TSTP Solution File: SYN938+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN938+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 30 00:01:19 EDT 2022
% Result : Theorem 0.20s 0.48s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN938+1 : TPTP v8.1.0. Released v3.1.0.
% 0.13/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n011.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Sep 5 09:33:15 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.20/0.34 Usage: tptp [options] [-file:]file
% 0.20/0.34 -h, -? prints this message.
% 0.20/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.20/0.34 -m, -model generate model.
% 0.20/0.34 -p, -proof generate proof.
% 0.20/0.34 -c, -core generate unsat core of named formulas.
% 0.20/0.34 -st, -statistics display statistics.
% 0.20/0.34 -t:timeout set timeout (in second).
% 0.20/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.20/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.20/0.34 -<param>:<value> configuration parameter and value.
% 0.20/0.34 -o:<output-file> file to place output in.
% 0.20/0.48 % SZS status Theorem
% 0.20/0.48 % SZS output start Proof
% 0.20/0.48 tff(p1_type, type, (
% 0.20/0.48 p1: $i > $o)).
% 0.20/0.48 tff(tptp_fun_X_20_type, type, (
% 0.20/0.48 tptp_fun_X_20: $i)).
% 0.20/0.48 tff(q1_type, type, (
% 0.20/0.48 q1: $i > $o)).
% 0.20/0.48 tff(tptp_fun_B_12_type, type, (
% 0.20/0.48 tptp_fun_B_12: $i)).
% 0.20/0.48 tff(tptp_fun_A_13_type, type, (
% 0.20/0.48 tptp_fun_A_13: $i)).
% 0.20/0.48 tff(tptp_fun_Y_16_type, type, (
% 0.20/0.48 tptp_fun_Y_16: $i > $i)).
% 0.20/0.48 tff(tptp_fun_Y_15_type, type, (
% 0.20/0.48 tptp_fun_Y_15: $i > $i)).
% 0.20/0.48 tff(r1_type, type, (
% 0.20/0.48 r1: $i > $o)).
% 0.20/0.48 tff(elem_148_type, type, (
% 0.20/0.48 elem_148: $i)).
% 0.20/0.48 tff(tptp_fun_Y_41_type, type, (
% 0.20/0.48 tptp_fun_Y_41: $i > $i)).
% 0.20/0.48 tff(elem_159_type, type, (
% 0.20/0.48 elem_159: $i)).
% 0.20/0.48 tff(tptp_fun_Y_52_type, type, (
% 0.20/0.48 tptp_fun_Y_52: $i)).
% 0.20/0.48 tff(k!0_type, type, (
% 0.20/0.48 k!0: $o)).
% 0.20/0.48 tff(tptp_fun_A_48_type, type, (
% 0.20/0.48 tptp_fun_A_48: $i)).
% 0.20/0.48 tff(tptp_fun_B_21_type, type, (
% 0.20/0.48 tptp_fun_B_21: $i)).
% 0.20/0.48 tff(tptp_fun_A_22_type, type, (
% 0.20/0.48 tptp_fun_A_22: $i)).
% 0.20/0.48 tff(tptp_fun_X_35_type, type, (
% 0.20/0.48 tptp_fun_X_35: $i)).
% 0.20/0.48 tff(tptp_fun_B_18_type, type, (
% 0.20/0.48 tptp_fun_B_18: $i)).
% 0.20/0.48 tff(tptp_fun_A_19_type, type, (
% 0.20/0.48 tptp_fun_A_19: $i)).
% 0.20/0.48 tff(tptp_fun_Y_36_type, type, (
% 0.20/0.48 tptp_fun_Y_36: $i)).
% 0.20/0.48 tff(p_type, type, (
% 0.20/0.48 p: ( $i * $i ) > $o)).
% 0.20/0.48 tff(tptp_fun_X_37_type, type, (
% 0.20/0.48 tptp_fun_X_37: $i > $i)).
% 0.20/0.48 tff(elem_90_type, type, (
% 0.20/0.48 elem_90: $i)).
% 0.20/0.48 tff(tptp_fun_C_3_type, type, (
% 0.20/0.48 tptp_fun_C_3: $i)).
% 0.20/0.48 tff(tptp_fun_B_4_type, type, (
% 0.20/0.48 tptp_fun_B_4: $i)).
% 0.20/0.48 tff(f_type, type, (
% 0.20/0.48 f: $i > $i)).
% 0.20/0.48 tff(tptp_fun_B_42_type, type, (
% 0.20/0.48 tptp_fun_B_42: $i)).
% 0.20/0.48 tff(tptp_fun_C_2_type, type, (
% 0.20/0.48 tptp_fun_C_2: $i)).
% 0.20/0.48 tff(tptp_fun_B_1_type, type, (
% 0.20/0.48 tptp_fun_B_1: $i)).
% 0.20/0.48 tff(a_type, type, (
% 0.20/0.48 a: ( $i * $i ) > $o)).
% 0.20/0.48 tff(tptp_fun_Y_30_type, type, (
% 0.20/0.48 tptp_fun_Y_30: $i)).
% 0.20/0.48 tff(tptp_fun_X_29_type, type, (
% 0.20/0.48 tptp_fun_X_29: $i)).
% 0.20/0.48 tff(tptp_fun_Y_27_type, type, (
% 0.20/0.48 tptp_fun_Y_27: $i)).
% 0.20/0.48 tff(tptp_fun_X_28_type, type, (
% 0.20/0.48 tptp_fun_X_28: $i)).
% 0.20/0.48 tff(tptp_fun_Y_14_type, type, (
% 0.20/0.48 tptp_fun_Y_14: $i)).
% 0.20/0.48 tff(tptp_fun_Y_25_type, type, (
% 0.20/0.48 tptp_fun_Y_25: $i)).
% 0.20/0.48 tff(s_type, type, (
% 0.20/0.48 s: ( $i * $i ) > $o)).
% 0.20/0.48 tff(tptp_fun_A_8_type, type, (
% 0.20/0.48 tptp_fun_A_8: $i)).
% 0.20/0.48 tff(e_type, type, (
% 0.20/0.48 e: $i > $o)).
% 0.20/0.48 tff(g_type, type, (
% 0.20/0.48 g: $i > $o)).
% 0.20/0.48 tff(c_type, type, (
% 0.20/0.48 c: $i > $o)).
% 0.20/0.48 tff(tptp_fun_B_6_type, type, (
% 0.20/0.48 tptp_fun_B_6: $i)).
% 0.20/0.48 tff(tptp_fun_Y_34_type, type, (
% 0.20/0.48 tptp_fun_Y_34: $i)).
% 0.20/0.48 tff(tptp_fun_X_33_type, type, (
% 0.20/0.48 tptp_fun_X_33: $i)).
% 0.20/0.48 tff(s1_type, type, (
% 0.20/0.48 s1: $i > $o)).
% 0.20/0.48 tff(tptp_fun_A_50_type, type, (
% 0.20/0.48 tptp_fun_A_50: $i)).
% 0.20/0.48 tff(tptp_fun_B_49_type, type, (
% 0.20/0.48 tptp_fun_B_49: $i)).
% 0.20/0.48 tff(tptp_fun_Y_46_type, type, (
% 0.20/0.48 tptp_fun_Y_46: $i)).
% 0.20/0.48 tff(tptp_fun_X_45_type, type, (
% 0.20/0.48 tptp_fun_X_45: $i)).
% 0.20/0.48 tff(tptp_fun_A_44_type, type, (
% 0.20/0.48 tptp_fun_A_44: $i)).
% 0.20/0.48 tff(tptp_fun_B_43_type, type, (
% 0.20/0.48 tptp_fun_B_43: $i)).
% 0.20/0.48 tff(b_type, type, (
% 0.20/0.48 b: $i > $o)).
% 0.20/0.48 tff(a1_type, type, (
% 0.20/0.48 a1: $i > $o)).
% 0.20/0.48 tff(tptp_fun_X_23_type, type, (
% 0.20/0.48 tptp_fun_X_23: $i)).
% 0.20/0.48 tff(tptp_fun_Y_17_type, type, (
% 0.20/0.48 tptp_fun_Y_17: $i > $i)).
% 0.20/0.48 tff(elem_72_type, type, (
% 0.20/0.48 elem_72: $i)).
% 0.20/0.48 tff(tptp_fun_X_7_type, type, (
% 0.20/0.48 tptp_fun_X_7: $i)).
% 0.20/0.48 tff(q_type, type, (
% 0.20/0.48 q: ( $i * $i ) > $o)).
% 0.20/0.48 tff(tptp_fun_B_51_type, type, (
% 0.20/0.48 tptp_fun_B_51: $i)).
% 0.20/0.48 tff(tptp_fun_C_5_type, type, (
% 0.20/0.48 tptp_fun_C_5: $i)).
% 0.20/0.48 tff(tptp_fun_X_47_type, type, (
% 0.20/0.48 tptp_fun_X_47: $i)).
% 0.20/0.48 tff(tptp_fun_X_24_type, type, (
% 0.20/0.48 tptp_fun_X_24: $i)).
% 0.20/0.48 tff(a_member_of_type, type, (
% 0.20/0.48 a_member_of: ( $i * $i ) > $o)).
% 0.20/0.48 tff(tptp_fun_Z_38_type, type, (
% 0.20/0.48 tptp_fun_Z_38: ( $i * $i ) > $i)).
% 0.20/0.48 tff(eq_type, type, (
% 0.20/0.48 eq: ( $i * $i ) > $o)).
% 0.20/0.48 tff(tptp_fun_A_40_type, type, (
% 0.20/0.48 tptp_fun_A_40: $i)).
% 0.20/0.48 tff(tptp_fun_B_39_type, type, (
% 0.20/0.48 tptp_fun_B_39: $i)).
% 0.20/0.48 tff(r_type, type, (
% 0.20/0.48 r: ( $i * $i ) > $o)).
% 0.20/0.48 tff(tptp_fun_C_9_type, type, (
% 0.20/0.48 tptp_fun_C_9: $i)).
% 0.20/0.48 tff(tptp_fun_B_10_type, type, (
% 0.20/0.48 tptp_fun_B_10: $i)).
% 0.20/0.48 tff(tptp_fun_A_11_type, type, (
% 0.20/0.48 tptp_fun_A_11: $i)).
% 0.20/0.48 tff(tptp_fun_B_31_type, type, (
% 0.20/0.48 tptp_fun_B_31: $i)).
% 0.20/0.48 tff(tptp_fun_A_32_type, type, (
% 0.20/0.48 tptp_fun_A_32: $i)).
% 0.20/0.48 tff(tptp_fun_X_26_type, type, (
% 0.20/0.48 tptp_fun_X_26: $i)).
% 0.20/0.48 tff(a0_type, type, (
% 0.20/0.48 a0: $o)).
% 0.20/0.48 tff(b0_type, type, (
% 0.20/0.48 b0: $o)).
% 0.20/0.48 tff(g0_type, type, (
% 0.20/0.48 g0: $o)).
% 0.20/0.48 tff(f0_type, type, (
% 0.20/0.48 f0: $o)).
% 0.20/0.48 tff(z_type, type, (
% 0.20/0.48 z: $i)).
% 0.20/0.48 tff(q0_type, type, (
% 0.20/0.48 q0: $o)).
% 0.20/0.48 tff(1,assumption,(~p1(A!13)), introduced(assumption)).
% 0.20/0.48 tff(2,assumption,(~((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X)))))))), introduced(assumption)).
% 0.20/0.48 tff(3,plain,
% 0.20/0.48 (((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X))))))) | ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(4,plain,
% 0.20/0.48 (![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[3, 2])).
% 0.20/0.48 tff(5,plain,
% 0.20/0.48 ((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (~(r1(elem!148) | p1(tptp_fun_Y_15(elem!148))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(6,plain,
% 0.20/0.48 (~(r1(elem!148) | p1(tptp_fun_Y_15(elem!148)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[5, 4])).
% 0.20/0.48 tff(7,plain,
% 0.20/0.48 ((r1(elem!148) | p1(tptp_fun_Y_15(elem!148))) | (~p1(tptp_fun_Y_15(elem!148)))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(8,plain,
% 0.20/0.48 (~p1(tptp_fun_Y_15(elem!148))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[7, 6])).
% 0.20/0.48 tff(9,plain,
% 0.20/0.48 (((~p1(tptp_fun_Y_15(elem!148))) | (~q1(tptp_fun_Y_16(tptp_fun_Y_15(elem!148))))) | p1(tptp_fun_Y_15(elem!148))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(10,plain,
% 0.20/0.48 ((~p1(tptp_fun_Y_15(elem!148))) | (~q1(tptp_fun_Y_16(tptp_fun_Y_15(elem!148))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.20/0.48 tff(11,plain,
% 0.20/0.48 (((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X))))))) | ![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X)))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(12,plain,
% 0.20/0.48 (![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X)))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[11, 2])).
% 0.20/0.48 tff(13,plain,
% 0.20/0.48 ((~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X)))))) | (~((~p1(tptp_fun_Y_15(elem!148))) | (~q1(tptp_fun_Y_16(tptp_fun_Y_15(elem!148))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(14,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[13, 12, 10])).
% 0.20/0.48 tff(15,plain,((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(16,assumption,(![X: $i] : (~((~p1(X)) | p1(tptp_fun_Y_41(X))))), introduced(assumption)).
% 0.20/0.48 tff(17,plain,
% 0.20/0.48 ((~![X: $i] : (~((~p1(X)) | p1(tptp_fun_Y_41(X))))) | (~((~p1(elem!159)) | p1(tptp_fun_Y_41(elem!159))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(18,plain,
% 0.20/0.48 (~((~p1(elem!159)) | p1(tptp_fun_Y_41(elem!159)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.20/0.48 tff(19,plain,
% 0.20/0.48 (((~p1(elem!159)) | p1(tptp_fun_Y_41(elem!159))) | (~p1(tptp_fun_Y_41(elem!159)))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(20,plain,
% 0.20/0.48 (~p1(tptp_fun_Y_41(elem!159))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.20/0.48 tff(21,plain,
% 0.20/0.48 (((~p1(tptp_fun_Y_41(elem!159))) | p1(tptp_fun_Y_41(tptp_fun_Y_41(elem!159)))) | p1(tptp_fun_Y_41(elem!159))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(22,plain,
% 0.20/0.48 ((~p1(tptp_fun_Y_41(elem!159))) | p1(tptp_fun_Y_41(tptp_fun_Y_41(elem!159)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.20/0.48 tff(23,plain,
% 0.20/0.48 ((~![X: $i] : (~((~p1(X)) | p1(tptp_fun_Y_41(X))))) | (~((~p1(tptp_fun_Y_41(elem!159))) | p1(tptp_fun_Y_41(tptp_fun_Y_41(elem!159)))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(24,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[23, 16, 22])).
% 0.20/0.48 tff(25,plain,(~![X: $i] : (~((~p1(X)) | p1(tptp_fun_Y_41(X))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(26,assumption,(~((~(r1(Y!52) | (~q1(Y!52)))) | (~![X: $i] : (q1(X) | (~p1(X)))) | (~![Z: $i] : (~(r1(Z) | (~p1(Z))))))), introduced(assumption)).
% 0.20/0.48 tff(27,plain,
% 0.20/0.48 (((~(r1(Y!52) | (~q1(Y!52)))) | (~![X: $i] : (q1(X) | (~p1(X)))) | (~![Z: $i] : (~(r1(Z) | (~p1(Z)))))) | ![Z: $i] : (~(r1(Z) | (~p1(Z))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(28,plain,
% 0.20/0.48 (![Z: $i] : (~(r1(Z) | (~p1(Z))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.20/0.48 tff(29,assumption,(r1(Y!52) | (~p1(Y!52))), introduced(assumption)).
% 0.20/0.48 tff(30,assumption,(![Z: $i] : (~(r1(Z) | (~p1(Z))))), introduced(assumption)).
% 0.20/0.48 tff(31,plain,
% 0.20/0.48 ((~![Z: $i] : (~(r1(Z) | (~p1(Z))))) | (~(r1(Y!52) | (~p1(Y!52))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(32,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[31, 30, 29])).
% 0.20/0.48 tff(33,plain,((~(r1(Y!52) | (~p1(Y!52)))) | (~![Z: $i] : (~(r1(Z) | (~p1(Z)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(34,plain,
% 0.20/0.48 (~(r1(Y!52) | (~p1(Y!52)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[33, 28])).
% 0.20/0.48 tff(35,plain,
% 0.20/0.48 ((r1(Y!52) | (~p1(Y!52))) | p1(Y!52)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(36,plain,
% 0.20/0.48 (p1(Y!52)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.20/0.48 tff(37,plain,
% 0.20/0.48 (((~(r1(Y!52) | (~q1(Y!52)))) | (~![X: $i] : (q1(X) | (~p1(X)))) | (~![Z: $i] : (~(r1(Z) | (~p1(Z)))))) | (r1(Y!52) | (~q1(Y!52)))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(38,plain,
% 0.20/0.48 (r1(Y!52) | (~q1(Y!52))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[37, 26])).
% 0.20/0.48 tff(39,plain,
% 0.20/0.48 ((r1(Y!52) | (~p1(Y!52))) | (~r1(Y!52))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(40,plain,
% 0.20/0.48 (~r1(Y!52)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[39, 34])).
% 0.20/0.48 tff(41,plain,
% 0.20/0.48 ((~(r1(Y!52) | (~q1(Y!52)))) | r1(Y!52) | (~q1(Y!52))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(42,plain,
% 0.20/0.48 (~q1(Y!52)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[41, 40, 38])).
% 0.20/0.48 tff(43,plain,
% 0.20/0.48 (((~(r1(Y!52) | (~q1(Y!52)))) | (~![X: $i] : (q1(X) | (~p1(X)))) | (~![Z: $i] : (~(r1(Z) | (~p1(Z)))))) | ![X: $i] : (q1(X) | (~p1(X)))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(44,plain,
% 0.20/0.48 (![X: $i] : (q1(X) | (~p1(X)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[43, 26])).
% 0.20/0.48 tff(45,plain,
% 0.20/0.48 (((~![X: $i] : (q1(X) | (~p1(X)))) | (q1(Y!52) | (~p1(Y!52)))) <=> ((~![X: $i] : (q1(X) | (~p1(X)))) | q1(Y!52) | (~p1(Y!52)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(46,plain,
% 0.20/0.48 ((~![X: $i] : (q1(X) | (~p1(X)))) | (q1(Y!52) | (~p1(Y!52)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(47,plain,
% 0.20/0.48 ((~![X: $i] : (q1(X) | (~p1(X)))) | q1(Y!52) | (~p1(Y!52))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.48 tff(48,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[47, 44, 42, 36])).
% 0.20/0.48 tff(49,plain,((~(r1(Y!52) | (~q1(Y!52)))) | (~![X: $i] : (q1(X) | (~p1(X)))) | (~![Z: $i] : (~(r1(Z) | (~p1(Z)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(50,assumption,(~(q1(A!48) | (~k!0) | (~![X: $i] : (~((~p1(X)) | (~q1(X))))))), introduced(assumption)).
% 0.20/0.48 tff(51,plain,
% 0.20/0.48 ((q1(A!48) | (~k!0) | (~![X: $i] : (~((~p1(X)) | (~q1(X)))))) | (~q1(A!48))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(52,plain,
% 0.20/0.48 (~q1(A!48)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.20/0.48 tff(53,plain,
% 0.20/0.48 (((~p1(A!48)) | (~q1(A!48))) | q1(A!48)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(54,plain,
% 0.20/0.48 ((~p1(A!48)) | (~q1(A!48))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.20/0.48 tff(55,plain,
% 0.20/0.48 ((q1(A!48) | (~k!0) | (~![X: $i] : (~((~p1(X)) | (~q1(X)))))) | ![X: $i] : (~((~p1(X)) | (~q1(X))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(56,plain,
% 0.20/0.48 (![X: $i] : (~((~p1(X)) | (~q1(X))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[55, 50])).
% 0.20/0.48 tff(57,plain,
% 0.20/0.48 ((~![X: $i] : (~((~p1(X)) | (~q1(X))))) | (~((~p1(A!48)) | (~q1(A!48))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(58,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[57, 56, 54])).
% 0.20/0.48 tff(59,plain,(q1(A!48) | (~k!0) | (~![X: $i] : (~((~p1(X)) | (~q1(X)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(60,assumption,(~((~![Z: $i] : (p1(Z) | (~q1(Z)))) | (~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))))), introduced(assumption)).
% 0.20/0.48 tff(61,plain,
% 0.20/0.48 (((~![Z: $i] : (p1(Z) | (~q1(Z)))) | (~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X))))))) | ![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(62,plain,
% 0.20/0.48 (![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.20/0.48 tff(63,plain,
% 0.20/0.48 (((~![Z: $i] : (p1(Z) | (~q1(Z)))) | (~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X))))))) | ![Z: $i] : (p1(Z) | (~q1(Z)))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(64,plain,
% 0.20/0.48 (![Z: $i] : (p1(Z) | (~q1(Z)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[63, 60])).
% 0.20/0.48 tff(65,assumption,(![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))), introduced(assumption)).
% 0.20/0.48 tff(66,plain,
% 0.20/0.48 (((~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))) | (~(p1(B!21) | (~q1(A!22))))) <=> ((~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))) | (~(p1(B!21) | (~q1(A!22)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(67,plain,
% 0.20/0.48 (($false | (~(p1(B!21) | (~q1(A!22))))) <=> (~(p1(B!21) | (~q1(A!22))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(68,plain,
% 0.20/0.48 ((~$true) <=> $false),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(69,plain,
% 0.20/0.48 ((p1(A!22) | (~p1(A!22))) <=> $true),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(70,plain,
% 0.20/0.48 ((~(p1(A!22) | (~p1(A!22)))) <=> (~$true)),
% 0.20/0.48 inference(monotonicity,[status(thm)],[69])).
% 0.20/0.48 tff(71,plain,
% 0.20/0.48 ((~(p1(A!22) | (~p1(A!22)))) <=> $false),
% 0.20/0.48 inference(transitivity,[status(thm)],[70, 68])).
% 0.20/0.48 tff(72,plain,
% 0.20/0.48 (((~(p1(A!22) | (~p1(A!22)))) | (~(p1(B!21) | (~q1(A!22))))) <=> ($false | (~(p1(B!21) | (~q1(A!22)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[71])).
% 0.20/0.48 tff(73,plain,
% 0.20/0.48 (((~(p1(A!22) | (~p1(A!22)))) | (~(p1(B!21) | (~q1(A!22))))) <=> (~(p1(B!21) | (~q1(A!22))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[72, 67])).
% 0.20/0.48 tff(74,plain,
% 0.20/0.48 (((~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))) | ((~(p1(A!22) | (~p1(A!22)))) | (~(p1(B!21) | (~q1(A!22)))))) <=> ((~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))) | (~(p1(B!21) | (~q1(A!22)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[73])).
% 0.20/0.48 tff(75,plain,
% 0.20/0.48 (((~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))) | ((~(p1(A!22) | (~p1(A!22)))) | (~(p1(B!21) | (~q1(A!22)))))) <=> ((~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))) | (~(p1(B!21) | (~q1(A!22)))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[74, 66])).
% 0.20/0.48 tff(76,plain,
% 0.20/0.48 ((~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))) | ((~(p1(A!22) | (~p1(A!22)))) | (~(p1(B!21) | (~q1(A!22)))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(77,plain,
% 0.20/0.48 ((~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))) | (~(p1(B!21) | (~q1(A!22))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.20/0.48 tff(78,plain,
% 0.20/0.48 (~(p1(B!21) | (~q1(A!22)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[77, 65])).
% 0.20/0.48 tff(79,assumption,(~p1(A!22)), introduced(assumption)).
% 0.20/0.48 tff(80,assumption,(![Z: $i] : (p1(Z) | (~q1(Z)))), introduced(assumption)).
% 0.20/0.48 tff(81,plain,
% 0.20/0.48 (((~![Z: $i] : (p1(Z) | (~q1(Z)))) | (p1(A!22) | (~q1(A!22)))) <=> ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | p1(A!22) | (~q1(A!22)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(82,plain,
% 0.20/0.48 ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | (p1(A!22) | (~q1(A!22)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(83,plain,
% 0.20/0.48 ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | p1(A!22) | (~q1(A!22))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.48 tff(84,plain,
% 0.20/0.48 (~q1(A!22)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[83, 80, 79])).
% 0.20/0.48 tff(85,plain,
% 0.20/0.48 ((p1(B!21) | (~q1(A!22))) | q1(A!22)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(86,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[85, 84, 78])).
% 0.20/0.48 tff(87,plain,(p1(A!22) | (~![Z: $i] : (p1(Z) | (~q1(Z)))) | (~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(88,plain,
% 0.20/0.48 (p1(A!22)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[87, 64, 62])).
% 0.20/0.48 tff(89,plain,
% 0.20/0.48 ((p1(A!22) | (~p1(B!21))) | (~p1(A!22))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(90,plain,
% 0.20/0.48 (p1(A!22) | (~p1(B!21))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.20/0.48 tff(91,plain,
% 0.20/0.48 (((~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))) | ((~(p1(A!22) | (~p1(B!21)))) | (~(p1(B!21) | (~q1(B!21)))))) <=> ((~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))) | (~(p1(A!22) | (~p1(B!21)))) | (~(p1(B!21) | (~q1(B!21)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(92,plain,
% 0.20/0.49 ((~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))) | ((~(p1(A!22) | (~p1(B!21)))) | (~(p1(B!21) | (~q1(B!21)))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(93,plain,
% 0.20/0.49 ((~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))) | (~(p1(A!22) | (~p1(B!21)))) | (~(p1(B!21) | (~q1(B!21))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.20/0.49 tff(94,plain,
% 0.20/0.49 (~(p1(B!21) | (~q1(B!21)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[93, 62, 90])).
% 0.20/0.49 tff(95,plain,
% 0.20/0.49 (~(p1(B!21) | (~q1(A!22)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[77, 62])).
% 0.20/0.49 tff(96,plain,
% 0.20/0.49 ((p1(B!21) | (~q1(A!22))) | (~p1(B!21))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(97,plain,
% 0.20/0.49 (~p1(B!21)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.20/0.49 tff(98,plain,
% 0.20/0.49 (((~![Z: $i] : (p1(Z) | (~q1(Z)))) | (p1(B!21) | (~q1(B!21)))) <=> ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | p1(B!21) | (~q1(B!21)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(99,plain,
% 0.20/0.49 ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | (p1(B!21) | (~q1(B!21)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(100,plain,
% 0.20/0.49 ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | p1(B!21) | (~q1(B!21))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.20/0.49 tff(101,plain,
% 0.20/0.49 (~q1(B!21)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[100, 64, 97])).
% 0.20/0.49 tff(102,plain,
% 0.20/0.49 ((p1(B!21) | (~q1(B!21))) | q1(B!21)),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(103,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[102, 101, 94])).
% 0.20/0.49 tff(104,plain,((~![Z: $i] : (p1(Z) | (~q1(Z)))) | (~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(105,assumption,(~p1(X!35)), introduced(assumption)).
% 0.20/0.49 tff(106,plain,
% 0.20/0.49 ((r1(X!35) | (~p1(X!35))) | p1(X!35)),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(107,plain,
% 0.20/0.49 (r1(X!35) | (~p1(X!35))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.20/0.49 tff(108,plain,
% 0.20/0.49 ((~![Z: $i] : (~(r1(Z) | (~p1(Z))))) | (~(r1(X!35) | (~p1(X!35))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(109,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[108, 30, 107])).
% 0.20/0.49 tff(110,plain,((~![Z: $i] : (~(r1(Z) | (~p1(Z))))) | p1(X!35)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(111,plain,
% 0.20/0.49 (~![Z: $i] : (~(r1(Z) | (~p1(Z))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[110, 105])).
% 0.20/0.49 tff(112,plain,
% 0.20/0.49 ((~(r1(Y!52) | (~q1(Y!52)))) | (~![X: $i] : (q1(X) | (~p1(X)))) | (~![Z: $i] : (~(r1(Z) | (~p1(Z)))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[27, 111])).
% 0.20/0.49 tff(113,plain,
% 0.20/0.49 (((~p1(X!35)) | (~q1(X!35))) | p1(X!35)),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(114,plain,
% 0.20/0.49 ((~p1(X!35)) | (~q1(X!35))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[113, 105])).
% 0.20/0.49 tff(115,assumption,(![X: $i] : (~((~p1(X)) | (~q1(X))))), introduced(assumption)).
% 0.20/0.49 tff(116,plain,
% 0.20/0.49 ((~![X: $i] : (~((~p1(X)) | (~q1(X))))) | (~((~p1(X!35)) | (~q1(X!35))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(117,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[116, 115, 114])).
% 0.20/0.49 tff(118,plain,((~![X: $i] : (~((~p1(X)) | (~q1(X))))) | p1(X!35)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(119,plain,
% 0.20/0.49 (~![X: $i] : (~((~p1(X)) | (~q1(X))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[118, 105])).
% 0.20/0.49 tff(120,plain,
% 0.20/0.49 (q1(A!48) | (~k!0) | (~![X: $i] : (~((~p1(X)) | (~q1(X)))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[55, 119])).
% 0.20/0.49 tff(121,plain,
% 0.20/0.49 (((~p1(X!35)) | (~q1(tptp_fun_Y_16(X!35)))) | p1(X!35)),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(122,plain,
% 0.20/0.49 ((~p1(X!35)) | (~q1(tptp_fun_Y_16(X!35)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[121, 105])).
% 0.20/0.49 tff(123,assumption,(![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X)))))), introduced(assumption)).
% 0.20/0.49 tff(124,plain,
% 0.20/0.49 ((~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X)))))) | (~((~p1(X!35)) | (~q1(tptp_fun_Y_16(X!35)))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(125,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[124, 123, 122])).
% 0.20/0.49 tff(126,plain,((~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X)))))) | p1(X!35)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(127,plain,
% 0.20/0.49 (~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X)))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[126, 105])).
% 0.20/0.49 tff(128,plain,
% 0.20/0.49 ((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X))))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[11, 127])).
% 0.20/0.49 tff(129,plain,
% 0.20/0.49 ((p1(A!19) | (~p1(X!35))) | p1(X!35)),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(130,plain,
% 0.20/0.49 (p1(A!19) | (~p1(X!35))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[129, 105])).
% 0.20/0.49 tff(131,assumption,(~((~![Y: $i] : (p1(Y) | (~q1(Y)))) | (~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))))), introduced(assumption)).
% 0.20/0.49 tff(132,plain,
% 0.20/0.49 (((~![Y: $i] : (p1(Y) | (~q1(Y)))) | (~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X))))))) | ![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(133,plain,
% 0.20/0.49 (![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[132, 131])).
% 0.20/0.49 tff(134,plain,
% 0.20/0.49 (((~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))) | ((~(p1(A!19) | (~p1(X!35)))) | (~(p1(B!18) | (~q1(X!35)))))) <=> ((~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))) | (~(p1(A!19) | (~p1(X!35)))) | (~(p1(B!18) | (~q1(X!35)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(135,plain,
% 0.20/0.49 ((~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))) | ((~(p1(A!19) | (~p1(X!35)))) | (~(p1(B!18) | (~q1(X!35)))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(136,plain,
% 0.20/0.49 ((~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))) | (~(p1(A!19) | (~p1(X!35)))) | (~(p1(B!18) | (~q1(X!35))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.20/0.49 tff(137,plain,
% 0.20/0.49 (~(p1(B!18) | (~q1(X!35)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[136, 133, 130])).
% 0.20/0.49 tff(138,plain,
% 0.20/0.49 (((~![Y: $i] : (p1(Y) | (~q1(Y)))) | (~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X))))))) | ![Y: $i] : (p1(Y) | (~q1(Y)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(139,plain,
% 0.20/0.49 (![Y: $i] : (p1(Y) | (~q1(Y)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[138, 131])).
% 0.20/0.49 tff(140,plain,
% 0.20/0.49 (((~![Y: $i] : (p1(Y) | (~q1(Y)))) | (p1(X!35) | (~q1(X!35)))) <=> ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | p1(X!35) | (~q1(X!35)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(141,plain,
% 0.20/0.49 ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | (p1(X!35) | (~q1(X!35)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(142,plain,
% 0.20/0.49 ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | p1(X!35) | (~q1(X!35))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.20/0.49 tff(143,plain,
% 0.20/0.49 (~q1(X!35)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[142, 139, 105])).
% 0.20/0.49 tff(144,plain,
% 0.20/0.49 ((p1(B!18) | (~q1(X!35))) | q1(X!35)),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(145,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[144, 143, 137])).
% 0.20/0.49 tff(146,plain,(((~![Y: $i] : (p1(Y) | (~q1(Y)))) | (~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X))))))) | p1(X!35)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(147,plain,
% 0.20/0.49 ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | (~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X))))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[146, 105])).
% 0.20/0.49 tff(148,plain,
% 0.20/0.49 (((~p1(X!35)) | (~![Y: $i] : (~p1(Y)))) | p1(X!35)),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(149,plain,
% 0.20/0.49 ((~p1(X!35)) | (~![Y: $i] : (~p1(Y)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[148, 105])).
% 0.20/0.49 tff(150,plain,
% 0.20/0.49 ((p1(A!22) | (~p1(X!35))) | p1(X!35)),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(151,plain,
% 0.20/0.49 (p1(A!22) | (~p1(X!35))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[150, 105])).
% 0.20/0.49 tff(152,plain,
% 0.20/0.49 (((~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))) | ((~(p1(A!22) | (~p1(X!35)))) | (~(p1(B!21) | (~q1(X!35)))))) <=> ((~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))) | (~(p1(A!22) | (~p1(X!35)))) | (~(p1(B!21) | (~q1(X!35)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(153,plain,
% 0.20/0.49 ((~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))) | ((~(p1(A!22) | (~p1(X!35)))) | (~(p1(B!21) | (~q1(X!35)))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(154,plain,
% 0.20/0.49 ((~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))) | (~(p1(A!22) | (~p1(X!35)))) | (~(p1(B!21) | (~q1(X!35))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.20/0.49 tff(155,plain,
% 0.20/0.49 (~(p1(B!21) | (~q1(X!35)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[154, 62, 151])).
% 0.20/0.49 tff(156,plain,
% 0.20/0.49 (((~![Z: $i] : (p1(Z) | (~q1(Z)))) | (p1(X!35) | (~q1(X!35)))) <=> ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | p1(X!35) | (~q1(X!35)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(157,plain,
% 0.20/0.49 ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | (p1(X!35) | (~q1(X!35)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(158,plain,
% 0.20/0.49 ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | p1(X!35) | (~q1(X!35))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.20/0.49 tff(159,plain,
% 0.20/0.49 (~q1(X!35)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[158, 64, 105])).
% 0.20/0.49 tff(160,plain,
% 0.20/0.49 ((p1(B!21) | (~q1(X!35))) | q1(X!35)),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(161,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[160, 159, 155])).
% 0.20/0.49 tff(162,plain,(((~![Z: $i] : (p1(Z) | (~q1(Z)))) | (~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X))))))) | p1(X!35)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(163,plain,
% 0.20/0.49 ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | (~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X))))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[162, 105])).
% 0.20/0.49 tff(164,assumption,(~((~(p1(X!35) | p1(Y!36))) | (~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))))), introduced(assumption)).
% 0.20/0.49 tff(165,plain,
% 0.20/0.49 (((~(p1(X!35) | p1(Y!36))) | (~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y))))) | (p1(X!35) | p1(Y!36))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(166,plain,
% 0.20/0.49 (p1(X!35) | p1(Y!36)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[165, 164])).
% 0.20/0.49 tff(167,plain,
% 0.20/0.49 ((~(p1(X!35) | p1(Y!36))) | p1(X!35) | p1(Y!36)),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(168,plain,
% 0.20/0.49 (p1(Y!36)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[167, 166, 105])).
% 0.20/0.49 tff(169,assumption,(~![X: $i] : (~p1(X))), introduced(assumption)).
% 0.20/0.49 tff(170,plain,
% 0.20/0.49 (((~(p1(X!35) | p1(Y!36))) | (~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y))))) | (![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(171,plain,
% 0.20/0.49 (![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[170, 164])).
% 0.20/0.49 tff(172,plain,
% 0.20/0.49 ((~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))) | ![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(173,plain,
% 0.20/0.49 (![Y: $i] : (~p1(Y))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[172, 171, 169])).
% 0.20/0.49 tff(174,plain,
% 0.20/0.49 ((~![Y: $i] : (~p1(Y))) | (~p1(Y!36))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(175,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[174, 173, 168])).
% 0.20/0.49 tff(176,plain,(((~(p1(X!35) | p1(Y!36))) | (~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y))))) | ![X: $i] : (~p1(X)) | p1(X!35)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(177,plain,
% 0.20/0.49 (![X: $i] : (~p1(X))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[176, 164, 105])).
% 0.20/0.49 tff(178,plain,
% 0.20/0.49 ((~![X: $i] : (~p1(X))) | (~p1(Y!36))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(179,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[178, 168, 177])).
% 0.20/0.49 tff(180,plain,(((~(p1(X!35) | p1(Y!36))) | (~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y))))) | p1(X!35)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(181,plain,
% 0.20/0.49 ((~(p1(X!35) | p1(Y!36))) | (~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[180, 105])).
% 0.20/0.49 tff(182,assumption,(![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))), introduced(assumption)).
% 0.20/0.49 tff(183,assumption,(~![W: $i] : (~p(W, elem!90))), introduced(assumption)).
% 0.20/0.49 tff(184,plain,
% 0.20/0.49 (((~p(elem!90, tptp_fun_X_37(tptp_fun_X_37(elem!90)))) | (~![W: $i] : (~p(W, elem!90)))) | ![W: $i] : (~p(W, elem!90))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(185,plain,
% 0.20/0.49 ((~p(elem!90, tptp_fun_X_37(tptp_fun_X_37(elem!90)))) | (~![W: $i] : (~p(W, elem!90)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[184, 183])).
% 0.20/0.49 tff(186,plain,
% 0.20/0.49 (((~p(elem!90, tptp_fun_X_37(elem!90))) | (~![W: $i] : (~p(W, elem!90)))) | ![W: $i] : (~p(W, elem!90))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(187,plain,
% 0.20/0.49 ((~p(elem!90, tptp_fun_X_37(elem!90))) | (~![W: $i] : (~p(W, elem!90)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[186, 183])).
% 0.20/0.49 tff(188,plain,
% 0.20/0.49 (((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~((~p(elem!90, elem!90)) | p(elem!90, tptp_fun_X_37(elem!90)))) | (~((~p(elem!90, tptp_fun_X_37(elem!90))) | (~![W: $i] : (~p(W, elem!90))))))) <=> ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))) | (~((~p(elem!90, elem!90)) | p(elem!90, tptp_fun_X_37(elem!90)))) | (~((~p(elem!90, tptp_fun_X_37(elem!90))) | (~![W: $i] : (~p(W, elem!90))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(189,plain,
% 0.20/0.49 (((~((~p(elem!90, elem!90)) | p(elem!90, tptp_fun_X_37(elem!90)) | (~p(elem!90, elem!90)))) | (~((~p(elem!90, tptp_fun_X_37(elem!90))) | (~![W: $i] : (~p(W, elem!90)))))) <=> ((~((~p(elem!90, elem!90)) | p(elem!90, tptp_fun_X_37(elem!90)))) | (~((~p(elem!90, tptp_fun_X_37(elem!90))) | (~![W: $i] : (~p(W, elem!90))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(190,plain,
% 0.20/0.49 (((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~((~p(elem!90, elem!90)) | p(elem!90, tptp_fun_X_37(elem!90)) | (~p(elem!90, elem!90)))) | (~((~p(elem!90, tptp_fun_X_37(elem!90))) | (~![W: $i] : (~p(W, elem!90))))))) <=> ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~((~p(elem!90, elem!90)) | p(elem!90, tptp_fun_X_37(elem!90)))) | (~((~p(elem!90, tptp_fun_X_37(elem!90))) | (~![W: $i] : (~p(W, elem!90)))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[189])).
% 0.20/0.49 tff(191,plain,
% 0.20/0.49 (((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~((~p(elem!90, elem!90)) | p(elem!90, tptp_fun_X_37(elem!90)) | (~p(elem!90, elem!90)))) | (~((~p(elem!90, tptp_fun_X_37(elem!90))) | (~![W: $i] : (~p(W, elem!90))))))) <=> ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))) | (~((~p(elem!90, elem!90)) | p(elem!90, tptp_fun_X_37(elem!90)))) | (~((~p(elem!90, tptp_fun_X_37(elem!90))) | (~![W: $i] : (~p(W, elem!90))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[190, 188])).
% 0.20/0.49 tff(192,plain,
% 0.20/0.49 ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~((~p(elem!90, elem!90)) | p(elem!90, tptp_fun_X_37(elem!90)) | (~p(elem!90, elem!90)))) | (~((~p(elem!90, tptp_fun_X_37(elem!90))) | (~![W: $i] : (~p(W, elem!90))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(193,plain,
% 0.20/0.49 ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))) | (~((~p(elem!90, elem!90)) | p(elem!90, tptp_fun_X_37(elem!90)))) | (~((~p(elem!90, tptp_fun_X_37(elem!90))) | (~![W: $i] : (~p(W, elem!90)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.20/0.49 tff(194,plain,
% 0.20/0.49 (~((~p(elem!90, elem!90)) | p(elem!90, tptp_fun_X_37(elem!90)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[193, 182, 187])).
% 0.20/0.49 tff(195,plain,
% 0.20/0.49 (((~p(elem!90, elem!90)) | p(elem!90, tptp_fun_X_37(elem!90))) | (~p(elem!90, tptp_fun_X_37(elem!90)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(196,plain,
% 0.20/0.49 (~p(elem!90, tptp_fun_X_37(elem!90))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[195, 194])).
% 0.20/0.49 tff(197,plain,
% 0.20/0.49 (((~p(elem!90, tptp_fun_X_37(elem!90))) | p(elem!90, tptp_fun_X_37(tptp_fun_X_37(elem!90))) | (~p(tptp_fun_X_37(elem!90), elem!90))) | p(elem!90, tptp_fun_X_37(elem!90))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(198,plain,
% 0.20/0.49 ((~p(elem!90, tptp_fun_X_37(elem!90))) | p(elem!90, tptp_fun_X_37(tptp_fun_X_37(elem!90))) | (~p(tptp_fun_X_37(elem!90), elem!90))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[197, 196])).
% 0.20/0.49 tff(199,plain,
% 0.20/0.49 (((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~((~p(elem!90, tptp_fun_X_37(elem!90))) | p(elem!90, tptp_fun_X_37(tptp_fun_X_37(elem!90))) | (~p(tptp_fun_X_37(elem!90), elem!90)))) | (~((~p(elem!90, tptp_fun_X_37(tptp_fun_X_37(elem!90)))) | (~![W: $i] : (~p(W, elem!90))))))) <=> ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))) | (~((~p(elem!90, tptp_fun_X_37(elem!90))) | p(elem!90, tptp_fun_X_37(tptp_fun_X_37(elem!90))) | (~p(tptp_fun_X_37(elem!90), elem!90)))) | (~((~p(elem!90, tptp_fun_X_37(tptp_fun_X_37(elem!90)))) | (~![W: $i] : (~p(W, elem!90))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(200,plain,
% 0.20/0.49 ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~((~p(elem!90, tptp_fun_X_37(elem!90))) | p(elem!90, tptp_fun_X_37(tptp_fun_X_37(elem!90))) | (~p(tptp_fun_X_37(elem!90), elem!90)))) | (~((~p(elem!90, tptp_fun_X_37(tptp_fun_X_37(elem!90)))) | (~![W: $i] : (~p(W, elem!90))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(201,plain,
% 0.20/0.49 ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))) | (~((~p(elem!90, tptp_fun_X_37(elem!90))) | p(elem!90, tptp_fun_X_37(tptp_fun_X_37(elem!90))) | (~p(tptp_fun_X_37(elem!90), elem!90)))) | (~((~p(elem!90, tptp_fun_X_37(tptp_fun_X_37(elem!90)))) | (~![W: $i] : (~p(W, elem!90)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.20/0.49 tff(202,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[201, 182, 198, 185])).
% 0.20/0.49 tff(203,plain,((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))) | ![W: $i] : (~p(W, elem!90))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(204,plain,
% 0.20/0.49 (![W: $i] : (~p(W, elem!90))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[203, 182])).
% 0.20/0.49 tff(205,assumption,(p(tptp_fun_X_37(elem!90), elem!90)), introduced(assumption)).
% 0.20/0.49 tff(206,assumption,(![W: $i] : (~p(W, elem!90))), introduced(assumption)).
% 0.20/0.49 tff(207,plain,
% 0.20/0.49 ((~![W: $i] : (~p(W, elem!90))) | (~p(tptp_fun_X_37(elem!90), elem!90))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(208,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[207, 206, 205])).
% 0.20/0.49 tff(209,plain,((~p(tptp_fun_X_37(elem!90), elem!90)) | (~![W: $i] : (~p(W, elem!90)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(210,plain,
% 0.20/0.49 (~p(tptp_fun_X_37(elem!90), elem!90)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[209, 204])).
% 0.20/0.49 tff(211,plain,
% 0.20/0.49 (((~p(elem!90, tptp_fun_X_37(elem!90))) | (~p(tptp_fun_X_37(elem!90), elem!90)) | p(tptp_fun_X_37(elem!90), tptp_fun_X_37(elem!90))) | p(tptp_fun_X_37(elem!90), elem!90)),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(212,plain,
% 0.20/0.49 ((~p(elem!90, tptp_fun_X_37(elem!90))) | (~p(tptp_fun_X_37(elem!90), elem!90)) | p(tptp_fun_X_37(elem!90), tptp_fun_X_37(elem!90))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[211, 210])).
% 0.20/0.49 tff(213,assumption,((~p(elem!90, tptp_fun_X_37(elem!90))) | (~p(tptp_fun_X_37(elem!90), elem!90)) | p(tptp_fun_X_37(elem!90), tptp_fun_X_37(elem!90))), introduced(assumption)).
% 0.20/0.49 tff(214,assumption,(~((~p(tptp_fun_X_37(elem!90), tptp_fun_X_37(elem!90))) | (~![W: $i] : (~p(W, tptp_fun_X_37(elem!90)))))), introduced(assumption)).
% 0.20/0.49 tff(215,plain,
% 0.20/0.49 (((~p(tptp_fun_X_37(elem!90), tptp_fun_X_37(elem!90))) | (~![W: $i] : (~p(W, tptp_fun_X_37(elem!90))))) | ![W: $i] : (~p(W, tptp_fun_X_37(elem!90)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(216,plain,
% 0.20/0.49 (![W: $i] : (~p(W, tptp_fun_X_37(elem!90)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[215, 214])).
% 0.20/0.49 tff(217,plain,
% 0.20/0.49 (((~p(tptp_fun_X_37(elem!90), tptp_fun_X_37(elem!90))) | (~![W: $i] : (~p(W, tptp_fun_X_37(elem!90))))) | p(tptp_fun_X_37(elem!90), tptp_fun_X_37(elem!90))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(218,plain,
% 0.20/0.49 (p(tptp_fun_X_37(elem!90), tptp_fun_X_37(elem!90))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[217, 214])).
% 0.20/0.49 tff(219,plain,
% 0.20/0.49 ((~![W: $i] : (~p(W, tptp_fun_X_37(elem!90)))) | (~p(tptp_fun_X_37(elem!90), tptp_fun_X_37(elem!90)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(220,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[219, 218, 216])).
% 0.20/0.49 tff(221,plain,((~p(tptp_fun_X_37(elem!90), tptp_fun_X_37(elem!90))) | (~![W: $i] : (~p(W, tptp_fun_X_37(elem!90))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(222,plain,
% 0.20/0.49 (((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~((~p(elem!90, tptp_fun_X_37(elem!90))) | (~p(tptp_fun_X_37(elem!90), elem!90)) | p(tptp_fun_X_37(elem!90), tptp_fun_X_37(elem!90)))) | (~((~p(tptp_fun_X_37(elem!90), tptp_fun_X_37(elem!90))) | (~![W: $i] : (~p(W, tptp_fun_X_37(elem!90)))))))) <=> ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))) | (~((~p(elem!90, tptp_fun_X_37(elem!90))) | (~p(tptp_fun_X_37(elem!90), elem!90)) | p(tptp_fun_X_37(elem!90), tptp_fun_X_37(elem!90)))) | (~((~p(tptp_fun_X_37(elem!90), tptp_fun_X_37(elem!90))) | (~![W: $i] : (~p(W, tptp_fun_X_37(elem!90)))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(223,plain,
% 0.20/0.49 (((~((~p(tptp_fun_X_37(elem!90), elem!90)) | p(tptp_fun_X_37(elem!90), tptp_fun_X_37(elem!90)) | (~p(elem!90, tptp_fun_X_37(elem!90))))) | (~((~p(tptp_fun_X_37(elem!90), tptp_fun_X_37(elem!90))) | (~![W: $i] : (~p(W, tptp_fun_X_37(elem!90))))))) <=> ((~((~p(elem!90, tptp_fun_X_37(elem!90))) | (~p(tptp_fun_X_37(elem!90), elem!90)) | p(tptp_fun_X_37(elem!90), tptp_fun_X_37(elem!90)))) | (~((~p(tptp_fun_X_37(elem!90), tptp_fun_X_37(elem!90))) | (~![W: $i] : (~p(W, tptp_fun_X_37(elem!90)))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(224,plain,
% 0.20/0.49 (((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~((~p(tptp_fun_X_37(elem!90), elem!90)) | p(tptp_fun_X_37(elem!90), tptp_fun_X_37(elem!90)) | (~p(elem!90, tptp_fun_X_37(elem!90))))) | (~((~p(tptp_fun_X_37(elem!90), tptp_fun_X_37(elem!90))) | (~![W: $i] : (~p(W, tptp_fun_X_37(elem!90)))))))) <=> ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~((~p(elem!90, tptp_fun_X_37(elem!90))) | (~p(tptp_fun_X_37(elem!90), elem!90)) | p(tptp_fun_X_37(elem!90), tptp_fun_X_37(elem!90)))) | (~((~p(tptp_fun_X_37(elem!90), tptp_fun_X_37(elem!90))) | (~![W: $i] : (~p(W, tptp_fun_X_37(elem!90))))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[223])).
% 0.20/0.49 tff(225,plain,
% 0.20/0.49 (((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~((~p(tptp_fun_X_37(elem!90), elem!90)) | p(tptp_fun_X_37(elem!90), tptp_fun_X_37(elem!90)) | (~p(elem!90, tptp_fun_X_37(elem!90))))) | (~((~p(tptp_fun_X_37(elem!90), tptp_fun_X_37(elem!90))) | (~![W: $i] : (~p(W, tptp_fun_X_37(elem!90)))))))) <=> ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))) | (~((~p(elem!90, tptp_fun_X_37(elem!90))) | (~p(tptp_fun_X_37(elem!90), elem!90)) | p(tptp_fun_X_37(elem!90), tptp_fun_X_37(elem!90)))) | (~((~p(tptp_fun_X_37(elem!90), tptp_fun_X_37(elem!90))) | (~![W: $i] : (~p(W, tptp_fun_X_37(elem!90)))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[224, 222])).
% 0.20/0.50 tff(226,plain,
% 0.20/0.50 ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~((~p(tptp_fun_X_37(elem!90), elem!90)) | p(tptp_fun_X_37(elem!90), tptp_fun_X_37(elem!90)) | (~p(elem!90, tptp_fun_X_37(elem!90))))) | (~((~p(tptp_fun_X_37(elem!90), tptp_fun_X_37(elem!90))) | (~![W: $i] : (~p(W, tptp_fun_X_37(elem!90)))))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(227,plain,
% 0.20/0.50 ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))) | (~((~p(elem!90, tptp_fun_X_37(elem!90))) | (~p(tptp_fun_X_37(elem!90), elem!90)) | p(tptp_fun_X_37(elem!90), tptp_fun_X_37(elem!90)))) | (~((~p(tptp_fun_X_37(elem!90), tptp_fun_X_37(elem!90))) | (~![W: $i] : (~p(W, tptp_fun_X_37(elem!90))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.20/0.50 tff(228,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[227, 182, 221, 213])).
% 0.20/0.50 tff(229,plain,((~((~p(elem!90, tptp_fun_X_37(elem!90))) | (~p(tptp_fun_X_37(elem!90), elem!90)) | p(tptp_fun_X_37(elem!90), tptp_fun_X_37(elem!90)))) | (~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y)))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(230,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[229, 212, 182])).
% 0.20/0.50 tff(231,plain,(~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(232,assumption,(~((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3)))))))))))))), introduced(assumption)).
% 0.20/0.50 tff(233,plain,
% 0.20/0.50 (((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3))))))))))))) | ![Z: $i] : q1(f(Z))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(234,plain,
% 0.20/0.50 (![Z: $i] : q1(f(Z))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[233, 232])).
% 0.20/0.50 tff(235,plain,
% 0.20/0.50 ((~![Z: $i] : q1(f(Z))) | q1(f(X!35))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(236,plain,
% 0.20/0.50 (q1(f(X!35))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[235, 234])).
% 0.20/0.50 tff(237,plain,
% 0.20/0.50 (((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3))))))))))))) | ![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3)))))))))))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(238,plain,
% 0.20/0.50 (![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3)))))))))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[237, 232])).
% 0.20/0.50 tff(239,plain,
% 0.20/0.50 (((~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3)))))))))))) | ((~q1(f(X!35))) | (~((~p1(f(C!3))) | (~((~p1(f(X!35))) | (~((~r1(C!3)) | (~((~r1(B!4)) | (~r1(C!3)))))))))))) <=> ((~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3)))))))))))) | (~q1(f(X!35))) | (~((~p1(f(C!3))) | (~((~p1(f(X!35))) | (~((~r1(C!3)) | (~((~r1(B!4)) | (~r1(C!3)))))))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(240,plain,
% 0.20/0.50 ((~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3)))))))))))) | ((~q1(f(X!35))) | (~((~p1(f(C!3))) | (~((~p1(f(X!35))) | (~((~r1(C!3)) | (~((~r1(B!4)) | (~r1(C!3)))))))))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(241,plain,
% 0.20/0.50 ((~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3)))))))))))) | (~q1(f(X!35))) | (~((~p1(f(C!3))) | (~((~p1(f(X!35))) | (~((~r1(C!3)) | (~((~r1(B!4)) | (~r1(C!3))))))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[240, 239])).
% 0.20/0.50 tff(242,plain,
% 0.20/0.50 (~((~p1(f(C!3))) | (~((~p1(f(X!35))) | (~((~r1(C!3)) | (~((~r1(B!4)) | (~r1(C!3)))))))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[241, 238, 236])).
% 0.20/0.50 tff(243,plain,
% 0.20/0.50 (((~p1(f(C!3))) | (~((~p1(f(X!35))) | (~((~r1(C!3)) | (~((~r1(B!4)) | (~r1(C!3))))))))) | ((~p1(f(X!35))) | (~((~r1(C!3)) | (~((~r1(B!4)) | (~r1(C!3)))))))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(244,plain,
% 0.20/0.50 ((~p1(f(X!35))) | (~((~r1(C!3)) | (~((~r1(B!4)) | (~r1(C!3))))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[243, 242])).
% 0.20/0.50 tff(245,plain,
% 0.20/0.50 ((~![Z: $i] : q1(f(Z))) | q1(f(B!42))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
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% 0.20/0.50 inference(unit_resolution,[status(thm)],[235, 280])).
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% 0.20/0.50 (((~![X: $i, Y: $i] : ((~q1(X)) | (~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))))) | ((~((~r1(X!35)) | (~((~r1(B!1)) | (~r1(C!2)))))) | (~q1(f(X!35))))) <=> ((~![X: $i, Y: $i] : ((~q1(X)) | (~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))))) | (~((~r1(X!35)) | (~((~r1(B!1)) | (~r1(C!2)))))) | (~q1(f(X!35))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(303,plain,
% 0.20/0.50 (((~q1(f(X!35))) | $false | (~((~r1(X!35)) | (~((~r1(B!1)) | (~r1(C!2))))))) <=> ((~((~r1(X!35)) | (~((~r1(B!1)) | (~r1(C!2)))))) | (~q1(f(X!35))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(304,plain,
% 0.20/0.50 ((p1(f(X!35)) | (~p1(f(X!35)))) <=> $true),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(305,plain,
% 0.20/0.50 ((~(p1(f(X!35)) | (~p1(f(X!35))))) <=> (~$true)),
% 0.20/0.50 inference(monotonicity,[status(thm)],[304])).
% 0.20/0.50 tff(306,plain,
% 0.20/0.50 ((~(p1(f(X!35)) | (~p1(f(X!35))))) <=> $false),
% 0.20/0.50 inference(transitivity,[status(thm)],[305, 68])).
% 0.20/0.50 tff(307,plain,
% 0.20/0.50 (((~q1(f(X!35))) | (~(p1(f(X!35)) | (~p1(f(X!35))))) | (~((~r1(X!35)) | (~((~r1(B!1)) | (~r1(C!2))))))) <=> ((~q1(f(X!35))) | $false | (~((~r1(X!35)) | (~((~r1(B!1)) | (~r1(C!2)))))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[306])).
% 0.20/0.50 tff(308,plain,
% 0.20/0.50 (((~q1(f(X!35))) | (~(p1(f(X!35)) | (~p1(f(X!35))))) | (~((~r1(X!35)) | (~((~r1(B!1)) | (~r1(C!2))))))) <=> ((~((~r1(X!35)) | (~((~r1(B!1)) | (~r1(C!2)))))) | (~q1(f(X!35))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[307, 303])).
% 0.20/0.50 tff(309,plain,
% 0.20/0.50 (((~![X: $i, Y: $i] : ((~q1(X)) | (~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))))) | ((~q1(f(X!35))) | (~(p1(f(X!35)) | (~p1(f(X!35))))) | (~((~r1(X!35)) | (~((~r1(B!1)) | (~r1(C!2)))))))) <=> ((~![X: $i, Y: $i] : ((~q1(X)) | (~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))))) | ((~((~r1(X!35)) | (~((~r1(B!1)) | (~r1(C!2)))))) | (~q1(f(X!35)))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[308])).
% 0.20/0.50 tff(310,plain,
% 0.20/0.50 (((~![X: $i, Y: $i] : ((~q1(X)) | (~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))))) | ((~q1(f(X!35))) | (~(p1(f(X!35)) | (~p1(f(X!35))))) | (~((~r1(X!35)) | (~((~r1(B!1)) | (~r1(C!2)))))))) <=> ((~![X: $i, Y: $i] : ((~q1(X)) | (~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))))) | (~((~r1(X!35)) | (~((~r1(B!1)) | (~r1(C!2)))))) | (~q1(f(X!35))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[309, 302])).
% 0.20/0.50 tff(311,plain,
% 0.20/0.50 ((~![X: $i, Y: $i] : ((~q1(X)) | (~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))))) | ((~q1(f(X!35))) | (~(p1(f(X!35)) | (~p1(f(X!35))))) | (~((~r1(X!35)) | (~((~r1(B!1)) | (~r1(C!2)))))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(312,plain,
% 0.20/0.50 ((~![X: $i, Y: $i] : ((~q1(X)) | (~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))))) | (~((~r1(X!35)) | (~((~r1(B!1)) | (~r1(C!2)))))) | (~q1(f(X!35)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[311, 310])).
% 0.20/0.50 tff(313,plain,
% 0.20/0.50 (~((~r1(X!35)) | (~((~r1(B!1)) | (~r1(C!2)))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[312, 286, 301])).
% 0.20/0.50 tff(314,plain,
% 0.20/0.50 (((~r1(X!35)) | (~((~r1(B!1)) | (~r1(C!2))))) | ((~r1(B!1)) | (~r1(C!2)))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(315,plain,
% 0.20/0.50 ((~r1(B!1)) | (~r1(C!2))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[314, 313])).
% 0.20/0.50 tff(316,plain,
% 0.20/0.50 ((~((~r1(B!1)) | (~r1(C!2)))) | (~r1(B!1)) | (~r1(C!2))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(317,plain,
% 0.20/0.50 (~r1(B!1)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[316, 315, 300])).
% 0.20/0.50 tff(318,plain,
% 0.20/0.50 (((~r1(B!1)) | (~((~r1(B!1)) | (~r1(C!2))))) | r1(B!1)),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(319,plain,
% 0.20/0.50 ((~r1(B!1)) | (~((~r1(B!1)) | (~r1(C!2))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[318, 317])).
% 0.20/0.50 tff(320,plain,
% 0.20/0.50 (((~![X: $i, Y: $i] : ((~q1(X)) | (~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))))) | ((~((~r1(B!1)) | (~((~r1(B!1)) | (~r1(C!2)))))) | (~q1(f(B!1))))) <=> ((~![X: $i, Y: $i] : ((~q1(X)) | (~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))))) | (~((~r1(B!1)) | (~((~r1(B!1)) | (~r1(C!2)))))) | (~q1(f(B!1))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(321,plain,
% 0.20/0.50 (((~q1(f(B!1))) | $false | (~((~r1(B!1)) | (~((~r1(B!1)) | (~r1(C!2))))))) <=> ((~((~r1(B!1)) | (~((~r1(B!1)) | (~r1(C!2)))))) | (~q1(f(B!1))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(322,plain,
% 0.20/0.50 ((p1(f(B!1)) | (~p1(f(B!1)))) <=> $true),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(323,plain,
% 0.20/0.50 ((~(p1(f(B!1)) | (~p1(f(B!1))))) <=> (~$true)),
% 0.20/0.50 inference(monotonicity,[status(thm)],[322])).
% 0.20/0.50 tff(324,plain,
% 0.20/0.50 ((~(p1(f(B!1)) | (~p1(f(B!1))))) <=> $false),
% 0.20/0.50 inference(transitivity,[status(thm)],[323, 68])).
% 0.20/0.50 tff(325,plain,
% 0.20/0.50 (((~q1(f(B!1))) | (~(p1(f(B!1)) | (~p1(f(B!1))))) | (~((~r1(B!1)) | (~((~r1(B!1)) | (~r1(C!2))))))) <=> ((~q1(f(B!1))) | $false | (~((~r1(B!1)) | (~((~r1(B!1)) | (~r1(C!2)))))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[324])).
% 0.20/0.50 tff(326,plain,
% 0.20/0.50 (((~q1(f(B!1))) | (~(p1(f(B!1)) | (~p1(f(B!1))))) | (~((~r1(B!1)) | (~((~r1(B!1)) | (~r1(C!2))))))) <=> ((~((~r1(B!1)) | (~((~r1(B!1)) | (~r1(C!2)))))) | (~q1(f(B!1))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[325, 321])).
% 0.20/0.50 tff(327,plain,
% 0.20/0.50 (((~![X: $i, Y: $i] : ((~q1(X)) | (~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))))) | ((~q1(f(B!1))) | (~(p1(f(B!1)) | (~p1(f(B!1))))) | (~((~r1(B!1)) | (~((~r1(B!1)) | (~r1(C!2)))))))) <=> ((~![X: $i, Y: $i] : ((~q1(X)) | (~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))))) | ((~((~r1(B!1)) | (~((~r1(B!1)) | (~r1(C!2)))))) | (~q1(f(B!1)))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[326])).
% 0.20/0.50 tff(328,plain,
% 0.20/0.50 (((~![X: $i, Y: $i] : ((~q1(X)) | (~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))))) | ((~q1(f(B!1))) | (~(p1(f(B!1)) | (~p1(f(B!1))))) | (~((~r1(B!1)) | (~((~r1(B!1)) | (~r1(C!2)))))))) <=> ((~![X: $i, Y: $i] : ((~q1(X)) | (~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))))) | (~((~r1(B!1)) | (~((~r1(B!1)) | (~r1(C!2)))))) | (~q1(f(B!1))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[327, 320])).
% 0.20/0.50 tff(329,plain,
% 0.20/0.50 ((~![X: $i, Y: $i] : ((~q1(X)) | (~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))))) | ((~q1(f(B!1))) | (~(p1(f(B!1)) | (~p1(f(B!1))))) | (~((~r1(B!1)) | (~((~r1(B!1)) | (~r1(C!2)))))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(330,plain,
% 0.20/0.50 ((~![X: $i, Y: $i] : ((~q1(X)) | (~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))))) | (~((~r1(B!1)) | (~((~r1(B!1)) | (~r1(C!2)))))) | (~q1(f(B!1)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[329, 328])).
% 0.20/0.50 tff(331,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[330, 286, 319, 282])).
% 0.20/0.50 tff(332,plain,((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2))))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(333,plain,
% 0.20/0.50 (((~p1(X!35)) | p1(tptp_fun_Y_41(X!35))) | p1(X!35)),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(334,plain,
% 0.20/0.50 ((~p1(X!35)) | p1(tptp_fun_Y_41(X!35))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[333, 105])).
% 0.20/0.50 tff(335,plain,
% 0.20/0.50 ((~![X: $i] : (~((~p1(X)) | p1(tptp_fun_Y_41(X))))) | (~((~p1(X!35)) | p1(tptp_fun_Y_41(X!35))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(336,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[335, 16, 334])).
% 0.20/0.50 tff(337,plain,((~![X: $i] : (~((~p1(X)) | p1(tptp_fun_Y_41(X))))) | p1(X!35)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(338,plain,
% 0.20/0.50 (~![X: $i] : (~((~p1(X)) | p1(tptp_fun_Y_41(X))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[337, 105])).
% 0.20/0.50 tff(339,assumption,(![X: $i] : p1(X)), introduced(assumption)).
% 0.20/0.50 tff(340,plain,
% 0.20/0.50 ((~![X: $i] : p1(X)) | p1(X!35)),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(341,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[340, 339, 105])).
% 0.20/0.50 tff(342,plain,((~![X: $i] : p1(X)) | p1(X!35)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(343,plain,
% 0.20/0.50 (~![X: $i] : p1(X)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[342, 105])).
% 0.20/0.50 tff(344,assumption,(~((~(a(X!28, Y!27) | a(X!29, Y!30))) | (~(![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))))), introduced(assumption)).
% 0.20/0.50 tff(345,plain,
% 0.20/0.50 (((~(a(X!28, Y!27) | a(X!29, Y!30))) | (~(![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y))))) | (![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(346,plain,
% 0.20/0.51 (![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[345, 344])).
% 0.20/0.51 tff(347,assumption,(~a(X!28, Y!27)), introduced(assumption)).
% 0.20/0.51 tff(348,plain,
% 0.20/0.51 (((~(a(X!28, Y!27) | a(X!29, Y!30))) | (~(![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y))))) | (a(X!28, Y!27) | a(X!29, Y!30))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(349,plain,
% 0.20/0.51 (a(X!28, Y!27) | a(X!29, Y!30)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[348, 344])).
% 0.20/0.51 tff(350,plain,
% 0.20/0.51 ((~(a(X!28, Y!27) | a(X!29, Y!30))) | a(X!28, Y!27) | a(X!29, Y!30)),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(351,plain,
% 0.20/0.51 (a(X!29, Y!30)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[350, 349, 347])).
% 0.20/0.51 tff(352,assumption,(![Y: $i, X: $i] : (~a(X, Y))), introduced(assumption)).
% 0.20/0.51 tff(353,assumption,(a(X!29, Y!30)), introduced(assumption)).
% 0.20/0.51 tff(354,plain,
% 0.20/0.51 ((~![Y: $i, X: $i] : (~a(X, Y))) | (~a(X!29, Y!30))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(355,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[354, 353, 352])).
% 0.20/0.51 tff(356,plain,((~![Y: $i, X: $i] : (~a(X, Y))) | (~a(X!29, Y!30))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(357,plain,
% 0.20/0.51 (~![Y: $i, X: $i] : (~a(X, Y))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[356, 351])).
% 0.20/0.51 tff(358,plain,
% 0.20/0.51 ((~(![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))) | ![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(359,plain,
% 0.20/0.51 (![X: $i, Y: $i] : (~a(X, Y))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[358, 357, 346])).
% 0.20/0.51 tff(360,plain,
% 0.20/0.51 ((~![X: $i, Y: $i] : (~a(X, Y))) | (~a(X!29, Y!30))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(361,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[360, 351, 359])).
% 0.20/0.51 tff(362,plain,(((~(a(X!28, Y!27) | a(X!29, Y!30))) | (~(![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y))))) | a(X!28, Y!27)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(363,plain,
% 0.20/0.51 (a(X!28, Y!27)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[362, 344])).
% 0.20/0.51 tff(364,assumption,(![X: $i, Y: $i] : (~a(X, Y))), introduced(assumption)).
% 0.20/0.51 tff(365,assumption,(a(X!28, Y!27)), introduced(assumption)).
% 0.20/0.51 tff(366,plain,
% 0.20/0.51 ((~![X: $i, Y: $i] : (~a(X, Y))) | (~a(X!28, Y!27))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(367,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[366, 365, 364])).
% 0.20/0.51 tff(368,plain,((~![X: $i, Y: $i] : (~a(X, Y))) | (~a(X!28, Y!27))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(369,plain,
% 0.20/0.51 (~![X: $i, Y: $i] : (~a(X, Y))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[368, 363])).
% 0.20/0.51 tff(370,plain,
% 0.20/0.51 (![Y: $i, X: $i] : (~a(X, Y))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[358, 369, 346])).
% 0.20/0.51 tff(371,plain,
% 0.20/0.51 ((~![Y: $i, X: $i] : (~a(X, Y))) | (~a(X!28, Y!27))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(372,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[371, 363, 370])).
% 0.20/0.51 tff(373,plain,((~(a(X!28, Y!27) | a(X!29, Y!30))) | (~(![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(374,assumption,((~(r1(Y!52) | (~q1(Y!52)))) | (~![X: $i] : (q1(X) | (~p1(X)))) | (~![Z: $i] : (~(r1(Z) | (~p1(Z)))))), introduced(assumption)).
% 0.20/0.51 tff(375,assumption,(~![X: $i] : p1(X)), introduced(assumption)).
% 0.20/0.51 tff(376,plain,
% 0.20/0.51 (((~q1(Y!14)) | (~![X: $i] : p1(X)) | (~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z)))))) | ![X: $i] : p1(X)),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(377,plain,
% 0.20/0.51 ((~q1(Y!14)) | (~![X: $i] : p1(X)) | (~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z)))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[376, 375])).
% 0.20/0.51 tff(378,assumption,(q1(A!48) | (~k!0) | (~![X: $i] : (~((~p1(X)) | (~q1(X)))))), introduced(assumption)).
% 0.20/0.51 tff(379,plain,
% 0.20/0.51 (((~![X: $i] : p1(X)) | (~![Y: $i] : (~p1(Y)))) | ![X: $i] : p1(X)),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(380,plain,
% 0.20/0.51 ((~![X: $i] : p1(X)) | (~![Y: $i] : (~p1(Y)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[379, 375])).
% 0.20/0.51 tff(381,assumption,((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X))))))), introduced(assumption)).
% 0.20/0.51 tff(382,assumption,((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3))))))))))))), introduced(assumption)).
% 0.20/0.51 tff(383,assumption,((~p1(X!35)) | (~![Y: $i] : (~p1(Y)))), introduced(assumption)).
% 0.20/0.51 tff(384,plain,
% 0.20/0.51 (((~![X: $i] : p1(X)) | (~((~p1(A!13)) | (~p1(B!12))))) | ![X: $i] : p1(X)),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(385,plain,
% 0.20/0.51 ((~![X: $i] : p1(X)) | (~((~p1(A!13)) | (~p1(B!12))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[384, 375])).
% 0.20/0.51 tff(386,assumption,((~(a(X!28, Y!27) | a(X!29, Y!30))) | (~(![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y))))), introduced(assumption)).
% 0.20/0.51 tff(387,assumption,((~(p1(X!35) | p1(Y!36))) | (~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y))))), introduced(assumption)).
% 0.20/0.51 tff(388,assumption,((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2))))))))), introduced(assumption)).
% 0.20/0.51 tff(389,assumption,(~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))), introduced(assumption)).
% 0.20/0.51 tff(390,assumption,((~![Y: $i] : (p1(Y) | (~q1(Y)))) | (~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X))))))), introduced(assumption)).
% 0.20/0.51 tff(391,assumption,(~![X: $i] : (~((~p1(X)) | p1(tptp_fun_Y_41(X))))), introduced(assumption)).
% 0.20/0.51 tff(392,assumption,((~![Z: $i] : (p1(Z) | (~q1(Z)))) | (~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X))))))), introduced(assumption)).
% 0.20/0.51 tff(393,plain,
% 0.20/0.51 (((~![X: $i] : (a(X, Y!25) <=> (~a(X, X)))) | $false) <=> (~![X: $i] : (a(X, Y!25) <=> (~a(X, X))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(394,plain,
% 0.20/0.51 ((a(Y!25, Y!25) <=> (~a(Y!25, Y!25))) <=> $false),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(395,plain,
% 0.20/0.51 (((~![X: $i] : (a(X, Y!25) <=> (~a(X, X)))) | (a(Y!25, Y!25) <=> (~a(Y!25, Y!25)))) <=> ((~![X: $i] : (a(X, Y!25) <=> (~a(X, X)))) | $false)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[394])).
% 0.20/0.51 tff(396,plain,
% 0.20/0.51 (((~![X: $i] : (a(X, Y!25) <=> (~a(X, X)))) | (a(Y!25, Y!25) <=> (~a(Y!25, Y!25)))) <=> (~![X: $i] : (a(X, Y!25) <=> (~a(X, X))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[395, 393])).
% 0.20/0.51 tff(397,plain,
% 0.20/0.51 ((~![X: $i] : (a(X, Y!25) <=> (~a(X, X)))) | (a(Y!25, Y!25) <=> (~a(Y!25, Y!25)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(398,plain,
% 0.20/0.51 (~![X: $i] : (a(X, Y!25) <=> (~a(X, X)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[397, 396])).
% 0.20/0.51 tff(399,assumption,(![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y))))))), introduced(assumption)).
% 0.20/0.51 tff(400,plain,
% 0.20/0.51 (((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y))))))) | (~((~p1(A!8)) | (~e(A!8)) | (~(g(B!6) | (~e(B!6)) | c(f(B!6)))) | (~((~p1(B!6)) | (~c(B!6)))) | (~(p1(f(A!8)) | (~s(A!8, f(A!8))))) | (~((~g(f(A!8))) | (~p1(f(A!8))))) | (~(s(f(A!8), f(f(A!8))) | (~e(f(A!8))) | g(f(A!8))))))) <=> ((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y))))))) | (~((~p1(A!8)) | (~e(A!8)) | (~(g(B!6) | (~e(B!6)) | c(f(B!6)))) | (~((~p1(B!6)) | (~c(B!6)))) | (~(p1(f(A!8)) | (~s(A!8, f(A!8))))) | (~((~g(f(A!8))) | (~p1(f(A!8))))) | (~(s(f(A!8), f(f(A!8))) | (~e(f(A!8))) | g(f(A!8)))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(401,plain,
% 0.20/0.51 ((~((~((~p1(B!6)) | (~c(B!6)))) | (~((~p1(f(A!8))) | (~g(f(A!8))))) | (~p1(A!8)) | (~e(A!8)) | (~(s(f(A!8), f(f(A!8))) | g(f(A!8)) | (~e(f(A!8))))) | (~(c(f(B!6)) | g(B!6) | (~e(B!6)))) | (~(p1(f(A!8)) | (~s(A!8, f(A!8))))))) <=> (~((~p1(A!8)) | (~e(A!8)) | (~(g(B!6) | (~e(B!6)) | c(f(B!6)))) | (~((~p1(B!6)) | (~c(B!6)))) | (~(p1(f(A!8)) | (~s(A!8, f(A!8))))) | (~((~g(f(A!8))) | (~p1(f(A!8))))) | (~(s(f(A!8), f(f(A!8))) | (~e(f(A!8))) | g(f(A!8))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(402,plain,
% 0.20/0.51 (((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y))))))) | (~((~((~p1(B!6)) | (~c(B!6)))) | (~((~p1(f(A!8))) | (~g(f(A!8))))) | (~p1(A!8)) | (~e(A!8)) | (~(s(f(A!8), f(f(A!8))) | g(f(A!8)) | (~e(f(A!8))))) | (~(c(f(B!6)) | g(B!6) | (~e(B!6)))) | (~(p1(f(A!8)) | (~s(A!8, f(A!8)))))))) <=> ((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y))))))) | (~((~p1(A!8)) | (~e(A!8)) | (~(g(B!6) | (~e(B!6)) | c(f(B!6)))) | (~((~p1(B!6)) | (~c(B!6)))) | (~(p1(f(A!8)) | (~s(A!8, f(A!8))))) | (~((~g(f(A!8))) | (~p1(f(A!8))))) | (~(s(f(A!8), f(f(A!8))) | (~e(f(A!8))) | g(f(A!8)))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[401])).
% 0.20/0.51 tff(403,plain,
% 0.20/0.51 (((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y))))))) | (~((~((~p1(B!6)) | (~c(B!6)))) | (~((~p1(f(A!8))) | (~g(f(A!8))))) | (~p1(A!8)) | (~e(A!8)) | (~(s(f(A!8), f(f(A!8))) | g(f(A!8)) | (~e(f(A!8))))) | (~(c(f(B!6)) | g(B!6) | (~e(B!6)))) | (~(p1(f(A!8)) | (~s(A!8, f(A!8)))))))) <=> ((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y))))))) | (~((~p1(A!8)) | (~e(A!8)) | (~(g(B!6) | (~e(B!6)) | c(f(B!6)))) | (~((~p1(B!6)) | (~c(B!6)))) | (~(p1(f(A!8)) | (~s(A!8, f(A!8))))) | (~((~g(f(A!8))) | (~p1(f(A!8))))) | (~(s(f(A!8), f(f(A!8))) | (~e(f(A!8))) | g(f(A!8)))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[402, 400])).
% 0.20/0.51 tff(404,plain,
% 0.20/0.51 ((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y))))))) | (~((~((~p1(B!6)) | (~c(B!6)))) | (~((~p1(f(A!8))) | (~g(f(A!8))))) | (~p1(A!8)) | (~e(A!8)) | (~(s(f(A!8), f(f(A!8))) | g(f(A!8)) | (~e(f(A!8))))) | (~(c(f(B!6)) | g(B!6) | (~e(B!6)))) | (~(p1(f(A!8)) | (~s(A!8, f(A!8)))))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(405,plain,
% 0.20/0.51 ((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y))))))) | (~((~p1(A!8)) | (~e(A!8)) | (~(g(B!6) | (~e(B!6)) | c(f(B!6)))) | (~((~p1(B!6)) | (~c(B!6)))) | (~(p1(f(A!8)) | (~s(A!8, f(A!8))))) | (~((~g(f(A!8))) | (~p1(f(A!8))))) | (~(s(f(A!8), f(f(A!8))) | (~e(f(A!8))) | g(f(A!8))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[404, 403])).
% 0.20/0.51 tff(406,plain,
% 0.20/0.51 (~((~p1(A!8)) | (~e(A!8)) | (~(g(B!6) | (~e(B!6)) | c(f(B!6)))) | (~((~p1(B!6)) | (~c(B!6)))) | (~(p1(f(A!8)) | (~s(A!8, f(A!8))))) | (~((~g(f(A!8))) | (~p1(f(A!8))))) | (~(s(f(A!8), f(f(A!8))) | (~e(f(A!8))) | g(f(A!8)))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[405, 399])).
% 0.20/0.51 tff(407,plain,
% 0.20/0.51 (((~p1(A!8)) | (~e(A!8)) | (~(g(B!6) | (~e(B!6)) | c(f(B!6)))) | (~((~p1(B!6)) | (~c(B!6)))) | (~(p1(f(A!8)) | (~s(A!8, f(A!8))))) | (~((~g(f(A!8))) | (~p1(f(A!8))))) | (~(s(f(A!8), f(f(A!8))) | (~e(f(A!8))) | g(f(A!8))))) | (p1(f(A!8)) | (~s(A!8, f(A!8))))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(408,plain,
% 0.20/0.51 (p1(f(A!8)) | (~s(A!8, f(A!8)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[407, 406])).
% 0.20/0.51 tff(409,plain,
% 0.20/0.51 (((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y))))))) | (~((~p1(A!8)) | (~e(A!8)) | (~((~p1(X!35)) | (~c(X!35)))) | (~((~p1(X!35)) | (~g(X!35)))) | (~(g(B!6) | (~e(B!6)) | c(f(B!6)))) | (~(p1(B!6) | (~s(A!8, B!6)))) | (~((~e(A!8)) | s(A!8, f(A!8)) | g(A!8)))))) <=> ((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y))))))) | (~((~p1(A!8)) | (~e(A!8)) | (~((~p1(X!35)) | (~c(X!35)))) | (~((~p1(X!35)) | (~g(X!35)))) | (~(g(B!6) | (~e(B!6)) | c(f(B!6)))) | (~(p1(B!6) | (~s(A!8, B!6)))) | (~((~e(A!8)) | s(A!8, f(A!8)) | g(A!8))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(410,plain,
% 0.20/0.51 ((~((~((~p1(X!35)) | (~c(X!35)))) | (~((~p1(X!35)) | (~g(X!35)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(A!8, f(A!8)) | g(A!8) | (~e(A!8)))) | (~(c(f(B!6)) | g(B!6) | (~e(B!6)))) | (~(p1(B!6) | (~s(A!8, B!6)))))) <=> (~((~p1(A!8)) | (~e(A!8)) | (~((~p1(X!35)) | (~c(X!35)))) | (~((~p1(X!35)) | (~g(X!35)))) | (~(g(B!6) | (~e(B!6)) | c(f(B!6)))) | (~(p1(B!6) | (~s(A!8, B!6)))) | (~((~e(A!8)) | s(A!8, f(A!8)) | g(A!8)))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(411,plain,
% 0.20/0.51 (((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y))))))) | (~((~((~p1(X!35)) | (~c(X!35)))) | (~((~p1(X!35)) | (~g(X!35)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(A!8, f(A!8)) | g(A!8) | (~e(A!8)))) | (~(c(f(B!6)) | g(B!6) | (~e(B!6)))) | (~(p1(B!6) | (~s(A!8, B!6))))))) <=> ((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y))))))) | (~((~p1(A!8)) | (~e(A!8)) | (~((~p1(X!35)) | (~c(X!35)))) | (~((~p1(X!35)) | (~g(X!35)))) | (~(g(B!6) | (~e(B!6)) | c(f(B!6)))) | (~(p1(B!6) | (~s(A!8, B!6)))) | (~((~e(A!8)) | s(A!8, f(A!8)) | g(A!8))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[410])).
% 0.20/0.51 tff(412,plain,
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% 0.20/0.51 inference(transitivity,[status(thm)],[411, 409])).
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% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
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% 0.20/0.52 inference(modus_ponens,[status(thm)],[413, 412])).
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% 0.20/0.52 inference(unit_resolution,[status(thm)],[414, 399])).
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% 0.20/0.52 inference(tautology,[status(thm)],[])).
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% 0.20/0.52 inference(unit_resolution,[status(thm)],[416, 415])).
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% 0.20/0.52 inference(tautology,[status(thm)],[])).
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% 0.20/0.52 (e(A!8)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[418, 415])).
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% 0.20/0.52 inference(rewrite,[status(thm)],[])).
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% 0.20/0.52 inference(rewrite,[status(thm)],[])).
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% 0.20/0.52 inference(monotonicity,[status(thm)],[421])).
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% 0.20/0.52 inference(transitivity,[status(thm)],[422, 420])).
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% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
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% 0.20/0.52 inference(modus_ponens,[status(thm)],[424, 423])).
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% 0.20/0.52 inference(tautology,[status(thm)],[])).
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% 0.20/0.52 inference(tautology,[status(thm)],[])).
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% 0.20/0.52 inference(unit_resolution,[status(thm)],[429, 415])).
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% 0.20/0.52 inference(tautology,[status(thm)],[])).
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% 0.20/0.52 inference(rewrite,[status(thm)],[])).
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% 0.20/0.52 inference(rewrite,[status(thm)],[])).
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% 0.20/0.52 inference(monotonicity,[status(thm)],[438])).
% 0.20/0.52 tff(440,plain,
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% 0.20/0.52 inference(transitivity,[status(thm)],[439, 437])).
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% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
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% 0.20/0.52 inference(modus_ponens,[status(thm)],[441, 440])).
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% 0.20/0.52 inference(unit_resolution,[status(thm)],[442, 399])).
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% 0.20/0.53 inference(tautology,[status(thm)],[])).
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% 0.20/0.53 inference(unit_resolution,[status(thm)],[444, 443])).
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% 0.20/0.53 inference(tautology,[status(thm)],[])).
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% 0.20/0.53 (c(f(A!8))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[446, 432, 419, 445])).
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% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(449,plain,
% 0.20/0.53 (~((~c(f(A!8))) | (~p1(f(A!8))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[448, 447, 436])).
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% 0.20/0.53 inference(tautology,[status(thm)],[])).
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% 0.20/0.53 inference(unit_resolution,[status(thm)],[450, 449])).
% 0.20/0.53 tff(452,plain,
% 0.20/0.53 (((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y))))))) | (~((~p1(A!8)) | (~e(A!8)) | (~((~p1(X!35)) | (~g(X!35)))) | (~(s(B!6, f(B!6)) | g(B!6) | (~e(B!6)))) | (~(p1(X!35) | (~s(A!8, X!35)))) | (~(g(B!6) | (~e(B!6)) | c(f(B!6)))) | (~((~c(f(A!8))) | (~p1(f(A!8)))))))) <=> ((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y))))))) | (~((~p1(A!8)) | (~e(A!8)) | (~((~p1(X!35)) | (~g(X!35)))) | (~(s(B!6, f(B!6)) | g(B!6) | (~e(B!6)))) | (~(p1(X!35) | (~s(A!8, X!35)))) | (~(g(B!6) | (~e(B!6)) | c(f(B!6)))) | (~((~c(f(A!8))) | (~p1(f(A!8))))))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
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% 0.20/0.53 ((~((~((~p1(f(A!8))) | (~c(f(A!8))))) | (~((~p1(X!35)) | (~g(X!35)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(B!6, f(B!6)) | g(B!6) | (~e(B!6)))) | (~(c(f(B!6)) | g(B!6) | (~e(B!6)))) | (~(p1(X!35) | (~s(A!8, X!35)))))) <=> (~((~p1(A!8)) | (~e(A!8)) | (~((~p1(X!35)) | (~g(X!35)))) | (~(s(B!6, f(B!6)) | g(B!6) | (~e(B!6)))) | (~(p1(X!35) | (~s(A!8, X!35)))) | (~(g(B!6) | (~e(B!6)) | c(f(B!6)))) | (~((~c(f(A!8))) | (~p1(f(A!8)))))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
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% 0.20/0.53 (((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y))))))) | (~((~((~p1(f(A!8))) | (~c(f(A!8))))) | (~((~p1(X!35)) | (~g(X!35)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(B!6, f(B!6)) | g(B!6) | (~e(B!6)))) | (~(c(f(B!6)) | g(B!6) | (~e(B!6)))) | (~(p1(X!35) | (~s(A!8, X!35))))))) <=> ((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y))))))) | (~((~p1(A!8)) | (~e(A!8)) | (~((~p1(X!35)) | (~g(X!35)))) | (~(s(B!6, f(B!6)) | g(B!6) | (~e(B!6)))) | (~(p1(X!35) | (~s(A!8, X!35)))) | (~(g(B!6) | (~e(B!6)) | c(f(B!6)))) | (~((~c(f(A!8))) | (~p1(f(A!8))))))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[453])).
% 0.20/0.53 tff(455,plain,
% 0.20/0.53 (((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y))))))) | (~((~((~p1(f(A!8))) | (~c(f(A!8))))) | (~((~p1(X!35)) | (~g(X!35)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(B!6, f(B!6)) | g(B!6) | (~e(B!6)))) | (~(c(f(B!6)) | g(B!6) | (~e(B!6)))) | (~(p1(X!35) | (~s(A!8, X!35))))))) <=> ((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y))))))) | (~((~p1(A!8)) | (~e(A!8)) | (~((~p1(X!35)) | (~g(X!35)))) | (~(s(B!6, f(B!6)) | g(B!6) | (~e(B!6)))) | (~(p1(X!35) | (~s(A!8, X!35)))) | (~(g(B!6) | (~e(B!6)) | c(f(B!6)))) | (~((~c(f(A!8))) | (~p1(f(A!8))))))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[454, 452])).
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% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
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% 0.20/0.53 inference(modus_ponens,[status(thm)],[456, 455])).
% 0.20/0.53 tff(458,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[457, 399, 451])).
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% 0.20/0.53 tff(460,plain,
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% 0.20/0.53 inference(tautology,[status(thm)],[])).
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% 0.20/0.53 inference(unit_resolution,[status(thm)],[460, 375])).
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% 0.20/0.53 (((~![X: $i] : p1(X)) | (~((~p1(X!33)) | (~p1(Y!34))))) | ![X: $i] : p1(X)),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(463,plain,
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% 0.20/0.53 inference(unit_resolution,[status(thm)],[462, 375])).
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% 0.20/0.53 inference(rewrite,[status(thm)],[])).
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% 0.20/0.53 ((~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(f(B!6))) | p(f(B!6), A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(B!42)) | p(B!49, B!42))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(f(B!6), B!42))))) <=> (~((~s1(A!50)) | p(A!50, B!49) | (~q1(A!50)) | (~q1(B!49)) | (~r1(A!50)) | (~r1(B!49)) | (~((~q1(f(B!6))) | p(f(B!6), A!50))) | (~((~s1(A!50)) | p(f(B!6), B!42))) | (~((~r1(B!42)) | p(B!49, B!42)))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(467,plain,
% 0.20/0.53 (((~![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y)))))) | (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(f(B!6))) | p(f(B!6), A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(B!42)) | p(B!49, B!42))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(f(B!6), B!42)))))) <=> ((~![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y)))))) | (~((~s1(A!50)) | p(A!50, B!49) | (~q1(A!50)) | (~q1(B!49)) | (~r1(A!50)) | (~r1(B!49)) | (~((~q1(f(B!6))) | p(f(B!6), A!50))) | (~((~s1(A!50)) | p(f(B!6), B!42))) | (~((~r1(B!42)) | p(B!49, B!42))))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[466])).
% 0.20/0.53 tff(468,plain,
% 0.20/0.53 (((~![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y)))))) | (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(f(B!6))) | p(f(B!6), A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(B!42)) | p(B!49, B!42))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(f(B!6), B!42)))))) <=> ((~![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y)))))) | (~((~s1(A!50)) | p(A!50, B!49) | (~q1(A!50)) | (~q1(B!49)) | (~r1(A!50)) | (~r1(B!49)) | (~((~q1(f(B!6))) | p(f(B!6), A!50))) | (~((~s1(A!50)) | p(f(B!6), B!42))) | (~((~r1(B!42)) | p(B!49, B!42))))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[467, 465])).
% 0.20/0.53 tff(469,plain,
% 0.20/0.53 ((~![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y)))))) | (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(f(B!6))) | p(f(B!6), A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(B!42)) | p(B!49, B!42))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(f(B!6), B!42)))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(470,plain,
% 0.20/0.53 ((~![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y)))))) | (~((~s1(A!50)) | p(A!50, B!49) | (~q1(A!50)) | (~q1(B!49)) | (~r1(A!50)) | (~r1(B!49)) | (~((~q1(f(B!6))) | p(f(B!6), A!50))) | (~((~s1(A!50)) | p(f(B!6), B!42))) | (~((~r1(B!42)) | p(B!49, B!42)))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[469, 468])).
% 0.20/0.53 tff(471,plain,
% 0.20/0.53 (~((~s1(A!50)) | p(A!50, B!49) | (~q1(A!50)) | (~q1(B!49)) | (~r1(A!50)) | (~r1(B!49)) | (~((~q1(f(B!6))) | p(f(B!6), A!50))) | (~((~s1(A!50)) | p(f(B!6), B!42))) | (~((~r1(B!42)) | p(B!49, B!42))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[470, 464])).
% 0.20/0.53 tff(472,plain,
% 0.20/0.53 (((~s1(A!50)) | p(A!50, B!49) | (~q1(A!50)) | (~q1(B!49)) | (~r1(A!50)) | (~r1(B!49)) | (~((~q1(f(B!6))) | p(f(B!6), A!50))) | (~((~s1(A!50)) | p(f(B!6), B!42))) | (~((~r1(B!42)) | p(B!49, B!42)))) | (~p(A!50, B!49))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(473,plain,
% 0.20/0.53 (~p(A!50, B!49)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[472, 471])).
% 0.20/0.53 tff(474,plain,
% 0.20/0.53 (((~s1(A!50)) | p(A!50, B!49) | (~q1(A!50)) | (~q1(B!49)) | (~r1(A!50)) | (~r1(B!49)) | (~((~q1(f(B!6))) | p(f(B!6), A!50))) | (~((~s1(A!50)) | p(f(B!6), B!42))) | (~((~r1(B!42)) | p(B!49, B!42)))) | s1(A!50)),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(475,plain,
% 0.20/0.53 (s1(A!50)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[474, 471])).
% 0.20/0.53 tff(476,plain,
% 0.20/0.53 ((~((~s1(A!50)) | p(A!50, B!49))) | (~s1(A!50)) | p(A!50, B!49)),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(477,plain,
% 0.20/0.53 (~((~s1(A!50)) | p(A!50, B!49))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[476, 475, 473])).
% 0.20/0.53 tff(478,plain,
% 0.20/0.53 (((~s1(A!50)) | p(A!50, B!49) | (~q1(A!50)) | (~q1(B!49)) | (~r1(A!50)) | (~r1(B!49)) | (~((~r1(B!49)) | p(B!49, B!49))) | (~((~q1(A!50)) | p(A!50, A!50))) | (~((~s1(A!50)) | p(A!50, B!49)))) | ((~s1(A!50)) | p(A!50, B!49))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(479,plain,
% 0.20/0.53 ((~s1(A!50)) | p(A!50, B!49) | (~q1(A!50)) | (~q1(B!49)) | (~r1(A!50)) | (~r1(B!49)) | (~((~r1(B!49)) | p(B!49, B!49))) | (~((~q1(A!50)) | p(A!50, A!50))) | (~((~s1(A!50)) | p(A!50, B!49)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[478, 477])).
% 0.20/0.53 tff(480,plain,
% 0.20/0.53 (((~![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y)))))) | (~((~s1(A!50)) | p(A!50, B!49) | (~q1(A!50)) | (~q1(B!49)) | (~r1(A!50)) | (~r1(B!49)) | (~((~r1(B!49)) | p(B!49, B!49))) | (~((~q1(A!50)) | p(A!50, A!50))) | (~((~s1(A!50)) | p(A!50, B!49)))))) <=> ((~![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y)))))) | (~((~s1(A!50)) | p(A!50, B!49) | (~q1(A!50)) | (~q1(B!49)) | (~r1(A!50)) | (~r1(B!49)) | (~((~r1(B!49)) | p(B!49, B!49))) | (~((~q1(A!50)) | p(A!50, A!50))) | (~((~s1(A!50)) | p(A!50, B!49))))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(481,plain,
% 0.20/0.53 ((~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(A!50)) | p(A!50, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(B!49)) | p(B!49, B!49))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(A!50, B!49))))) <=> (~((~s1(A!50)) | p(A!50, B!49) | (~q1(A!50)) | (~q1(B!49)) | (~r1(A!50)) | (~r1(B!49)) | (~((~r1(B!49)) | p(B!49, B!49))) | (~((~q1(A!50)) | p(A!50, A!50))) | (~((~s1(A!50)) | p(A!50, B!49)))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(482,plain,
% 0.20/0.53 (((~![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y)))))) | (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(A!50)) | p(A!50, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(B!49)) | p(B!49, B!49))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(A!50, B!49)))))) <=> ((~![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y)))))) | (~((~s1(A!50)) | p(A!50, B!49) | (~q1(A!50)) | (~q1(B!49)) | (~r1(A!50)) | (~r1(B!49)) | (~((~r1(B!49)) | p(B!49, B!49))) | (~((~q1(A!50)) | p(A!50, A!50))) | (~((~s1(A!50)) | p(A!50, B!49))))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[481])).
% 0.20/0.53 tff(483,plain,
% 0.20/0.53 (((~![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y)))))) | (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(A!50)) | p(A!50, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(B!49)) | p(B!49, B!49))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(A!50, B!49)))))) <=> ((~![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y)))))) | (~((~s1(A!50)) | p(A!50, B!49) | (~q1(A!50)) | (~q1(B!49)) | (~r1(A!50)) | (~r1(B!49)) | (~((~r1(B!49)) | p(B!49, B!49))) | (~((~q1(A!50)) | p(A!50, A!50))) | (~((~s1(A!50)) | p(A!50, B!49))))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[482, 480])).
% 0.20/0.53 tff(484,plain,
% 0.20/0.53 ((~![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y)))))) | (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(A!50)) | p(A!50, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(B!49)) | p(B!49, B!49))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(A!50, B!49)))))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(485,plain,
% 0.20/0.54 ((~![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y)))))) | (~((~s1(A!50)) | p(A!50, B!49) | (~q1(A!50)) | (~q1(B!49)) | (~r1(A!50)) | (~r1(B!49)) | (~((~r1(B!49)) | p(B!49, B!49))) | (~((~q1(A!50)) | p(A!50, A!50))) | (~((~s1(A!50)) | p(A!50, B!49)))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[484, 483])).
% 0.20/0.54 tff(486,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[485, 464, 479])).
% 0.20/0.54 tff(487,plain,(~![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(488,assumption,(~((~![Y: $i] : p(X!45, Y)) | (~![X: $i] : (~p(X, Y!46))))), introduced(assumption)).
% 0.20/0.54 tff(489,plain,
% 0.20/0.54 (((~![Y: $i] : p(X!45, Y)) | (~![X: $i] : (~p(X, Y!46)))) | ![X: $i] : (~p(X, Y!46))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(490,plain,
% 0.20/0.54 (![X: $i] : (~p(X, Y!46))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[489, 488])).
% 0.20/0.54 tff(491,plain,
% 0.20/0.54 ((~![X: $i] : (~p(X, Y!46))) | (~p(X!45, Y!46))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(492,plain,
% 0.20/0.54 (~p(X!45, Y!46)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[491, 490])).
% 0.20/0.54 tff(493,plain,
% 0.20/0.54 (((~![Y: $i] : p(X!45, Y)) | (~![X: $i] : (~p(X, Y!46)))) | ![Y: $i] : p(X!45, Y)),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(494,plain,
% 0.20/0.54 (![Y: $i] : p(X!45, Y)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[493, 488])).
% 0.20/0.54 tff(495,plain,
% 0.20/0.54 ((~![Y: $i] : p(X!45, Y)) | p(X!45, Y!46)),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(496,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[495, 494, 492])).
% 0.20/0.54 tff(497,plain,((~![Y: $i] : p(X!45, Y)) | (~![X: $i] : (~p(X, Y!46)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(498,assumption,(![X: $i, Y: $i] : (~(r1(B!43) | (~p1(A!44)) | (~(r1(Y) | (~p1(X))))))), introduced(assumption)).
% 0.20/0.54 tff(499,plain,
% 0.20/0.54 ((~![X: $i, Y: $i] : (~(r1(B!43) | (~p1(A!44)) | (~(r1(Y) | (~p1(X))))))) | (~(r1(B!43) | (~p1(A!44)) | (~(r1(B!42) | (~p1(X!35))))))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(500,plain,
% 0.20/0.54 (~(r1(B!43) | (~p1(A!44)) | (~(r1(B!42) | (~p1(X!35)))))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[499, 498])).
% 0.20/0.54 tff(501,plain,
% 0.20/0.54 ((r1(B!43) | (~p1(A!44)) | (~(r1(B!42) | (~p1(X!35))))) | p1(A!44)),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(502,plain,
% 0.20/0.54 (p1(A!44)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[501, 500])).
% 0.20/0.54 tff(503,plain,
% 0.20/0.54 ((r1(B!43) | (~p1(A!44)) | (~(r1(B!42) | (~p1(X!35))))) | (~r1(B!43))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(504,plain,
% 0.20/0.54 (~r1(B!43)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[503, 500])).
% 0.20/0.54 tff(505,plain,
% 0.20/0.54 ((~(r1(B!43) | (~p1(A!44)))) | r1(B!43) | (~p1(A!44))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(506,plain,
% 0.20/0.54 (~(r1(B!43) | (~p1(A!44)))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[505, 504, 502])).
% 0.20/0.54 tff(507,plain,
% 0.20/0.54 ((r1(B!43) | (~p1(A!44)) | (~(r1(B!43) | (~p1(A!44))))) | (r1(B!43) | (~p1(A!44)))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(508,plain,
% 0.20/0.54 (r1(B!43) | (~p1(A!44)) | (~(r1(B!43) | (~p1(A!44))))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[507, 506])).
% 0.20/0.54 tff(509,plain,
% 0.20/0.54 ((~![X: $i, Y: $i] : (~(r1(B!43) | (~p1(A!44)) | (~(r1(Y) | (~p1(X))))))) | (~(r1(B!43) | (~p1(A!44)) | (~(r1(B!43) | (~p1(A!44))))))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(510,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[509, 498, 508])).
% 0.20/0.54 tff(511,plain,(~![X: $i, Y: $i] : (~(r1(B!43) | (~p1(A!44)) | (~(r1(Y) | (~p1(X))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(512,plain,
% 0.20/0.54 (((~![Y: $i] : (~(p1(Y) | (~p1(X!35))))) | $false) <=> (~![Y: $i] : (~(p1(Y) | (~p1(X!35)))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(513,plain,
% 0.20/0.54 ((p1(X!35) | (~p1(X!35))) <=> $true),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(514,plain,
% 0.20/0.54 ((~(p1(X!35) | (~p1(X!35)))) <=> (~$true)),
% 0.20/0.54 inference(monotonicity,[status(thm)],[513])).
% 0.20/0.54 tff(515,plain,
% 0.20/0.54 ((~(p1(X!35) | (~p1(X!35)))) <=> $false),
% 0.20/0.54 inference(transitivity,[status(thm)],[514, 68])).
% 0.20/0.54 tff(516,plain,
% 0.20/0.54 (((~![Y: $i] : (~(p1(Y) | (~p1(X!35))))) | (~(p1(X!35) | (~p1(X!35))))) <=> ((~![Y: $i] : (~(p1(Y) | (~p1(X!35))))) | $false)),
% 0.20/0.54 inference(monotonicity,[status(thm)],[515])).
% 0.20/0.54 tff(517,plain,
% 0.20/0.54 (((~![Y: $i] : (~(p1(Y) | (~p1(X!35))))) | (~(p1(X!35) | (~p1(X!35))))) <=> (~![Y: $i] : (~(p1(Y) | (~p1(X!35)))))),
% 0.20/0.54 inference(transitivity,[status(thm)],[516, 512])).
% 0.20/0.54 tff(518,plain,
% 0.20/0.54 ((~![Y: $i] : (~(p1(Y) | (~p1(X!35))))) | (~(p1(X!35) | (~p1(X!35))))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(519,plain,
% 0.20/0.54 (~![Y: $i] : (~(p1(Y) | (~p1(X!35))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[518, 517])).
% 0.20/0.54 tff(520,assumption,(![Y: $i] : (~(p1(Y) | (~p1(X!35))))), introduced(assumption)).
% 0.20/0.54 tff(521,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[520, 519])).
% 0.20/0.54 tff(522,plain,(~![Y: $i] : (~(p1(Y) | (~p1(X!35))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(523,assumption,(~((~a1(X!23)) | (~![X: $i] : (b(X) | (~a1(X)))) | (~![X: $i] : (~b(X))))), introduced(assumption)).
% 0.20/0.54 tff(524,plain,
% 0.20/0.54 (((~a1(X!23)) | (~![X: $i] : (b(X) | (~a1(X)))) | (~![X: $i] : (~b(X)))) | ![X: $i] : (b(X) | (~a1(X)))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(525,plain,
% 0.20/0.54 (![X: $i] : (b(X) | (~a1(X)))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[524, 523])).
% 0.20/0.54 tff(526,plain,
% 0.20/0.54 (((~a1(X!23)) | (~![X: $i] : (b(X) | (~a1(X)))) | (~![X: $i] : (~b(X)))) | a1(X!23)),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(527,plain,
% 0.20/0.54 (a1(X!23)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[526, 523])).
% 0.20/0.54 tff(528,plain,
% 0.20/0.54 (((~![X: $i] : (b(X) | (~a1(X)))) | (b(X!23) | (~a1(X!23)))) <=> ((~![X: $i] : (b(X) | (~a1(X)))) | b(X!23) | (~a1(X!23)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(529,plain,
% 0.20/0.54 ((~![X: $i] : (b(X) | (~a1(X)))) | (b(X!23) | (~a1(X!23)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(530,plain,
% 0.20/0.54 ((~![X: $i] : (b(X) | (~a1(X)))) | b(X!23) | (~a1(X!23))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[529, 528])).
% 0.20/0.54 tff(531,plain,
% 0.20/0.54 (b(X!23)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[530, 527, 525])).
% 0.20/0.54 tff(532,plain,
% 0.20/0.54 (((~a1(X!23)) | (~![X: $i] : (b(X) | (~a1(X)))) | (~![X: $i] : (~b(X)))) | ![X: $i] : (~b(X))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(533,plain,
% 0.20/0.54 (![X: $i] : (~b(X))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[532, 523])).
% 0.20/0.54 tff(534,plain,
% 0.20/0.54 ((~![X: $i] : (~b(X))) | (~b(X!23))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(535,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[534, 533, 531])).
% 0.20/0.54 tff(536,plain,((~a1(X!23)) | (~![X: $i] : (b(X) | (~a1(X)))) | (~![X: $i] : (~b(X)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(537,assumption,(~((~![X: $i] : (~((~a(X, tptp_fun_Y_17(X))) | (~a(tptp_fun_Y_17(X), tptp_fun_Y_17(X)))))) | (~![Z: $i] : (~a(Z, Z))))), introduced(assumption)).
% 0.20/0.54 tff(538,plain,
% 0.20/0.54 (((~![X: $i] : (~((~a(X, tptp_fun_Y_17(X))) | (~a(tptp_fun_Y_17(X), tptp_fun_Y_17(X)))))) | (~![Z: $i] : (~a(Z, Z)))) | ![X: $i] : (~((~a(X, tptp_fun_Y_17(X))) | (~a(tptp_fun_Y_17(X), tptp_fun_Y_17(X)))))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(539,plain,
% 0.20/0.54 (![X: $i] : (~((~a(X, tptp_fun_Y_17(X))) | (~a(tptp_fun_Y_17(X), tptp_fun_Y_17(X)))))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[538, 537])).
% 0.20/0.54 tff(540,plain,
% 0.20/0.54 ((~![X: $i] : (~((~a(X, tptp_fun_Y_17(X))) | (~a(tptp_fun_Y_17(X), tptp_fun_Y_17(X)))))) | (~((~a(elem!72, tptp_fun_Y_17(elem!72))) | (~a(tptp_fun_Y_17(elem!72), tptp_fun_Y_17(elem!72)))))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(541,plain,
% 0.20/0.54 (~((~a(elem!72, tptp_fun_Y_17(elem!72))) | (~a(tptp_fun_Y_17(elem!72), tptp_fun_Y_17(elem!72))))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[540, 539])).
% 0.20/0.54 tff(542,plain,
% 0.20/0.54 (((~a(elem!72, tptp_fun_Y_17(elem!72))) | (~a(tptp_fun_Y_17(elem!72), tptp_fun_Y_17(elem!72)))) | a(tptp_fun_Y_17(elem!72), tptp_fun_Y_17(elem!72))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(543,plain,
% 0.20/0.54 (a(tptp_fun_Y_17(elem!72), tptp_fun_Y_17(elem!72))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[542, 541])).
% 0.20/0.54 tff(544,plain,
% 0.20/0.54 (((~![X: $i] : (~((~a(X, tptp_fun_Y_17(X))) | (~a(tptp_fun_Y_17(X), tptp_fun_Y_17(X)))))) | (~![Z: $i] : (~a(Z, Z)))) | ![Z: $i] : (~a(Z, Z))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(545,plain,
% 0.20/0.54 (![Z: $i] : (~a(Z, Z))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[544, 537])).
% 0.20/0.54 tff(546,plain,
% 0.20/0.54 ((~![Z: $i] : (~a(Z, Z))) | (~a(tptp_fun_Y_17(elem!72), tptp_fun_Y_17(elem!72)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(547,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[546, 545, 543])).
% 0.20/0.54 tff(548,plain,((~![X: $i] : (~((~a(X, tptp_fun_Y_17(X))) | (~a(tptp_fun_Y_17(X), tptp_fun_Y_17(X)))))) | (~![Z: $i] : (~a(Z, Z)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(549,assumption,(~(q1(B!42) | (~r1(B!42)) | (~![X: $i] : (q1(X) | (~p1(X)))) | (~![Y: $i] : (p1(Y) | (~r1(Y)))))), introduced(assumption)).
% 0.20/0.54 tff(550,plain,
% 0.20/0.54 ((q1(B!42) | (~r1(B!42)) | (~![X: $i] : (q1(X) | (~p1(X)))) | (~![Y: $i] : (p1(Y) | (~r1(Y))))) | ![Y: $i] : (p1(Y) | (~r1(Y)))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(551,plain,
% 0.20/0.54 (![Y: $i] : (p1(Y) | (~r1(Y)))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[550, 549])).
% 0.20/0.54 tff(552,plain,
% 0.20/0.54 ((q1(B!42) | (~r1(B!42)) | (~![X: $i] : (q1(X) | (~p1(X)))) | (~![Y: $i] : (p1(Y) | (~r1(Y))))) | r1(B!42)),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(553,plain,
% 0.20/0.54 (r1(B!42)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[552, 549])).
% 0.20/0.54 tff(554,plain,
% 0.20/0.54 (((~![Y: $i] : (p1(Y) | (~r1(Y)))) | (p1(B!42) | (~r1(B!42)))) <=> ((~![Y: $i] : (p1(Y) | (~r1(Y)))) | p1(B!42) | (~r1(B!42)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(555,plain,
% 0.20/0.54 ((~![Y: $i] : (p1(Y) | (~r1(Y)))) | (p1(B!42) | (~r1(B!42)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(556,plain,
% 0.20/0.54 ((~![Y: $i] : (p1(Y) | (~r1(Y)))) | p1(B!42) | (~r1(B!42))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[555, 554])).
% 0.20/0.54 tff(557,plain,
% 0.20/0.54 (p1(B!42)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[556, 553, 551])).
% 0.20/0.54 tff(558,plain,
% 0.20/0.54 ((q1(B!42) | (~r1(B!42)) | (~![X: $i] : (q1(X) | (~p1(X)))) | (~![Y: $i] : (p1(Y) | (~r1(Y))))) | (~q1(B!42))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(559,plain,
% 0.20/0.54 (~q1(B!42)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[558, 549])).
% 0.20/0.54 tff(560,plain,
% 0.20/0.54 ((q1(B!42) | (~r1(B!42)) | (~![X: $i] : (q1(X) | (~p1(X)))) | (~![Y: $i] : (p1(Y) | (~r1(Y))))) | ![X: $i] : (q1(X) | (~p1(X)))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(561,plain,
% 0.20/0.54 (![X: $i] : (q1(X) | (~p1(X)))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[560, 549])).
% 0.20/0.54 tff(562,plain,
% 0.20/0.54 (((~![X: $i] : (q1(X) | (~p1(X)))) | (q1(B!42) | (~p1(B!42)))) <=> ((~![X: $i] : (q1(X) | (~p1(X)))) | q1(B!42) | (~p1(B!42)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(563,plain,
% 0.20/0.54 ((~![X: $i] : (q1(X) | (~p1(X)))) | (q1(B!42) | (~p1(B!42)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(564,plain,
% 0.20/0.54 ((~![X: $i] : (q1(X) | (~p1(X)))) | q1(B!42) | (~p1(B!42))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[563, 562])).
% 0.20/0.54 tff(565,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[564, 561, 559, 557])).
% 0.20/0.54 tff(566,plain,(q1(B!42) | (~r1(B!42)) | (~![X: $i] : (q1(X) | (~p1(X)))) | (~![Y: $i] : (p1(Y) | (~r1(Y))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(567,assumption,(~(b(X!7) | (~a1(X!7)) | (~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (~![X: $i] : ((~a1(X)) | (~c(X)))))), introduced(assumption)).
% 0.20/0.54 tff(568,plain,
% 0.20/0.54 ((b(X!7) | (~a1(X!7)) | (~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (~![X: $i] : ((~a1(X)) | (~c(X))))) | ![X: $i] : ((~a1(X)) | (~c(X)))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(569,plain,
% 0.20/0.54 (![X: $i] : ((~a1(X)) | (~c(X)))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[568, 567])).
% 0.20/0.54 tff(570,plain,
% 0.20/0.54 ((b(X!7) | (~a1(X!7)) | (~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (~![X: $i] : ((~a1(X)) | (~c(X))))) | a1(X!7)),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(571,plain,
% 0.20/0.54 (a1(X!7)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[570, 567])).
% 0.20/0.54 tff(572,plain,
% 0.20/0.54 (((~![X: $i] : ((~a1(X)) | (~c(X)))) | ((~a1(X!7)) | (~c(X!7)))) <=> ((~![X: $i] : ((~a1(X)) | (~c(X)))) | (~a1(X!7)) | (~c(X!7)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(573,plain,
% 0.20/0.54 ((~![X: $i] : ((~a1(X)) | (~c(X)))) | ((~a1(X!7)) | (~c(X!7)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(574,plain,
% 0.20/0.54 ((~![X: $i] : ((~a1(X)) | (~c(X)))) | (~a1(X!7)) | (~c(X!7))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[573, 572])).
% 0.20/0.54 tff(575,plain,
% 0.20/0.54 (~c(X!7)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[574, 571, 569])).
% 0.20/0.54 tff(576,plain,
% 0.20/0.54 ((b(X!7) | (~a1(X!7)) | (~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (~![X: $i] : ((~a1(X)) | (~c(X))))) | ![X: $i] : (c(X) | b(X) | (~a1(X)))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(577,plain,
% 0.20/0.54 (![X: $i] : (c(X) | b(X) | (~a1(X)))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[576, 567])).
% 0.20/0.54 tff(578,plain,
% 0.20/0.54 ((b(X!7) | (~a1(X!7)) | (~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (~![X: $i] : ((~a1(X)) | (~c(X))))) | (~b(X!7))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(579,plain,
% 0.20/0.54 (~b(X!7)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[578, 567])).
% 0.20/0.54 tff(580,plain,
% 0.20/0.54 (((~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (b(X!7) | (~a1(X!7)) | c(X!7))) <=> ((~![X: $i] : (c(X) | b(X) | (~a1(X)))) | b(X!7) | (~a1(X!7)) | c(X!7))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(581,plain,
% 0.20/0.54 ((c(X!7) | b(X!7) | (~a1(X!7))) <=> (b(X!7) | (~a1(X!7)) | c(X!7))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(582,plain,
% 0.20/0.54 (((~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (c(X!7) | b(X!7) | (~a1(X!7)))) <=> ((~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (b(X!7) | (~a1(X!7)) | c(X!7)))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[581])).
% 0.20/0.54 tff(583,plain,
% 0.20/0.54 (((~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (c(X!7) | b(X!7) | (~a1(X!7)))) <=> ((~![X: $i] : (c(X) | b(X) | (~a1(X)))) | b(X!7) | (~a1(X!7)) | c(X!7))),
% 0.20/0.54 inference(transitivity,[status(thm)],[582, 580])).
% 0.20/0.54 tff(584,plain,
% 0.20/0.54 ((~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (c(X!7) | b(X!7) | (~a1(X!7)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(585,plain,
% 0.20/0.54 ((~![X: $i] : (c(X) | b(X) | (~a1(X)))) | b(X!7) | (~a1(X!7)) | c(X!7)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[584, 583])).
% 0.20/0.54 tff(586,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[585, 579, 571, 577, 575])).
% 0.20/0.54 tff(587,plain,(b(X!7) | (~a1(X!7)) | (~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (~![X: $i] : ((~a1(X)) | (~c(X))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(588,assumption,(~((~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))) | (~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))))), introduced(assumption)).
% 0.20/0.54 tff(589,plain,
% 0.20/0.54 (((~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))) | (~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y)))))) | ![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(590,plain,
% 0.20/0.54 (![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[589, 588])).
% 0.20/0.54 tff(591,assumption,(p(f(B!51), B!51)), introduced(assumption)).
% 0.20/0.54 tff(592,assumption,(![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))), introduced(assumption)).
% 0.20/0.54 tff(593,plain,
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% 0.20/0.54 inference(rewrite,[status(thm)],[])).
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% 0.20/0.54 inference(rewrite,[status(thm)],[])).
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% 0.20/0.54 ((~((~q(f(B!51), B!51)) | q(f(B!51), B!51))) <=> $false),
% 0.20/0.54 inference(transitivity,[status(thm)],[596, 68])).
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% 0.20/0.54 inference(monotonicity,[status(thm)],[597])).
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% 0.20/0.54 inference(transitivity,[status(thm)],[598, 594])).
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% 0.20/0.54 inference(monotonicity,[status(thm)],[599])).
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% 0.20/0.54 inference(transitivity,[status(thm)],[600, 593])).
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% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
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% 0.20/0.54 inference(modus_ponens,[status(thm)],[602, 601])).
% 0.20/0.54 tff(604,plain,
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% 0.20/0.54 inference(unit_resolution,[status(thm)],[603, 592, 591])).
% 0.20/0.54 tff(605,plain,((~p(f(B!51), B!51)) | (~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(606,plain,
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% 0.20/0.54 inference(unit_resolution,[status(thm)],[605, 590])).
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% 0.20/0.54 inference(unit_resolution,[status(thm)],[607, 588])).
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% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(610,plain,
% 0.20/0.54 (($false | p(f(B!51), B!51)) <=> p(f(B!51), B!51)),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
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% 0.20/0.54 inference(rewrite,[status(thm)],[])).
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% 0.20/0.54 inference(monotonicity,[status(thm)],[611])).
% 0.20/0.54 tff(613,plain,
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% 0.20/0.54 inference(transitivity,[status(thm)],[612, 68])).
% 0.20/0.54 tff(614,plain,
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% 0.20/0.54 inference(monotonicity,[status(thm)],[613])).
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% 0.20/0.54 (((~(r1(B!51) | (~r1(B!51)))) | p(f(B!51), B!51)) <=> p(f(B!51), B!51)),
% 0.20/0.54 inference(transitivity,[status(thm)],[614, 610])).
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% 0.20/0.54 inference(monotonicity,[status(thm)],[615])).
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% 0.20/0.54 inference(transitivity,[status(thm)],[616, 609])).
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% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(619,plain,
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% 0.20/0.54 inference(modus_ponens,[status(thm)],[618, 617])).
% 0.20/0.54 tff(620,plain,
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% 0.20/0.54 inference(unit_resolution,[status(thm)],[619, 608, 606])).
% 0.20/0.54 tff(621,plain,((~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))) | (~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(622,assumption,(~((~q1(f(B!6))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5)))))))))))))), introduced(assumption)).
% 0.20/0.54 tff(623,plain,
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% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(624,plain,
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% 0.20/0.54 inference(unit_resolution,[status(thm)],[623, 622])).
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% 0.20/0.54 inference(tautology,[status(thm)],[])).
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% 0.20/0.54 inference(unit_resolution,[status(thm)],[625, 622])).
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% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
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% 0.20/0.54 inference(modus_ponens,[status(thm)],[634, 633])).
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% 0.20/0.55 inference(unit_resolution,[status(thm)],[641, 640])).
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% 0.20/0.55 inference(unit_resolution,[status(thm)],[643, 640])).
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% 0.20/0.55 inference(tautology,[status(thm)],[])).
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% 0.20/0.55 inference(unit_resolution,[status(thm)],[647, 638, 646])).
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% 0.20/0.55 inference(unit_resolution,[status(thm)],[649, 648])).
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% 0.20/0.55 inference(unit_resolution,[status(thm)],[655, 654])).
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% 0.20/0.55 (![X: $i, Y: $i] : p(X, Y)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[657, 654])).
% 0.20/0.55 tff(659,plain,
% 0.20/0.55 ((~![X: $i, Y: $i] : p(X, Y)) | p(X!47, X!47)),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(660,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[659, 658, 656])).
% 0.20/0.55 tff(661,plain,((~![X: $i, Y: $i] : p(X, Y)) | p(X!47, X!47)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(662,assumption,(~((~p1(X!35)) | (~![Z: $i] : (~p1(Z))))), introduced(assumption)).
% 0.20/0.55 tff(663,plain,
% 0.20/0.55 (((~p1(X!35)) | (~![Z: $i] : (~p1(Z)))) | ![Z: $i] : (~p1(Z))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(664,plain,
% 0.20/0.55 (![Z: $i] : (~p1(Z))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[663, 662])).
% 0.20/0.55 tff(665,plain,
% 0.20/0.55 (((~p1(X!35)) | (~![Z: $i] : (~p1(Z)))) | p1(X!35)),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(666,plain,
% 0.20/0.55 (p1(X!35)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[665, 662])).
% 0.20/0.55 tff(667,plain,
% 0.20/0.55 ((~![Z: $i] : (~p1(Z))) | (~p1(X!35))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(668,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[667, 666, 664])).
% 0.20/0.55 tff(669,plain,((~p1(X!35)) | (~![Z: $i] : (~p1(Z)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(670,assumption,(~((~(b(X!24) | (~a1(X!24)))) | (~![X: $i] : (~b(X))) | (~![X: $i] : a1(X)))), introduced(assumption)).
% 0.20/0.55 tff(671,plain,
% 0.20/0.55 (((~(b(X!24) | (~a1(X!24)))) | (~![X: $i] : (~b(X))) | (~![X: $i] : a1(X))) | (b(X!24) | (~a1(X!24)))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(672,plain,
% 0.20/0.55 (b(X!24) | (~a1(X!24))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[671, 670])).
% 0.20/0.55 tff(673,plain,
% 0.20/0.55 (((~(b(X!24) | (~a1(X!24)))) | (~![X: $i] : (~b(X))) | (~![X: $i] : a1(X))) | ![X: $i] : a1(X)),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(674,plain,
% 0.20/0.55 (![X: $i] : a1(X)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[673, 670])).
% 0.20/0.55 tff(675,assumption,(![X: $i] : a1(X)), introduced(assumption)).
% 0.20/0.55 tff(676,assumption,(~a1(X!24)), introduced(assumption)).
% 0.20/0.55 tff(677,plain,
% 0.20/0.55 ((~![X: $i] : a1(X)) | a1(X!24)),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(678,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[677, 676, 675])).
% 0.20/0.55 tff(679,plain,(a1(X!24) | (~![X: $i] : a1(X))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(680,plain,
% 0.20/0.55 (a1(X!24)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[679, 674])).
% 0.20/0.55 tff(681,plain,
% 0.20/0.55 ((~(b(X!24) | (~a1(X!24)))) | b(X!24) | (~a1(X!24))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(682,plain,
% 0.20/0.55 (b(X!24)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[681, 680, 672])).
% 0.20/0.55 tff(683,plain,
% 0.20/0.55 (((~(b(X!24) | (~a1(X!24)))) | (~![X: $i] : (~b(X))) | (~![X: $i] : a1(X))) | ![X: $i] : (~b(X))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(684,plain,
% 0.20/0.55 (![X: $i] : (~b(X))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[683, 670])).
% 0.20/0.55 tff(685,plain,
% 0.20/0.55 ((~![X: $i] : (~b(X))) | (~b(X!24))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(686,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[685, 684, 682])).
% 0.20/0.55 tff(687,plain,((~(b(X!24) | (~a1(X!24)))) | (~![X: $i] : (~b(X))) | (~![X: $i] : a1(X))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(688,assumption,(~((~eq(A!40, B!39)) | eq(B!39, A!40) | (~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | ((~a_member_of(tptp_fun_Z_38(Y, X), X)) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))))))), introduced(assumption)).
% 0.20/0.55 tff(689,plain,
% 0.20/0.55 (((~eq(A!40, B!39)) | eq(B!39, A!40) | (~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | ((~a_member_of(tptp_fun_Z_38(Y, X), X)) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))))))) | ![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | ((~a_member_of(tptp_fun_Z_38(Y, X), X)) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(690,plain,
% 0.20/0.55 (![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | ((~a_member_of(tptp_fun_Z_38(Y, X), X)) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[689, 688])).
% 0.20/0.55 tff(691,plain,
% 0.20/0.55 ((~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | ((~a_member_of(tptp_fun_Z_38(Y, X), X)) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))))) | (~((~((~eq(A!40, B!39)) | ![Z: $i] : (a_member_of(Z, A!40) <=> a_member_of(Z, B!39)))) | (~(eq(A!40, B!39) | ((~a_member_of(tptp_fun_Z_38(B!39, A!40), A!40)) <=> a_member_of(tptp_fun_Z_38(B!39, A!40), B!39))))))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(692,plain,
% 0.20/0.55 (~((~((~eq(A!40, B!39)) | ![Z: $i] : (a_member_of(Z, A!40) <=> a_member_of(Z, B!39)))) | (~(eq(A!40, B!39) | ((~a_member_of(tptp_fun_Z_38(B!39, A!40), A!40)) <=> a_member_of(tptp_fun_Z_38(B!39, A!40), B!39)))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[691, 690])).
% 0.20/0.55 tff(693,plain,
% 0.20/0.55 (((~((~eq(A!40, B!39)) | ![Z: $i] : (a_member_of(Z, A!40) <=> a_member_of(Z, B!39)))) | (~(eq(A!40, B!39) | ((~a_member_of(tptp_fun_Z_38(B!39, A!40), A!40)) <=> a_member_of(tptp_fun_Z_38(B!39, A!40), B!39))))) | ((~eq(A!40, B!39)) | ![Z: $i] : (a_member_of(Z, A!40) <=> a_member_of(Z, B!39)))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(694,plain,
% 0.20/0.55 ((~eq(A!40, B!39)) | ![Z: $i] : (a_member_of(Z, A!40) <=> a_member_of(Z, B!39))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[693, 692])).
% 0.20/0.55 tff(695,plain,
% 0.20/0.55 (((~eq(A!40, B!39)) | eq(B!39, A!40) | (~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | ((~a_member_of(tptp_fun_Z_38(Y, X), X)) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))))))) | eq(A!40, B!39)),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(696,plain,
% 0.20/0.55 (eq(A!40, B!39)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[695, 688])).
% 0.20/0.55 tff(697,plain,
% 0.20/0.55 ((~((~eq(A!40, B!39)) | ![Z: $i] : (a_member_of(Z, A!40) <=> a_member_of(Z, B!39)))) | (~eq(A!40, B!39)) | ![Z: $i] : (a_member_of(Z, A!40) <=> a_member_of(Z, B!39))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(698,plain,
% 0.20/0.55 ((~((~eq(A!40, B!39)) | ![Z: $i] : (a_member_of(Z, A!40) <=> a_member_of(Z, B!39)))) | ![Z: $i] : (a_member_of(Z, A!40) <=> a_member_of(Z, B!39))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[697, 696])).
% 0.20/0.55 tff(699,plain,
% 0.20/0.55 (![Z: $i] : (a_member_of(Z, A!40) <=> a_member_of(Z, B!39))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[698, 694])).
% 0.20/0.55 tff(700,plain,
% 0.20/0.55 ((~![Z: $i] : (a_member_of(Z, A!40) <=> a_member_of(Z, B!39))) | (a_member_of(tptp_fun_Z_38(A!40, B!39), A!40) <=> a_member_of(tptp_fun_Z_38(A!40, B!39), B!39))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(701,plain,
% 0.20/0.55 (a_member_of(tptp_fun_Z_38(A!40, B!39), A!40) <=> a_member_of(tptp_fun_Z_38(A!40, B!39), B!39)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[700, 699])).
% 0.20/0.55 tff(702,plain,
% 0.20/0.55 ((~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | ((~a_member_of(tptp_fun_Z_38(Y, X), X)) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))))) | (~((~((~eq(B!39, A!40)) | ![Z: $i] : (a_member_of(Z, B!39) <=> a_member_of(Z, A!40)))) | (~(eq(B!39, A!40) | ((~a_member_of(tptp_fun_Z_38(A!40, B!39), B!39)) <=> a_member_of(tptp_fun_Z_38(A!40, B!39), A!40))))))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(703,plain,
% 0.20/0.55 (~((~((~eq(B!39, A!40)) | ![Z: $i] : (a_member_of(Z, B!39) <=> a_member_of(Z, A!40)))) | (~(eq(B!39, A!40) | ((~a_member_of(tptp_fun_Z_38(A!40, B!39), B!39)) <=> a_member_of(tptp_fun_Z_38(A!40, B!39), A!40)))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[702, 690])).
% 0.20/0.55 tff(704,plain,
% 0.20/0.55 (((~((~eq(B!39, A!40)) | ![Z: $i] : (a_member_of(Z, B!39) <=> a_member_of(Z, A!40)))) | (~(eq(B!39, A!40) | ((~a_member_of(tptp_fun_Z_38(A!40, B!39), B!39)) <=> a_member_of(tptp_fun_Z_38(A!40, B!39), A!40))))) | (eq(B!39, A!40) | ((~a_member_of(tptp_fun_Z_38(A!40, B!39), B!39)) <=> a_member_of(tptp_fun_Z_38(A!40, B!39), A!40)))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(705,plain,
% 0.20/0.55 (eq(B!39, A!40) | ((~a_member_of(tptp_fun_Z_38(A!40, B!39), B!39)) <=> a_member_of(tptp_fun_Z_38(A!40, B!39), A!40))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[704, 703])).
% 0.20/0.55 tff(706,plain,
% 0.20/0.55 (((~eq(A!40, B!39)) | eq(B!39, A!40) | (~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | ((~a_member_of(tptp_fun_Z_38(Y, X), X)) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))))))) | (~eq(B!39, A!40))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(707,plain,
% 0.20/0.55 (~eq(B!39, A!40)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[706, 688])).
% 0.20/0.55 tff(708,plain,
% 0.20/0.55 ((~(eq(B!39, A!40) | ((~a_member_of(tptp_fun_Z_38(A!40, B!39), B!39)) <=> a_member_of(tptp_fun_Z_38(A!40, B!39), A!40)))) | eq(B!39, A!40) | ((~a_member_of(tptp_fun_Z_38(A!40, B!39), B!39)) <=> a_member_of(tptp_fun_Z_38(A!40, B!39), A!40))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(709,plain,
% 0.20/0.55 ((~(eq(B!39, A!40) | ((~a_member_of(tptp_fun_Z_38(A!40, B!39), B!39)) <=> a_member_of(tptp_fun_Z_38(A!40, B!39), A!40)))) | ((~a_member_of(tptp_fun_Z_38(A!40, B!39), B!39)) <=> a_member_of(tptp_fun_Z_38(A!40, B!39), A!40))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[708, 707])).
% 0.20/0.55 tff(710,plain,
% 0.20/0.55 ((~a_member_of(tptp_fun_Z_38(A!40, B!39), B!39)) <=> a_member_of(tptp_fun_Z_38(A!40, B!39), A!40)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[709, 705])).
% 0.20/0.55 tff(711,assumption,(a_member_of(tptp_fun_Z_38(A!40, B!39), A!40) <=> a_member_of(tptp_fun_Z_38(A!40, B!39), B!39)), introduced(assumption)).
% 0.20/0.55 tff(712,assumption,(~a_member_of(tptp_fun_Z_38(A!40, B!39), A!40)), introduced(assumption)).
% 0.20/0.55 tff(713,assumption,((~a_member_of(tptp_fun_Z_38(A!40, B!39), B!39)) <=> a_member_of(tptp_fun_Z_38(A!40, B!39), A!40)), introduced(assumption)).
% 0.20/0.55 tff(714,plain,
% 0.20/0.55 ((~((~a_member_of(tptp_fun_Z_38(A!40, B!39), B!39)) <=> a_member_of(tptp_fun_Z_38(A!40, B!39), A!40))) | a_member_of(tptp_fun_Z_38(A!40, B!39), B!39) | a_member_of(tptp_fun_Z_38(A!40, B!39), A!40)),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(715,plain,
% 0.20/0.55 (a_member_of(tptp_fun_Z_38(A!40, B!39), B!39)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[714, 712, 713])).
% 0.20/0.55 tff(716,plain,
% 0.20/0.55 ((~(a_member_of(tptp_fun_Z_38(A!40, B!39), A!40) <=> a_member_of(tptp_fun_Z_38(A!40, B!39), B!39))) | a_member_of(tptp_fun_Z_38(A!40, B!39), A!40) | (~a_member_of(tptp_fun_Z_38(A!40, B!39), B!39))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(717,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[716, 715, 712, 711])).
% 0.20/0.55 tff(718,plain,(a_member_of(tptp_fun_Z_38(A!40, B!39), A!40) | (~(a_member_of(tptp_fun_Z_38(A!40, B!39), A!40) <=> a_member_of(tptp_fun_Z_38(A!40, B!39), B!39))) | (~((~a_member_of(tptp_fun_Z_38(A!40, B!39), B!39)) <=> a_member_of(tptp_fun_Z_38(A!40, B!39), A!40)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(719,plain,
% 0.20/0.55 (a_member_of(tptp_fun_Z_38(A!40, B!39), A!40)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[718, 701, 710])).
% 0.20/0.55 tff(720,plain,
% 0.20/0.55 ((~((~a_member_of(tptp_fun_Z_38(A!40, B!39), B!39)) <=> a_member_of(tptp_fun_Z_38(A!40, B!39), A!40))) | (~a_member_of(tptp_fun_Z_38(A!40, B!39), B!39)) | (~a_member_of(tptp_fun_Z_38(A!40, B!39), A!40))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(721,plain,
% 0.20/0.55 (~a_member_of(tptp_fun_Z_38(A!40, B!39), B!39)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[720, 719, 710])).
% 0.20/0.55 tff(722,plain,
% 0.20/0.55 ((~(a_member_of(tptp_fun_Z_38(A!40, B!39), A!40) <=> a_member_of(tptp_fun_Z_38(A!40, B!39), B!39))) | (~a_member_of(tptp_fun_Z_38(A!40, B!39), A!40)) | a_member_of(tptp_fun_Z_38(A!40, B!39), B!39)),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(723,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[722, 721, 719, 701])).
% 0.20/0.55 tff(724,plain,((~eq(A!40, B!39)) | eq(B!39, A!40) | (~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | ((~a_member_of(tptp_fun_Z_38(Y, X), X)) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(725,assumption,(~((~a1(X!23)) | (~![X: $i] : b(X)) | (~![X: $i] : ((~a1(X)) | (~b(X)))))), introduced(assumption)).
% 0.20/0.55 tff(726,plain,
% 0.20/0.55 (((~a1(X!23)) | (~![X: $i] : b(X)) | (~![X: $i] : ((~a1(X)) | (~b(X))))) | ![X: $i] : ((~a1(X)) | (~b(X)))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(727,plain,
% 0.20/0.55 (![X: $i] : ((~a1(X)) | (~b(X)))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[726, 725])).
% 0.20/0.55 tff(728,plain,
% 0.20/0.55 (((~a1(X!23)) | (~![X: $i] : b(X)) | (~![X: $i] : ((~a1(X)) | (~b(X))))) | a1(X!23)),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(729,plain,
% 0.20/0.55 (a1(X!23)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[728, 725])).
% 0.20/0.55 tff(730,plain,
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% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(731,plain,
% 0.20/0.55 ((~![X: $i] : ((~a1(X)) | (~b(X)))) | ((~a1(X!23)) | (~b(X!23)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(732,plain,
% 0.20/0.55 ((~![X: $i] : ((~a1(X)) | (~b(X)))) | (~a1(X!23)) | (~b(X!23))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[731, 730])).
% 0.20/0.55 tff(733,plain,
% 0.20/0.55 (~b(X!23)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[732, 729, 727])).
% 0.20/0.55 tff(734,plain,
% 0.20/0.55 (((~a1(X!23)) | (~![X: $i] : b(X)) | (~![X: $i] : ((~a1(X)) | (~b(X))))) | ![X: $i] : b(X)),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(735,plain,
% 0.20/0.55 (![X: $i] : b(X)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[734, 725])).
% 0.20/0.55 tff(736,plain,
% 0.20/0.55 ((~![X: $i] : b(X)) | b(X!23)),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(737,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[736, 735, 733])).
% 0.20/0.55 tff(738,plain,((~a1(X!23)) | (~![X: $i] : b(X)) | (~![X: $i] : ((~a1(X)) | (~b(X))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(739,assumption,(~((~s1(A!11)) | (~s1(B!10)) | (~r(B!10, C!9)) | (~![X: $i] : (p1(X) | (~s1(X)))) | (~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y)))))), introduced(assumption)).
% 0.20/0.55 tff(740,plain,
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% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(741,plain,
% 0.20/0.55 (![X: $i] : (p1(X) | (~s1(X)))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[740, 739])).
% 0.20/0.55 tff(742,plain,
% 0.20/0.55 (((~s1(A!11)) | (~s1(B!10)) | (~r(B!10, C!9)) | (~![X: $i] : (p1(X) | (~s1(X)))) | (~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y))))) | s1(B!10)),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(743,plain,
% 0.20/0.55 (s1(B!10)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[742, 739])).
% 0.20/0.55 tff(744,plain,
% 0.20/0.55 (((~![X: $i] : (p1(X) | (~s1(X)))) | (p1(B!10) | (~s1(B!10)))) <=> ((~![X: $i] : (p1(X) | (~s1(X)))) | p1(B!10) | (~s1(B!10)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(745,plain,
% 0.20/0.55 ((~![X: $i] : (p1(X) | (~s1(X)))) | (p1(B!10) | (~s1(B!10)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(746,plain,
% 0.20/0.55 ((~![X: $i] : (p1(X) | (~s1(X)))) | p1(B!10) | (~s1(B!10))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[745, 744])).
% 0.20/0.55 tff(747,plain,
% 0.20/0.55 (p1(B!10)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[746, 743, 741])).
% 0.20/0.55 tff(748,plain,
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% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(749,plain,
% 0.20/0.55 (![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[748, 739])).
% 0.20/0.55 tff(750,plain,
% 0.20/0.55 (((~s1(A!11)) | (~s1(B!10)) | (~r(B!10, C!9)) | (~![X: $i] : (p1(X) | (~s1(X)))) | (~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y))))) | r(B!10, C!9)),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(751,plain,
% 0.20/0.55 (r(B!10, C!9)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[750, 739])).
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% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(753,plain,
% 0.20/0.55 ((~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | ((~r(B!10, C!9)) | q(B!10, C!9))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(754,plain,
% 0.20/0.55 ((~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~r(B!10, C!9)) | q(B!10, C!9)),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[753, 752])).
% 0.20/0.55 tff(755,plain,
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% 0.20/0.55 inference(unit_resolution,[status(thm)],[754, 751, 749])).
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% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(757,plain,
% 0.20/0.55 (![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y)))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[756, 739])).
% 0.20/0.55 tff(758,plain,
% 0.20/0.55 (((~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y)))) | ((~p1(B!10)) | (~q(B!10, C!9)))) <=> ((~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y)))) | (~p1(B!10)) | (~q(B!10, C!9)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(759,plain,
% 0.20/0.55 ((~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y)))) | ((~p1(B!10)) | (~q(B!10, C!9)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(760,plain,
% 0.20/0.55 ((~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y)))) | (~p1(B!10)) | (~q(B!10, C!9))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[759, 758])).
% 0.20/0.55 tff(761,plain,
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% 0.20/0.55 inference(unit_resolution,[status(thm)],[760, 757, 755, 747])).
% 0.20/0.55 tff(762,plain,((~s1(A!11)) | (~s1(B!10)) | (~r(B!10, C!9)) | (~![X: $i] : (p1(X) | (~s1(X)))) | (~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(763,assumption,(~((~![X: $i] : p1(X)) | (~((~p1(A!32)) | (~p1(B!31)))))), introduced(assumption)).
% 0.20/0.55 tff(764,plain,
% 0.20/0.55 (((~![X: $i] : p1(X)) | (~((~p1(A!32)) | (~p1(B!31))))) | ((~p1(A!32)) | (~p1(B!31)))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
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% 0.20/0.55 inference(unit_resolution,[status(thm)],[764, 763])).
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% 0.20/0.55 inference(tautology,[status(thm)],[])).
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% 0.20/0.55 inference(unit_resolution,[status(thm)],[766, 763])).
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% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
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% 0.20/0.55 inference(unit_resolution,[status(thm)],[769, 339, 768])).
% 0.20/0.55 tff(771,plain,(p1(B!31) | (~![X: $i] : p1(X))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(772,plain,
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% 0.20/0.55 inference(unit_resolution,[status(thm)],[771, 767])).
% 0.20/0.55 tff(773,plain,
% 0.20/0.55 ((~((~p1(A!32)) | (~p1(B!31)))) | (~p1(A!32)) | (~p1(B!31))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
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% 0.20/0.55 inference(unit_resolution,[status(thm)],[773, 772, 765])).
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% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
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% 0.20/0.55 inference(unit_resolution,[status(thm)],[775, 767, 774])).
% 0.20/0.55 tff(777,plain,((~![X: $i] : p1(X)) | (~((~p1(A!32)) | (~p1(B!31))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(778,assumption,(~((~b(X!26)) | (~![X: $i] : (~(a1(X) | b(X)))))), introduced(assumption)).
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% 0.20/0.55 (((~b(X!26)) | (~![X: $i] : (~(a1(X) | b(X))))) | b(X!26)),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
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% 0.20/0.55 inference(unit_resolution,[status(thm)],[779, 778])).
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% 0.20/0.55 inference(tautology,[status(thm)],[])).
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% 0.20/0.55 (((~b(X!26)) | (~![X: $i] : (~(a1(X) | b(X))))) | ![X: $i] : (~(a1(X) | b(X)))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
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% 0.20/0.55 inference(unit_resolution,[status(thm)],[783, 778])).
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% 0.20/0.55 ((~![X: $i] : (~(a1(X) | b(X)))) | (~(a1(X!26) | b(X!26)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
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% 0.20/0.55 inference(unit_resolution,[status(thm)],[785, 784, 782])).
% 0.20/0.55 tff(787,plain,((~b(X!26)) | (~![X: $i] : (~(a1(X) | b(X))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(788,assumption,(~((~b0) | (a0 <=> b0) | (~a0))), introduced(assumption)).
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% 0.20/0.55 tff(790,plain,
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% 0.20/0.55 inference(unit_resolution,[status(thm)],[789, 788])).
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% 0.20/0.55 (((~b0) | (a0 <=> b0) | (~a0)) | b0),
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% 0.20/0.55 inference(unit_resolution,[status(thm)],[791, 788])).
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% 0.20/0.55 inference(tautology,[status(thm)],[])).
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% 0.20/0.55 inference(unit_resolution,[status(thm)],[793, 788])).
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% 0.20/0.55 ((a0 <=> b0) | (~a0) | (~b0)),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
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% 0.20/0.55 inference(unit_resolution,[status(thm)],[795, 794, 792, 790])).
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% 0.20/0.55 tff(798,plain,
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(~((~r1(B!4)) | (~r1(C!3)))))))))))))) | (~((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))))))) | (~((~![X: $i] : p1(X)) | (~((~p1(A!13)) | (~p1(B!12)))))) | ![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y)))))) | (~((~![X: $i] : (~((~a(X, tptp_fun_Y_17(X))) | (~a(tptp_fun_Y_17(X), tptp_fun_Y_17(X)))))) | (~![Z: $i] : (~a(Z, Z))))) | (~((~![Y: $i] : (p1(Y) | (~q1(Y)))) | (~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))))) | (~((~![X: $i] : p1(X)) | (~![Y: $i] : (~p1(Y))))) | (~(q1(X!20) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X)))))) | (~((~![Z: $i] : (p1(Z) | (~q1(Z)))) | (~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))))) | (~((~b(X!26)) | (~![X: $i] : (~(a1(X) | b(X)))))) | (~((~(a(X!28, 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| (~(b(X!7) | (~a1(X!7)) | (~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (~![X: $i] : ((~a1(X)) | (~c(X)))))) | (~((~s1(A!11)) | (~s1(B!10)) | (~r(B!10, C!9)) | (~![X: $i] : (p1(X) | (~s1(X)))) | (~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y)))))) | (~((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X)))))))) | (~((~a1(X!23)) | (~![X: $i] : b(X)) | (~![X: $i] : ((~a1(X)) | (~b(X)))))) | (~((~eq(A!40, B!39)) | eq(B!39, A!40) | (~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | ((~a_member_of(tptp_fun_Z_38(Y, X), X)) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))))))) | ![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y)))))) | (~(q1(A!48) | (~k!0) | (~![X: $i] : (~((~p1(X)) | (~q1(X))))))) | (~((~a1(X!23)) | (~![X: $i] : (b(X) | (~a1(X)))) | (~![X: $i] : (~b(X))))) | (~((~(b(X!24) | (~a1(X!24)))) | (~![X: $i] : (~b(X))) | (~![X: $i] : a1(X)))) | (~((~q1(Y!14)) | (~![X: $i] : p1(X)) | (~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))))) | (~(q1(B!42) | (~r1(B!42)) | (~![X: $i] : (q1(X) | (~p1(X)))) | (~![Y: $i] : (p1(Y) | (~r1(Y)))))) | (~((~(r1(Y!52) | (~q1(Y!52)))) | (~![X: $i] : (q1(X) | (~p1(X)))) | (~![Z: $i] : (~(r1(Z) | (~p1(Z))))))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(799,plain,
% 0.20/0.56 ((~((~![X: $i] : (q1(X) | (~p1(X)))) | (~(r1(Y!52) | (~q1(Y!52)))) | (~![Z: $i] : (~(r1(Z) | (~p1(Z))))))) <=> (~((~(r1(Y!52) | (~q1(Y!52)))) | (~![X: $i] : (q1(X) | (~p1(X)))) | (~![Z: $i] : (~(r1(Z) | (~p1(Z)))))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(800,plain,
% 0.20/0.56 ((~(q1(A!48) | (~k!0) | (~![X: $i] : (~((~p1(X)) | (~q1(X))))))) <=> (~(q1(A!48) | (~k!0) | (~![X: $i] : (~((~p1(X)) | (~q1(X)))))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(801,plain,
% 0.20/0.56 ((~((~![X: $i] : (q1(X) | (~p1(X)))) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | q1(B!42) | (~r1(B!42)))) <=> (~(q1(B!42) | (~r1(B!42)) | (~![X: $i] : (q1(X) | (~p1(X)))) | (~![Y: $i] : (p1(Y) | (~r1(Y))))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(802,plain,
% 0.20/0.56 ((~((~eq(A!40, B!39)) | eq(B!39, A!40) | (~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | ((~a_member_of(tptp_fun_Z_38(Y, X), X)) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))))))) <=> (~((~eq(A!40, B!39)) | eq(B!39, A!40) | (~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | ((~a_member_of(tptp_fun_Z_38(Y, X), X)) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))))))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(803,plain,
% 0.20/0.56 ((~![X: $i] : ((~a1(X)) | (~b(X)))) <=> (~![X: $i] : ((~a1(X)) | (~b(X))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(804,plain,
% 0.20/0.56 ((~![X: $i] : b(X)) <=> (~![X: $i] : b(X))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
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% 0.20/0.56 (((~a1(X!23)) | (~![X: $i] : b(X)) | (~![X: $i] : ((~a1(X)) | (~b(X))))) <=> ((~a1(X!23)) | (~![X: $i] : b(X)) | (~![X: $i] : ((~a1(X)) | (~b(X)))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[804, 803])).
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% 0.20/0.56 ((~((~a1(X!23)) | (~![X: $i] : b(X)) | (~![X: $i] : ((~a1(X)) | (~b(X)))))) <=> (~((~a1(X!23)) | (~![X: $i] : b(X)) | (~![X: $i] : ((~a1(X)) | (~b(X))))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[805])).
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% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(808,plain,
% 0.20/0.56 ((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) <=> (~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z)))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(809,plain,
% 0.20/0.56 (((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X))))))) <=> ((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X)))))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[808, 807])).
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% 0.20/0.56 ((~((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X)))))))) <=> (~((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X))))))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[809])).
% 0.20/0.56 tff(811,plain,
% 0.20/0.56 ((~((~![X: $i] : p1(X)) | (~q1(Y!14)) | (~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))))) <=> (~((~q1(Y!14)) | (~![X: $i] : p1(X)) | (~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z)))))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(812,plain,
% 0.20/0.56 ((~((~s1(A!11)) | (~s1(B!10)) | (~r(B!10, C!9)) | (~![X: $i] : (p1(X) | (~s1(X)))) | (~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y)))))) <=> (~((~s1(A!11)) | (~s1(B!10)) | (~r(B!10, C!9)) | (~![X: $i] : (p1(X) | (~s1(X)))) | (~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y))))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
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% 0.20/0.56 ((~(b(X!7) | (~a1(X!7)) | (~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (~![X: $i] : ((~a1(X)) | (~c(X)))))) <=> (~(b(X!7) | (~a1(X!7)) | (~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (~![X: $i] : ((~a1(X)) | (~c(X))))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(814,plain,
% 0.20/0.56 ((~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5)))))))))))) <=> (~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5))))))))))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(815,plain,
% 0.20/0.56 (((~q1(f(B!6))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5))))))))))))) <=> ((~q1(f(B!6))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5)))))))))))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[814])).
% 0.20/0.56 tff(816,plain,
% 0.20/0.56 ((~((~q1(f(B!6))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5)))))))))))))) <=> (~((~q1(f(B!6))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5))))))))))))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[815])).
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% 0.20/0.56 ((~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))) <=> (~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y)))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(818,plain,
% 0.20/0.56 ((~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))) <=> (~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(819,plain,
% 0.20/0.56 (((~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))) | (~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y)))))) <=> ((~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))) | (~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[818, 817])).
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% 0.20/0.56 inference(monotonicity,[status(thm)],[819])).
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% 0.20/0.56 ((~((~b0) | (a0 <=> b0) | (~a0))) <=> (~((~b0) | (a0 <=> b0) | (~a0)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(822,plain,
% 0.20/0.56 ((~![X: $i, Y: $i] : p(X, Y)) <=> (~![X: $i, Y: $i] : p(X, Y))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(823,plain,
% 0.20/0.56 (((~![X: $i, Y: $i] : p(X, Y)) | p(X!47, X!47)) <=> ((~![X: $i, Y: $i] : p(X, Y)) | p(X!47, X!47))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[822])).
% 0.20/0.56 tff(824,plain,
% 0.20/0.56 ((~((~![X: $i, Y: $i] : p(X, Y)) | p(X!47, X!47))) <=> (~((~![X: $i, Y: $i] : p(X, Y)) | p(X!47, X!47)))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[823])).
% 0.20/0.56 tff(825,plain,
% 0.20/0.56 ((~![Y: $i] : (~p1(Y))) <=> (~![Y: $i] : (~p1(Y)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(826,plain,
% 0.20/0.56 (((~p1(X!35)) | (~![Y: $i] : (~p1(Y)))) <=> ((~p1(X!35)) | (~![Y: $i] : (~p1(Y))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[825])).
% 0.20/0.56 tff(827,plain,
% 0.20/0.56 ((~((~p1(X!35)) | (~![Y: $i] : (~p1(Y))))) <=> (~((~p1(X!35)) | (~![Y: $i] : (~p1(Y)))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[826])).
% 0.20/0.56 tff(828,plain,
% 0.20/0.56 ((~![X: $i] : (~p(X, Y!46))) <=> (~![X: $i] : (~p(X, Y!46)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(829,plain,
% 0.20/0.56 ((~![Y: $i] : p(X!45, Y)) <=> (~![Y: $i] : p(X!45, Y))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(830,plain,
% 0.20/0.56 (((~![Y: $i] : p(X!45, Y)) | (~![X: $i] : (~p(X, Y!46)))) <=> ((~![Y: $i] : p(X!45, Y)) | (~![X: $i] : (~p(X, Y!46))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[829, 828])).
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% 0.20/0.56 ((~((~![Y: $i] : p(X!45, Y)) | (~![X: $i] : (~p(X, Y!46))))) <=> (~((~![Y: $i] : p(X!45, Y)) | (~![X: $i] : (~p(X, Y!46)))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[830])).
% 0.20/0.56 tff(832,plain,
% 0.20/0.56 ((~![Z: $i] : (~p1(Z))) <=> (~![Z: $i] : (~p1(Z)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(833,plain,
% 0.20/0.56 (((~p1(X!35)) | (~![Z: $i] : (~p1(Z)))) <=> ((~p1(X!35)) | (~![Z: $i] : (~p1(Z))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[832])).
% 0.20/0.56 tff(834,plain,
% 0.20/0.56 ((~((~p1(X!35)) | (~![Z: $i] : (~p1(Z))))) <=> (~((~p1(X!35)) | (~![Z: $i] : (~p1(Z)))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[833])).
% 0.20/0.56 tff(835,plain,
% 0.20/0.56 ((![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y))) <=> (![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(836,plain,
% 0.20/0.56 ((~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))) <=> (~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[835])).
% 0.20/0.56 tff(837,plain,
% 0.20/0.56 (((~(p1(X!35) | p1(Y!36))) | (~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y))))) <=> ((~(p1(X!35) | p1(Y!36))) | (~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[836])).
% 0.20/0.56 tff(838,plain,
% 0.20/0.56 ((~((~(p1(X!35) | p1(Y!36))) | (~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))))) <=> (~((~(p1(X!35) | p1(Y!36))) | (~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y))))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[837])).
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% 0.20/0.56 ((~![X: $i] : p1(X)) <=> (~![X: $i] : p1(X))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(840,plain,
% 0.20/0.56 (((~![X: $i] : p1(X)) | (~((~p1(X!33)) | (~p1(Y!34))))) <=> ((~![X: $i] : p1(X)) | (~((~p1(X!33)) | (~p1(Y!34)))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[839])).
% 0.20/0.56 tff(841,plain,
% 0.20/0.56 ((~((~![X: $i] : p1(X)) | (~((~p1(X!33)) | (~p1(Y!34)))))) <=> (~((~![X: $i] : p1(X)) | (~((~p1(X!33)) | (~p1(Y!34))))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[840])).
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% 0.20/0.56 (((~![X: $i] : p1(X)) | (~((~p1(A!32)) | (~p1(B!31))))) <=> ((~![X: $i] : p1(X)) | (~((~p1(A!32)) | (~p1(B!31)))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[839])).
% 0.20/0.56 tff(843,plain,
% 0.20/0.56 ((~((~![X: $i] : p1(X)) | (~((~p1(A!32)) | (~p1(B!31)))))) <=> (~((~![X: $i] : p1(X)) | (~((~p1(A!32)) | (~p1(B!31))))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[842])).
% 0.20/0.56 tff(844,plain,
% 0.20/0.56 ((![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y))) <=> (![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(845,plain,
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% 0.20/0.56 inference(monotonicity,[status(thm)],[844])).
% 0.20/0.56 tff(846,plain,
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% 0.20/0.56 inference(monotonicity,[status(thm)],[845])).
% 0.20/0.56 tff(847,plain,
% 0.20/0.56 ((~((~(a(X!28, Y!27) | a(X!29, Y!30))) | (~(![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))))) <=> (~((~(a(X!28, Y!27) | a(X!29, Y!30))) | (~(![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y))))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[846])).
% 0.20/0.56 tff(848,plain,
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% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(849,plain,
% 0.20/0.56 (((~b(X!26)) | (~![X: $i] : (~(a1(X) | b(X))))) <=> ((~b(X!26)) | (~![X: $i] : (~(a1(X) | b(X)))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[848])).
% 0.20/0.56 tff(850,plain,
% 0.20/0.56 ((~((~b(X!26)) | (~![X: $i] : (~(a1(X) | b(X)))))) <=> (~((~b(X!26)) | (~![X: $i] : (~(a1(X) | b(X))))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[849])).
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% 0.20/0.56 inference(rewrite,[status(thm)],[])).
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% 0.20/0.56 inference(rewrite,[status(thm)],[])).
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% 0.20/0.56 inference(rewrite,[status(thm)],[])).
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% 0.20/0.56 ((~![Z: $i] : (p1(Z) | (~q1(Z)))) <=> (~![Z: $i] : (p1(Z) | (~q1(Z))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
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% 0.20/0.56 inference(monotonicity,[status(thm)],[854, 853])).
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% 0.20/0.56 inference(monotonicity,[status(thm)],[855])).
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% 0.20/0.56 ((~![X: $i] : (q1(X) | (~p1(X)))) <=> (~![X: $i] : (q1(X) | (~p1(X))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(858,plain,
% 0.20/0.56 ((q1(X!20) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) <=> (q1(X!20) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X)))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[839, 857])).
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% 0.20/0.56 inference(monotonicity,[status(thm)],[858])).
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% 0.20/0.56 inference(monotonicity,[status(thm)],[839, 825])).
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% 0.20/0.56 inference(monotonicity,[status(thm)],[860])).
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% 0.20/0.57 inference(rewrite,[status(thm)],[])).
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% 0.20/0.57 inference(rewrite,[status(thm)],[])).
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% 0.20/0.57 inference(monotonicity,[status(thm)],[864])).
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% 0.20/0.57 inference(rewrite,[status(thm)],[])).
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% 0.20/0.57 inference(monotonicity,[status(thm)],[839])).
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% 0.20/0.57 inference(monotonicity,[status(thm)],[867])).
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% 0.20/0.57 inference(rewrite,[status(thm)],[])).
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% 0.20/0.57 inference(rewrite,[status(thm)],[])).
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% 0.20/0.57 inference(monotonicity,[status(thm)],[870, 869])).
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% 0.20/0.57 inference(monotonicity,[status(thm)],[870, 873])).
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% 0.20/0.57 inference(monotonicity,[status(thm)],[874])).
% 0.20/0.57 tff(876,plain,
% 0.20/0.57 ((![X: $i] : (a(X, Y!25) <=> (~a(X, X))) | ![X: $i, Y: $i] : (~(r1(B!43) | (~p1(A!44)) | (~(r1(Y) | (~p1(X)))))) | ![X: $i] : (~((~p1(X)) | p1(tptp_fun_Y_41(X)))) | (~((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3)))))))))))))) | (~((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))))))) | (~((~![X: $i] : p1(X)) | (~((~p1(A!13)) | (~p1(B!12)))))) | ![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y)))))) | (~((~![X: $i] : (~((~a(X, tptp_fun_Y_17(X))) | (~a(tptp_fun_Y_17(X), tptp_fun_Y_17(X)))))) | (~![Z: $i] : (~a(Z, Z))))) | (~((~![Y: $i] : (p1(Y) | (~q1(Y)))) | (~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))))) | (~((~![X: $i] : p1(X)) | (~![Y: $i] : (~p1(Y))))) | (~(q1(X!20) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X)))))) | (~((~![Z: $i] : (p1(Z) | (~q1(Z)))) | (~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))))) | (~((~![X: $i] : (b(X) | (~a1(X)))) | (~![X: $i] : (~b(X))) | (~a1(X!23)))) | (~((~![X: $i] : a1(X)) | (~![X: $i] : (~b(X))) | (~(b(X!24) | (~a1(X!24)))))) | (~((~b(X!26)) | (~![X: $i] : (~(a1(X) | b(X)))))) | (~((~(a(X!28, Y!27) | a(X!29, Y!30))) | (~(![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))))) | (~((~![X: $i] : p1(X)) | (~((~p1(A!32)) | (~p1(B!31)))))) | (~((~![X: $i] : p1(X)) | (~((~p1(X!33)) | (~p1(Y!34)))))) | (~((~(p1(X!35) | p1(Y!36))) | (~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))))) | (~((~p1(X!35)) | (~![Z: $i] : (~p1(Z))))) | ![Y: $i] : (~(p1(Y) | (~p1(X!35)))) | (~((~![Y: $i] : p(X!45, Y)) | (~![X: $i] : (~p(X, Y!46))))) | (~((~p1(X!35)) | (~![Y: $i] : (~p1(Y))))) | (~((~![X: $i, Y: $i] : p(X, Y)) | p(X!47, X!47))) | (~((~b0) | (a0 <=> b0) | (~a0))) | ![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y))))) | (~((~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))) | (~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))))) | (~((~q1(f(B!6))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5)))))))))))))) | (~(b(X!7) | (~a1(X!7)) | (~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (~![X: $i] : ((~a1(X)) | (~c(X)))))) | (~((~s1(A!11)) | (~s1(B!10)) | (~r(B!10, C!9)) | (~![X: $i] : (p1(X) | (~s1(X)))) | (~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y)))))) | (~((~![X: $i] : p1(X)) | (~q1(Y!14)) | (~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))))) | (~((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X)))))))) | (~((~a1(X!23)) | (~![X: $i] : b(X)) | (~![X: $i] : ((~a1(X)) | (~b(X)))))) | (~((~eq(A!40, B!39)) | eq(B!39, A!40) | (~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | ((~a_member_of(tptp_fun_Z_38(Y, X), X)) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))))))) | ![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y)))))) | (~((~![X: $i] : (q1(X) | (~p1(X)))) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | q1(B!42) | (~r1(B!42)))) | (~(q1(A!48) | (~k!0) | (~![X: $i] : (~((~p1(X)) | (~q1(X))))))) | (~((~![X: $i] : (q1(X) | (~p1(X)))) | (~(r1(Y!52) | (~q1(Y!52)))) | (~![Z: $i] : (~(r1(Z) | (~p1(Z)))))))) <=> (![X: $i] : (a(X, Y!25) <=> (~a(X, X))) | ![X: $i, Y: $i] : (~(r1(B!43) | (~p1(A!44)) | (~(r1(Y) | (~p1(X)))))) | ![X: $i] : (~((~p1(X)) | p1(tptp_fun_Y_41(X)))) | (~((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3)))))))))))))) | (~((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))))))) | (~((~![X: $i] : p1(X)) | (~((~p1(A!13)) | (~p1(B!12)))))) | ![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y)))))) | (~((~![X: $i] : (~((~a(X, tptp_fun_Y_17(X))) | (~a(tptp_fun_Y_17(X), tptp_fun_Y_17(X)))))) | (~![Z: $i] : (~a(Z, Z))))) | (~((~![Y: $i] : (p1(Y) | (~q1(Y)))) | (~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))))) | (~((~![X: $i] : p1(X)) | (~![Y: $i] : (~p1(Y))))) | (~(q1(X!20) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X)))))) | (~((~![Z: $i] : (p1(Z) | (~q1(Z)))) | (~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))))) | (~((~a1(X!23)) | (~![X: $i] : (b(X) | (~a1(X)))) | (~![X: $i] : (~b(X))))) | (~((~(b(X!24) | (~a1(X!24)))) | (~![X: $i] : (~b(X))) | (~![X: $i] : a1(X)))) | (~((~b(X!26)) | (~![X: $i] : (~(a1(X) | b(X)))))) | (~((~(a(X!28, Y!27) | a(X!29, Y!30))) | (~(![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))))) | (~((~![X: $i] : p1(X)) | (~((~p1(A!32)) | (~p1(B!31)))))) | (~((~![X: $i] : p1(X)) | (~((~p1(X!33)) | (~p1(Y!34)))))) | (~((~(p1(X!35) | p1(Y!36))) | (~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))))) | (~((~p1(X!35)) | (~![Z: $i] : (~p1(Z))))) | ![Y: $i] : (~(p1(Y) | (~p1(X!35)))) | (~((~![Y: $i] : p(X!45, Y)) | (~![X: $i] : (~p(X, Y!46))))) | (~((~p1(X!35)) | (~![Y: $i] : (~p1(Y))))) | (~((~![X: $i, Y: $i] : p(X, Y)) | p(X!47, X!47))) | (~((~b0) | (a0 <=> b0) | (~a0))) | ![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y))))) | (~((~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))) | (~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))))) | (~((~q1(f(B!6))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5)))))))))))))) | (~(b(X!7) | (~a1(X!7)) | (~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (~![X: $i] : ((~a1(X)) | (~c(X)))))) | (~((~s1(A!11)) | (~s1(B!10)) | (~r(B!10, C!9)) | (~![X: $i] : (p1(X) | (~s1(X)))) | (~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y)))))) | (~((~q1(Y!14)) | (~![X: $i] : p1(X)) | (~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))))) | (~((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X)))))))) | (~((~a1(X!23)) | (~![X: $i] : b(X)) | (~![X: $i] : ((~a1(X)) | (~b(X)))))) | (~((~eq(A!40, B!39)) | eq(B!39, A!40) | (~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | ((~a_member_of(tptp_fun_Z_38(Y, X), X)) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))))))) | ![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y)))))) | (~(q1(B!42) | (~r1(B!42)) | (~![X: $i] : (q1(X) | (~p1(X)))) | (~![Y: $i] : (p1(Y) | (~r1(Y)))))) | (~(q1(A!48) | (~k!0) | (~![X: $i] : (~((~p1(X)) | (~q1(X))))))) | (~((~(r1(Y!52) | (~q1(Y!52)))) | (~![X: $i] : (q1(X) | (~p1(X)))) | (~![Z: $i] : (~(r1(Z) | (~p1(Z))))))))),
% 0.48/0.57 inference(monotonicity,[status(thm)],[875, 872, 868, 866, 865, 861, 859, 856, 852, 851, 850, 847, 843, 841, 838, 834, 831, 827, 824, 821, 820, 816, 813, 812, 811, 810, 806, 802, 801, 800, 799])).
% 0.48/0.57 tff(877,plain,
% 0.48/0.57 ((![X: $i] : (a(X, Y!25) <=> (~a(X, X))) | ![X: $i, Y: $i] : (~(r1(B!43) | (~p1(A!44)) | (~(r1(Y) | (~p1(X)))))) | ![X: $i] : (~((~p1(X)) | p1(tptp_fun_Y_41(X)))) | (~((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3)))))))))))))) | (~((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))))))) | (~((~![X: $i] : p1(X)) | (~((~p1(A!13)) | (~p1(B!12)))))) | ![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y)))))) | (~((~![X: $i] : (~((~a(X, tptp_fun_Y_17(X))) | (~a(tptp_fun_Y_17(X), tptp_fun_Y_17(X)))))) | (~![Z: $i] : (~a(Z, Z))))) | (~((~![Y: $i] : (p1(Y) | (~q1(Y)))) | (~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))))) | (~((~![X: $i] : p1(X)) | (~![Y: $i] : (~p1(Y))))) | (~(q1(X!20) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X)))))) | (~((~![Z: $i] : (p1(Z) | (~q1(Z)))) | (~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))))) | (~((~![X: $i] : (b(X) | (~a1(X)))) | (~![X: $i] : (~b(X))) | (~a1(X!23)))) | (~((~![X: $i] : a1(X)) | (~![X: $i] : (~b(X))) | (~(b(X!24) | (~a1(X!24)))))) | (~((~b(X!26)) | (~![X: $i] : (~(a1(X) | b(X)))))) | (~((~(a(X!28, Y!27) | a(X!29, Y!30))) | (~(![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))))) | (~((~![X: $i] : p1(X)) | (~((~p1(A!32)) | (~p1(B!31)))))) | (~((~![X: $i] : p1(X)) | (~((~p1(X!33)) | (~p1(Y!34)))))) | (~((~(p1(X!35) | p1(Y!36))) | (~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))))) | (~((~p1(X!35)) | (~![Z: $i] : (~p1(Z))))) | ![Y: $i] : (~(p1(Y) | (~p1(X!35)))) | (~((~![Y: $i] : p(X!45, Y)) | (~![X: $i] : (~p(X, Y!46))))) | (~((~p1(X!35)) | (~![Y: $i] : (~p1(Y))))) | (~((~![X: $i, Y: $i] : p(X, Y)) | p(X!47, X!47))) | (~((~b0) | (a0 <=> b0) | (~a0))) | ![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y))))) | (~((~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))) | (~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))))) | (~((~q1(f(B!6))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5)))))))))))))) | (~(b(X!7) | (~a1(X!7)) | (~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (~![X: $i] : ((~a1(X)) | (~c(X)))))) | (~((~s1(A!11)) | (~s1(B!10)) | (~r(B!10, C!9)) | (~![X: $i] : (p1(X) | (~s1(X)))) | (~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y)))))) | (~((~![X: $i] : p1(X)) | (~q1(Y!14)) | (~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))))) | (~((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X)))))))) | (~((~a1(X!23)) | (~![X: $i] : b(X)) | (~![X: $i] : ((~a1(X)) | (~b(X)))))) | (~((~eq(A!40, B!39)) | eq(B!39, A!40) | (~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | ((~a_member_of(tptp_fun_Z_38(Y, X), X)) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))))))) | ![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y)))))) | (~((~![X: $i] : (q1(X) | (~p1(X)))) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | q1(B!42) | (~r1(B!42)))) | (~(q1(A!48) | (~k!0) | (~![X: $i] : (~((~p1(X)) | (~q1(X))))))) | (~((~![X: $i] : (q1(X) | (~p1(X)))) | (~(r1(Y!52) | (~q1(Y!52)))) | (~![Z: $i] : (~(r1(Z) | (~p1(Z)))))))) <=> ((~((~b0) | (a0 <=> b0) | (~a0))) | ![X: $i] : (a(X, Y!25) <=> (~a(X, X))) | ![X: $i, Y: $i] : (~(r1(B!43) | (~p1(A!44)) | (~(r1(Y) | (~p1(X)))))) | ![X: $i] : (~((~p1(X)) | p1(tptp_fun_Y_41(X)))) | (~((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3)))))))))))))) | (~((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))))))) | (~((~![X: $i] : p1(X)) | (~((~p1(A!13)) | (~p1(B!12)))))) | ![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y)))))) | (~((~![X: $i] : (~((~a(X, tptp_fun_Y_17(X))) | (~a(tptp_fun_Y_17(X), tptp_fun_Y_17(X)))))) | (~![Z: $i] : (~a(Z, Z))))) | (~((~![Y: $i] : (p1(Y) | (~q1(Y)))) | (~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))))) | (~((~![X: $i] : p1(X)) | (~![Y: $i] : (~p1(Y))))) | (~(q1(X!20) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X)))))) | (~((~![Z: $i] : (p1(Z) | (~q1(Z)))) | (~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))))) | (~((~b(X!26)) | (~![X: $i] : (~(a1(X) | b(X)))))) | (~((~(a(X!28, 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| (~(b(X!7) | (~a1(X!7)) | (~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (~![X: $i] : ((~a1(X)) | (~c(X)))))) | (~((~s1(A!11)) | (~s1(B!10)) | (~r(B!10, C!9)) | (~![X: $i] : (p1(X) | (~s1(X)))) | (~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y)))))) | (~((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X)))))))) | (~((~a1(X!23)) | (~![X: $i] : b(X)) | (~![X: $i] : ((~a1(X)) | (~b(X)))))) | (~((~eq(A!40, B!39)) | eq(B!39, A!40) | (~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | ((~a_member_of(tptp_fun_Z_38(Y, X), X)) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))))))) | ![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y)))))) | (~(q1(A!48) | (~k!0) | (~![X: $i] : (~((~p1(X)) | (~q1(X))))))) | (~((~a1(X!23)) | (~![X: $i] : (b(X) | (~a1(X)))) | (~![X: $i] : (~b(X))))) | (~((~(b(X!24) | (~a1(X!24)))) | (~![X: $i] : (~b(X))) | (~![X: $i] : a1(X)))) | (~((~q1(Y!14)) | (~![X: $i] : p1(X)) | (~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))))) | (~(q1(B!42) | (~r1(B!42)) | (~![X: $i] : (q1(X) | (~p1(X)))) | (~![Y: $i] : (p1(Y) | (~r1(Y)))))) | (~((~(r1(Y!52) | (~q1(Y!52)))) | (~![X: $i] : (q1(X) | (~p1(X)))) | (~![Z: $i] : (~(r1(Z) | (~p1(Z))))))))),
% 0.48/0.58 inference(transitivity,[status(thm)],[876, 798])).
% 0.48/0.58 tff(878,plain,
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| (~![X: $i] : ((~a1(X)) | (~b(X)))))) | (~((~eq(A!40, B!39)) | eq(B!39, A!40) | (~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | ((~a_member_of(tptp_fun_Z_38(Y, X), X)) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))))))) | ![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y)))))) | (~((~![X: $i] : (q1(X) | (~p1(X)))) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | q1(B!42) | (~r1(B!42)))) | (~(q1(A!48) | (~k!0) | (~![X: $i] : (~((~p1(X)) | (~q1(X))))))) | (~((~![X: $i] : (q1(X) | (~p1(X)))) | (~(r1(Y!52) | (~q1(Y!52)))) | (~![Z: $i] : (~(r1(Z) | (~p1(Z)))))))) <=> (![X: $i] : (a(X, Y!25) <=> (~a(X, X))) | ![X: $i, Y: $i] : (~(r1(B!43) | (~p1(A!44)) | (~(r1(Y) | (~p1(X)))))) | ![X: $i] : (~((~p1(X)) | p1(tptp_fun_Y_41(X)))) | (~((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3)))))))))))))) | (~((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))))))) | (~((~![X: $i] : p1(X)) | (~((~p1(A!13)) | (~p1(B!12)))))) | ![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y)))))) | (~((~![X: $i] : (~((~a(X, tptp_fun_Y_17(X))) | (~a(tptp_fun_Y_17(X), tptp_fun_Y_17(X)))))) | (~![Z: $i] : (~a(Z, Z))))) | (~((~![Y: $i] : (p1(Y) | (~q1(Y)))) | (~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))))) | (~((~![X: $i] : p1(X)) | (~![Y: $i] : (~p1(Y))))) | (~(q1(X!20) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X)))))) | (~((~![Z: $i] : (p1(Z) | (~q1(Z)))) | (~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))))) | (~((~![X: $i] : (b(X) | (~a1(X)))) | (~![X: $i] : (~b(X))) | (~a1(X!23)))) | 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Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))))) | (~((~q1(f(B!6))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5)))))))))))))) | (~(b(X!7) | (~a1(X!7)) | (~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (~![X: $i] : ((~a1(X)) | (~c(X)))))) | (~((~s1(A!11)) | (~s1(B!10)) | (~r(B!10, C!9)) | (~![X: $i] : (p1(X) | (~s1(X)))) | (~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y)))))) | (~((~![X: $i] : p1(X)) | (~q1(Y!14)) | (~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))))) | (~((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X)))))))) | (~((~a1(X!23)) | (~![X: $i] : b(X)) | (~![X: $i] : ((~a1(X)) | (~b(X)))))) | (~((~eq(A!40, B!39)) | eq(B!39, A!40) | (~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | ((~a_member_of(tptp_fun_Z_38(Y, X), X)) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))))))) | ![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y)))))) | (~((~![X: $i] : (q1(X) | (~p1(X)))) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | q1(B!42) | (~r1(B!42)))) | (~(q1(A!48) | (~k!0) | (~![X: $i] : (~((~p1(X)) | (~q1(X))))))) | (~((~![X: $i] : (q1(X) | (~p1(X)))) | (~(r1(Y!52) | (~q1(Y!52)))) | (~![Z: $i] : (~(r1(Z) | (~p1(Z))))))))),
% 0.48/0.58 inference(rewrite,[status(thm)],[])).
% 0.48/0.58 tff(879,plain,
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((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))))) | (~((~![X: $i] : (b(X) | (~a1(X)))) | (~![X: $i] : (~b(X))) | (~a1(X!23)))) | (~((~![X: $i] : a1(X)) | (~![X: $i] : (~b(X))) | (~(b(X!24) | (~a1(X!24)))))) | ![X: $i] : (a(X, Y!25) <=> (~a(X, X))) | (~((~b(X!26)) | (~![X: $i] : (~(a1(X) | b(X)))))) | (~((~(a(X!28, Y!27) | a(X!29, Y!30))) | (~(![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))))) | (~((~![X: $i] : p1(X)) | (~((~p1(A!32)) | (~p1(B!31)))))) | (~((~![X: $i] : p1(X)) | (~((~p1(X!33)) | (~p1(Y!34)))))) | (~((~(p1(X!35) | p1(Y!36))) | (~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))))) | (~((~p1(X!35)) | (~![Z: $i] : (~p1(Z))))) | ![X: $i, Y: $i] : (~(r1(B!43) | (~p1(A!44)) | (~(r1(Y) | (~p1(X)))))) | ![Y: $i] : (~(p1(Y) | (~p1(X!35)))) | (~((~![Y: $i] : p(X!45, Y)) | (~![X: $i] : (~p(X, Y!46))))) | (~((~p1(X!35)) | (~![Y: $i] : (~p1(Y))))) | (~((~![X: $i, Y: $i] : p(X, Y)) | p(X!47, X!47))) | (~((~b0) | (a0 <=> b0) | (~a0))) | ![X: $i, Y: $i] : (~((~s1(A!50)) | 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$i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y)))))) | (~((~eq(A!40, B!39)) | eq(B!39, A!40) | (~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | ((~a_member_of(tptp_fun_Z_38(Y, X), X)) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))))))) | (~((~![X: $i] : (q1(X) | (~p1(X)))) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | q1(B!42) | (~r1(B!42)))) | ![X: $i] : (~((~p1(X)) | p1(tptp_fun_Y_41(X)))) | (~(q1(A!48) | (~k!0) | (~![X: $i] : (~((~p1(X)) | (~q1(X))))))) | (~((~![X: $i] : (q1(X) | (~p1(X)))) | (~(r1(Y!52) | (~q1(Y!52)))) | (~![Z: $i] : (~(r1(Z) | (~p1(Z)))))))) <=> (![X: $i] : (a(X, Y!25) <=> (~a(X, X))) | ![X: $i, Y: $i] : (~(r1(B!43) | (~p1(A!44)) | (~(r1(Y) | (~p1(X)))))) | ![X: $i] : (~((~p1(X)) | p1(tptp_fun_Y_41(X)))) | (~((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3)))))))))))))) | (~((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))))))) | (~((~![X: $i] : p1(X)) | (~((~p1(A!13)) | (~p1(B!12)))))) | ![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y)))))) | (~((~![X: $i] : (~((~a(X, tptp_fun_Y_17(X))) | (~a(tptp_fun_Y_17(X), tptp_fun_Y_17(X)))))) | (~![Z: $i] : (~a(Z, Z))))) | (~((~![Y: $i] : (p1(Y) | (~q1(Y)))) | (~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))))) | (~((~![X: $i] : p1(X)) | (~![Y: $i] : (~p1(Y))))) | (~(q1(X!20) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X)))))) | (~((~![Z: $i] : (p1(Z) | (~q1(Z)))) | (~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))))) | (~((~![X: $i] : (b(X) | (~a1(X)))) | (~![X: $i] : (~b(X))) | (~a1(X!23)))) | 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Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))))) | (~((~q1(f(B!6))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5)))))))))))))) | (~(b(X!7) | (~a1(X!7)) | (~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (~![X: $i] : ((~a1(X)) | (~c(X)))))) | (~((~s1(A!11)) | (~s1(B!10)) | (~r(B!10, C!9)) | (~![X: $i] : (p1(X) | (~s1(X)))) | (~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y)))))) | (~((~![X: $i] : p1(X)) | (~q1(Y!14)) | (~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))))) | (~((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X)))))))) | (~((~a1(X!23)) | (~![X: $i] : b(X)) | (~![X: $i] : ((~a1(X)) | (~b(X)))))) | (~((~eq(A!40, B!39)) | eq(B!39, A!40) | (~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | ((~a_member_of(tptp_fun_Z_38(Y, X), X)) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))))))) | ![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y)))))) | (~((~![X: $i] : (q1(X) | (~p1(X)))) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | q1(B!42) | (~r1(B!42)))) | (~(q1(A!48) | (~k!0) | (~![X: $i] : (~((~p1(X)) | (~q1(X))))))) | (~((~![X: $i] : (q1(X) | (~p1(X)))) | (~(r1(Y!52) | (~q1(Y!52)))) | (~![Z: $i] : (~(r1(Z) | (~p1(Z))))))))),
% 0.50/0.58 inference(rewrite,[status(thm)],[])).
% 0.50/0.58 tff(880,plain,
% 0.50/0.58 ((![X: $i] : (q1(X) | (~p1(X))) & (r1(Y!52) | (~q1(Y!52))) & ![Z: $i] : (~(r1(Z) | (~p1(Z))))) <=> (~((~![X: $i] : (q1(X) | (~p1(X)))) | (~(r1(Y!52) | (~q1(Y!52)))) | (~![Z: $i] : (~(r1(Z) | (~p1(Z)))))))),
% 0.50/0.58 inference(rewrite,[status(thm)],[])).
% 0.50/0.58 tff(881,plain,
% 0.50/0.58 (((~q1(A!48)) & k!0 & ![X: $i] : (~((~p1(X)) | (~q1(X))))) <=> (~(q1(A!48) | (~k!0) | (~![X: $i] : (~((~p1(X)) | (~q1(X)))))))),
% 0.50/0.58 inference(rewrite,[status(thm)],[])).
% 0.50/0.58 tff(882,plain,
% 0.50/0.58 (^[X: $i] : rewrite((p1(X) & q1(X)) <=> (~((~p1(X)) | (~q1(X)))))),
% 0.50/0.58 inference(bind,[status(th)],[])).
% 0.50/0.58 tff(883,plain,
% 0.50/0.58 (![X: $i] : (p1(X) & q1(X)) <=> ![X: $i] : (~((~p1(X)) | (~q1(X))))),
% 0.50/0.58 inference(quant_intro,[status(thm)],[882])).
% 0.50/0.58 tff(884,plain,
% 0.50/0.58 (((~q1(A!48)) & k!0 & ![X: $i] : (p1(X) & q1(X))) <=> ((~q1(A!48)) & k!0 & ![X: $i] : (~((~p1(X)) | (~q1(X)))))),
% 0.50/0.58 inference(monotonicity,[status(thm)],[883])).
% 0.50/0.58 tff(885,plain,
% 0.50/0.58 (((~q1(A!48)) & k!0 & ![X: $i] : (p1(X) & q1(X))) <=> (~(q1(A!48) | (~k!0) | (~![X: $i] : (~((~p1(X)) | (~q1(X)))))))),
% 0.50/0.58 inference(transitivity,[status(thm)],[884, 881])).
% 0.50/0.58 tff(886,plain,
% 0.50/0.58 (((~q1(B!42)) & ![Y: $i] : (p1(Y) | (~r1(Y))) & ![X: $i] : (q1(X) | (~p1(X))) & r1(B!42)) <=> (~((~![X: $i] : (q1(X) | (~p1(X)))) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | q1(B!42) | (~r1(B!42))))),
% 0.50/0.58 inference(rewrite,[status(thm)],[])).
% 0.50/0.58 tff(887,plain,
% 0.50/0.58 ((![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | ((~a_member_of(tptp_fun_Z_38(Y, X), X)) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))))) & (~((~eq(A!40, B!39)) | eq(B!39, A!40)))) <=> (~((~eq(A!40, B!39)) | eq(B!39, A!40) | (~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | ((~a_member_of(tptp_fun_Z_38(Y, X), X)) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))))))))),
% 0.50/0.58 inference(rewrite,[status(thm)],[])).
% 0.50/0.58 tff(888,plain,
% 0.50/0.58 (^[X: $i, Y: $i] : trans(monotonicity(rewrite(((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) <=> ((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))), ((((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(X, Y) | ((~a_member_of(tptp_fun_Z_38(Y, X), X)) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))) <=> (((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(X, Y) | ((~a_member_of(tptp_fun_Z_38(Y, X), X)) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))))), rewrite((((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(X, Y) | ((~a_member_of(tptp_fun_Z_38(Y, X), X)) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))) <=> (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | ((~a_member_of(tptp_fun_Z_38(Y, X), X)) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))))), ((((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(X, Y) | ((~a_member_of(tptp_fun_Z_38(Y, X), X)) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))) <=> (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | ((~a_member_of(tptp_fun_Z_38(Y, X), X)) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))))))),
% 0.50/0.58 inference(bind,[status(th)],[])).
% 0.50/0.58 tff(889,plain,
% 0.50/0.58 (![X: $i, Y: $i] : (((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(X, Y) | ((~a_member_of(tptp_fun_Z_38(Y, X), X)) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))) <=> ![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | ((~a_member_of(tptp_fun_Z_38(Y, X), X)) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))))),
% 0.50/0.59 inference(quant_intro,[status(thm)],[888])).
% 0.50/0.59 tff(890,plain,
% 0.50/0.59 ((![X: $i, Y: $i] : (((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(X, Y) | ((~a_member_of(tptp_fun_Z_38(Y, X), X)) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))) & (~((~eq(A!40, B!39)) | eq(B!39, A!40)))) <=> (![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | ((~a_member_of(tptp_fun_Z_38(Y, X), X)) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))))) & (~((~eq(A!40, B!39)) | eq(B!39, A!40))))),
% 0.50/0.59 inference(monotonicity,[status(thm)],[889])).
% 0.50/0.59 tff(891,plain,
% 0.50/0.59 ((![X: $i, Y: $i] : (((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(X, Y) | ((~a_member_of(tptp_fun_Z_38(Y, X), X)) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))) & (~((~eq(A!40, B!39)) | eq(B!39, A!40)))) <=> (~((~eq(A!40, B!39)) | eq(B!39, A!40) | (~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | ((~a_member_of(tptp_fun_Z_38(Y, X), X)) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))))))))),
% 0.50/0.59 inference(transitivity,[status(thm)],[890, 887])).
% 0.50/0.59 tff(892,plain,
% 0.50/0.59 (^[Z: $i, Y: $i] : rewrite(((~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_37(Z)))) | (p(Y, tptp_fun_X_37(Z)) & ![W: $i] : (~p(W, Y)))) <=> ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y)))))))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(893,plain,
% 0.50/0.59 (![Z: $i, Y: $i] : ((~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_37(Z)))) | (p(Y, tptp_fun_X_37(Z)) & ![W: $i] : (~p(W, Y)))) <=> ![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))),
% 0.50/0.59 inference(quant_intro,[status(thm)],[892])).
% 0.50/0.59 tff(894,plain,
% 0.50/0.59 ((a1(X!23) & ![X: $i] : b(X) & ![X: $i] : ((~a1(X)) | (~b(X)))) <=> (~((~a1(X!23)) | (~![X: $i] : b(X)) | (~![X: $i] : ((~a1(X)) | (~b(X))))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(895,plain,
% 0.50/0.59 (^[X: $i] : trans(monotonicity(rewrite((a1(X) & b(X)) <=> (~((~a1(X)) | (~b(X))))), ((~(a1(X) & b(X))) <=> (~(~((~a1(X)) | (~b(X))))))), rewrite((~(~((~a1(X)) | (~b(X))))) <=> ((~a1(X)) | (~b(X)))), ((~(a1(X) & b(X))) <=> ((~a1(X)) | (~b(X)))))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(896,plain,
% 0.50/0.59 (![X: $i] : (~(a1(X) & b(X))) <=> ![X: $i] : ((~a1(X)) | (~b(X)))),
% 0.50/0.59 inference(quant_intro,[status(thm)],[895])).
% 0.50/0.59 tff(897,plain,
% 0.50/0.59 ((a1(X!23) & ![X: $i] : b(X) & ![X: $i] : (~(a1(X) & b(X)))) <=> (a1(X!23) & ![X: $i] : b(X) & ![X: $i] : ((~a1(X)) | (~b(X))))),
% 0.50/0.59 inference(monotonicity,[status(thm)],[896])).
% 0.50/0.59 tff(898,plain,
% 0.50/0.59 ((a1(X!23) & ![X: $i] : b(X) & ![X: $i] : (~(a1(X) & b(X)))) <=> (~((~a1(X!23)) | (~![X: $i] : b(X)) | (~![X: $i] : ((~a1(X)) | (~b(X))))))),
% 0.50/0.59 inference(transitivity,[status(thm)],[897, 894])).
% 0.50/0.59 tff(899,plain,
% 0.50/0.59 ((![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X))))) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) <=> (~((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X))))))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(900,plain,
% 0.50/0.59 (^[X: $i] : rewrite((p1(X) & q1(tptp_fun_Y_16(X))) <=> (~((~p1(X)) | (~q1(tptp_fun_Y_16(X))))))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(901,plain,
% 0.50/0.59 (![X: $i] : (p1(X) & q1(tptp_fun_Y_16(X))) <=> ![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X)))))),
% 0.50/0.59 inference(quant_intro,[status(thm)],[900])).
% 0.50/0.59 tff(902,plain,
% 0.50/0.59 ((![X: $i] : (p1(X) & q1(tptp_fun_Y_16(X))) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) <=> (![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X))))) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z)))))),
% 0.50/0.59 inference(monotonicity,[status(thm)],[901])).
% 0.50/0.59 tff(903,plain,
% 0.50/0.59 ((![X: $i] : (p1(X) & q1(tptp_fun_Y_16(X))) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) <=> (~((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X))))))))),
% 0.50/0.59 inference(transitivity,[status(thm)],[902, 899])).
% 0.50/0.59 tff(904,plain,
% 0.50/0.59 ((![X: $i] : p1(X) & q1(Y!14) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) <=> (~((~![X: $i] : p1(X)) | (~q1(Y!14)) | (~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z)))))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(905,plain,
% 0.50/0.59 ((s1(A!11) & s1(B!10) & r(B!10, C!9) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)) & ![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y)))) <=> (~((~s1(A!11)) | (~s1(B!10)) | (~r(B!10, C!9)) | (~![X: $i] : (p1(X) | (~s1(X)))) | (~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y))))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(906,plain,
% 0.50/0.59 (^[X: $i, Y: $i] : trans(monotonicity(rewrite((p1(X) & q(X, Y)) <=> (~((~p1(X)) | (~q(X, Y))))), ((~(p1(X) & q(X, Y))) <=> (~(~((~p1(X)) | (~q(X, Y))))))), rewrite((~(~((~p1(X)) | (~q(X, Y))))) <=> ((~p1(X)) | (~q(X, Y)))), ((~(p1(X) & q(X, Y))) <=> ((~p1(X)) | (~q(X, Y)))))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(907,plain,
% 0.50/0.59 (![X: $i, Y: $i] : (~(p1(X) & q(X, Y))) <=> ![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y)))),
% 0.50/0.59 inference(quant_intro,[status(thm)],[906])).
% 0.50/0.59 tff(908,plain,
% 0.50/0.59 ((s1(A!11) & s1(B!10) & r(B!10, C!9) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)) & ![X: $i, Y: $i] : (~(p1(X) & q(X, Y)))) <=> (s1(A!11) & s1(B!10) & r(B!10, C!9) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)) & ![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y))))),
% 0.50/0.59 inference(monotonicity,[status(thm)],[907])).
% 0.50/0.59 tff(909,plain,
% 0.50/0.59 ((s1(A!11) & s1(B!10) & r(B!10, C!9) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)) & ![X: $i, Y: $i] : (~(p1(X) & q(X, Y)))) <=> (~((~s1(A!11)) | (~s1(B!10)) | (~r(B!10, C!9)) | (~![X: $i] : (p1(X) | (~s1(X)))) | (~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y))))))),
% 0.50/0.59 inference(transitivity,[status(thm)],[908, 905])).
% 0.50/0.59 tff(910,plain,
% 0.50/0.59 ((![X: $i] : (c(X) | b(X) | (~a1(X))) & (~(b(X!7) | (~a1(X!7)))) & ![X: $i] : ((~a1(X)) | (~c(X)))) <=> (~(b(X!7) | (~a1(X!7)) | (~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (~![X: $i] : ((~a1(X)) | (~c(X))))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(911,plain,
% 0.50/0.59 (^[X: $i] : trans(monotonicity(rewrite((a1(X) & c(X)) <=> (~((~a1(X)) | (~c(X))))), ((~(a1(X) & c(X))) <=> (~(~((~a1(X)) | (~c(X))))))), rewrite((~(~((~a1(X)) | (~c(X))))) <=> ((~a1(X)) | (~c(X)))), ((~(a1(X) & c(X))) <=> ((~a1(X)) | (~c(X)))))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(912,plain,
% 0.50/0.59 (![X: $i] : (~(a1(X) & c(X))) <=> ![X: $i] : ((~a1(X)) | (~c(X)))),
% 0.50/0.59 inference(quant_intro,[status(thm)],[911])).
% 0.50/0.59 tff(913,plain,
% 0.50/0.59 ((![X: $i] : (c(X) | b(X) | (~a1(X))) & (~(b(X!7) | (~a1(X!7)))) & ![X: $i] : (~(a1(X) & c(X)))) <=> (![X: $i] : (c(X) | b(X) | (~a1(X))) & (~(b(X!7) | (~a1(X!7)))) & ![X: $i] : ((~a1(X)) | (~c(X))))),
% 0.50/0.59 inference(monotonicity,[status(thm)],[912])).
% 0.50/0.59 tff(914,plain,
% 0.50/0.59 ((![X: $i] : (c(X) | b(X) | (~a1(X))) & (~(b(X!7) | (~a1(X!7)))) & ![X: $i] : (~(a1(X) & c(X)))) <=> (~(b(X!7) | (~a1(X!7)) | (~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (~![X: $i] : ((~a1(X)) | (~c(X))))))),
% 0.50/0.59 inference(transitivity,[status(thm)],[913, 910])).
% 0.50/0.59 tff(915,plain,
% 0.50/0.59 ((q1(f(B!6)) & ![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5)))))))))))) <=> (~((~q1(f(B!6))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5))))))))))))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(916,plain,
% 0.50/0.59 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!6) & r1(C!5))))) <=> ((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5)))))))))), ((((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!6) & r1(C!5))))) & q1(X)) <=> (((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5))))))))) & q1(X)))), rewrite((((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5))))))))) & q1(X)) <=> (~((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5))))))))))))), ((((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!6) & r1(C!5))))) & q1(X)) <=> (~((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5)))))))))))))), ((~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!6) & r1(C!5))))) & q1(X))) <=> (~(~((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5))))))))))))))), rewrite((~(~((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5))))))))))))) <=> ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5)))))))))))), ((~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!6) & r1(C!5))))) & q1(X))) <=> ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5)))))))))))))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(917,plain,
% 0.50/0.59 (![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!6) & r1(C!5))))) & q1(X))) <=> ![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5)))))))))))),
% 0.50/0.59 inference(quant_intro,[status(thm)],[916])).
% 0.50/0.59 tff(918,plain,
% 0.50/0.59 ((q1(f(B!6)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!6) & r1(C!5))))) & q1(X)))) <=> (q1(f(B!6)) & ![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5))))))))))))),
% 0.50/0.59 inference(monotonicity,[status(thm)],[917])).
% 0.50/0.59 tff(919,plain,
% 0.50/0.59 ((q1(f(B!6)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!6) & r1(C!5))))) & q1(X)))) <=> (~((~q1(f(B!6))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5))))))))))))))),
% 0.50/0.59 inference(transitivity,[status(thm)],[918, 915])).
% 0.50/0.59 tff(920,plain,
% 0.50/0.59 ((![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y)) & ![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))) <=> (~((~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))) | (~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y)))))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(921,plain,
% 0.50/0.59 (^[X: $i, Y: $i] : trans(monotonicity(rewrite((p(X, Y) & ((~q(f(B!51), B!51)) | q(X, Y))) <=> (~((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y)))))), ((~(p(X, Y) & ((~q(f(B!51), B!51)) | q(X, Y)))) <=> (~(~((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y)))))))), rewrite((~(~((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y)))))) <=> ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))), ((~(p(X, Y) & ((~q(f(B!51), B!51)) | q(X, Y)))) <=> ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(922,plain,
% 0.50/0.59 (![X: $i, Y: $i] : (~(p(X, Y) & ((~q(f(B!51), B!51)) | q(X, Y)))) <=> ![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))),
% 0.50/0.59 inference(quant_intro,[status(thm)],[921])).
% 0.50/0.59 tff(923,plain,
% 0.50/0.59 ((![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y)) & ![X: $i, Y: $i] : (~(p(X, Y) & ((~q(f(B!51), B!51)) | q(X, Y))))) <=> (![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y)) & ![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y)))))),
% 0.50/0.59 inference(monotonicity,[status(thm)],[922])).
% 0.50/0.59 tff(924,plain,
% 0.50/0.59 ((![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y)) & ![X: $i, Y: $i] : (~(p(X, Y) & ((~q(f(B!51), B!51)) | q(X, Y))))) <=> (~((~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))) | (~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y)))))))),
% 0.50/0.59 inference(transitivity,[status(thm)],[923, 920])).
% 0.50/0.59 tff(925,plain,
% 0.50/0.59 (^[X: $i, Y: $i] : rewrite((~((~(((~q1(X)) | p(X, A!50)) & q1(A!50) & q1(B!49) & ((~r1(Y)) | p(B!49, Y)) & r1(A!50) & r1(B!49) & ((~s1(A!50)) | p(X, Y)) & s1(A!50))) | p(A!50, B!49))) <=> (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y))))))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(926,plain,
% 0.50/0.59 (![X: $i, Y: $i] : (~((~(((~q1(X)) | p(X, A!50)) & q1(A!50) & q1(B!49) & ((~r1(Y)) | p(B!49, Y)) & r1(A!50) & r1(B!49) & ((~s1(A!50)) | p(X, Y)) & s1(A!50))) | p(A!50, B!49))) <=> ![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y)))))),
% 0.50/0.59 inference(quant_intro,[status(thm)],[925])).
% 0.50/0.59 tff(927,plain,
% 0.50/0.59 ((~((~(a0 & b0)) | (a0 <=> b0))) <=> (~((~b0) | (a0 <=> b0) | (~a0)))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(928,plain,
% 0.50/0.59 ((![X: $i, Y: $i] : p(X, Y) & (~p(X!47, X!47))) <=> (~((~![X: $i, Y: $i] : p(X, Y)) | p(X!47, X!47)))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(929,plain,
% 0.50/0.59 ((p1(X!35) & ![Y: $i] : (~p1(Y))) <=> (~((~p1(X!35)) | (~![Y: $i] : (~p1(Y)))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(930,plain,
% 0.50/0.59 ((![Y: $i] : p(X!45, Y) & ![X: $i] : (~p(X, Y!46))) <=> (~((~![Y: $i] : p(X!45, Y)) | (~![X: $i] : (~p(X, Y!46)))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(931,plain,
% 0.50/0.59 (^[Y: $i] : rewrite(((~p1(Y)) & p1(X!35)) <=> (~(p1(Y) | (~p1(X!35)))))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(932,plain,
% 0.50/0.59 (![Y: $i] : ((~p1(Y)) & p1(X!35)) <=> ![Y: $i] : (~(p1(Y) | (~p1(X!35))))),
% 0.50/0.59 inference(quant_intro,[status(thm)],[931])).
% 0.50/0.59 tff(933,plain,
% 0.50/0.59 ((p1(X!35) & ![Z: $i] : (~p1(Z))) <=> (~((~p1(X!35)) | (~![Z: $i] : (~p1(Z)))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(934,plain,
% 0.50/0.59 (((p1(X!35) | p1(Y!36)) & (![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))) <=> (~((~(p1(X!35) | p1(Y!36))) | (~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y))))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(935,plain,
% 0.50/0.59 ((![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y))) <=> (![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(936,plain,
% 0.50/0.59 (((p1(X!35) | p1(Y!36)) & (![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))) <=> ((p1(X!35) | p1(Y!36)) & (![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y))))),
% 0.50/0.59 inference(monotonicity,[status(thm)],[935])).
% 0.50/0.59 tff(937,plain,
% 0.50/0.59 (((p1(X!35) | p1(Y!36)) & (![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))) <=> (~((~(p1(X!35) | p1(Y!36))) | (~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y))))))),
% 0.50/0.59 inference(transitivity,[status(thm)],[936, 934])).
% 0.50/0.59 tff(938,plain,
% 0.50/0.59 ((![X: $i] : p1(X) & ((~p1(X!33)) | (~p1(Y!34)))) <=> (~((~![X: $i] : p1(X)) | (~((~p1(X!33)) | (~p1(Y!34))))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(939,plain,
% 0.50/0.59 ((![X: $i] : p1(X) & ((~p1(A!32)) | (~p1(B!31)))) <=> (~((~![X: $i] : p1(X)) | (~((~p1(A!32)) | (~p1(B!31))))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(940,plain,
% 0.50/0.59 ((~(~((~p1(A!32)) | (~p1(B!31))))) <=> ((~p1(A!32)) | (~p1(B!31)))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(941,plain,
% 0.50/0.59 ((p1(A!32) & p1(B!31)) <=> (~((~p1(A!32)) | (~p1(B!31))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(942,plain,
% 0.50/0.59 ((~(p1(A!32) & p1(B!31))) <=> (~(~((~p1(A!32)) | (~p1(B!31)))))),
% 0.50/0.59 inference(monotonicity,[status(thm)],[941])).
% 0.50/0.59 tff(943,plain,
% 0.50/0.59 ((~(p1(A!32) & p1(B!31))) <=> ((~p1(A!32)) | (~p1(B!31)))),
% 0.50/0.59 inference(transitivity,[status(thm)],[942, 940])).
% 0.50/0.59 tff(944,plain,
% 0.50/0.59 ((![X: $i] : p1(X) & (~(p1(A!32) & p1(B!31)))) <=> (![X: $i] : p1(X) & ((~p1(A!32)) | (~p1(B!31))))),
% 0.50/0.59 inference(monotonicity,[status(thm)],[943])).
% 0.50/0.59 tff(945,plain,
% 0.50/0.59 ((![X: $i] : p1(X) & (~(p1(A!32) & p1(B!31)))) <=> (~((~![X: $i] : p1(X)) | (~((~p1(A!32)) | (~p1(B!31))))))),
% 0.50/0.59 inference(transitivity,[status(thm)],[944, 939])).
% 0.50/0.59 tff(946,plain,
% 0.50/0.59 (((a(X!28, Y!27) | a(X!29, Y!30)) & (![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))) <=> (~((~(a(X!28, Y!27) | a(X!29, Y!30))) | (~(![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y))))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(947,plain,
% 0.50/0.59 ((![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y))) <=> (![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(948,plain,
% 0.50/0.59 (((a(X!28, Y!27) | a(X!29, Y!30)) & (![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))) <=> ((a(X!28, Y!27) | a(X!29, Y!30)) & (![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y))))),
% 0.50/0.59 inference(monotonicity,[status(thm)],[947])).
% 0.50/0.59 tff(949,plain,
% 0.50/0.59 (((a(X!28, Y!27) | a(X!29, Y!30)) & (![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))) <=> (~((~(a(X!28, Y!27) | a(X!29, Y!30))) | (~(![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y))))))),
% 0.50/0.59 inference(transitivity,[status(thm)],[948, 946])).
% 0.50/0.59 tff(950,plain,
% 0.50/0.59 ((b(X!26) & ![X: $i] : (~(a1(X) | b(X)))) <=> (~((~b(X!26)) | (~![X: $i] : (~(a1(X) | b(X))))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(951,plain,
% 0.50/0.59 ((![X: $i] : (~b(X)) & ![X: $i] : a1(X) & (b(X!24) | (~a1(X!24)))) <=> (~((~![X: $i] : a1(X)) | (~![X: $i] : (~b(X))) | (~(b(X!24) | (~a1(X!24))))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(952,plain,
% 0.50/0.59 ((![X: $i] : (~b(X)) & ![X: $i] : (b(X) | (~a1(X))) & a1(X!23)) <=> (~((~![X: $i] : (b(X) | (~a1(X)))) | (~![X: $i] : (~b(X))) | (~a1(X!23))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(953,plain,
% 0.50/0.59 ((![Z: $i] : (p1(Z) | (~q1(Z))) & ![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))) <=> (~((~![Z: $i] : (p1(Z) | (~q1(Z)))) | (~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X))))))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(954,plain,
% 0.50/0.59 (^[X: $i] : trans(monotonicity(rewrite(((p1(A!22) | (~p1(X))) & (p1(B!21) | (~q1(X)))) <=> (~((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X))))))), ((~((p1(A!22) | (~p1(X))) & (p1(B!21) | (~q1(X))))) <=> (~(~((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X))))))))), rewrite((~(~((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X))))))) <=> ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))), ((~((p1(A!22) | (~p1(X))) & (p1(B!21) | (~q1(X))))) <=> ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(955,plain,
% 0.50/0.59 (![X: $i] : (~((p1(A!22) | (~p1(X))) & (p1(B!21) | (~q1(X))))) <=> ![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))),
% 0.50/0.59 inference(quant_intro,[status(thm)],[954])).
% 0.50/0.59 tff(956,plain,
% 0.50/0.59 ((![Z: $i] : (p1(Z) | (~q1(Z))) & ![X: $i] : (~((p1(A!22) | (~p1(X))) & (p1(B!21) | (~q1(X)))))) <=> (![Z: $i] : (p1(Z) | (~q1(Z))) & ![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X))))))),
% 0.50/0.59 inference(monotonicity,[status(thm)],[955])).
% 0.50/0.59 tff(957,plain,
% 0.50/0.59 ((![Z: $i] : (p1(Z) | (~q1(Z))) & ![X: $i] : (~((p1(A!22) | (~p1(X))) & (p1(B!21) | (~q1(X)))))) <=> (~((~![Z: $i] : (p1(Z) | (~q1(Z)))) | (~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X))))))))),
% 0.50/0.59 inference(transitivity,[status(thm)],[956, 953])).
% 0.50/0.59 tff(958,plain,
% 0.50/0.59 (((~q1(X!20)) & ![X: $i] : p1(X) & ![X: $i] : (q1(X) | (~p1(X)))) <=> (~(q1(X!20) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(959,plain,
% 0.50/0.59 ((![X: $i] : p1(X) & ![Y: $i] : (~p1(Y))) <=> (~((~![X: $i] : p1(X)) | (~![Y: $i] : (~p1(Y)))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(960,plain,
% 0.50/0.59 ((![Y: $i] : (p1(Y) | (~q1(Y))) & ![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))) <=> (~((~![Y: $i] : (p1(Y) | (~q1(Y)))) | (~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X))))))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(961,plain,
% 0.50/0.59 (^[X: $i] : trans(monotonicity(rewrite(((p1(A!19) | (~p1(X))) & (p1(B!18) | (~q1(X)))) <=> (~((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X))))))), ((~((p1(A!19) | (~p1(X))) & (p1(B!18) | (~q1(X))))) <=> (~(~((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X))))))))), rewrite((~(~((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X))))))) <=> ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))), ((~((p1(A!19) | (~p1(X))) & (p1(B!18) | (~q1(X))))) <=> ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(962,plain,
% 0.50/0.59 (![X: $i] : (~((p1(A!19) | (~p1(X))) & (p1(B!18) | (~q1(X))))) <=> ![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))),
% 0.50/0.59 inference(quant_intro,[status(thm)],[961])).
% 0.50/0.59 tff(963,plain,
% 0.50/0.59 ((![Y: $i] : (p1(Y) | (~q1(Y))) & ![X: $i] : (~((p1(A!19) | (~p1(X))) & (p1(B!18) | (~q1(X)))))) <=> (![Y: $i] : (p1(Y) | (~q1(Y))) & ![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X))))))),
% 0.50/0.59 inference(monotonicity,[status(thm)],[962])).
% 0.50/0.59 tff(964,plain,
% 0.50/0.59 ((![Y: $i] : (p1(Y) | (~q1(Y))) & ![X: $i] : (~((p1(A!19) | (~p1(X))) & (p1(B!18) | (~q1(X)))))) <=> (~((~![Y: $i] : (p1(Y) | (~q1(Y)))) | (~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X))))))))),
% 0.50/0.59 inference(transitivity,[status(thm)],[963, 960])).
% 0.50/0.59 tff(965,plain,
% 0.50/0.59 ((![X: $i] : (~((~a(X, tptp_fun_Y_17(X))) | (~a(tptp_fun_Y_17(X), tptp_fun_Y_17(X))))) & ![Z: $i] : (~a(Z, Z))) <=> (~((~![X: $i] : (~((~a(X, tptp_fun_Y_17(X))) | (~a(tptp_fun_Y_17(X), tptp_fun_Y_17(X)))))) | (~![Z: $i] : (~a(Z, Z)))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(966,plain,
% 0.50/0.59 (^[X: $i] : rewrite((a(X, tptp_fun_Y_17(X)) & a(tptp_fun_Y_17(X), tptp_fun_Y_17(X))) <=> (~((~a(X, tptp_fun_Y_17(X))) | (~a(tptp_fun_Y_17(X), tptp_fun_Y_17(X))))))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(967,plain,
% 0.50/0.59 (![X: $i] : (a(X, tptp_fun_Y_17(X)) & a(tptp_fun_Y_17(X), tptp_fun_Y_17(X))) <=> ![X: $i] : (~((~a(X, tptp_fun_Y_17(X))) | (~a(tptp_fun_Y_17(X), tptp_fun_Y_17(X)))))),
% 0.50/0.59 inference(quant_intro,[status(thm)],[966])).
% 0.50/0.59 tff(968,plain,
% 0.50/0.59 ((![X: $i] : (a(X, tptp_fun_Y_17(X)) & a(tptp_fun_Y_17(X), tptp_fun_Y_17(X))) & ![Z: $i] : (~a(Z, Z))) <=> (![X: $i] : (~((~a(X, tptp_fun_Y_17(X))) | (~a(tptp_fun_Y_17(X), tptp_fun_Y_17(X))))) & ![Z: $i] : (~a(Z, Z)))),
% 0.50/0.59 inference(monotonicity,[status(thm)],[967])).
% 0.50/0.59 tff(969,plain,
% 0.50/0.59 ((![X: $i] : (a(X, tptp_fun_Y_17(X)) & a(tptp_fun_Y_17(X), tptp_fun_Y_17(X))) & ![Z: $i] : (~a(Z, Z))) <=> (~((~![X: $i] : (~((~a(X, tptp_fun_Y_17(X))) | (~a(tptp_fun_Y_17(X), tptp_fun_Y_17(X)))))) | (~![Z: $i] : (~a(Z, Z)))))),
% 0.50/0.59 inference(transitivity,[status(thm)],[968, 965])).
% 0.50/0.59 tff(970,plain,
% 0.50/0.59 ((![X: $i] : p1(X) & ((~p1(A!13)) | (~p1(B!12)))) <=> (~((~![X: $i] : p1(X)) | (~((~p1(A!13)) | (~p1(B!12))))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(971,plain,
% 0.50/0.59 ((~(~((~p1(A!13)) | (~p1(B!12))))) <=> ((~p1(A!13)) | (~p1(B!12)))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(972,plain,
% 0.50/0.59 ((p1(A!13) & p1(B!12)) <=> (~((~p1(A!13)) | (~p1(B!12))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(973,plain,
% 0.50/0.59 ((~(p1(A!13) & p1(B!12))) <=> (~(~((~p1(A!13)) | (~p1(B!12)))))),
% 0.50/0.59 inference(monotonicity,[status(thm)],[972])).
% 0.50/0.59 tff(974,plain,
% 0.50/0.59 ((~(p1(A!13) & p1(B!12))) <=> ((~p1(A!13)) | (~p1(B!12)))),
% 0.50/0.59 inference(transitivity,[status(thm)],[973, 971])).
% 0.50/0.59 tff(975,plain,
% 0.50/0.59 ((![X: $i] : p1(X) & (~(p1(A!13) & p1(B!12)))) <=> (![X: $i] : p1(X) & ((~p1(A!13)) | (~p1(B!12))))),
% 0.50/0.59 inference(monotonicity,[status(thm)],[974])).
% 0.50/0.59 tff(976,plain,
% 0.50/0.59 ((![X: $i] : p1(X) & (~(p1(A!13) & p1(B!12)))) <=> (~((~![X: $i] : p1(X)) | (~((~p1(A!13)) | (~p1(B!12))))))),
% 0.50/0.59 inference(transitivity,[status(thm)],[975, 970])).
% 0.50/0.59 tff(977,plain,
% 0.50/0.59 (^[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : rewrite((~((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A!8) & e(A!8) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A!8, Y))))))) <=> (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y)))))))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(978,plain,
% 0.50/0.59 (![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A!8) & e(A!8) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A!8, Y))))))) <=> ![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y))))))),
% 0.50/0.59 inference(quant_intro,[status(thm)],[977])).
% 0.50/0.59 tff(979,plain,
% 0.50/0.59 ((![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : ((~q1(X)) | (~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))))) <=> (~((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2))))))))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(980,plain,
% 0.50/0.59 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~r1(Y)) | (r1(B!1) & r1(C!2))) <=> ((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))), (((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B!1) & r1(C!2))) & q1(X)) <=> ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2))))) & q1(X)))), rewrite(((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2))))) & q1(X)) <=> (~((~q1(X)) | (~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2))))))))), (((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B!1) & r1(C!2))) & q1(X)) <=> (~((~q1(X)) | (~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))))))), ((~((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B!1) & r1(C!2))) & q1(X))) <=> (~(~((~q1(X)) | (~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2))))))))))), rewrite((~(~((~q1(X)) | (~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2))))))))) <=> ((~q1(X)) | (~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))))), ((~((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B!1) & r1(C!2))) & q1(X))) <=> ((~q1(X)) | (~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))))))),
% 0.50/0.60 inference(bind,[status(th)],[])).
% 0.50/0.60 tff(981,plain,
% 0.50/0.60 (![X: $i, Y: $i] : (~((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B!1) & r1(C!2))) & q1(X))) <=> ![X: $i, Y: $i] : ((~q1(X)) | (~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))))),
% 0.50/0.60 inference(quant_intro,[status(thm)],[980])).
% 0.50/0.60 tff(982,plain,
% 0.50/0.60 ((![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B!1) & r1(C!2))) & q1(X)))) <=> (![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : ((~q1(X)) | (~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2))))))))),
% 0.50/0.60 inference(monotonicity,[status(thm)],[981])).
% 0.50/0.60 tff(983,plain,
% 0.50/0.60 ((![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B!1) & r1(C!2))) & q1(X)))) <=> (~((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2))))))))))),
% 0.50/0.60 inference(transitivity,[status(thm)],[982, 979])).
% 0.50/0.60 tff(984,plain,
% 0.50/0.60 ((![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3)))))))))))) <=> (~((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3))))))))))))))),
% 0.50/0.60 inference(rewrite,[status(thm)],[])).
% 0.50/0.60 tff(985,plain,
% 0.50/0.60 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!4) & r1(C!3))))) <=> ((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3)))))))))), ((((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!4) & r1(C!3))))) & q1(X)) <=> (((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3))))))))) & q1(X)))), rewrite((((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3))))))))) & q1(X)) <=> (~((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3))))))))))))), ((((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!4) & r1(C!3))))) & q1(X)) <=> (~((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3)))))))))))))), ((~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!4) & r1(C!3))))) & q1(X))) <=> (~(~((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3))))))))))))))), rewrite((~(~((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3))))))))))))) <=> ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3)))))))))))), ((~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!4) & r1(C!3))))) & q1(X))) <=> ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3)))))))))))))),
% 0.50/0.60 inference(bind,[status(th)],[])).
% 0.50/0.60 tff(986,plain,
% 0.50/0.60 (![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!4) & r1(C!3))))) & q1(X))) <=> ![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3)))))))))))),
% 0.50/0.60 inference(quant_intro,[status(thm)],[985])).
% 0.50/0.60 tff(987,plain,
% 0.50/0.60 ((![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!4) & r1(C!3))))) & q1(X)))) <=> (![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3))))))))))))),
% 0.50/0.60 inference(monotonicity,[status(thm)],[986])).
% 0.50/0.60 tff(988,plain,
% 0.50/0.60 ((![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!4) & r1(C!3))))) & q1(X)))) <=> (~((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3))))))))))))))),
% 0.50/0.60 inference(transitivity,[status(thm)],[987, 984])).
% 0.50/0.60 tff(989,plain,
% 0.50/0.60 (((![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!4) & r1(C!3))))) & q1(X)))) | (![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B!1) & r1(C!2))) & q1(X)))) | ![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A!8) & e(A!8) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A!8, Y))))))) | (![X: $i] : p1(X) & (~(p1(A!13) & p1(B!12)))) | (![X: $i] : (a(X, tptp_fun_Y_17(X)) & a(tptp_fun_Y_17(X), tptp_fun_Y_17(X))) & ![Z: $i] : (~a(Z, Z))) | (![Y: $i] : (p1(Y) | (~q1(Y))) & ![X: $i] : (~((p1(A!19) | (~p1(X))) & (p1(B!18) | (~q1(X)))))) | (![X: $i] : p1(X) & ![Y: $i] : (~p1(Y))) | ((~q1(X!20)) & ![X: $i] : p1(X) & ![X: $i] : (q1(X) | (~p1(X)))) | (![Z: $i] : (p1(Z) | (~q1(Z))) & ![X: $i] : (~((p1(A!22) | (~p1(X))) & (p1(B!21) | (~q1(X)))))) | (![X: $i] : (~b(X)) & ![X: $i] : (b(X) | (~a1(X))) & a1(X!23)) | (![X: $i] : (~b(X)) & ![X: $i] : a1(X) & (b(X!24) | (~a1(X!24)))) | ![X: $i] : (a(X, Y!25) <=> (~a(X, X))) | (b(X!26) & ![X: $i] : (~(a1(X) | b(X)))) | ((a(X!28, Y!27) | a(X!29, Y!30)) & (![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))) | (![X: $i] : p1(X) & (~(p1(A!32) & p1(B!31)))) | (![X: $i] : p1(X) & ((~p1(X!33)) | (~p1(Y!34)))) | ((p1(X!35) | p1(Y!36)) & (![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))) | (p1(X!35) & ![Z: $i] : (~p1(Z))) | ![X: $i, Y: $i] : (~(r1(B!43) | (~p1(A!44)) | (~(r1(Y) | (~p1(X)))))) | ![Y: $i] : ((~p1(Y)) & p1(X!35)) | (![Y: $i] : p(X!45, Y) & ![X: $i] : (~p(X, Y!46))) | (p1(X!35) & ![Y: $i] : (~p1(Y))) | (![X: $i, Y: $i] : p(X, Y) & (~p(X!47, X!47))) | (~((~(a0 & b0)) | (a0 <=> b0))) | ![X: $i, Y: $i] : (~((~(((~q1(X)) | p(X, A!50)) & q1(A!50) & q1(B!49) & ((~r1(Y)) | p(B!49, Y)) & r1(A!50) & r1(B!49) & ((~s1(A!50)) | p(X, Y)) & s1(A!50))) | p(A!50, B!49))) | (![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y)) & ![X: $i, Y: $i] : (~(p(X, Y) & ((~q(f(B!51), B!51)) | q(X, Y))))) | (q1(f(B!6)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!6) & r1(C!5))))) & q1(X)))) | (![X: $i] : (c(X) | b(X) | (~a1(X))) & (~(b(X!7) | (~a1(X!7)))) & ![X: $i] : (~(a1(X) & c(X)))) | (s1(A!11) & s1(B!10) & r(B!10, C!9) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)) & ![X: $i, Y: $i] : (~(p1(X) & q(X, Y)))) | (![X: $i] : p1(X) & q1(Y!14) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (![X: $i] : (p1(X) & q1(tptp_fun_Y_16(X))) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (a1(X!23) & ![X: $i] : b(X) & ![X: $i] : (~(a1(X) & b(X)))) | ![Z: $i, Y: $i] : ((~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_37(Z)))) | (p(Y, tptp_fun_X_37(Z)) & ![W: $i] : (~p(W, Y)))) | (![X: $i, Y: $i] : (((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(X, Y) | ((~a_member_of(tptp_fun_Z_38(Y, X), X)) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))) & (~((~eq(A!40, B!39)) | eq(B!39, A!40)))) | ((~q1(B!42)) & ![Y: $i] : (p1(Y) | (~r1(Y))) & ![X: $i] : (q1(X) | (~p1(X))) & r1(B!42)) | ![X: $i] : (~((~p1(X)) | p1(tptp_fun_Y_41(X)))) | ((~q1(A!48)) & k!0 & ![X: $i] : (p1(X) & q1(X))) | (![X: $i] : (q1(X) | (~p1(X))) & (r1(Y!52) | (~q1(Y!52))) & ![Z: $i] : (~(r1(Z) | (~p1(Z)))))) <=> ((~((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3)))))))))))))) | (~((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))))))) | ![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y)))))) | (~((~![X: $i] : p1(X)) | (~((~p1(A!13)) | (~p1(B!12)))))) | (~((~![X: $i] : (~((~a(X, tptp_fun_Y_17(X))) | (~a(tptp_fun_Y_17(X), tptp_fun_Y_17(X)))))) | (~![Z: $i] : (~a(Z, Z))))) | (~((~![Y: $i] : (p1(Y) | (~q1(Y)))) | (~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))))) | (~((~![X: $i] : p1(X)) | (~![Y: $i] : (~p1(Y))))) | (~(q1(X!20) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X)))))) | (~((~![Z: $i] : (p1(Z) | (~q1(Z)))) | (~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))))) | (~((~![X: $i] : (b(X) | (~a1(X)))) | (~![X: $i] : (~b(X))) | (~a1(X!23)))) | (~((~![X: $i] : a1(X)) | (~![X: $i] : (~b(X))) | (~(b(X!24) | (~a1(X!24)))))) | ![X: $i] : (a(X, Y!25) <=> (~a(X, X))) | (~((~b(X!26)) | (~![X: $i] : (~(a1(X) | b(X)))))) | (~((~(a(X!28, Y!27) | a(X!29, Y!30))) | (~(![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))))) | (~((~![X: $i] : p1(X)) | (~((~p1(A!32)) | (~p1(B!31)))))) | (~((~![X: $i] : p1(X)) | (~((~p1(X!33)) | (~p1(Y!34)))))) | (~((~(p1(X!35) | p1(Y!36))) | (~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))))) | (~((~p1(X!35)) | (~![Z: $i] : (~p1(Z))))) | ![X: $i, Y: $i] : (~(r1(B!43) | (~p1(A!44)) | (~(r1(Y) | (~p1(X)))))) | ![Y: $i] : (~(p1(Y) | (~p1(X!35)))) | (~((~![Y: $i] : p(X!45, Y)) | (~![X: $i] : (~p(X, Y!46))))) | (~((~p1(X!35)) | (~![Y: $i] : (~p1(Y))))) | (~((~![X: $i, Y: $i] : p(X, Y)) | p(X!47, X!47))) | (~((~b0) | (a0 <=> b0) | (~a0))) | ![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y))))) | (~((~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))) | (~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))))) | (~((~q1(f(B!6))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5)))))))))))))) | (~(b(X!7) | (~a1(X!7)) | (~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (~![X: $i] : ((~a1(X)) | (~c(X)))))) | (~((~s1(A!11)) | (~s1(B!10)) | (~r(B!10, C!9)) | (~![X: $i] : (p1(X) | (~s1(X)))) | (~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y)))))) | (~((~![X: $i] : p1(X)) | (~q1(Y!14)) | (~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))))) | (~((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X)))))))) | (~((~a1(X!23)) | (~![X: $i] : b(X)) | (~![X: $i] : ((~a1(X)) | (~b(X)))))) | ![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y)))))) | (~((~eq(A!40, B!39)) | eq(B!39, A!40) | (~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | ((~a_member_of(tptp_fun_Z_38(Y, X), X)) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))))))) | (~((~![X: $i] : (q1(X) | (~p1(X)))) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | q1(B!42) | (~r1(B!42)))) | ![X: $i] : (~((~p1(X)) | p1(tptp_fun_Y_41(X)))) | (~(q1(A!48) | (~k!0) | (~![X: $i] : (~((~p1(X)) | (~q1(X))))))) | (~((~![X: $i] : (q1(X) | (~p1(X)))) | (~(r1(Y!52) | (~q1(Y!52)))) | (~![Z: $i] : (~(r1(Z) | (~p1(Z))))))))),
% 0.50/0.60 inference(monotonicity,[status(thm)],[988, 983, 978, 976, 969, 964, 959, 958, 957, 952, 951, 950, 949, 945, 938, 937, 933, 932, 930, 929, 928, 927, 926, 924, 919, 914, 909, 904, 903, 898, 893, 891, 886, 885, 880])).
% 0.50/0.60 tff(990,plain,
% 0.50/0.60 (((![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!4) & r1(C!3))))) & q1(X)))) | (![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B!1) & r1(C!2))) & q1(X)))) | ![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A!8) & e(A!8) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A!8, Y))))))) | (![X: $i] : p1(X) & (~(p1(A!13) & p1(B!12)))) | (![X: $i] : (a(X, tptp_fun_Y_17(X)) & a(tptp_fun_Y_17(X), tptp_fun_Y_17(X))) & ![Z: $i] : (~a(Z, Z))) | (![Y: $i] : (p1(Y) | (~q1(Y))) & ![X: $i] : (~((p1(A!19) | (~p1(X))) & (p1(B!18) | (~q1(X)))))) | (![X: $i] : p1(X) & ![Y: $i] : (~p1(Y))) | ((~q1(X!20)) & ![X: $i] : p1(X) & ![X: $i] : (q1(X) | (~p1(X)))) | (![Z: $i] : (p1(Z) | (~q1(Z))) & ![X: $i] : (~((p1(A!22) | (~p1(X))) & (p1(B!21) | (~q1(X)))))) | (![X: $i] : (~b(X)) & ![X: $i] : (b(X) | (~a1(X))) & a1(X!23)) | (![X: $i] : (~b(X)) & ![X: $i] : a1(X) & (b(X!24) | (~a1(X!24)))) | ![X: $i] : (a(X, Y!25) <=> (~a(X, X))) | (b(X!26) & ![X: $i] : (~(a1(X) | b(X)))) | ((a(X!28, Y!27) | a(X!29, Y!30)) & (![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))) | (![X: $i] : p1(X) & (~(p1(A!32) & p1(B!31)))) | (![X: $i] : p1(X) & ((~p1(X!33)) | (~p1(Y!34)))) | ((p1(X!35) | p1(Y!36)) & (![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))) | (p1(X!35) & ![Z: $i] : (~p1(Z))) | ![X: $i, Y: $i] : (~(r1(B!43) | (~p1(A!44)) | (~(r1(Y) | (~p1(X)))))) | ![Y: $i] : ((~p1(Y)) & p1(X!35)) | (![Y: $i] : p(X!45, Y) & ![X: $i] : (~p(X, Y!46))) | (p1(X!35) & ![Y: $i] : (~p1(Y))) | (![X: $i, Y: $i] : p(X, Y) & (~p(X!47, X!47))) | (~((~(a0 & b0)) | (a0 <=> b0))) | ![X: $i, Y: $i] : (~((~(((~q1(X)) | p(X, A!50)) & q1(A!50) & q1(B!49) & ((~r1(Y)) | p(B!49, Y)) & r1(A!50) & r1(B!49) & ((~s1(A!50)) | p(X, Y)) & s1(A!50))) | p(A!50, B!49))) | (![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y)) & ![X: $i, Y: $i] : (~(p(X, Y) & ((~q(f(B!51), B!51)) | q(X, Y))))) | (q1(f(B!6)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!6) & r1(C!5))))) & q1(X)))) | (![X: $i] : (c(X) | b(X) | (~a1(X))) & (~(b(X!7) | (~a1(X!7)))) & ![X: $i] : (~(a1(X) & c(X)))) | (s1(A!11) & s1(B!10) & r(B!10, C!9) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)) & ![X: $i, Y: $i] : (~(p1(X) & q(X, Y)))) | (![X: $i] : p1(X) & q1(Y!14) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (![X: $i] : (p1(X) & q1(tptp_fun_Y_16(X))) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (a1(X!23) & ![X: $i] : b(X) & ![X: $i] : (~(a1(X) & b(X)))) | ![Z: $i, Y: $i] : ((~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_37(Z)))) | (p(Y, tptp_fun_X_37(Z)) & ![W: $i] : (~p(W, Y)))) | (![X: $i, Y: $i] : (((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(X, Y) | ((~a_member_of(tptp_fun_Z_38(Y, X), X)) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))) & (~((~eq(A!40, B!39)) | eq(B!39, A!40)))) | ((~q1(B!42)) & ![Y: $i] : (p1(Y) | (~r1(Y))) & ![X: $i] : (q1(X) | (~p1(X))) & r1(B!42)) | ![X: $i] : (~((~p1(X)) | p1(tptp_fun_Y_41(X)))) | ((~q1(A!48)) & k!0 & ![X: $i] : (p1(X) & q1(X))) | (![X: $i] : (q1(X) | (~p1(X))) & (r1(Y!52) | (~q1(Y!52))) & ![Z: $i] : (~(r1(Z) | (~p1(Z)))))) <=> (![X: $i] : (a(X, Y!25) <=> (~a(X, X))) | ![X: $i, Y: $i] : (~(r1(B!43) | (~p1(A!44)) | (~(r1(Y) | (~p1(X)))))) | ![X: $i] : (~((~p1(X)) | p1(tptp_fun_Y_41(X)))) | (~((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3)))))))))))))) | (~((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))))))) | (~((~![X: $i] : p1(X)) | (~((~p1(A!13)) | (~p1(B!12)))))) | ![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y)))))) | (~((~![X: $i] : (~((~a(X, tptp_fun_Y_17(X))) | (~a(tptp_fun_Y_17(X), tptp_fun_Y_17(X)))))) | (~![Z: $i] : (~a(Z, Z))))) | (~((~![Y: $i] : (p1(Y) | (~q1(Y)))) | (~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))))) | (~((~![X: $i] : p1(X)) | (~![Y: $i] : (~p1(Y))))) | (~(q1(X!20) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X)))))) | (~((~![Z: $i] : (p1(Z) | (~q1(Z)))) | (~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))))) | (~((~![X: $i] : (b(X) | (~a1(X)))) | (~![X: $i] : (~b(X))) | (~a1(X!23)))) | (~((~![X: $i] : a1(X)) | (~![X: $i] : (~b(X))) | (~(b(X!24) | (~a1(X!24)))))) | (~((~b(X!26)) | (~![X: $i] : (~(a1(X) | b(X)))))) | (~((~(a(X!28, Y!27) | a(X!29, Y!30))) | (~(![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))))) | (~((~![X: $i] : p1(X)) | (~((~p1(A!32)) | (~p1(B!31)))))) | (~((~![X: $i] : p1(X)) | (~((~p1(X!33)) | (~p1(Y!34)))))) | (~((~(p1(X!35) | p1(Y!36))) | (~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))))) | (~((~p1(X!35)) | (~![Z: $i] : (~p1(Z))))) | ![Y: $i] : (~(p1(Y) | (~p1(X!35)))) | (~((~![Y: $i] : p(X!45, Y)) | (~![X: $i] : (~p(X, Y!46))))) | (~((~p1(X!35)) | (~![Y: $i] : (~p1(Y))))) | (~((~![X: $i, Y: $i] : p(X, Y)) | p(X!47, X!47))) | (~((~b0) | (a0 <=> b0) | (~a0))) | ![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y))))) | (~((~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))) | (~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))))) | (~((~q1(f(B!6))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5)))))))))))))) | (~(b(X!7) | (~a1(X!7)) | (~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (~![X: $i] : ((~a1(X)) | (~c(X)))))) | (~((~s1(A!11)) | (~s1(B!10)) | (~r(B!10, C!9)) | (~![X: $i] : (p1(X) | (~s1(X)))) | (~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y)))))) | (~((~![X: $i] : p1(X)) | (~q1(Y!14)) | (~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))))) | (~((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X)))))))) | (~((~a1(X!23)) | (~![X: $i] : b(X)) | (~![X: $i] : ((~a1(X)) | (~b(X)))))) | (~((~eq(A!40, B!39)) | eq(B!39, A!40) | (~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | ((~a_member_of(tptp_fun_Z_38(Y, X), X)) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))))))) | ![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y)))))) | (~((~![X: $i] : (q1(X) | (~p1(X)))) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | q1(B!42) | (~r1(B!42)))) | (~(q1(A!48) | (~k!0) | (~![X: $i] : (~((~p1(X)) | (~q1(X))))))) | (~((~![X: $i] : (q1(X) | (~p1(X)))) | (~(r1(Y!52) | (~q1(Y!52)))) | (~![Z: $i] : (~(r1(Z) | (~p1(Z))))))))),
% 0.50/0.61 inference(transitivity,[status(thm)],[989, 879])).
% 0.50/0.61 tff(991,plain,
% 0.50/0.61 (((![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B!1) & r1(C!2))) & q1(X)))) | (![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!4) & r1(C!3))))) & q1(X)))) | (q1(f(B!6)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!6) & r1(C!5))))) & q1(X)))) | (![X: $i] : (c(X) | b(X) | (~a1(X))) & (~(b(X!7) | (~a1(X!7)))) & ![X: $i] : (~(a1(X) & c(X)))) | ![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A!8) & e(A!8) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A!8, Y))))))) | (s1(A!11) & s1(B!10) & r(B!10, C!9) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)) & ![X: $i, Y: $i] : (~(p1(X) & q(X, Y)))) | (![X: $i] : p1(X) & (~(p1(A!13) & p1(B!12)))) | (![X: $i] : p1(X) & q1(Y!14) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (![X: $i] : (p1(X) & q1(tptp_fun_Y_16(X))) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (![X: $i] : (a(X, tptp_fun_Y_17(X)) & a(tptp_fun_Y_17(X), tptp_fun_Y_17(X))) & ![Z: $i] : (~a(Z, Z))) | (![Y: $i] : (p1(Y) | (~q1(Y))) & ![X: $i] : (~((p1(A!19) | (~p1(X))) & (p1(B!18) | (~q1(X)))))) | (![X: $i] : p1(X) & ![Y: $i] : (~p1(Y))) | ((~q1(X!20)) & ![X: $i] : p1(X) & ![X: $i] : (q1(X) | (~p1(X)))) | (![Z: $i] : (p1(Z) | (~q1(Z))) & ![X: $i] : (~((p1(A!22) | (~p1(X))) & (p1(B!21) | (~q1(X)))))) | (![X: $i] : (~b(X)) & ![X: $i] : (b(X) | (~a1(X))) & a1(X!23)) | (![X: $i] : (~b(X)) & ![X: $i] : a1(X) & (b(X!24) | (~a1(X!24)))) | ![X: $i] : (a(X, Y!25) <=> (~a(X, X))) | (a1(X!23) & ![X: $i] : b(X) & ![X: $i] : (~(a1(X) & b(X)))) | (b(X!26) & ![X: $i] : (~(a1(X) | b(X)))) | ((a(X!28, Y!27) | a(X!29, Y!30)) & (![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))) | (![X: $i] : p1(X) & (~(p1(A!32) & p1(B!31)))) | (![X: $i] : p1(X) & ((~p1(X!33)) | (~p1(Y!34)))) | ((p1(X!35) | p1(Y!36)) & (![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))) | (p1(X!35) & ![Z: $i] : (~p1(Z))) | ![Z: $i, Y: $i] : ((~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_37(Z)))) | (p(Y, tptp_fun_X_37(Z)) & ![W: $i] : (~p(W, Y)))) | (![X: $i, Y: $i] : (((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(X, Y) | ((~a_member_of(tptp_fun_Z_38(Y, X), X)) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))) & (~((~eq(A!40, B!39)) | eq(B!39, A!40)))) | ![X: $i] : (~((~p1(X)) | p1(tptp_fun_Y_41(X)))) | ((~q1(B!42)) & ![Y: $i] : (p1(Y) | (~r1(Y))) & ![X: $i] : (q1(X) | (~p1(X))) & r1(B!42)) | ![X: $i, Y: $i] : (~(r1(B!43) | (~p1(A!44)) | (~(r1(Y) | (~p1(X)))))) | ![Y: $i] : ((~p1(Y)) & p1(X!35)) | (![Y: $i] : p(X!45, Y) & ![X: $i] : (~p(X, Y!46))) | (p1(X!35) & ![Y: $i] : (~p1(Y))) | (![X: $i, Y: $i] : p(X, Y) & (~p(X!47, X!47))) | ((~q1(A!48)) & k!0 & ![X: $i] : (p1(X) & q1(X))) | (~((~(a0 & b0)) | (a0 <=> b0))) | ![X: $i, Y: $i] : (~((~(((~q1(X)) | p(X, A!50)) & q1(A!50) & q1(B!49) & ((~r1(Y)) | p(B!49, Y)) & r1(A!50) & r1(B!49) & ((~s1(A!50)) | p(X, Y)) & s1(A!50))) | p(A!50, B!49))) | (![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y)) & ![X: $i, Y: $i] : (~(p(X, Y) & ((~q(f(B!51), B!51)) | q(X, Y))))) | (![X: $i] : (q1(X) | (~p1(X))) & (r1(Y!52) | (~q1(Y!52))) & ![Z: $i] : (~(r1(Z) | (~p1(Z)))))) <=> ((![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!4) & r1(C!3))))) & q1(X)))) | (![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B!1) & r1(C!2))) & q1(X)))) | ![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A!8) & e(A!8) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A!8, Y))))))) | (![X: $i] : p1(X) & (~(p1(A!13) & p1(B!12)))) | (![X: $i] : (a(X, tptp_fun_Y_17(X)) & a(tptp_fun_Y_17(X), tptp_fun_Y_17(X))) & ![Z: $i] : (~a(Z, Z))) | (![Y: $i] : (p1(Y) | (~q1(Y))) & ![X: $i] : (~((p1(A!19) | (~p1(X))) & (p1(B!18) | (~q1(X)))))) | (![X: $i] : p1(X) & ![Y: $i] : (~p1(Y))) | ((~q1(X!20)) & ![X: $i] : p1(X) & ![X: $i] : (q1(X) | (~p1(X)))) | (![Z: $i] : (p1(Z) | (~q1(Z))) & ![X: $i] : (~((p1(A!22) | (~p1(X))) & (p1(B!21) | (~q1(X)))))) | (![X: $i] : (~b(X)) & ![X: $i] : (b(X) | (~a1(X))) & a1(X!23)) | (![X: $i] : (~b(X)) & ![X: $i] : a1(X) & (b(X!24) | (~a1(X!24)))) | ![X: $i] : (a(X, Y!25) <=> (~a(X, X))) | (b(X!26) & ![X: $i] : (~(a1(X) | b(X)))) | ((a(X!28, Y!27) | a(X!29, Y!30)) & (![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))) | (![X: $i] : p1(X) & (~(p1(A!32) & p1(B!31)))) | (![X: $i] : p1(X) & ((~p1(X!33)) | (~p1(Y!34)))) | ((p1(X!35) | p1(Y!36)) & (![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))) | (p1(X!35) & ![Z: $i] : (~p1(Z))) | ![X: $i, Y: $i] : (~(r1(B!43) | (~p1(A!44)) | (~(r1(Y) | (~p1(X)))))) | ![Y: $i] : ((~p1(Y)) & p1(X!35)) | (![Y: $i] : p(X!45, Y) & ![X: $i] : (~p(X, Y!46))) | (p1(X!35) & ![Y: $i] : (~p1(Y))) | (![X: $i, Y: $i] : p(X, Y) & (~p(X!47, X!47))) | (~((~(a0 & b0)) | (a0 <=> b0))) | ![X: $i, Y: $i] : (~((~(((~q1(X)) | p(X, A!50)) & q1(A!50) & q1(B!49) & ((~r1(Y)) | p(B!49, Y)) & r1(A!50) & r1(B!49) & ((~s1(A!50)) | p(X, Y)) & s1(A!50))) | p(A!50, B!49))) | (![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y)) & ![X: $i, Y: $i] : (~(p(X, Y) & ((~q(f(B!51), B!51)) | q(X, Y))))) | (q1(f(B!6)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!6) & r1(C!5))))) & q1(X)))) | (![X: $i] : (c(X) | b(X) | (~a1(X))) & (~(b(X!7) | (~a1(X!7)))) & ![X: $i] : (~(a1(X) & c(X)))) | (s1(A!11) & s1(B!10) & r(B!10, C!9) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)) & ![X: $i, Y: $i] : (~(p1(X) & q(X, Y)))) | (![X: $i] : p1(X) & q1(Y!14) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (![X: $i] : (p1(X) & q1(tptp_fun_Y_16(X))) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (a1(X!23) & ![X: $i] : b(X) & ![X: $i] : (~(a1(X) & b(X)))) | ![Z: $i, Y: $i] : ((~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_37(Z)))) | (p(Y, tptp_fun_X_37(Z)) & ![W: $i] : (~p(W, Y)))) | (![X: $i, Y: $i] : (((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(X, Y) | ((~a_member_of(tptp_fun_Z_38(Y, X), X)) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))) & (~((~eq(A!40, B!39)) | eq(B!39, A!40)))) | ((~q1(B!42)) & ![Y: $i] : (p1(Y) | (~r1(Y))) & ![X: $i] : (q1(X) | (~p1(X))) & r1(B!42)) | ![X: $i] : (~((~p1(X)) | p1(tptp_fun_Y_41(X)))) | ((~q1(A!48)) & k!0 & ![X: $i] : (p1(X) & q1(X))) | (![X: $i] : (q1(X) | (~p1(X))) & (r1(Y!52) | (~q1(Y!52))) & ![Z: $i] : (~(r1(Z) | (~p1(Z))))))),
% 0.50/0.61 inference(rewrite,[status(thm)],[])).
% 0.50/0.61 tff(992,plain,
% 0.50/0.61 (((![X: $i] : (q1(X) | (~p1(X))) & (r1(Y!52) | (~q1(Y!52)))) & ![Z: $i] : (~(r1(Z) | (~p1(Z))))) <=> (![X: $i] : (q1(X) | (~p1(X))) & (r1(Y!52) | (~q1(Y!52))) & ![Z: $i] : (~(r1(Z) | (~p1(Z)))))),
% 0.50/0.61 inference(rewrite,[status(thm)],[])).
% 0.50/0.61 tff(993,plain,
% 0.50/0.61 ((![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y)) & ![X: $i, Y: $i] : (~(p(X, Y) & ((~q(f(B!51), B!51)) | q(X, Y))))) <=> (![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y)) & ![X: $i, Y: $i] : (~(p(X, Y) & ((~q(f(B!51), B!51)) | q(X, Y)))))),
% 0.50/0.61 inference(rewrite,[status(thm)],[])).
% 0.50/0.61 tff(994,plain,
% 0.50/0.61 (((~q1(A!48)) & (k!0 & ![X: $i] : (p1(X) & q1(X)))) <=> ((~q1(A!48)) & k!0 & ![X: $i] : (p1(X) & q1(X)))),
% 0.50/0.61 inference(rewrite,[status(thm)],[])).
% 0.50/0.61 tff(995,plain,
% 0.50/0.61 ((k!0 & ![X: $i] : (p1(X) & q1(X))) <=> (k!0 & ![X: $i] : (p1(X) & q1(X)))),
% 0.50/0.61 inference(rewrite,[status(thm)],[])).
% 0.50/0.61 tff(996,plain,
% 0.50/0.61 (((~q1(A!48)) & (k!0 & ![X: $i] : (p1(X) & q1(X)))) <=> ((~q1(A!48)) & (k!0 & ![X: $i] : (p1(X) & q1(X))))),
% 0.50/0.61 inference(monotonicity,[status(thm)],[995])).
% 0.50/0.61 tff(997,plain,
% 0.50/0.61 (((~q1(A!48)) & (k!0 & ![X: $i] : (p1(X) & q1(X)))) <=> ((~q1(A!48)) & k!0 & ![X: $i] : (p1(X) & q1(X)))),
% 0.50/0.61 inference(transitivity,[status(thm)],[996, 994])).
% 0.50/0.61 tff(998,plain,
% 0.50/0.61 ((![X: $i, Y: $i] : p(X, Y) & (~p(X!47, X!47))) <=> (![X: $i, Y: $i] : p(X, Y) & (~p(X!47, X!47)))),
% 0.50/0.61 inference(rewrite,[status(thm)],[])).
% 0.50/0.61 tff(999,plain,
% 0.50/0.61 ((![Y: $i] : p(X!45, Y) & ![X: $i] : (~p(X, Y!46))) <=> (![Y: $i] : p(X!45, Y) & ![X: $i] : (~p(X, Y!46)))),
% 0.50/0.61 inference(rewrite,[status(thm)],[])).
% 0.50/0.61 tff(1000,plain,
% 0.50/0.61 (((~q1(B!42)) & ![Y: $i] : (p1(Y) | (~r1(Y))) & (![X: $i] : (q1(X) | (~p1(X))) & r1(B!42))) <=> ((~q1(B!42)) & ![Y: $i] : (p1(Y) | (~r1(Y))) & ![X: $i] : (q1(X) | (~p1(X))) & r1(B!42))),
% 0.50/0.61 inference(rewrite,[status(thm)],[])).
% 0.50/0.61 tff(1001,plain,
% 0.50/0.61 (^[X: $i] : rewrite((~(p1(tptp_fun_Y_41(X)) | (~p1(X)))) <=> (~((~p1(X)) | p1(tptp_fun_Y_41(X)))))),
% 0.50/0.61 inference(bind,[status(th)],[])).
% 0.50/0.61 tff(1002,plain,
% 0.50/0.61 (![X: $i] : (~(p1(tptp_fun_Y_41(X)) | (~p1(X)))) <=> ![X: $i] : (~((~p1(X)) | p1(tptp_fun_Y_41(X))))),
% 0.50/0.61 inference(quant_intro,[status(thm)],[1001])).
% 0.50/0.61 tff(1003,plain,
% 0.50/0.61 ((![X: $i, Y: $i] : (((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))) & (~((~eq(A!40, B!39)) | eq(B!39, A!40)))) <=> (![X: $i, Y: $i] : (((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(X, Y) | ((~a_member_of(tptp_fun_Z_38(Y, X), X)) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))) & (~((~eq(A!40, B!39)) | eq(B!39, A!40))))),
% 0.50/0.61 inference(rewrite,[status(thm)],[])).
% 0.50/0.61 tff(1004,plain,
% 0.50/0.61 (![Z: $i] : ![Y: $i] : ((~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_37(Z)))) | (p(Y, tptp_fun_X_37(Z)) & ![W: $i] : (~p(W, Y)))) <=> ![Z: $i, Y: $i] : ((~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_37(Z)))) | (p(Y, tptp_fun_X_37(Z)) & ![W: $i] : (~p(W, Y))))),
% 0.50/0.61 inference(pull_quant,[status(thm)],[])).
% 0.50/0.61 tff(1005,plain,
% 0.50/0.61 (^[Z: $i] : quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(rewrite(((~(~p(Y, tptp_fun_X_37(Z)))) & ![W: $i] : (~p(W, Y))) <=> (p(Y, tptp_fun_X_37(Z)) & ![W: $i] : (~p(W, Y)))), ((((~(~p(Y, tptp_fun_X_37(Z)))) & ![W: $i] : (~p(W, Y))) | (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_37(Z))))) <=> ((p(Y, tptp_fun_X_37(Z)) & ![W: $i] : (~p(W, Y))) | (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_37(Z))))))), rewrite(((p(Y, tptp_fun_X_37(Z)) & ![W: $i] : (~p(W, Y))) | (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_37(Z))))) <=> ((~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_37(Z)))) | (p(Y, tptp_fun_X_37(Z)) & ![W: $i] : (~p(W, Y))))), ((((~(~p(Y, tptp_fun_X_37(Z)))) & ![W: $i] : (~p(W, Y))) | (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_37(Z))))) <=> ((~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_37(Z)))) | (p(Y, tptp_fun_X_37(Z)) & ![W: $i] : (~p(W, Y))))))), (![Y: $i] : (((~(~p(Y, tptp_fun_X_37(Z)))) & ![W: $i] : (~p(W, Y))) | (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_37(Z))))) <=> ![Y: $i] : ((~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_37(Z)))) | (p(Y, tptp_fun_X_37(Z)) & ![W: $i] : (~p(W, Y))))))),
% 0.50/0.61 inference(bind,[status(th)],[])).
% 0.50/0.61 tff(1006,plain,
% 0.50/0.61 (![Z: $i] : ![Y: $i] : (((~(~p(Y, tptp_fun_X_37(Z)))) & ![W: $i] : (~p(W, Y))) | (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_37(Z))))) <=> ![Z: $i] : ![Y: $i] : ((~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_37(Z)))) | (p(Y, tptp_fun_X_37(Z)) & ![W: $i] : (~p(W, Y))))),
% 0.50/0.61 inference(quant_intro,[status(thm)],[1005])).
% 0.50/0.61 tff(1007,plain,
% 0.50/0.61 (![Z: $i] : ![Y: $i] : (((~(~p(Y, tptp_fun_X_37(Z)))) & ![W: $i] : (~p(W, Y))) | (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_37(Z))))) <=> ![Z: $i, Y: $i] : ((~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_37(Z)))) | (p(Y, tptp_fun_X_37(Z)) & ![W: $i] : (~p(W, Y))))),
% 0.50/0.61 inference(transitivity,[status(thm)],[1006, 1004])).
% 0.50/0.61 tff(1008,plain,
% 0.50/0.61 ((p1(X!35) & ![Z: $i] : (~p1(Z))) <=> (p1(X!35) & ![Z: $i] : (~p1(Z)))),
% 0.50/0.61 inference(rewrite,[status(thm)],[])).
% 0.50/0.61 tff(1009,plain,
% 0.50/0.61 ((b(X!26) & ![X: $i] : (~(a1(X) | b(X)))) <=> (b(X!26) & ![X: $i] : (~(a1(X) | b(X))))),
% 0.50/0.61 inference(rewrite,[status(thm)],[])).
% 0.50/0.61 tff(1010,plain,
% 0.50/0.61 (((a1(X!23) & ![X: $i] : b(X)) & ![X: $i] : (~(a1(X) & b(X)))) <=> (a1(X!23) & ![X: $i] : b(X) & ![X: $i] : (~(a1(X) & b(X))))),
% 0.50/0.61 inference(rewrite,[status(thm)],[])).
% 0.50/0.61 tff(1011,plain,
% 0.50/0.61 ((a1(X!23) & ![X: $i] : b(X)) <=> (a1(X!23) & ![X: $i] : b(X))),
% 0.50/0.61 inference(rewrite,[status(thm)],[])).
% 0.50/0.61 tff(1012,plain,
% 0.50/0.61 (((a1(X!23) & ![X: $i] : b(X)) & ![X: $i] : (~(a1(X) & b(X)))) <=> ((a1(X!23) & ![X: $i] : b(X)) & ![X: $i] : (~(a1(X) & b(X))))),
% 0.50/0.61 inference(monotonicity,[status(thm)],[1011])).
% 0.50/0.61 tff(1013,plain,
% 0.50/0.61 (((a1(X!23) & ![X: $i] : b(X)) & ![X: $i] : (~(a1(X) & b(X)))) <=> (a1(X!23) & ![X: $i] : b(X) & ![X: $i] : (~(a1(X) & b(X))))),
% 0.50/0.61 inference(transitivity,[status(thm)],[1012, 1010])).
% 0.50/0.61 tff(1014,plain,
% 0.50/0.61 ((![X: $i] : (~b(X)) & ![X: $i] : a1(X) & (b(X!24) | (~a1(X!24)))) <=> (![X: $i] : (~b(X)) & ![X: $i] : a1(X) & (b(X!24) | (~a1(X!24))))),
% 0.50/0.61 inference(rewrite,[status(thm)],[])).
% 0.50/0.61 tff(1015,plain,
% 0.50/0.61 ((![X: $i] : (~b(X)) & ![X: $i] : (b(X) | (~a1(X))) & a1(X!23)) <=> (![X: $i] : (~b(X)) & ![X: $i] : (b(X) | (~a1(X))) & a1(X!23))),
% 0.50/0.61 inference(rewrite,[status(thm)],[])).
% 0.50/0.61 tff(1016,plain,
% 0.50/0.61 ((![Z: $i] : (p1(Z) | (~q1(Z))) & ![X: $i] : (~((p1(A!22) | (~p1(X))) & (p1(B!21) | (~q1(X)))))) <=> (![Z: $i] : (p1(Z) | (~q1(Z))) & ![X: $i] : (~((p1(A!22) | (~p1(X))) & (p1(B!21) | (~q1(X))))))),
% 0.50/0.61 inference(rewrite,[status(thm)],[])).
% 0.50/0.61 tff(1017,plain,
% 0.50/0.61 (((~q1(X!20)) & ![X: $i] : p1(X) & ![X: $i] : (q1(X) | (~p1(X)))) <=> ((~q1(X!20)) & ![X: $i] : p1(X) & ![X: $i] : (q1(X) | (~p1(X))))),
% 0.50/0.61 inference(rewrite,[status(thm)],[])).
% 0.50/0.61 tff(1018,plain,
% 0.50/0.61 ((![X: $i] : p1(X) & ![Y: $i] : (~p1(Y))) <=> (![X: $i] : p1(X) & ![Y: $i] : (~p1(Y)))),
% 0.50/0.61 inference(rewrite,[status(thm)],[])).
% 0.50/0.61 tff(1019,plain,
% 0.50/0.61 ((![Y: $i] : (p1(Y) | (~q1(Y))) & ![X: $i] : (~((p1(A!19) | (~p1(X))) & (p1(B!18) | (~q1(X)))))) <=> (![Y: $i] : (p1(Y) | (~q1(Y))) & ![X: $i] : (~((p1(A!19) | (~p1(X))) & (p1(B!18) | (~q1(X))))))),
% 0.50/0.61 inference(rewrite,[status(thm)],[])).
% 0.50/0.61 tff(1020,plain,
% 0.50/0.61 ((![X: $i] : (a(X, tptp_fun_Y_17(X)) & a(tptp_fun_Y_17(X), tptp_fun_Y_17(X))) & ![Z: $i] : (~a(Z, Z))) <=> (![X: $i] : (a(X, tptp_fun_Y_17(X)) & a(tptp_fun_Y_17(X), tptp_fun_Y_17(X))) & ![Z: $i] : (~a(Z, Z)))),
% 0.50/0.61 inference(rewrite,[status(thm)],[])).
% 0.50/0.61 tff(1021,plain,
% 0.50/0.61 ((![X: $i] : (p1(X) & q1(tptp_fun_Y_16(X))) & ![Z: $i] : (~(p1(tptp_fun_Y_15(Z)) | r1(Z)))) <=> (![X: $i] : (p1(X) & q1(tptp_fun_Y_16(X))) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z)))))),
% 0.50/0.61 inference(rewrite,[status(thm)],[])).
% 0.50/0.61 tff(1022,plain,
% 0.50/0.61 (((![X: $i] : p1(X) & q1(Y!14)) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) <=> (![X: $i] : p1(X) & q1(Y!14) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z)))))),
% 0.50/0.61 inference(rewrite,[status(thm)],[])).
% 0.50/0.61 tff(1023,plain,
% 0.50/0.61 (^[Z: $i] : rewrite((~(p1(tptp_fun_Y_15(Z)) | r1(Z))) <=> (~(r1(Z) | p1(tptp_fun_Y_15(Z)))))),
% 0.50/0.61 inference(bind,[status(th)],[])).
% 0.50/0.61 tff(1024,plain,
% 0.50/0.61 (![Z: $i] : (~(p1(tptp_fun_Y_15(Z)) | r1(Z))) <=> ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))),
% 0.50/0.61 inference(quant_intro,[status(thm)],[1023])).
% 0.50/0.61 tff(1025,plain,
% 0.50/0.61 (((![X: $i] : p1(X) & q1(Y!14)) & ![Z: $i] : (~(p1(tptp_fun_Y_15(Z)) | r1(Z)))) <=> ((![X: $i] : p1(X) & q1(Y!14)) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z)))))),
% 0.50/0.61 inference(monotonicity,[status(thm)],[1024])).
% 0.50/0.61 tff(1026,plain,
% 0.50/0.61 (((![X: $i] : p1(X) & q1(Y!14)) & ![Z: $i] : (~(p1(tptp_fun_Y_15(Z)) | r1(Z)))) <=> (![X: $i] : p1(X) & q1(Y!14) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z)))))),
% 0.50/0.61 inference(transitivity,[status(thm)],[1025, 1022])).
% 0.50/0.61 tff(1027,plain,
% 0.50/0.61 ((![X: $i] : p1(X) & (~(p1(A!13) & p1(B!12)))) <=> (![X: $i] : p1(X) & (~(p1(A!13) & p1(B!12))))),
% 0.50/0.61 inference(rewrite,[status(thm)],[])).
% 0.50/0.61 tff(1028,plain,
% 0.50/0.61 (((s1(A!11) & s1(B!10) & r(B!10, C!9) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) & ![X: $i, Y: $i] : (~(p1(X) & q(X, Y)))) <=> (s1(A!11) & s1(B!10) & r(B!10, C!9) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)) & ![X: $i, Y: $i] : (~(p1(X) & q(X, Y))))),
% 0.50/0.61 inference(rewrite,[status(thm)],[])).
% 0.50/0.61 tff(1029,plain,
% 0.50/0.61 ((s1(A!11) & s1(B!10) & r(B!10, C!9) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) <=> (s1(A!11) & s1(B!10) & r(B!10, C!9) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))),
% 0.50/0.61 inference(rewrite,[status(thm)],[])).
% 0.50/0.61 tff(1030,plain,
% 0.50/0.61 (((s1(A!11) & s1(B!10) & r(B!10, C!9) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) & ![X: $i, Y: $i] : (~(p1(X) & q(X, Y)))) <=> ((s1(A!11) & s1(B!10) & r(B!10, C!9) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) & ![X: $i, Y: $i] : (~(p1(X) & q(X, Y))))),
% 0.50/0.61 inference(monotonicity,[status(thm)],[1029])).
% 0.50/0.61 tff(1031,plain,
% 0.50/0.61 (((s1(A!11) & s1(B!10) & r(B!10, C!9) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) & ![X: $i, Y: $i] : (~(p1(X) & q(X, Y)))) <=> (s1(A!11) & s1(B!10) & r(B!10, C!9) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)) & ![X: $i, Y: $i] : (~(p1(X) & q(X, Y))))),
% 0.50/0.61 inference(transitivity,[status(thm)],[1030, 1028])).
% 0.50/0.61 tff(1032,plain,
% 0.50/0.61 (((![X: $i] : (c(X) | b(X) | (~a1(X))) & (~(b(X!7) | (~a1(X!7))))) & ![X: $i] : (~(a1(X) & c(X)))) <=> (![X: $i] : (c(X) | b(X) | (~a1(X))) & (~(b(X!7) | (~a1(X!7)))) & ![X: $i] : (~(a1(X) & c(X))))),
% 0.50/0.61 inference(rewrite,[status(thm)],[])).
% 0.50/0.61 tff(1033,plain,
% 0.50/0.61 ((![X: $i] : (c(X) | b(X) | (~a1(X))) & (~(b(X!7) | (~a1(X!7))))) <=> (![X: $i] : (c(X) | b(X) | (~a1(X))) & (~(b(X!7) | (~a1(X!7)))))),
% 0.50/0.61 inference(rewrite,[status(thm)],[])).
% 0.50/0.61 tff(1034,plain,
% 0.50/0.61 (((![X: $i] : (c(X) | b(X) | (~a1(X))) & (~(b(X!7) | (~a1(X!7))))) & ![X: $i] : (~(a1(X) & c(X)))) <=> ((![X: $i] : (c(X) | b(X) | (~a1(X))) & (~(b(X!7) | (~a1(X!7))))) & ![X: $i] : (~(a1(X) & c(X))))),
% 0.50/0.61 inference(monotonicity,[status(thm)],[1033])).
% 0.50/0.61 tff(1035,plain,
% 0.50/0.61 (((![X: $i] : (c(X) | b(X) | (~a1(X))) & (~(b(X!7) | (~a1(X!7))))) & ![X: $i] : (~(a1(X) & c(X)))) <=> (![X: $i] : (c(X) | b(X) | (~a1(X))) & (~(b(X!7) | (~a1(X!7)))) & ![X: $i] : (~(a1(X) & c(X))))),
% 0.50/0.61 inference(transitivity,[status(thm)],[1034, 1032])).
% 0.50/0.61 tff(1036,plain,
% 0.50/0.61 (((~(~q1(f(B!6)))) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!6) & r1(C!5))))) & q1(X)))) <=> (q1(f(B!6)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!6) & r1(C!5))))) & q1(X))))),
% 0.50/0.61 inference(rewrite,[status(thm)],[])).
% 0.50/0.62 tff(1037,plain,
% 0.50/0.62 ((![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!4) & r1(C!3))))) & q1(X)))) <=> (![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!4) & r1(C!3))))) & q1(X))))),
% 0.50/0.62 inference(rewrite,[status(thm)],[])).
% 0.50/0.62 tff(1038,plain,
% 0.50/0.62 ((![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B!1) & r1(C!2))) & q1(X)))) <=> (![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B!1) & r1(C!2))) & q1(X))))),
% 0.50/0.62 inference(rewrite,[status(thm)],[])).
% 0.50/0.62 tff(1039,plain,
% 0.50/0.62 (((![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B!1) & r1(C!2))) & q1(X)))) | (![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!4) & r1(C!3))))) & q1(X)))) | ((~(~q1(f(B!6)))) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!6) & r1(C!5))))) & q1(X)))) | ((![X: $i] : (c(X) | b(X) | (~a1(X))) & (~(b(X!7) | (~a1(X!7))))) & ![X: $i] : (~(a1(X) & c(X)))) | ![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A!8) & e(A!8) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A!8, Y))))))) | ((s1(A!11) & s1(B!10) & r(B!10, C!9) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) & ![X: $i, Y: $i] : (~(p1(X) & q(X, Y)))) | (![X: $i] : p1(X) & (~(p1(A!13) & p1(B!12)))) | ((![X: $i] : p1(X) & q1(Y!14)) & ![Z: $i] : (~(p1(tptp_fun_Y_15(Z)) | r1(Z)))) | (![X: $i] : (p1(X) & q1(tptp_fun_Y_16(X))) & ![Z: $i] : (~(p1(tptp_fun_Y_15(Z)) | r1(Z)))) | (![X: $i] : (a(X, tptp_fun_Y_17(X)) & a(tptp_fun_Y_17(X), tptp_fun_Y_17(X))) & ![Z: $i] : (~a(Z, Z))) | (![Y: $i] : (p1(Y) | (~q1(Y))) & ![X: $i] : (~((p1(A!19) | (~p1(X))) & (p1(B!18) | (~q1(X)))))) | (![X: $i] : p1(X) & ![Y: $i] : (~p1(Y))) | ((~q1(X!20)) & ![X: $i] : p1(X) & ![X: $i] : (q1(X) | (~p1(X)))) | (![Z: $i] : (p1(Z) | (~q1(Z))) & ![X: $i] : (~((p1(A!22) | (~p1(X))) & (p1(B!21) | (~q1(X)))))) | (![X: $i] : (~b(X)) & ![X: $i] : (b(X) | (~a1(X))) & a1(X!23)) | (![X: $i] : (~b(X)) & ![X: $i] : a1(X) & (b(X!24) | (~a1(X!24)))) | ![X: $i] : (a(X, Y!25) <=> (~a(X, X))) | ((a1(X!23) & ![X: $i] : b(X)) & ![X: $i] : (~(a1(X) & b(X)))) | (b(X!26) & ![X: $i] : (~(a1(X) | b(X)))) | ((a(X!28, Y!27) | a(X!29, Y!30)) & (![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))) | (![X: $i] : p1(X) & (~(p1(A!32) & p1(B!31)))) | (![X: $i] : p1(X) & ((~p1(X!33)) | (~p1(Y!34)))) | ((p1(X!35) | p1(Y!36)) & (![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))) | (p1(X!35) & ![Z: $i] : (~p1(Z))) | ![Z: $i] : ![Y: $i] : (((~(~p(Y, tptp_fun_X_37(Z)))) & ![W: $i] : (~p(W, Y))) | (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_37(Z))))) | (![X: $i, Y: $i] : (((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))) & (~((~eq(A!40, B!39)) | eq(B!39, A!40)))) | ![X: $i] : (~(p1(tptp_fun_Y_41(X)) | (~p1(X)))) | ((~q1(B!42)) & ![Y: $i] : (p1(Y) | (~r1(Y))) & (![X: $i] : (q1(X) | (~p1(X))) & r1(B!42))) | ![X: $i, Y: $i] : (~(r1(B!43) | (~p1(A!44)) | (~(r1(Y) | (~p1(X)))))) | ![Y: $i] : ((~p1(Y)) & p1(X!35)) | (![Y: $i] : p(X!45, Y) & ![X: $i] : (~p(X, Y!46))) | (p1(X!35) & ![Y: $i] : (~p1(Y))) | (![X: $i, Y: $i] : p(X, Y) & (~p(X!47, X!47))) | ((~q1(A!48)) & (k!0 & ![X: $i] : (p1(X) & q1(X)))) | (~((~(a0 & b0)) | (a0 <=> b0))) | ![X: $i, Y: $i] : (~((~(((~q1(X)) | p(X, A!50)) & q1(A!50) & q1(B!49) & ((~r1(Y)) | p(B!49, Y)) & r1(A!50) & r1(B!49) & ((~s1(A!50)) | p(X, Y)) & s1(A!50))) | p(A!50, B!49))) | (![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y)) & ![X: $i, Y: $i] : (~(p(X, Y) & ((~q(f(B!51), B!51)) | q(X, Y))))) | ((![X: $i] : (q1(X) | (~p1(X))) & (r1(Y!52) | (~q1(Y!52)))) & ![Z: $i] : (~(r1(Z) | (~p1(Z)))))) <=> ((![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B!1) & r1(C!2))) & q1(X)))) | (![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!4) & r1(C!3))))) & q1(X)))) | (q1(f(B!6)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!6) & r1(C!5))))) & q1(X)))) | (![X: $i] : (c(X) | b(X) | (~a1(X))) & (~(b(X!7) | (~a1(X!7)))) & ![X: $i] : (~(a1(X) & c(X)))) | ![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A!8) & e(A!8) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A!8, Y))))))) | (s1(A!11) & s1(B!10) & r(B!10, C!9) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)) & ![X: $i, Y: $i] : (~(p1(X) & q(X, Y)))) | (![X: $i] : p1(X) & (~(p1(A!13) & p1(B!12)))) | (![X: $i] : p1(X) & q1(Y!14) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (![X: $i] : (p1(X) & q1(tptp_fun_Y_16(X))) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (![X: $i] : (a(X, tptp_fun_Y_17(X)) & a(tptp_fun_Y_17(X), tptp_fun_Y_17(X))) & ![Z: $i] : (~a(Z, Z))) | (![Y: $i] : (p1(Y) | (~q1(Y))) & ![X: $i] : (~((p1(A!19) | (~p1(X))) & (p1(B!18) | (~q1(X)))))) | (![X: $i] : p1(X) & ![Y: $i] : (~p1(Y))) | ((~q1(X!20)) & ![X: $i] : p1(X) & ![X: $i] : (q1(X) | (~p1(X)))) | (![Z: $i] : (p1(Z) | (~q1(Z))) & ![X: $i] : (~((p1(A!22) | (~p1(X))) & (p1(B!21) | (~q1(X)))))) | (![X: $i] : (~b(X)) & ![X: $i] : (b(X) | (~a1(X))) & a1(X!23)) | (![X: $i] : (~b(X)) & ![X: $i] : a1(X) & (b(X!24) | (~a1(X!24)))) | ![X: $i] : (a(X, Y!25) <=> (~a(X, X))) | (a1(X!23) & ![X: $i] : b(X) & ![X: $i] : (~(a1(X) & b(X)))) | (b(X!26) & ![X: $i] : (~(a1(X) | b(X)))) | ((a(X!28, Y!27) | a(X!29, Y!30)) & (![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))) | (![X: $i] : p1(X) & (~(p1(A!32) & p1(B!31)))) | (![X: $i] : p1(X) & ((~p1(X!33)) | (~p1(Y!34)))) | ((p1(X!35) | p1(Y!36)) & (![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))) | (p1(X!35) & ![Z: $i] : (~p1(Z))) | ![Z: $i, Y: $i] : ((~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_37(Z)))) | (p(Y, tptp_fun_X_37(Z)) & ![W: $i] : (~p(W, Y)))) | (![X: $i, Y: $i] : (((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(X, Y) | ((~a_member_of(tptp_fun_Z_38(Y, X), X)) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))) & (~((~eq(A!40, B!39)) | eq(B!39, A!40)))) | ![X: $i] : (~((~p1(X)) | p1(tptp_fun_Y_41(X)))) | ((~q1(B!42)) & ![Y: $i] : (p1(Y) | (~r1(Y))) & ![X: $i] : (q1(X) | (~p1(X))) & r1(B!42)) | ![X: $i, Y: $i] : (~(r1(B!43) | (~p1(A!44)) | (~(r1(Y) | (~p1(X)))))) | ![Y: $i] : ((~p1(Y)) & p1(X!35)) | (![Y: $i] : p(X!45, Y) & ![X: $i] : (~p(X, Y!46))) | (p1(X!35) & ![Y: $i] : (~p1(Y))) | (![X: $i, Y: $i] : p(X, Y) & (~p(X!47, X!47))) | ((~q1(A!48)) & k!0 & ![X: $i] : (p1(X) & q1(X))) | (~((~(a0 & b0)) | (a0 <=> b0))) | ![X: $i, Y: $i] : (~((~(((~q1(X)) | p(X, A!50)) & q1(A!50) & q1(B!49) & ((~r1(Y)) | p(B!49, Y)) & r1(A!50) & r1(B!49) & ((~s1(A!50)) | p(X, Y)) & s1(A!50))) | p(A!50, B!49))) | (![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y)) & ![X: $i, Y: $i] : (~(p(X, Y) & ((~q(f(B!51), B!51)) | q(X, Y))))) | (![X: $i] : (q1(X) | (~p1(X))) & (r1(Y!52) | (~q1(Y!52))) & ![Z: $i] : (~(r1(Z) | (~p1(Z))))))),
% 0.50/0.62 inference(monotonicity,[status(thm)],[1038, 1037, 1036, 1035, 1031, 1027, 1026, 1021, 1020, 1019, 1018, 1017, 1016, 1015, 1014, 1013, 1009, 948, 936, 1008, 1007, 1003, 1002, 1000, 999, 998, 997, 993, 992])).
% 0.50/0.62 tff(1040,plain,
% 0.50/0.62 (((![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B!1) & r1(C!2))) & q1(X)))) | (![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!4) & r1(C!3))))) & q1(X)))) | ((~(~q1(f(B!6)))) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!6) & r1(C!5))))) & q1(X)))) | ((![X: $i] : (c(X) | b(X) | (~a1(X))) & (~(b(X!7) | (~a1(X!7))))) & ![X: $i] : (~(a1(X) & c(X)))) | ![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A!8) & e(A!8) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A!8, Y))))))) | ((s1(A!11) & s1(B!10) & r(B!10, C!9) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) & ![X: $i, Y: $i] : (~(p1(X) & q(X, Y)))) | (![X: $i] : p1(X) & (~(p1(A!13) & p1(B!12)))) | ((![X: $i] : p1(X) & q1(Y!14)) & ![Z: $i] : (~(p1(tptp_fun_Y_15(Z)) | r1(Z)))) | (![X: $i] : (p1(X) & q1(tptp_fun_Y_16(X))) & ![Z: $i] : (~(p1(tptp_fun_Y_15(Z)) | r1(Z)))) | (![X: $i] : (a(X, tptp_fun_Y_17(X)) & a(tptp_fun_Y_17(X), tptp_fun_Y_17(X))) & ![Z: $i] : (~a(Z, Z))) | (![Y: $i] : (p1(Y) | (~q1(Y))) & ![X: $i] : (~((p1(A!19) | (~p1(X))) & (p1(B!18) | (~q1(X)))))) | (![X: $i] : p1(X) & ![Y: $i] : (~p1(Y))) | ((~q1(X!20)) & ![X: $i] : p1(X) & ![X: $i] : (q1(X) | (~p1(X)))) | (![Z: $i] : (p1(Z) | (~q1(Z))) & ![X: $i] : (~((p1(A!22) | (~p1(X))) & (p1(B!21) | (~q1(X)))))) | (![X: $i] : (~b(X)) & ![X: $i] : (b(X) | (~a1(X))) & a1(X!23)) | (![X: $i] : (~b(X)) & ![X: $i] : a1(X) & (b(X!24) | (~a1(X!24)))) | ![X: $i] : (a(X, Y!25) <=> (~a(X, X))) | ((a1(X!23) & ![X: $i] : b(X)) & ![X: $i] : (~(a1(X) & b(X)))) | (b(X!26) & ![X: $i] : (~(a1(X) | b(X)))) | ((a(X!28, Y!27) | a(X!29, Y!30)) & (![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))) | (![X: $i] : p1(X) & (~(p1(A!32) & p1(B!31)))) | (![X: $i] : p1(X) & ((~p1(X!33)) | (~p1(Y!34)))) | ((p1(X!35) | p1(Y!36)) & (![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))) | (p1(X!35) & ![Z: $i] : (~p1(Z))) | ![Z: $i] : ![Y: $i] : (((~(~p(Y, tptp_fun_X_37(Z)))) & ![W: $i] : (~p(W, Y))) | (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_37(Z))))) | (![X: $i, Y: $i] : (((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))) & (~((~eq(A!40, B!39)) | eq(B!39, A!40)))) | ![X: $i] : (~(p1(tptp_fun_Y_41(X)) | (~p1(X)))) | ((~q1(B!42)) & ![Y: $i] : (p1(Y) | (~r1(Y))) & (![X: $i] : (q1(X) | (~p1(X))) & r1(B!42))) | ![X: $i, Y: $i] : (~(r1(B!43) | (~p1(A!44)) | (~(r1(Y) | (~p1(X)))))) | ![Y: $i] : ((~p1(Y)) & p1(X!35)) | (![Y: $i] : p(X!45, Y) & ![X: $i] : (~p(X, Y!46))) | (p1(X!35) & ![Y: $i] : (~p1(Y))) | (![X: $i, Y: $i] : p(X, Y) & (~p(X!47, X!47))) | ((~q1(A!48)) & (k!0 & ![X: $i] : (p1(X) & q1(X)))) | (~((~(a0 & b0)) | (a0 <=> b0))) | ![X: $i, Y: $i] : (~((~(((~q1(X)) | p(X, A!50)) & q1(A!50) & q1(B!49) & ((~r1(Y)) | p(B!49, Y)) & r1(A!50) & r1(B!49) & ((~s1(A!50)) | p(X, Y)) & s1(A!50))) | p(A!50, B!49))) | (![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y)) & ![X: $i, Y: $i] : (~(p(X, Y) & ((~q(f(B!51), B!51)) | q(X, Y))))) | ((![X: $i] : (q1(X) | (~p1(X))) & (r1(Y!52) | (~q1(Y!52)))) & ![Z: $i] : (~(r1(Z) | (~p1(Z)))))) <=> ((![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!4) & r1(C!3))))) & q1(X)))) | (![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B!1) & r1(C!2))) & q1(X)))) | ![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A!8) & e(A!8) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A!8, Y))))))) | (![X: $i] : p1(X) & (~(p1(A!13) & p1(B!12)))) | (![X: $i] : (a(X, tptp_fun_Y_17(X)) & a(tptp_fun_Y_17(X), tptp_fun_Y_17(X))) & ![Z: $i] : (~a(Z, Z))) | (![Y: $i] : (p1(Y) | (~q1(Y))) & ![X: $i] : (~((p1(A!19) | (~p1(X))) & (p1(B!18) | (~q1(X)))))) | (![X: $i] : p1(X) & ![Y: $i] : (~p1(Y))) | ((~q1(X!20)) & ![X: $i] : p1(X) & ![X: $i] : (q1(X) | (~p1(X)))) | (![Z: $i] : (p1(Z) | (~q1(Z))) & ![X: $i] : (~((p1(A!22) | (~p1(X))) & (p1(B!21) | (~q1(X)))))) | (![X: $i] : (~b(X)) & ![X: $i] : (b(X) | (~a1(X))) & a1(X!23)) | (![X: $i] : (~b(X)) & ![X: $i] : a1(X) & (b(X!24) | (~a1(X!24)))) | ![X: $i] : (a(X, Y!25) <=> (~a(X, X))) | (b(X!26) & ![X: $i] : (~(a1(X) | b(X)))) | ((a(X!28, Y!27) | a(X!29, Y!30)) & (![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))) | (![X: $i] : p1(X) & (~(p1(A!32) & p1(B!31)))) | (![X: $i] : p1(X) & ((~p1(X!33)) | (~p1(Y!34)))) | ((p1(X!35) | p1(Y!36)) & (![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))) | (p1(X!35) & ![Z: $i] : (~p1(Z))) | ![X: $i, Y: $i] : (~(r1(B!43) | (~p1(A!44)) | (~(r1(Y) | (~p1(X)))))) | ![Y: $i] : ((~p1(Y)) & p1(X!35)) | (![Y: $i] : p(X!45, Y) & ![X: $i] : (~p(X, Y!46))) | (p1(X!35) & ![Y: $i] : (~p1(Y))) | (![X: $i, Y: $i] : p(X, Y) & (~p(X!47, X!47))) | (~((~(a0 & b0)) | (a0 <=> b0))) | ![X: $i, Y: $i] : (~((~(((~q1(X)) | p(X, A!50)) & q1(A!50) & q1(B!49) & ((~r1(Y)) | p(B!49, Y)) & r1(A!50) & r1(B!49) & ((~s1(A!50)) | p(X, Y)) & s1(A!50))) | p(A!50, B!49))) | (![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y)) & ![X: $i, Y: $i] : (~(p(X, Y) & ((~q(f(B!51), B!51)) | q(X, Y))))) | (q1(f(B!6)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!6) & r1(C!5))))) & q1(X)))) | (![X: $i] : (c(X) | b(X) | (~a1(X))) & (~(b(X!7) | (~a1(X!7)))) & ![X: $i] : (~(a1(X) & c(X)))) | (s1(A!11) & s1(B!10) & r(B!10, C!9) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)) & ![X: $i, Y: $i] : (~(p1(X) & q(X, Y)))) | (![X: $i] : p1(X) & q1(Y!14) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (![X: $i] : (p1(X) & q1(tptp_fun_Y_16(X))) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (a1(X!23) & ![X: $i] : b(X) & ![X: $i] : (~(a1(X) & b(X)))) | ![Z: $i, Y: $i] : ((~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_37(Z)))) | (p(Y, tptp_fun_X_37(Z)) & ![W: $i] : (~p(W, Y)))) | (![X: $i, Y: $i] : (((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(X, Y) | ((~a_member_of(tptp_fun_Z_38(Y, X), X)) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))) & (~((~eq(A!40, B!39)) | eq(B!39, A!40)))) | ((~q1(B!42)) & ![Y: $i] : (p1(Y) | (~r1(Y))) & ![X: $i] : (q1(X) | (~p1(X))) & r1(B!42)) | ![X: $i] : (~((~p1(X)) | p1(tptp_fun_Y_41(X)))) | ((~q1(A!48)) & k!0 & ![X: $i] : (p1(X) & q1(X))) | (![X: $i] : (q1(X) | (~p1(X))) & (r1(Y!52) | (~q1(Y!52))) & ![Z: $i] : (~(r1(Z) | (~p1(Z))))))),
% 0.50/0.62 inference(transitivity,[status(thm)],[1039, 991])).
% 0.50/0.62 tff(1041,plain,
% 0.50/0.62 ((![C: $i, B: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B) & r1(C))) & q1(X))) & ![B: $i, C: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ![B: $i, C: $i] : ((~q1(f(B))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ((~(![X: $i] : (c(X) | b(X) | (~a1(X))) & (~![X: $i] : (b(X) | (~a1(X)))))) | ?[X: $i] : (a1(X) & c(X))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A) & e(A) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A, Y)))))) & ![A: $i, B: $i, C: $i] : ((~(s1(A) & s1(B) & r(B, C) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p1(X) & q(X, Y))) & ((~![X: $i] : p1(X)) | ![A: $i, B: $i] : (p1(A) & p1(B))) & ((~(![X: $i] : p1(X) & ?[Y: $i] : q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (p1(X) & q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)) & ![A: $i, B: $i] : ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & ((~![X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & (![X: $i] : q1(X) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) & ![A: $i, B: $i] : ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & (?[X: $i] : b(X) | (~![X: $i] : (b(X) | (~a1(X)))) | (~?[X: $i] : a1(X))) & (?[X: $i] : b(X) | (~![X: $i] : a1(X)) | (~?[X: $i] : (b(X) | (~a1(X))))) & (~?[Y: $i] : ![X: $i] : (a(X, Y) <=> (~a(X, X)))) & ((~(?[X: $i] : a1(X) & ![X: $i] : b(X))) | ?[X: $i] : (a1(X) & b(X))) & ((~?[X: $i] : b(X)) | ?[X: $i] : (a1(X) | b(X))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y)) & ![A: $i, B: $i] : ((~![X: $i] : p1(X)) | (p1(A) & p1(B))) & ((~![X: $i] : p1(X)) | (![X: $i] : p1(X) & ![Y: $i] : p1(Y))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y)) & ((~?[X: $i] : p1(X)) | ?[Z: $i] : p1(Z)) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))) & ((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) & ?[X: $i] : ![Y: $i] : (p1(Y) | (~p1(X))) & ![B: $i] : (q1(B) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | (~(![X: $i] : (q1(X) | (~p1(X))) & r1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (r1(B) | (~p1(A)) | (~(r1(Y) | (~p1(X))))) & ?[Y: $i] : (p1(Y) | (~?[X: $i] : p1(X))) & ((~?[X: $i] : ![Y: $i] : p(X, Y)) | ![Y: $i] : ?[X: $i] : p(X, Y)) & ((~?[X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & ((~![X: $i, Y: $i] : p(X, Y)) | ![X: $i] : p(X, X)) & ![A: $i] : (q1(A) | (~(k!0 & ![X: $i] : (p1(X) & q1(X))))) & ((~(a0 & b0)) | (a0 <=> b0)) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q1(X)) | p(X, A)) & q1(A) & q1(B) & ((~r1(Y)) | p(B, Y)) & r1(A) & r1(B) & ((~s1(A)) | p(X, Y)) & s1(A))) | p(A, B)) & ![B: $i] : ((~![Y: $i] : ((~(r1(Y) | (~r1(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))) & ((~(![X: $i] : (q1(X) | (~p1(X))) & ?[Y: $i] : (r1(Y) | (~q1(Y))))) | ?[Z: $i] : (r1(Z) | (~p1(Z))))) <=> (![C: $i, B: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B) & r1(C))) & q1(X))) & ![B: $i, C: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ![B: $i, C: $i] : ((~q1(f(B))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ((~(![X: $i] : (c(X) | b(X) | (~a1(X))) & (~![X: $i] : (b(X) | (~a1(X)))))) | ?[X: $i] : (a1(X) & c(X))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A) & e(A) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A, Y)))))) & ![A: $i, B: $i, C: $i] : ((~(s1(A) & s1(B) & r(B, C) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p1(X) & q(X, Y))) & ((~![X: $i] : p1(X)) | ![A: $i, B: $i] : (p1(A) & p1(B))) & ((~(![X: $i] : p1(X) & ?[Y: $i] : q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (p1(X) & q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)) & ![A: $i, B: $i] : ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & ((~![X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & (![X: $i] : q1(X) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) & ![A: $i, B: $i] : ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & (?[X: $i] : b(X) | (~![X: $i] : (b(X) | (~a1(X)))) | (~?[X: $i] : a1(X))) & (?[X: $i] : b(X) | (~![X: $i] : a1(X)) | (~?[X: $i] : (b(X) | (~a1(X))))) & (~?[Y: $i] : ![X: $i] : (a(X, Y) <=> (~a(X, X)))) & ((~(?[X: $i] : a1(X) & ![X: $i] : b(X))) | ?[X: $i] : (a1(X) & b(X))) & ((~?[X: $i] : b(X)) | ?[X: $i] : (a1(X) | b(X))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y)) & ![A: $i, B: $i] : ((~![X: $i] : p1(X)) | (p1(A) & p1(B))) & ((~![X: $i] : p1(X)) | (![X: $i] : p1(X) & ![Y: $i] : p1(Y))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y)) & ((~?[X: $i] : p1(X)) | ?[Z: $i] : p1(Z)) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))) & ((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) & ?[X: $i] : ![Y: $i] : (p1(Y) | (~p1(X))) & ![B: $i] : (q1(B) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | (~(![X: $i] : (q1(X) | (~p1(X))) & r1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (r1(B) | (~p1(A)) | (~(r1(Y) | (~p1(X))))) & ?[Y: $i] : (p1(Y) | (~?[X: $i] : p1(X))) & ((~?[X: $i] : ![Y: $i] : p(X, Y)) | ![Y: $i] : ?[X: $i] : p(X, Y)) & ((~?[X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & ((~![X: $i, Y: $i] : p(X, Y)) | ![X: $i] : p(X, X)) & ![A: $i] : (q1(A) | (~(k!0 & ![X: $i] : (p1(X) & q1(X))))) & ((~(a0 & b0)) | (a0 <=> b0)) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q1(X)) | p(X, A)) & q1(A) & q1(B) & ((~r1(Y)) | p(B, Y)) & r1(A) & r1(B) & ((~s1(A)) | p(X, Y)) & s1(A))) | p(A, B)) & ![B: $i] : ((~![Y: $i] : ((~(r1(Y) | (~r1(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))) & ((~(![X: $i] : (q1(X) | (~p1(X))) & ?[Y: $i] : (r1(Y) | (~q1(Y))))) | ?[Z: $i] : (r1(Z) | (~p1(Z)))))),
% 0.50/0.63 inference(rewrite,[status(thm)],[])).
% 0.50/0.63 tff(1042,plain,
% 0.50/0.63 ((~(![C: $i, B: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B) & r1(C))) & q1(X))) & ![B: $i, C: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ![B: $i, C: $i] : ((~q1(f(B))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ((~(![X: $i] : (c(X) | b(X) | (~a1(X))) & (~![X: $i] : (b(X) | (~a1(X)))))) | ?[X: $i] : (a1(X) & c(X))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A) & e(A) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A, Y)))))) & ![A: $i, B: $i, C: $i] : ((~(s1(A) & s1(B) & r(B, C) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p1(X) & q(X, Y))) & ((~![X: $i] : p1(X)) | ![A: $i, B: $i] : (p1(A) & p1(B))) & ((~(![X: $i] : p1(X) & ?[Y: $i] : q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (p1(X) & q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)) & ![A: $i, B: $i] : ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & ((~![X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & (![X: $i] : q1(X) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) & ![A: $i, B: $i] : ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & (?[X: $i] : b(X) | (~![X: $i] : (b(X) | (~a1(X)))) | (~?[X: $i] : a1(X))) & (?[X: $i] : b(X) | (~![X: $i] : a1(X)) | (~?[X: $i] : (b(X) | (~a1(X))))) & (~?[Y: $i] : ![X: $i] : (a(X, Y) <=> (~a(X, X)))) & ((~(?[X: $i] : a1(X) & ![X: $i] : b(X))) | ?[X: $i] : (a1(X) & b(X))) & ((~?[X: $i] : b(X)) | ?[X: $i] : (a1(X) | b(X))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y)) & ![A: $i, B: $i] : ((~![X: $i] : p1(X)) | (p1(A) & p1(B))) & ((~![X: $i] : p1(X)) | (![X: $i] : p1(X) & ![Y: $i] : p1(Y))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y)) & ((~?[X: $i] : p1(X)) | ?[Z: $i] : p1(Z)) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))) & ((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) & ?[X: $i] : ![Y: $i] : (p1(Y) | (~p1(X))) & ![B: $i] : (q1(B) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | (~(![X: $i] : (q1(X) | (~p1(X))) & r1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (r1(B) | (~p1(A)) | (~(r1(Y) | (~p1(X))))) & ?[Y: $i] : (p1(Y) | (~?[X: $i] : p1(X))) & ((~?[X: $i] : ![Y: $i] : p(X, Y)) | ![Y: $i] : ?[X: $i] : p(X, Y)) & ((~?[X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & ((~![X: $i, Y: $i] : p(X, Y)) | ![X: $i] : p(X, X)) & ![A: $i] : (q1(A) | (~(k!0 & ![X: $i] : (p1(X) & q1(X))))) & ((~(a0 & b0)) | (a0 <=> b0)) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q1(X)) | p(X, A)) & q1(A) & q1(B) & ((~r1(Y)) | p(B, Y)) & r1(A) & r1(B) & ((~s1(A)) | p(X, Y)) & s1(A))) | p(A, B)) & ![B: $i] : ((~![Y: $i] : ((~(r1(Y) | (~r1(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))) & ((~(![X: $i] : (q1(X) | (~p1(X))) & ?[Y: $i] : (r1(Y) | (~q1(Y))))) | ?[Z: $i] : (r1(Z) | (~p1(Z)))))) <=> (~(![C: $i, B: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B) & r1(C))) & q1(X))) & ![B: $i, C: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ![B: $i, C: $i] : ((~q1(f(B))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ((~(![X: $i] : (c(X) | b(X) | (~a1(X))) & (~![X: $i] : (b(X) | (~a1(X)))))) | ?[X: $i] : (a1(X) & c(X))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A) & e(A) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A, Y)))))) & ![A: $i, B: $i, C: $i] : ((~(s1(A) & s1(B) & r(B, C) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p1(X) & q(X, Y))) & ((~![X: $i] : p1(X)) | ![A: $i, B: $i] : (p1(A) & p1(B))) & ((~(![X: $i] : p1(X) & ?[Y: $i] : q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (p1(X) & q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)) & ![A: $i, B: $i] : ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & ((~![X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & (![X: $i] : q1(X) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) & ![A: $i, B: $i] : ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & (?[X: $i] : b(X) | (~![X: $i] : (b(X) | (~a1(X)))) | (~?[X: $i] : a1(X))) & (?[X: $i] : b(X) | (~![X: $i] : a1(X)) | (~?[X: $i] : (b(X) | (~a1(X))))) & (~?[Y: $i] : ![X: $i] : (a(X, Y) <=> (~a(X, X)))) & ((~(?[X: $i] : a1(X) & ![X: $i] : b(X))) | ?[X: $i] : (a1(X) & b(X))) & ((~?[X: $i] : b(X)) | ?[X: $i] : (a1(X) | b(X))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y)) & ![A: $i, B: $i] : ((~![X: $i] : p1(X)) | (p1(A) & p1(B))) & ((~![X: $i] : p1(X)) | (![X: $i] : p1(X) & ![Y: $i] : p1(Y))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y)) & ((~?[X: $i] : p1(X)) | ?[Z: $i] : p1(Z)) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))) & ((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) & ?[X: $i] : ![Y: $i] : (p1(Y) | (~p1(X))) & ![B: $i] : (q1(B) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | (~(![X: $i] : (q1(X) | (~p1(X))) & r1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (r1(B) | (~p1(A)) | (~(r1(Y) | (~p1(X))))) & ?[Y: $i] : (p1(Y) | (~?[X: $i] : p1(X))) & ((~?[X: $i] : ![Y: $i] : p(X, Y)) | ![Y: $i] : ?[X: $i] : p(X, Y)) & ((~?[X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & ((~![X: $i, Y: $i] : p(X, Y)) | ![X: $i] : p(X, X)) & ![A: $i] : (q1(A) | (~(k!0 & ![X: $i] : (p1(X) & q1(X))))) & ((~(a0 & b0)) | (a0 <=> b0)) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q1(X)) | p(X, A)) & q1(A) & q1(B) & ((~r1(Y)) | p(B, Y)) & r1(A) & r1(B) & ((~s1(A)) | p(X, Y)) & s1(A))) | p(A, B)) & ![B: $i] : ((~![Y: $i] : ((~(r1(Y) | (~r1(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))) & ((~(![X: $i] : (q1(X) | (~p1(X))) & ?[Y: $i] : (r1(Y) | (~q1(Y))))) | ?[Z: $i] : (r1(Z) | (~p1(Z))))))),
% 0.54/0.63 inference(monotonicity,[status(thm)],[1041])).
% 0.54/0.63 tff(1043,plain,
% 0.54/0.63 ((~(![C: $i, B: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B) & r1(C))) & q1(X))) & ![B: $i, C: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ![B: $i, C: $i] : ((~q1(f(B))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ((~(![X: $i] : (c(X) | b(X) | (~a1(X))) & (~![X: $i] : (b(X) | (~a1(X)))))) | ?[X: $i] : (a1(X) & c(X))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A) & e(A) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A, Y)))))) & ![A: $i, B: $i, C: $i] : ((~(s1(A) & s1(B) & r(B, C) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p1(X) & q(X, Y))) & ((~![X: $i] : p1(X)) | ![A: $i, B: $i] : (p1(A) & p1(B))) & ((~(![X: $i] : p1(X) & ?[Y: $i] : q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (p1(X) & q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)) & ![A: $i, B: $i] : ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & ((~![X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & (![X: $i] : q1(X) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) & ![A: $i, B: $i] : ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & (?[X: $i] : b(X) | (~![X: $i] : (b(X) | (~a1(X)))) | (~?[X: $i] : a1(X))) & (?[X: $i] : b(X) | (~![X: $i] : a1(X)) | (~?[X: $i] : (b(X) | (~a1(X))))) & (~?[Y: $i] : ![X: $i] : (a(X, Y) <=> (~a(X, X)))) & ((~(?[X: $i] : a1(X) & ![X: $i] : b(X))) | ?[X: $i] : (a1(X) & b(X))) & ((~?[X: $i] : b(X)) | ?[X: $i] : (a1(X) | b(X))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y)) & ![A: $i, B: $i] : ((~![X: $i] : p1(X)) | (p1(A) & p1(B))) & ((~![X: $i] : p1(X)) | (![X: $i] : p1(X) & ![Y: $i] : p1(Y))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y)) & ((~?[X: $i] : p1(X)) | ?[Z: $i] : p1(Z)) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))) & ((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) & ?[X: $i] : ![Y: $i] : (p1(Y) | (~p1(X))) & ![B: $i] : (q1(B) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | (~(![X: $i] : (q1(X) | (~p1(X))) & r1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (r1(B) | (~p1(A)) | (~(r1(Y) | (~p1(X))))) & ?[Y: $i] : (p1(Y) | (~?[X: $i] : p1(X))) & ((~?[X: $i] : ![Y: $i] : p(X, Y)) | ![Y: $i] : ?[X: $i] : p(X, Y)) & ((~?[X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & ((~![X: $i, Y: $i] : p(X, Y)) | ![X: $i] : p(X, X)) & ![A: $i] : (q1(A) | (~((f0 | g0) & ![X: $i] : (p1(X) & q1(X))))) & ((~(a0 & b0)) | (a0 <=> b0)) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q1(X)) | p(X, A)) & q1(A) & q1(B) & ((~r1(Y)) | p(B, Y)) & r1(A) & r1(B) & ((~s1(A)) | p(X, Y)) & s1(A))) | p(A, B)) & ![B: $i] : ((~![Y: $i] : ((~(r1(Y) | (~r1(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))) & ((~(![X: $i] : (q1(X) | (~p1(X))) & ?[Y: $i] : (r1(Y) | (~q1(Y))))) | ?[Z: $i] : (r1(Z) | (~p1(Z)))))) <=> (~(![C: $i, B: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B) & r1(C))) & q1(X))) & ![B: $i, C: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ![B: $i, C: $i] : ((~q1(f(B))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ((~(![X: $i] : (c(X) | b(X) | (~a1(X))) & (~![X: $i] : (b(X) | (~a1(X)))))) | ?[X: $i] : (a1(X) & c(X))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A) & e(A) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A, Y)))))) & ![A: $i, B: $i, C: $i] : ((~(s1(A) & s1(B) & r(B, C) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p1(X) & q(X, Y))) & ((~![X: $i] : p1(X)) | ![A: $i, B: $i] : (p1(A) & p1(B))) & ((~(![X: $i] : p1(X) & ?[Y: $i] : q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (p1(X) & q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)) & ![A: $i, B: $i] : ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & ((~![X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & (![X: $i] : q1(X) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) & ![A: $i, B: $i] : ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & (?[X: $i] : b(X) | (~![X: $i] : (b(X) | (~a1(X)))) | (~?[X: $i] : a1(X))) & (?[X: $i] : b(X) | (~![X: $i] : a1(X)) | (~?[X: $i] : (b(X) | (~a1(X))))) & (~?[Y: $i] : ![X: $i] : (a(X, Y) <=> (~a(X, X)))) & ((~(?[X: $i] : a1(X) & ![X: $i] : b(X))) | ?[X: $i] : (a1(X) & b(X))) & ((~?[X: $i] : b(X)) | ?[X: $i] : (a1(X) | b(X))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y)) & ![A: $i, B: $i] : ((~![X: $i] : p1(X)) | (p1(A) & p1(B))) & ((~![X: $i] : p1(X)) | (![X: $i] : p1(X) & ![Y: $i] : p1(Y))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y)) & ((~?[X: $i] : p1(X)) | ?[Z: $i] : p1(Z)) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))) & ((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) & ?[X: $i] : ![Y: $i] : (p1(Y) | (~p1(X))) & ![B: $i] : (q1(B) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | (~(![X: $i] : (q1(X) | (~p1(X))) & r1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (r1(B) | (~p1(A)) | (~(r1(Y) | (~p1(X))))) & ?[Y: $i] : (p1(Y) | (~?[X: $i] : p1(X))) & ((~?[X: $i] : ![Y: $i] : p(X, Y)) | ![Y: $i] : ?[X: $i] : p(X, Y)) & ((~?[X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & ((~![X: $i, Y: $i] : p(X, Y)) | ![X: $i] : p(X, X)) & ![A: $i] : (q1(A) | (~(k!0 & ![X: $i] : (p1(X) & q1(X))))) & ((~(a0 & b0)) | (a0 <=> b0)) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q1(X)) | p(X, A)) & q1(A) & q1(B) & ((~r1(Y)) | p(B, Y)) & r1(A) & r1(B) & ((~s1(A)) | p(X, Y)) & s1(A))) | p(A, B)) & ![B: $i] : ((~![Y: $i] : ((~(r1(Y) | (~r1(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))) & ((~(![X: $i] : (q1(X) | (~p1(X))) & ?[Y: $i] : (r1(Y) | (~q1(Y))))) | ?[Z: $i] : (r1(Z) | (~p1(Z))))))),
% 0.54/0.64 inference(rewrite,[status(thm)],[])).
% 0.54/0.64 tff(1044,plain,
% 0.54/0.64 ((![C: $i, B: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B) & r1(C))) & q1(X))) & ![B: $i, C: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ![B: $i, C: $i] : ((~q1(f(B))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ((~(![X: $i] : (c(X) | b(X) | (~a1(X))) & (~![X: $i] : (b(X) | (~a1(X)))))) | ?[X: $i] : (a1(X) & c(X))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A) & e(A) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A, Y)))))) & ![A: $i, B: $i, C: $i] : ((~(s1(A) & s1(B) & r(B, C) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p1(X) & q(X, Y))) & ((~![X: $i] : p1(X)) | ![A: $i, B: $i] : (p1(A) & p1(B))) & ((~(![X: $i] : p1(X) & ?[Y: $i] : q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (p1(X) & q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)) & ![A: $i, B: $i] : ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & ((~![X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & (![X: $i] : q1(X) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) & ![A: $i, B: $i] : ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & (?[X: $i] : b(X) | (~![X: $i] : (b(X) | (~a1(X)))) | (~?[X: $i] : a1(X))) & (?[X: $i] : b(X) | (~![X: $i] : a1(X)) | (~?[X: $i] : (b(X) | (~a1(X))))) & (~?[Y: $i] : ![X: $i] : (a(X, Y) <=> (~a(X, X)))) & ((~(?[X: $i] : a1(X) & ![X: $i] : b(X))) | ?[X: $i] : (a1(X) & b(X))) & ((~?[X: $i] : b(X)) | ?[X: $i] : (a1(X) | b(X))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y)) & ![A: $i, B: $i] : ((~![X: $i] : p1(X)) | (p1(A) & p1(B))) & ((~![X: $i] : p1(X)) | (![X: $i] : p1(X) & ![Y: $i] : p1(Y))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y)) & ((~?[X: $i] : p1(X)) | ?[Z: $i] : p1(Z)) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))) & ((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) & ?[X: $i] : ![Y: $i] : (p1(Y) | (~p1(X))) & ![B: $i] : (q1(B) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | (~(![X: $i] : (q1(X) | (~p1(X))) & r1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (r1(B) | (~p1(A)) | (~(r1(Y) | (~p1(X))))) & ?[Y: $i] : (p1(Y) | (~?[X: $i] : p1(X))) & ((~?[X: $i] : ![Y: $i] : p(X, Y)) | ![Y: $i] : ?[X: $i] : p(X, Y)) & ((~?[X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & ((~![X: $i, Y: $i] : p(X, Y)) | ![X: $i] : p(X, X)) & ![A: $i] : (q1(A) | (~((f0 | g0) & ![X: $i] : (p1(X) & q1(X))))) & ((~(a0 & b0)) | (a0 <=> b0)) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q1(X)) | p(X, A)) & q1(A) & q1(B) & ((~r1(Y)) | p(B, Y)) & r1(A) & r1(B) & ((~s1(A)) | p(X, Y)) & s1(A))) | p(A, B)) & ![B: $i] : ((~![Y: $i] : ((~(r1(Y) | (~r1(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))) & ((~(![X: $i] : (q1(X) | (~p1(X))) & ?[Y: $i] : (r1(Y) | (~q1(Y))))) | ?[Z: $i] : (r1(Z) | (~p1(Z))))) <=> (![C: $i, B: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B) & r1(C))) & q1(X))) & ![B: $i, C: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ![B: $i, C: $i] : ((~q1(f(B))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ((~(![X: $i] : (c(X) | b(X) | (~a1(X))) & (~![X: $i] : (b(X) | (~a1(X)))))) | ?[X: $i] : (a1(X) & c(X))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A) & e(A) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A, Y)))))) & ![A: $i, B: $i, C: $i] : ((~(s1(A) & s1(B) & r(B, C) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p1(X) & q(X, Y))) & ((~![X: $i] : p1(X)) | ![A: $i, B: $i] : (p1(A) & p1(B))) & ((~(![X: $i] : p1(X) & ?[Y: $i] : q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (p1(X) & q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)) & ![A: $i, B: $i] : ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & ((~![X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & (![X: $i] : q1(X) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) & ![A: $i, B: $i] : ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & (?[X: $i] : b(X) | (~![X: $i] : (b(X) | (~a1(X)))) | (~?[X: $i] : a1(X))) & (?[X: $i] : b(X) | (~![X: $i] : a1(X)) | (~?[X: $i] : (b(X) | (~a1(X))))) & (~?[Y: $i] : ![X: $i] : (a(X, Y) <=> (~a(X, X)))) & ((~(?[X: $i] : a1(X) & ![X: $i] : b(X))) | ?[X: $i] : (a1(X) & b(X))) & ((~?[X: $i] : b(X)) | ?[X: $i] : (a1(X) | b(X))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y)) & ![A: $i, B: $i] : ((~![X: $i] : p1(X)) | (p1(A) & p1(B))) & ((~![X: $i] : p1(X)) | (![X: $i] : p1(X) & ![Y: $i] : p1(Y))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y)) & ((~?[X: $i] : p1(X)) | ?[Z: $i] : p1(Z)) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))) & ((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) & ?[X: $i] : ![Y: $i] : (p1(Y) | (~p1(X))) & ![B: $i] : (q1(B) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | (~(![X: $i] : (q1(X) | (~p1(X))) & r1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (r1(B) | (~p1(A)) | (~(r1(Y) | (~p1(X))))) & ?[Y: $i] : (p1(Y) | (~?[X: $i] : p1(X))) & ((~?[X: $i] : ![Y: $i] : p(X, Y)) | ![Y: $i] : ?[X: $i] : p(X, Y)) & ((~?[X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & ((~![X: $i, Y: $i] : p(X, Y)) | ![X: $i] : p(X, X)) & ![A: $i] : (q1(A) | (~((f0 | g0) & ![X: $i] : (p1(X) & q1(X))))) & ((~(a0 & b0)) | (a0 <=> b0)) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q1(X)) | p(X, A)) & q1(A) & q1(B) & ((~r1(Y)) | p(B, Y)) & r1(A) & r1(B) & ((~s1(A)) | p(X, Y)) & s1(A))) | p(A, B)) & ![B: $i] : ((~![Y: $i] : ((~(r1(Y) | (~r1(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))) & ((~(![X: $i] : (q1(X) | (~p1(X))) & ?[Y: $i] : (r1(Y) | (~q1(Y))))) | ?[Z: $i] : (r1(Z) | (~p1(Z)))))),
% 0.54/0.64 inference(rewrite,[status(thm)],[])).
% 0.54/0.64 tff(1045,plain,
% 0.54/0.64 ((~(![C: $i, B: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B) & r1(C))) & q1(X))) & ![B: $i, C: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ![B: $i, C: $i] : ((~q1(f(B))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ((~(![X: $i] : (c(X) | b(X) | (~a1(X))) & (~![X: $i] : (b(X) | (~a1(X)))))) | ?[X: $i] : (a1(X) & c(X))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A) & e(A) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A, Y)))))) & ![A: $i, B: $i, C: $i] : ((~(s1(A) & s1(B) & r(B, C) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p1(X) & q(X, Y))) & ((~![X: $i] : p1(X)) | ![A: $i, B: $i] : (p1(A) & p1(B))) & ((~(![X: $i] : p1(X) & ?[Y: $i] : q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (p1(X) & q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)) & ![A: $i, B: $i] : ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & ((~![X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & (![X: $i] : q1(X) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) & ![A: $i, B: $i] : ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & (?[X: $i] : b(X) | (~![X: $i] : (b(X) | (~a1(X)))) | (~?[X: $i] : a1(X))) & (?[X: $i] : b(X) | (~![X: $i] : a1(X)) | (~?[X: $i] : (b(X) | (~a1(X))))) & (~?[Y: $i] : ![X: $i] : (a(X, Y) <=> (~a(X, X)))) & ((~(?[X: $i] : a1(X) & ![X: $i] : b(X))) | ?[X: $i] : (a1(X) & b(X))) & ((~?[X: $i] : b(X)) | ?[X: $i] : (a1(X) | b(X))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y)) & ![A: $i, B: $i] : ((~![X: $i] : p1(X)) | (p1(A) & p1(B))) & ((~![X: $i] : p1(X)) | (![X: $i] : p1(X) & ![Y: $i] : p1(Y))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y)) & ((~?[X: $i] : p1(X)) | ?[Z: $i] : p1(Z)) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))) & ((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) & ?[X: $i] : ![Y: $i] : (p1(Y) | (~p1(X))) & ![B: $i] : (q1(B) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | (~(![X: $i] : (q1(X) | (~p1(X))) & r1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (r1(B) | (~p1(A)) | (~(r1(Y) | (~p1(X))))) & ?[Y: $i] : (p1(Y) | (~?[X: $i] : p1(X))) & ((~?[X: $i] : ![Y: $i] : p(X, Y)) | ![Y: $i] : ?[X: $i] : p(X, Y)) & ((~?[X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & ((~![X: $i, Y: $i] : p(X, Y)) | ![X: $i] : p(X, X)) & ![A: $i] : (q1(A) | (~((f0 | g0) & ![X: $i] : (p1(X) & q1(X))))) & ((~(a0 & b0)) | (a0 <=> b0)) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q1(X)) | p(X, A)) & q1(A) & q1(B) & ((~r1(Y)) | p(B, Y)) & r1(A) & r1(B) & ((~s1(A)) | p(X, Y)) & s1(A))) | p(A, B)) & ![B: $i] : ((~![Y: $i] : ((~(r1(Y) | (~r1(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))) & ((~(![X: $i] : (q1(X) | (~p1(X))) & ?[Y: $i] : (r1(Y) | (~q1(Y))))) | ?[Z: $i] : (r1(Z) | (~p1(Z)))))) <=> (~(![C: $i, B: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B) & r1(C))) & q1(X))) & ![B: $i, C: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ![B: $i, C: $i] : ((~q1(f(B))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ((~(![X: $i] : (c(X) | b(X) | (~a1(X))) & (~![X: $i] : (b(X) | (~a1(X)))))) | ?[X: $i] : (a1(X) & c(X))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A) & e(A) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A, Y)))))) & ![A: $i, B: $i, C: $i] : ((~(s1(A) & s1(B) & r(B, C) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p1(X) & q(X, Y))) & ((~![X: $i] : p1(X)) | ![A: $i, B: $i] : (p1(A) & p1(B))) & ((~(![X: $i] : p1(X) & ?[Y: $i] : q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (p1(X) & q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)) & ![A: $i, B: $i] : ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & ((~![X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & (![X: $i] : q1(X) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) & ![A: $i, B: $i] : ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & (?[X: $i] : b(X) | (~![X: $i] : (b(X) | (~a1(X)))) | (~?[X: $i] : a1(X))) & (?[X: $i] : b(X) | (~![X: $i] : a1(X)) | (~?[X: $i] : (b(X) | (~a1(X))))) & (~?[Y: $i] : ![X: $i] : (a(X, Y) <=> (~a(X, X)))) & ((~(?[X: $i] : a1(X) & ![X: $i] : b(X))) | ?[X: $i] : (a1(X) & b(X))) & ((~?[X: $i] : b(X)) | ?[X: $i] : (a1(X) | b(X))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y)) & ![A: $i, B: $i] : ((~![X: $i] : p1(X)) | (p1(A) & p1(B))) & ((~![X: $i] : p1(X)) | (![X: $i] : p1(X) & ![Y: $i] : p1(Y))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y)) & ((~?[X: $i] : p1(X)) | ?[Z: $i] : p1(Z)) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))) & ((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) & ?[X: $i] : ![Y: $i] : (p1(Y) | (~p1(X))) & ![B: $i] : (q1(B) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | (~(![X: $i] : (q1(X) | (~p1(X))) & r1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (r1(B) | (~p1(A)) | (~(r1(Y) | (~p1(X))))) & ?[Y: $i] : (p1(Y) | (~?[X: $i] : p1(X))) & ((~?[X: $i] : ![Y: $i] : p(X, Y)) | ![Y: $i] : ?[X: $i] : p(X, Y)) & ((~?[X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & ((~![X: $i, Y: $i] : p(X, Y)) | ![X: $i] : p(X, X)) & ![A: $i] : (q1(A) | (~((f0 | g0) & ![X: $i] : (p1(X) & q1(X))))) & ((~(a0 & b0)) | (a0 <=> b0)) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q1(X)) | p(X, A)) & q1(A) & q1(B) & ((~r1(Y)) | p(B, Y)) & r1(A) & r1(B) & ((~s1(A)) | p(X, Y)) & s1(A))) | p(A, B)) & ![B: $i] : ((~![Y: $i] : ((~(r1(Y) | (~r1(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))) & ((~(![X: $i] : (q1(X) | (~p1(X))) & ?[Y: $i] : (r1(Y) | (~q1(Y))))) | ?[Z: $i] : (r1(Z) | (~p1(Z))))))),
% 0.56/0.64 inference(monotonicity,[status(thm)],[1044])).
% 0.56/0.64 tff(1046,plain,
% 0.56/0.64 ((~(![C: $i, B: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B) & r1(C))) & q1(X))) & ![B: $i, C: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ![B: $i, C: $i] : ((~q1(f(B))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ((~(![X: $i] : (c(X) | b(X) | (~a1(X))) & (~![X: $i] : (b(X) | (~a1(X)))))) | ?[X: $i] : (a1(X) & c(X))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A) & e(A) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A, Y)))))) & ![A: $i, B: $i, C: $i] : ((~(s1(A) & s1(B) & r(B, C) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p1(X) & q(X, Y))) & ((~![X: $i] : p1(X)) | ![A: $i, B: $i] : (p1(A) & p1(B))) & ((~(![X: $i] : p1(X) & ?[Y: $i] : q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (p1(X) & q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)) & ![A: $i, B: $i] : ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & ((~![X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & (![X: $i] : q1(X) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) & ![A: $i, B: $i] : ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & (?[X: $i] : b(X) | (~![X: $i] : (b(X) | (~a1(X)))) | (~?[X: $i] : a1(X))) & (?[X: $i] : b(X) | (~![X: $i] : a1(X)) | (~?[X: $i] : (b(X) | (~a1(X))))) & (~?[Y: $i] : ![X: $i] : (a(X, Y) <=> (~a(X, X)))) & ((~(?[X: $i] : a1(X) & ![X: $i] : b(X))) | ?[X: $i] : (a1(X) & b(X))) & ((~?[X: $i] : b(X)) | ?[X: $i] : (a1(X) | b(X))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y)) & ![A: $i, B: $i] : ((~![X: $i] : p1(X)) | (p1(A) & p1(B))) & ((~![X: $i] : p1(X)) | (![X: $i] : p1(X) & ![Y: $i] : p1(Y))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y)) & ((~?[X: $i] : p1(X)) | ?[Z: $i] : p1(Z)) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))) & ((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) & ?[X: $i] : ![Y: $i] : (p1(Y) | (~p1(X))) & ![B: $i] : (q1(B) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | (~(![X: $i] : (q1(X) | (~p1(X))) & r1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (r1(B) | (~p1(A)) | (~(r1(Y) | (~p1(X))))) & ?[Y: $i] : (p1(Y) | (~?[X: $i] : p1(X))) & ((~?[X: $i] : ![Y: $i] : p(X, Y)) | ![Y: $i] : ?[X: $i] : p(X, Y)) & ((~?[X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & ((~![X: $i, Y: $i] : p(X, Y)) | ![X: $i] : p(X, X)) & ![A: $i] : (q1(A) | (~((f0 | g0) & ![X: $i] : (p1(X) & q1(X))))) & (a0 | b0 | (a0 <=> b0)) & ((~(a0 & b0)) | (a0 <=> b0)) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q1(X)) | p(X, A)) & q1(A) & q1(B) & ((~r1(Y)) | p(B, Y)) & r1(A) & r1(B) & ((~s1(A)) | p(X, Y)) & s1(A))) | p(A, B)) & ![B: $i] : ((~![Y: $i] : ((~(r1(Y) | (~r1(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))) & ((~(![X: $i] : (q1(X) | (~p1(X))) & ?[Y: $i] : (r1(Y) | (~q1(Y))))) | ?[Z: $i] : (r1(Z) | (~p1(Z)))))) <=> (~(![C: $i, B: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B) & r1(C))) & q1(X))) & ![B: $i, C: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ![B: $i, C: $i] : ((~q1(f(B))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ((~(![X: $i] : (c(X) | b(X) | (~a1(X))) & (~![X: $i] : (b(X) | (~a1(X)))))) | ?[X: $i] : (a1(X) & c(X))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A) & e(A) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A, Y)))))) & ![A: $i, B: $i, C: $i] : ((~(s1(A) & s1(B) & r(B, C) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p1(X) & q(X, Y))) & ((~![X: $i] : p1(X)) | ![A: $i, B: $i] : (p1(A) & p1(B))) & ((~(![X: $i] : p1(X) & ?[Y: $i] : q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (p1(X) & q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)) & ![A: $i, B: $i] : ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & ((~![X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & (![X: $i] : q1(X) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) & ![A: $i, B: $i] : ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & (?[X: $i] : b(X) | (~![X: $i] : (b(X) | (~a1(X)))) | (~?[X: $i] : a1(X))) & (?[X: $i] : b(X) | (~![X: $i] : a1(X)) | (~?[X: $i] : (b(X) | (~a1(X))))) & (~?[Y: $i] : ![X: $i] : (a(X, Y) <=> (~a(X, X)))) & ((~(?[X: $i] : a1(X) & ![X: $i] : b(X))) | ?[X: $i] : (a1(X) & b(X))) & ((~?[X: $i] : b(X)) | ?[X: $i] : (a1(X) | b(X))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y)) & ![A: $i, B: $i] : ((~![X: $i] : p1(X)) | (p1(A) & p1(B))) & ((~![X: $i] : p1(X)) | (![X: $i] : p1(X) & ![Y: $i] : p1(Y))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y)) & ((~?[X: $i] : p1(X)) | ?[Z: $i] : p1(Z)) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))) & ((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) & ?[X: $i] : ![Y: $i] : (p1(Y) | (~p1(X))) & ![B: $i] : (q1(B) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | (~(![X: $i] : (q1(X) | (~p1(X))) & r1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (r1(B) | (~p1(A)) | (~(r1(Y) | (~p1(X))))) & ?[Y: $i] : (p1(Y) | (~?[X: $i] : p1(X))) & ((~?[X: $i] : ![Y: $i] : p(X, Y)) | ![Y: $i] : ?[X: $i] : p(X, Y)) & ((~?[X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & ((~![X: $i, Y: $i] : p(X, Y)) | ![X: $i] : p(X, X)) & ![A: $i] : (q1(A) | (~((f0 | g0) & ![X: $i] : (p1(X) & q1(X))))) & ((~(a0 & b0)) | (a0 <=> b0)) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q1(X)) | p(X, A)) & q1(A) & q1(B) & ((~r1(Y)) | p(B, Y)) & r1(A) & r1(B) & ((~s1(A)) | p(X, Y)) & s1(A))) | p(A, B)) & ![B: $i] : ((~![Y: $i] : ((~(r1(Y) | (~r1(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))) & ((~(![X: $i] : (q1(X) | (~p1(X))) & ?[Y: $i] : (r1(Y) | (~q1(Y))))) | ?[Z: $i] : (r1(Z) | (~p1(Z))))))),
% 0.56/0.65 inference(rewrite,[status(thm)],[])).
% 0.56/0.65 tff(1047,plain,
% 0.56/0.65 ((![C: $i, B: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B) & r1(C))) & q1(X))) & ![B: $i, C: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ![B: $i, C: $i] : ((~q1(f(B))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ((~(![X: $i] : (c(X) | b(X) | (~a1(X))) & (~![X: $i] : (b(X) | (~a1(X)))))) | ?[X: $i] : (a1(X) & c(X))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A) & e(A) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A, Y)))))) & ![A: $i, B: $i, C: $i] : ((~(s1(A) & s1(B) & r(B, C) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p1(X) & q(X, Y))) & ((~![X: $i] : p1(X)) | ![A: $i, B: $i] : (p1(A) & p1(B))) & ((~(![X: $i] : p1(X) & ?[Y: $i] : q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (p1(X) & q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)) & ![A: $i, B: $i] : ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & ((~![X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & (![X: $i] : q1(X) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) & ![A: $i, B: $i] : ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & (?[X: $i] : b(X) | (~![X: $i] : (b(X) | (~a1(X)))) | (~?[X: $i] : a1(X))) & (?[X: $i] : b(X) | (~![X: $i] : a1(X)) | (~?[X: $i] : (b(X) | (~a1(X))))) & (~?[Y: $i] : ![X: $i] : (a(X, Y) <=> (~a(X, X)))) & ((~(?[X: $i] : a1(X) & ![X: $i] : b(X))) | ?[X: $i] : (a1(X) & b(X))) & ((~?[X: $i] : b(X)) | ?[X: $i] : (a1(X) | b(X))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y)) & ![A: $i, B: $i] : ((~![X: $i] : p1(X)) | (p1(A) & p1(B))) & ((~![X: $i] : p1(X)) | (![X: $i] : p1(X) & ![Y: $i] : p1(Y))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y)) & ((~?[X: $i] : p1(X)) | ?[Z: $i] : p1(Z)) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))) & ((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) & ?[X: $i] : ![Y: $i] : (p1(Y) | (~p1(X))) & ![B: $i] : (q1(B) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | (~(![X: $i] : (q1(X) | (~p1(X))) & r1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (r1(B) | (~p1(A)) | (~(r1(Y) | (~p1(X))))) & ?[Y: $i] : (p1(Y) | (~?[X: $i] : p1(X))) & ((~?[X: $i] : ![Y: $i] : p(X, Y)) | ![Y: $i] : ?[X: $i] : p(X, Y)) & ((~?[X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & ((~![X: $i, Y: $i] : p(X, Y)) | ![X: $i] : p(X, X)) & ![A: $i] : (q1(A) | (~((f0 | g0) & ![X: $i] : (p1(X) & q1(X))))) & (a0 | b0 | (a0 <=> b0)) & ((~(a0 & b0)) | (a0 <=> b0)) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q1(X)) | p(X, A)) & q1(A) & q1(B) & ((~r1(Y)) | p(B, Y)) & r1(A) & r1(B) & ((~s1(A)) | p(X, Y)) & s1(A))) | p(A, B)) & ![B: $i] : ((~![Y: $i] : ((~(r1(Y) | (~r1(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))) & ((~(![X: $i] : (q1(X) | (~p1(X))) & ?[Y: $i] : (r1(Y) | (~q1(Y))))) | ?[Z: $i] : (r1(Z) | (~p1(Z))))) <=> (![C: $i, B: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B) & r1(C))) & q1(X))) & ![B: $i, C: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ![B: $i, C: $i] : ((~q1(f(B))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ((~(![X: $i] : (c(X) | b(X) | (~a1(X))) & (~![X: $i] : (b(X) | (~a1(X)))))) | ?[X: $i] : (a1(X) & c(X))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A) & e(A) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A, Y)))))) & ![A: $i, B: $i, C: $i] : ((~(s1(A) & s1(B) & r(B, C) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p1(X) & q(X, Y))) & ((~![X: $i] : p1(X)) | ![A: $i, B: $i] : (p1(A) & p1(B))) & ((~(![X: $i] : p1(X) & ?[Y: $i] : q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (p1(X) & q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)) & ![A: $i, B: $i] : ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & ((~![X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & (![X: $i] : q1(X) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) & ![A: $i, B: $i] : ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & (?[X: $i] : b(X) | (~![X: $i] : (b(X) | (~a1(X)))) | (~?[X: $i] : a1(X))) & (?[X: $i] : b(X) | (~![X: $i] : a1(X)) | (~?[X: $i] : (b(X) | (~a1(X))))) & (~?[Y: $i] : ![X: $i] : (a(X, Y) <=> (~a(X, X)))) & ((~(?[X: $i] : a1(X) & ![X: $i] : b(X))) | ?[X: $i] : (a1(X) & b(X))) & ((~?[X: $i] : b(X)) | ?[X: $i] : (a1(X) | b(X))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y)) & ![A: $i, B: $i] : ((~![X: $i] : p1(X)) | (p1(A) & p1(B))) & ((~![X: $i] : p1(X)) | (![X: $i] : p1(X) & ![Y: $i] : p1(Y))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y)) & ((~?[X: $i] : p1(X)) | ?[Z: $i] : p1(Z)) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))) & ((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) & ?[X: $i] : ![Y: $i] : (p1(Y) | (~p1(X))) & ![B: $i] : (q1(B) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | (~(![X: $i] : (q1(X) | (~p1(X))) & r1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (r1(B) | (~p1(A)) | (~(r1(Y) | (~p1(X))))) & ?[Y: $i] : (p1(Y) | (~?[X: $i] : p1(X))) & ((~?[X: $i] : ![Y: $i] : p(X, Y)) | ![Y: $i] : ?[X: $i] : p(X, Y)) & ((~?[X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & ((~![X: $i, Y: $i] : p(X, Y)) | ![X: $i] : p(X, X)) & ![A: $i] : (q1(A) | (~((f0 | g0) & ![X: $i] : (p1(X) & q1(X))))) & (a0 | b0 | (a0 <=> b0)) & ((~(a0 & b0)) | (a0 <=> b0)) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q1(X)) | p(X, A)) & q1(A) & q1(B) & ((~r1(Y)) | p(B, Y)) & r1(A) & r1(B) & ((~s1(A)) | p(X, Y)) & s1(A))) | p(A, B)) & ![B: $i] : ((~![Y: $i] : ((~(r1(Y) | (~r1(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))) & ((~(![X: $i] : (q1(X) | (~p1(X))) & ?[Y: $i] : (r1(Y) | (~q1(Y))))) | ?[Z: $i] : (r1(Z) | (~p1(Z)))))),
% 0.56/0.65 inference(rewrite,[status(thm)],[])).
% 0.56/0.65 tff(1048,plain,
% 0.56/0.65 ((~(![C: $i, B: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B) & r1(C))) & q1(X))) & ![B: $i, C: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ![B: $i, C: $i] : ((~q1(f(B))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ((~(![X: $i] : (c(X) | b(X) | (~a1(X))) & (~![X: $i] : (b(X) | (~a1(X)))))) | ?[X: $i] : (a1(X) & c(X))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A) & e(A) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A, Y)))))) & ![A: $i, B: $i, C: $i] : ((~(s1(A) & s1(B) & r(B, C) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p1(X) & q(X, Y))) & ((~![X: $i] : p1(X)) | ![A: $i, B: $i] : (p1(A) & p1(B))) & ((~(![X: $i] : p1(X) & ?[Y: $i] : q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (p1(X) & q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)) & ![A: $i, B: $i] : ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & ((~![X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & (![X: $i] : q1(X) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) & ![A: $i, B: $i] : ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & (?[X: $i] : b(X) | (~![X: $i] : (b(X) | (~a1(X)))) | (~?[X: $i] : a1(X))) & (?[X: $i] : b(X) | (~![X: $i] : a1(X)) | (~?[X: $i] : (b(X) | (~a1(X))))) & (~?[Y: $i] : ![X: $i] : (a(X, Y) <=> (~a(X, X)))) & ((~(?[X: $i] : a1(X) & ![X: $i] : b(X))) | ?[X: $i] : (a1(X) & b(X))) & ((~?[X: $i] : b(X)) | ?[X: $i] : (a1(X) | b(X))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y)) & ![A: $i, B: $i] : ((~![X: $i] : p1(X)) | (p1(A) & p1(B))) & ((~![X: $i] : p1(X)) | (![X: $i] : p1(X) & ![Y: $i] : p1(Y))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y)) & ((~?[X: $i] : p1(X)) | ?[Z: $i] : p1(Z)) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))) & ((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) & ?[X: $i] : ![Y: $i] : (p1(Y) | (~p1(X))) & ![B: $i] : (q1(B) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | (~(![X: $i] : (q1(X) | (~p1(X))) & r1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (r1(B) | (~p1(A)) | (~(r1(Y) | (~p1(X))))) & ?[Y: $i] : (p1(Y) | (~?[X: $i] : p1(X))) & ((~?[X: $i] : ![Y: $i] : p(X, Y)) | ![Y: $i] : ?[X: $i] : p(X, Y)) & ((~?[X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & ((~![X: $i, Y: $i] : p(X, Y)) | ![X: $i] : p(X, X)) & ![A: $i] : (q1(A) | (~((f0 | g0) & ![X: $i] : (p1(X) & q1(X))))) & (a0 | b0 | (a0 <=> b0)) & ((~(a0 & b0)) | (a0 <=> b0)) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q1(X)) | p(X, A)) & q1(A) & q1(B) & ((~r1(Y)) | p(B, Y)) & r1(A) & r1(B) & ((~s1(A)) | p(X, Y)) & s1(A))) | p(A, B)) & ![B: $i] : ((~![Y: $i] : ((~(r1(Y) | (~r1(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))) & ((~(![X: $i] : (q1(X) | (~p1(X))) & ?[Y: $i] : (r1(Y) | (~q1(Y))))) | ?[Z: $i] : (r1(Z) | (~p1(Z)))))) <=> (~(![C: $i, B: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B) & r1(C))) & q1(X))) & ![B: $i, C: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ![B: $i, C: $i] : ((~q1(f(B))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ((~(![X: $i] : (c(X) | b(X) | (~a1(X))) & (~![X: $i] : (b(X) | (~a1(X)))))) | ?[X: $i] : (a1(X) & c(X))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A) & e(A) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A, Y)))))) & ![A: $i, B: $i, C: $i] : ((~(s1(A) & s1(B) & r(B, C) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p1(X) & q(X, Y))) & ((~![X: $i] : p1(X)) | ![A: $i, B: $i] : (p1(A) & p1(B))) & ((~(![X: $i] : p1(X) & ?[Y: $i] : q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (p1(X) & q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)) & ![A: $i, B: $i] : ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & ((~![X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & (![X: $i] : q1(X) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) & ![A: $i, B: $i] : ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & (?[X: $i] : b(X) | (~![X: $i] : (b(X) | (~a1(X)))) | (~?[X: $i] : a1(X))) & (?[X: $i] : b(X) | (~![X: $i] : a1(X)) | (~?[X: $i] : (b(X) | (~a1(X))))) & (~?[Y: $i] : ![X: $i] : (a(X, Y) <=> (~a(X, X)))) & ((~(?[X: $i] : a1(X) & ![X: $i] : b(X))) | ?[X: $i] : (a1(X) & b(X))) & ((~?[X: $i] : b(X)) | ?[X: $i] : (a1(X) | b(X))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y)) & ![A: $i, B: $i] : ((~![X: $i] : p1(X)) | (p1(A) & p1(B))) & ((~![X: $i] : p1(X)) | (![X: $i] : p1(X) & ![Y: $i] : p1(Y))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y)) & ((~?[X: $i] : p1(X)) | ?[Z: $i] : p1(Z)) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))) & ((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) & ?[X: $i] : ![Y: $i] : (p1(Y) | (~p1(X))) & ![B: $i] : (q1(B) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | (~(![X: $i] : (q1(X) | (~p1(X))) & r1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (r1(B) | (~p1(A)) | (~(r1(Y) | (~p1(X))))) & ?[Y: $i] : (p1(Y) | (~?[X: $i] : p1(X))) & ((~?[X: $i] : ![Y: $i] : p(X, Y)) | ![Y: $i] : ?[X: $i] : p(X, Y)) & ((~?[X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & ((~![X: $i, Y: $i] : p(X, Y)) | ![X: $i] : p(X, X)) & ![A: $i] : (q1(A) | (~((f0 | g0) & ![X: $i] : (p1(X) & q1(X))))) & (a0 | b0 | (a0 <=> b0)) & ((~(a0 & b0)) | (a0 <=> b0)) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q1(X)) | p(X, A)) & q1(A) & q1(B) & ((~r1(Y)) | p(B, Y)) & r1(A) & r1(B) & ((~s1(A)) | p(X, Y)) & s1(A))) | p(A, B)) & ![B: $i] : ((~![Y: $i] : ((~(r1(Y) | (~r1(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))) & ((~(![X: $i] : (q1(X) | (~p1(X))) & ?[Y: $i] : (r1(Y) | (~q1(Y))))) | ?[Z: $i] : (r1(Z) | (~p1(Z))))))),
% 0.56/0.65 inference(monotonicity,[status(thm)],[1047])).
% 0.56/0.65 tff(1049,plain,
% 0.56/0.65 ((~((((((((((((((((((((((((((((((((((((((((((![C: $i, B: $i] : (![Z: $i] : q1(f(Z)) => ?[X: $i, Y: $i] : (((p1(f(Y)) => p1(X)) & (r1(Y) => (r1(B) & r1(C)))) & q1(X))) & ![B: $i, C: $i] : (![Z: $i] : q1(f(Z)) => ?[X: $i, Y: $i] : ((p1(f(Y)) => (p1(X) & (r1(Y) => (r1(B) & r1(C))))) & q1(X)))) & ![B: $i, C: $i] : (q1(f(B)) => ?[X: $i, Y: $i] : ((p1(f(Y)) => (p1(X) & (r1(Y) => (r1(B) & r1(C))))) & q1(X)))) & ((![X: $i] : (a1(X) => (b(X) | c(X))) & (~![X: $i] : (a1(X) => b(X)))) => ?[X: $i] : (a1(X) & c(X)))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (((((p1(A) & e(A)) & (e(X) => (g(X) | s(X, f(X))))) & (e(X2) => (g(X2) | c(f(X2))))) & (s(A, Y) => p1(Y))) => ((p1(X3) & g(X3)) | (p1(X4) & c(X4))))) & ![A: $i, B: $i, C: $i] : (((((s1(A) & s1(B)) & r(B, C)) & ![X: $i] : (s1(X) => p1(X))) & ![X: $i, Y: $i] : (r(X, Y) => q(X, Y))) => ?[X: $i, Y: $i] : (p1(X) & q(X, Y)))) & (![X: $i] : p1(X) => ![A: $i, B: $i] : (p1(A) & p1(B)))) & ((![X: $i] : p1(X) & ?[Y: $i] : q1(Y)) => ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z)))) & (![X: $i] : ?[Y: $i] : (p1(X) & q1(Y)) => ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z)))) & (![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y)) => ?[Z: $i] : a(Z, Z))) & ![A: $i, B: $i, C: $i] : (((((s1(A) & s1(B)) & r(B, C)) & ![X: $i] : (s1(X) => p1(X))) & ![X: $i, Y: $i] : (r(X, Y) => q(X, Y))) => ?[X: $i, Y: $i] : (p1(X) & q(X, Y)))) & ![A: $i, B: $i] : (![Y: $i] : (q1(Y) => p1(Y)) => ?[X: $i] : ((p1(X) => p1(A)) & (q1(X) => p1(B))))) & (?[X: $i] : p1(X) => (?[X: $i] : p1(X) & (a0 => ((b0 | (~b0)) & (q0 => q0)))))) & (![X: $i] : p1(X) => ?[Y: $i] : p1(Y))) & (![X: $i] : (p1(X) => q1(X)) => (![X: $i] : p1(X) => ![X: $i] : q1(X)))) & ![A: $i, B: $i] : (![Z: $i] : (q1(Z) => p1(Z)) => ?[X: $i] : ((p1(X) => p1(A)) & (q1(X) => p1(B))))) & (![X: $i] : (a1(X) => b(X)) => (?[X: $i] : a1(X) => ?[X: $i] : b(X)))) & (?[X: $i] : (a1(X) => b(X)) => (![X: $i] : a1(X) => ?[X: $i] : b(X)))) & (~?[Y: $i] : ![X: $i] : (a(X, Y) <=> (~a(X, X))))) & ((?[X: $i] : a1(X) & ![X: $i] : b(X)) => ?[X: $i] : (a1(X) & b(X)))) & (?[X: $i] : b(X) => ?[X: $i] : (a1(X) | b(X)))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y))) & ![A: $i, B: $i] : (![X: $i] : p1(X) => (p1(A) & p1(B)))) & (![X: $i] : p1(X) => (![X: $i] : p1(X) & ![Y: $i] : p1(Y)))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y))) & (?[X: $i] : p1(X) => ?[Z: $i] : p1(Z))) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : ((p(Y, X) => ?[W: $i] : p(W, Y)) & ((p(Z, Y) & p(Y, Z)) => p(Y, X)))) & (![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) => ![A: $i, B: $i] : (eq(A, B) => eq(B, A)))) & ![A: $i, B: $i] : (![Y: $i] : (q1(Y) => p1(Y)) => ?[X: $i] : ((p1(X) => p1(A)) & (q1(X) => p1(B))))) & ?[X: $i] : ![Y: $i] : (p1(X) => p1(Y))) & ![B: $i] : ((![X: $i] : (p1(X) => q1(X)) & r1(B)) => (![Y: $i] : (r1(Y) => p1(Y)) => q1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((p1(X) => r1(Y)) => (p1(A) => r1(B)))) & ?[Y: $i] : (?[X: $i] : p1(X) => p1(Y))) & (?[X: $i] : ![Y: $i] : p(X, Y) => ![Y: $i] : ?[X: $i] : p(X, Y))) & (p1(z) => p1(z))) & (?[X: $i] : p1(X) => ?[Y: $i] : p1(Y))) & (![X: $i, Y: $i] : p(X, Y) => ![X: $i] : p(X, X))) & ![A: $i] : (((f0 | g0) & ![X: $i] : (p1(X) & q1(X))) => q1(A))) & (((a0 <=> b0) | a0) | b0)) & ((a0 & b0) => (a0 <=> b0))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (((((((((q1(X) => p(X, A)) & q1(A)) & q1(B)) & (r1(Y) => p(B, Y))) & r1(A)) & r1(B)) & (s1(A) => p(X, Y))) & s1(A)) => p(A, B))) & ![B: $i] : (![Y: $i] : ((r1(B) => r1(Y)) => p(f(Y), Y)) => ?[X: $i, Y: $i] : (p(X, Y) & (q(f(B), B) => q(X, Y))))) & ((![X: $i] : (p1(X) => q1(X)) & ?[Y: $i] : (q1(Y) => r1(Y))) => ?[Z: $i] : (p1(Z) => r1(Z))))) <=> (~(![C: $i, B: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B) & r1(C))) & q1(X))) & ![B: $i, C: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ![B: $i, C: $i] : ((~q1(f(B))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ((~(![X: $i] : (c(X) | b(X) | (~a1(X))) & (~![X: $i] : (b(X) | (~a1(X)))))) | ?[X: $i] : (a1(X) & c(X))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A) & e(A) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A, Y)))))) & ![A: $i, B: $i, C: $i] : ((~(s1(A) & s1(B) & r(B, C) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p1(X) & q(X, Y))) & ((~![X: $i] : p1(X)) | ![A: $i, B: $i] : (p1(A) & p1(B))) & ((~(![X: $i] : p1(X) & ?[Y: $i] : q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (p1(X) & q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)) & ![A: $i, B: $i] : ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & ((~![X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & (![X: $i] : q1(X) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) & ![A: $i, B: $i] : ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & (?[X: $i] : b(X) | (~![X: $i] : (b(X) | (~a1(X)))) | (~?[X: $i] : a1(X))) & (?[X: $i] : b(X) | (~![X: $i] : a1(X)) | (~?[X: $i] : (b(X) | (~a1(X))))) & (~?[Y: $i] : ![X: $i] : (a(X, Y) <=> (~a(X, X)))) & ((~(?[X: $i] : a1(X) & ![X: $i] : b(X))) | ?[X: $i] : (a1(X) & b(X))) & ((~?[X: $i] : b(X)) | ?[X: $i] : (a1(X) | b(X))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y)) & ![A: $i, B: $i] : ((~![X: $i] : p1(X)) | (p1(A) & p1(B))) & ((~![X: $i] : p1(X)) | (![X: $i] : p1(X) & ![Y: $i] : p1(Y))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y)) & ((~?[X: $i] : p1(X)) | ?[Z: $i] : p1(Z)) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))) & ((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) & ?[X: $i] : ![Y: $i] : (p1(Y) | (~p1(X))) & ![B: $i] : (q1(B) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | (~(![X: $i] : (q1(X) | (~p1(X))) & r1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (r1(B) | (~p1(A)) | (~(r1(Y) | (~p1(X))))) & ?[Y: $i] : (p1(Y) | (~?[X: $i] : p1(X))) & ((~?[X: $i] : ![Y: $i] : p(X, Y)) | ![Y: $i] : ?[X: $i] : p(X, Y)) & ((~?[X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & ((~![X: $i, Y: $i] : p(X, Y)) | ![X: $i] : p(X, X)) & ![A: $i] : (q1(A) | (~((f0 | g0) & ![X: $i] : (p1(X) & q1(X))))) & (a0 | b0 | (a0 <=> b0)) & ((~(a0 & b0)) | (a0 <=> b0)) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q1(X)) | p(X, A)) & q1(A) & q1(B) & ((~r1(Y)) | p(B, Y)) & r1(A) & r1(B) & ((~s1(A)) | p(X, Y)) & s1(A))) | p(A, B)) & ![B: $i] : ((~![Y: $i] : ((~(r1(Y) | (~r1(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))) & ((~(![X: $i] : (q1(X) | (~p1(X))) & ?[Y: $i] : (r1(Y) | (~q1(Y))))) | ?[Z: $i] : (r1(Z) | (~p1(Z))))))),
% 0.56/0.66 inference(rewrite,[status(thm)],[])).
% 0.56/0.66 tff(1050,axiom,(~((((((((((((((((((((((((((((((((((((((((((![C: $i, B: $i] : (![Z: $i] : q1(f(Z)) => ?[X: $i, Y: $i] : (((p1(f(Y)) => p1(X)) & (r1(Y) => (r1(B) & r1(C)))) & q1(X))) & ![B: $i, C: $i] : (![Z: $i] : q1(f(Z)) => ?[X: $i, Y: $i] : ((p1(f(Y)) => (p1(X) & (r1(Y) => (r1(B) & r1(C))))) & q1(X)))) & ![B: $i, C: $i] : (q1(f(B)) => ?[X: $i, Y: $i] : ((p1(f(Y)) => (p1(X) & (r1(Y) => (r1(B) & r1(C))))) & q1(X)))) & ((![X: $i] : (a1(X) => (b(X) | c(X))) & (~![X: $i] : (a1(X) => b(X)))) => ?[X: $i] : (a1(X) & c(X)))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (((((p1(A) & e(A)) & (e(X) => (g(X) | s(X, f(X))))) & (e(X2) => (g(X2) | c(f(X2))))) & (s(A, Y) => p1(Y))) => ((p1(X3) & g(X3)) | (p1(X4) & c(X4))))) & ![A: $i, B: $i, C: $i] : (((((s1(A) & s1(B)) & r(B, C)) & ![X: $i] : (s1(X) => p1(X))) & ![X: $i, Y: $i] : (r(X, Y) => q(X, Y))) => ?[X: $i, Y: $i] : (p1(X) & q(X, Y)))) & (![X: $i] : p1(X) => ![A: $i, B: $i] : (p1(A) & p1(B)))) & ((![X: $i] : p1(X) & ?[Y: $i] : q1(Y)) => ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z)))) & (![X: $i] : ?[Y: $i] : (p1(X) & q1(Y)) => ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z)))) & (![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y)) => ?[Z: $i] : a(Z, Z))) & ![A: $i, B: $i, C: $i] : (((((s1(A) & s1(B)) & r(B, C)) & ![X: $i] : (s1(X) => p1(X))) & ![X: $i, Y: $i] : (r(X, Y) => q(X, Y))) => ?[X: $i, Y: $i] : (p1(X) & q(X, Y)))) & ![A: $i, B: $i] : (![Y: $i] : (q1(Y) => p1(Y)) => ?[X: $i] : ((p1(X) => p1(A)) & (q1(X) => p1(B))))) & (?[X: $i] : p1(X) => (?[X: $i] : p1(X) & (a0 => ((b0 | (~b0)) & (q0 => q0)))))) & (![X: $i] : p1(X) => ?[Y: $i] : p1(Y))) & (![X: $i] : (p1(X) => q1(X)) => (![X: $i] : p1(X) => ![X: $i] : q1(X)))) & ![A: $i, B: $i] : (![Z: $i] : (q1(Z) => p1(Z)) => ?[X: $i] : ((p1(X) => p1(A)) & (q1(X) => p1(B))))) & (![X: $i] : (a1(X) => b(X)) => (?[X: $i] : a1(X) => ?[X: $i] : b(X)))) & (?[X: $i] : (a1(X) => b(X)) => (![X: $i] : a1(X) => ?[X: $i] : b(X)))) & (~?[Y: $i] : ![X: $i] : (a(X, Y) <=> (~a(X, X))))) & ((?[X: $i] : a1(X) & ![X: $i] : b(X)) => ?[X: $i] : (a1(X) & b(X)))) & (?[X: $i] : b(X) => ?[X: $i] : (a1(X) | b(X)))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y))) & ![A: $i, B: $i] : (![X: $i] : p1(X) => (p1(A) & p1(B)))) & (![X: $i] : p1(X) => (![X: $i] : p1(X) & ![Y: $i] : p1(Y)))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y))) & (?[X: $i] : p1(X) => ?[Z: $i] : p1(Z))) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : ((p(Y, X) => ?[W: $i] : p(W, Y)) & ((p(Z, Y) & p(Y, Z)) => p(Y, X)))) & (![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) => ![A: $i, B: $i] : (eq(A, B) => eq(B, A)))) & ![A: $i, B: $i] : (![Y: $i] : (q1(Y) => p1(Y)) => ?[X: $i] : ((p1(X) => p1(A)) & (q1(X) => p1(B))))) & ?[X: $i] : ![Y: $i] : (p1(X) => p1(Y))) & ![B: $i] : ((![X: $i] : (p1(X) => q1(X)) & r1(B)) => (![Y: $i] : (r1(Y) => p1(Y)) => q1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((p1(X) => r1(Y)) => (p1(A) => r1(B)))) & ?[Y: $i] : (?[X: $i] : p1(X) => p1(Y))) & (?[X: $i] : ![Y: $i] : p(X, Y) => ![Y: $i] : ?[X: $i] : p(X, Y))) & (p1(z) => p1(z))) & (?[X: $i] : p1(X) => ?[Y: $i] : p1(Y))) & (![X: $i, Y: $i] : p(X, Y) => ![X: $i] : p(X, X))) & ![A: $i] : (((f0 | g0) & ![X: $i] : (p1(X) & q1(X))) => q1(A))) & (((a0 <=> b0) | a0) | b0)) & ((a0 & b0) => (a0 <=> b0))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (((((((((q1(X) => p(X, A)) & q1(A)) & q1(B)) & (r1(Y) => p(B, Y))) & r1(A)) & r1(B)) & (s1(A) => p(X, Y))) & s1(A)) => p(A, B))) & ![B: $i] : (![Y: $i] : ((r1(B) => r1(Y)) => p(f(Y), Y)) => ?[X: $i, Y: $i] : (p(X, Y) & (q(f(B), B) => q(X, Y))))) & ((![X: $i] : (p1(X) => q1(X)) & ?[Y: $i] : (q1(Y) => r1(Y))) => ?[Z: $i] : (p1(Z) => r1(Z))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.56/0.66 tff(1051,plain,
% 0.56/0.66 (~(![C: $i, B: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B) & r1(C))) & q1(X))) & ![B: $i, C: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ![B: $i, C: $i] : ((~q1(f(B))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ((~(![X: $i] : (c(X) | b(X) | (~a1(X))) & (~![X: $i] : (b(X) | (~a1(X)))))) | ?[X: $i] : (a1(X) & c(X))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A) & e(A) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A, Y)))))) & ![A: $i, B: $i, C: $i] : ((~(s1(A) & s1(B) & r(B, C) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p1(X) & q(X, Y))) & ((~![X: $i] : p1(X)) | ![A: $i, B: $i] : (p1(A) & p1(B))) & ((~(![X: $i] : p1(X) & ?[Y: $i] : q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (p1(X) & q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)) & ![A: $i, B: $i] : ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & ((~![X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & (![X: $i] : q1(X) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) & ![A: $i, B: $i] : ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & (?[X: $i] : b(X) | (~![X: $i] : (b(X) | (~a1(X)))) | (~?[X: $i] : a1(X))) & (?[X: $i] : b(X) | (~![X: $i] : a1(X)) | (~?[X: $i] : (b(X) | (~a1(X))))) & (~?[Y: $i] : ![X: $i] : (a(X, Y) <=> (~a(X, X)))) & ((~(?[X: $i] : a1(X) & ![X: $i] : b(X))) | ?[X: $i] : (a1(X) & b(X))) & ((~?[X: $i] : b(X)) | ?[X: $i] : (a1(X) | b(X))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y)) & ![A: $i, B: $i] : ((~![X: $i] : p1(X)) | (p1(A) & p1(B))) & ((~![X: $i] : p1(X)) | (![X: $i] : p1(X) & ![Y: $i] : p1(Y))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y)) & ((~?[X: $i] : p1(X)) | ?[Z: $i] : p1(Z)) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))) & ((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) & ?[X: $i] : ![Y: $i] : (p1(Y) | (~p1(X))) & ![B: $i] : (q1(B) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | (~(![X: $i] : (q1(X) | (~p1(X))) & r1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (r1(B) | (~p1(A)) | (~(r1(Y) | (~p1(X))))) & ?[Y: $i] : (p1(Y) | (~?[X: $i] : p1(X))) & ((~?[X: $i] : ![Y: $i] : p(X, Y)) | ![Y: $i] : ?[X: $i] : p(X, Y)) & ((~?[X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & ((~![X: $i, Y: $i] : p(X, Y)) | ![X: $i] : p(X, X)) & ![A: $i] : (q1(A) | (~((f0 | g0) & ![X: $i] : (p1(X) & q1(X))))) & (a0 | b0 | (a0 <=> b0)) & ((~(a0 & b0)) | (a0 <=> b0)) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q1(X)) | p(X, A)) & q1(A) & q1(B) & ((~r1(Y)) | p(B, Y)) & r1(A) & r1(B) & ((~s1(A)) | p(X, Y)) & s1(A))) | p(A, B)) & ![B: $i] : ((~![Y: $i] : ((~(r1(Y) | (~r1(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))) & ((~(![X: $i] : (q1(X) | (~p1(X))) & ?[Y: $i] : (r1(Y) | (~q1(Y))))) | ?[Z: $i] : (r1(Z) | (~p1(Z)))))),
% 0.56/0.66 inference(modus_ponens,[status(thm)],[1050, 1049])).
% 0.56/0.66 tff(1052,plain,
% 0.56/0.66 (~(![C: $i, B: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B) & r1(C))) & q1(X))) & ![B: $i, C: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ![B: $i, C: $i] : ((~q1(f(B))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ((~(![X: $i] : (c(X) | b(X) | (~a1(X))) & (~![X: $i] : (b(X) | (~a1(X)))))) | ?[X: $i] : (a1(X) & c(X))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A) & e(A) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A, Y)))))) & ![A: $i, B: $i, C: $i] : ((~(s1(A) & s1(B) & r(B, C) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p1(X) & q(X, Y))) & ((~![X: $i] : p1(X)) | ![A: $i, B: $i] : (p1(A) & p1(B))) & ((~(![X: $i] : p1(X) & ?[Y: $i] : q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (p1(X) & q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)) & ![A: $i, B: $i] : ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & ((~![X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & (![X: $i] : q1(X) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) & ![A: $i, B: $i] : ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & (?[X: $i] : b(X) | (~![X: $i] : (b(X) | (~a1(X)))) | (~?[X: $i] : a1(X))) & (?[X: $i] : b(X) | (~![X: $i] : a1(X)) | (~?[X: $i] : (b(X) | (~a1(X))))) & (~?[Y: $i] : ![X: $i] : (a(X, Y) <=> (~a(X, X)))) & ((~(?[X: $i] : a1(X) & ![X: $i] : b(X))) | ?[X: $i] : (a1(X) & b(X))) & ((~?[X: $i] : b(X)) | ?[X: $i] : (a1(X) | b(X))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y)) & ![A: $i, B: $i] : ((~![X: $i] : p1(X)) | (p1(A) & p1(B))) & ((~![X: $i] : p1(X)) | (![X: $i] : p1(X) & ![Y: $i] : p1(Y))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y)) & ((~?[X: $i] : p1(X)) | ?[Z: $i] : p1(Z)) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))) & ((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) & ?[X: $i] : ![Y: $i] : (p1(Y) | (~p1(X))) & ![B: $i] : (q1(B) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | (~(![X: $i] : (q1(X) | (~p1(X))) & r1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (r1(B) | (~p1(A)) | (~(r1(Y) | (~p1(X))))) & ?[Y: $i] : (p1(Y) | (~?[X: $i] : p1(X))) & ((~?[X: $i] : ![Y: $i] : p(X, Y)) | ![Y: $i] : ?[X: $i] : p(X, Y)) & ((~?[X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & ((~![X: $i, Y: $i] : p(X, Y)) | ![X: $i] : p(X, X)) & ![A: $i] : (q1(A) | (~((f0 | g0) & ![X: $i] : (p1(X) & q1(X))))) & (a0 | b0 | (a0 <=> b0)) & ((~(a0 & b0)) | (a0 <=> b0)) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q1(X)) | p(X, A)) & q1(A) & q1(B) & ((~r1(Y)) | p(B, Y)) & r1(A) & r1(B) & ((~s1(A)) | p(X, Y)) & s1(A))) | p(A, B)) & ![B: $i] : ((~![Y: $i] : ((~(r1(Y) | (~r1(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))) & ((~(![X: $i] : (q1(X) | (~p1(X))) & ?[Y: $i] : (r1(Y) | (~q1(Y))))) | ?[Z: $i] : (r1(Z) | (~p1(Z)))))),
% 0.56/0.66 inference(modus_ponens,[status(thm)],[1051, 1048])).
% 0.56/0.66 tff(1053,plain,
% 0.56/0.66 (~(![C: $i, B: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B) & r1(C))) & q1(X))) & ![B: $i, C: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ![B: $i, C: $i] : ((~q1(f(B))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ((~(![X: $i] : (c(X) | b(X) | (~a1(X))) & (~![X: $i] : (b(X) | (~a1(X)))))) | ?[X: $i] : (a1(X) & c(X))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A) & e(A) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A, Y)))))) & ![A: $i, B: $i, C: $i] : ((~(s1(A) & s1(B) & r(B, C) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p1(X) & q(X, Y))) & ((~![X: $i] : p1(X)) | ![A: $i, B: $i] : (p1(A) & p1(B))) & ((~(![X: $i] : p1(X) & ?[Y: $i] : q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (p1(X) & q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)) & ![A: $i, B: $i] : ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & ((~![X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & (![X: $i] : q1(X) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) & ![A: $i, B: $i] : ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & (?[X: $i] : b(X) | (~![X: $i] : (b(X) | (~a1(X)))) | (~?[X: $i] : a1(X))) & (?[X: $i] : b(X) | (~![X: $i] : a1(X)) | (~?[X: $i] : (b(X) | (~a1(X))))) & (~?[Y: $i] : ![X: $i] : (a(X, Y) <=> (~a(X, X)))) & ((~(?[X: $i] : a1(X) & ![X: $i] : b(X))) | ?[X: $i] : (a1(X) & b(X))) & ((~?[X: $i] : b(X)) | ?[X: $i] : (a1(X) | b(X))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y)) & ![A: $i, B: $i] : ((~![X: $i] : p1(X)) | (p1(A) & p1(B))) & ((~![X: $i] : p1(X)) | (![X: $i] : p1(X) & ![Y: $i] : p1(Y))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y)) & ((~?[X: $i] : p1(X)) | ?[Z: $i] : p1(Z)) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))) & ((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) & ?[X: $i] : ![Y: $i] : (p1(Y) | (~p1(X))) & ![B: $i] : (q1(B) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | (~(![X: $i] : (q1(X) | (~p1(X))) & r1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (r1(B) | (~p1(A)) | (~(r1(Y) | (~p1(X))))) & ?[Y: $i] : (p1(Y) | (~?[X: $i] : p1(X))) & ((~?[X: $i] : ![Y: $i] : p(X, Y)) | ![Y: $i] : ?[X: $i] : p(X, Y)) & ((~?[X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & ((~![X: $i, Y: $i] : p(X, Y)) | ![X: $i] : p(X, X)) & ![A: $i] : (q1(A) | (~((f0 | g0) & ![X: $i] : (p1(X) & q1(X))))) & ((~(a0 & b0)) | (a0 <=> b0)) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q1(X)) | p(X, A)) & q1(A) & q1(B) & ((~r1(Y)) | p(B, Y)) & r1(A) & r1(B) & ((~s1(A)) | p(X, Y)) & s1(A))) | p(A, B)) & ![B: $i] : ((~![Y: $i] : ((~(r1(Y) | (~r1(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))) & ((~(![X: $i] : (q1(X) | (~p1(X))) & ?[Y: $i] : (r1(Y) | (~q1(Y))))) | ?[Z: $i] : (r1(Z) | (~p1(Z)))))),
% 0.56/0.67 inference(modus_ponens,[status(thm)],[1052, 1046])).
% 0.56/0.67 tff(1054,plain,
% 0.56/0.67 (~(![C: $i, B: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B) & r1(C))) & q1(X))) & ![B: $i, C: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ![B: $i, C: $i] : ((~q1(f(B))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ((~(![X: $i] : (c(X) | b(X) | (~a1(X))) & (~![X: $i] : (b(X) | (~a1(X)))))) | ?[X: $i] : (a1(X) & c(X))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A) & e(A) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A, Y)))))) & ![A: $i, B: $i, C: $i] : ((~(s1(A) & s1(B) & r(B, C) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p1(X) & q(X, Y))) & ((~![X: $i] : p1(X)) | ![A: $i, B: $i] : (p1(A) & p1(B))) & ((~(![X: $i] : p1(X) & ?[Y: $i] : q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (p1(X) & q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)) & ![A: $i, B: $i] : ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & ((~![X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & (![X: $i] : q1(X) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) & ![A: $i, B: $i] : ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & (?[X: $i] : b(X) | (~![X: $i] : (b(X) | (~a1(X)))) | (~?[X: $i] : a1(X))) & (?[X: $i] : b(X) | (~![X: $i] : a1(X)) | (~?[X: $i] : (b(X) | (~a1(X))))) & (~?[Y: $i] : ![X: $i] : (a(X, Y) <=> (~a(X, X)))) & ((~(?[X: $i] : a1(X) & ![X: $i] : b(X))) | ?[X: $i] : (a1(X) & b(X))) & ((~?[X: $i] : b(X)) | ?[X: $i] : (a1(X) | b(X))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y)) & ![A: $i, B: $i] : ((~![X: $i] : p1(X)) | (p1(A) & p1(B))) & ((~![X: $i] : p1(X)) | (![X: $i] : p1(X) & ![Y: $i] : p1(Y))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y)) & ((~?[X: $i] : p1(X)) | ?[Z: $i] : p1(Z)) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))) & ((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) & ?[X: $i] : ![Y: $i] : (p1(Y) | (~p1(X))) & ![B: $i] : (q1(B) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | (~(![X: $i] : (q1(X) | (~p1(X))) & r1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (r1(B) | (~p1(A)) | (~(r1(Y) | (~p1(X))))) & ?[Y: $i] : (p1(Y) | (~?[X: $i] : p1(X))) & ((~?[X: $i] : ![Y: $i] : p(X, Y)) | ![Y: $i] : ?[X: $i] : p(X, Y)) & ((~?[X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & ((~![X: $i, Y: $i] : p(X, Y)) | ![X: $i] : p(X, X)) & ![A: $i] : (q1(A) | (~((f0 | g0) & ![X: $i] : (p1(X) & q1(X))))) & ((~(a0 & b0)) | (a0 <=> b0)) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q1(X)) | p(X, A)) & q1(A) & q1(B) & ((~r1(Y)) | p(B, Y)) & r1(A) & r1(B) & ((~s1(A)) | p(X, Y)) & s1(A))) | p(A, B)) & ![B: $i] : ((~![Y: $i] : ((~(r1(Y) | (~r1(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))) & ((~(![X: $i] : (q1(X) | (~p1(X))) & ?[Y: $i] : (r1(Y) | (~q1(Y))))) | ?[Z: $i] : (r1(Z) | (~p1(Z)))))),
% 0.56/0.67 inference(modus_ponens,[status(thm)],[1053, 1045])).
% 0.56/0.67 tff(1055,plain,
% 0.56/0.67 (~(![C: $i, B: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B) & r1(C))) & q1(X))) & ![B: $i, C: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ![B: $i, C: $i] : ((~q1(f(B))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ((~(![X: $i] : (c(X) | b(X) | (~a1(X))) & (~![X: $i] : (b(X) | (~a1(X)))))) | ?[X: $i] : (a1(X) & c(X))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A) & e(A) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A, Y)))))) & ![A: $i, B: $i, C: $i] : ((~(s1(A) & s1(B) & r(B, C) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p1(X) & q(X, Y))) & ((~![X: $i] : p1(X)) | ![A: $i, B: $i] : (p1(A) & p1(B))) & ((~(![X: $i] : p1(X) & ?[Y: $i] : q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (p1(X) & q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)) & ![A: $i, B: $i] : ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & ((~![X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & (![X: $i] : q1(X) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) & ![A: $i, B: $i] : ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & (?[X: $i] : b(X) | (~![X: $i] : (b(X) | (~a1(X)))) | (~?[X: $i] : a1(X))) & (?[X: $i] : b(X) | (~![X: $i] : a1(X)) | (~?[X: $i] : (b(X) | (~a1(X))))) & (~?[Y: $i] : ![X: $i] : (a(X, Y) <=> (~a(X, X)))) & ((~(?[X: $i] : a1(X) & ![X: $i] : b(X))) | ?[X: $i] : (a1(X) & b(X))) & ((~?[X: $i] : b(X)) | ?[X: $i] : (a1(X) | b(X))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y)) & ![A: $i, B: $i] : ((~![X: $i] : p1(X)) | (p1(A) & p1(B))) & ((~![X: $i] : p1(X)) | (![X: $i] : p1(X) & ![Y: $i] : p1(Y))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y)) & ((~?[X: $i] : p1(X)) | ?[Z: $i] : p1(Z)) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))) & ((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) & ?[X: $i] : ![Y: $i] : (p1(Y) | (~p1(X))) & ![B: $i] : (q1(B) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | (~(![X: $i] : (q1(X) | (~p1(X))) & r1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (r1(B) | (~p1(A)) | (~(r1(Y) | (~p1(X))))) & ?[Y: $i] : (p1(Y) | (~?[X: $i] : p1(X))) & ((~?[X: $i] : ![Y: $i] : p(X, Y)) | ![Y: $i] : ?[X: $i] : p(X, Y)) & ((~?[X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & ((~![X: $i, Y: $i] : p(X, Y)) | ![X: $i] : p(X, X)) & ![A: $i] : (q1(A) | (~(k!0 & ![X: $i] : (p1(X) & q1(X))))) & ((~(a0 & b0)) | (a0 <=> b0)) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q1(X)) | p(X, A)) & q1(A) & q1(B) & ((~r1(Y)) | p(B, Y)) & r1(A) & r1(B) & ((~s1(A)) | p(X, Y)) & s1(A))) | p(A, B)) & ![B: $i] : ((~![Y: $i] : ((~(r1(Y) | (~r1(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))) & ((~(![X: $i] : (q1(X) | (~p1(X))) & ?[Y: $i] : (r1(Y) | (~q1(Y))))) | ?[Z: $i] : (r1(Z) | (~p1(Z)))))),
% 0.56/0.67 inference(modus_ponens,[status(thm)],[1054, 1043])).
% 0.56/0.67 tff(1056,plain,
% 0.56/0.67 (~(![C: $i, B: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B) & r1(C))) & q1(X))) & ![B: $i, C: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ![B: $i, C: $i] : ((~q1(f(B))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ((~(![X: $i] : (c(X) | b(X) | (~a1(X))) & (~![X: $i] : (b(X) | (~a1(X)))))) | ?[X: $i] : (a1(X) & c(X))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A) & e(A) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A, Y)))))) & ![A: $i, B: $i, C: $i] : ((~(s1(A) & s1(B) & r(B, C) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p1(X) & q(X, Y))) & ((~![X: $i] : p1(X)) | ![A: $i, B: $i] : (p1(A) & p1(B))) & ((~(![X: $i] : p1(X) & ?[Y: $i] : q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (p1(X) & q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)) & ![A: $i, B: $i] : ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & ((~![X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & (![X: $i] : q1(X) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) & ![A: $i, B: $i] : ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & (?[X: $i] : b(X) | (~![X: $i] : (b(X) | (~a1(X)))) | (~?[X: $i] : a1(X))) & (?[X: $i] : b(X) | (~![X: $i] : a1(X)) | (~?[X: $i] : (b(X) | (~a1(X))))) & (~?[Y: $i] : ![X: $i] : (a(X, Y) <=> (~a(X, X)))) & ((~(?[X: $i] : a1(X) & ![X: $i] : b(X))) | ?[X: $i] : (a1(X) & b(X))) & ((~?[X: $i] : b(X)) | ?[X: $i] : (a1(X) | b(X))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y)) & ![A: $i, B: $i] : ((~![X: $i] : p1(X)) | (p1(A) & p1(B))) & ((~![X: $i] : p1(X)) | (![X: $i] : p1(X) & ![Y: $i] : p1(Y))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y)) & ((~?[X: $i] : p1(X)) | ?[Z: $i] : p1(Z)) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))) & ((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) & ?[X: $i] : ![Y: $i] : (p1(Y) | (~p1(X))) & ![B: $i] : (q1(B) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | (~(![X: $i] : (q1(X) | (~p1(X))) & r1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (r1(B) | (~p1(A)) | (~(r1(Y) | (~p1(X))))) & ?[Y: $i] : (p1(Y) | (~?[X: $i] : p1(X))) & ((~?[X: $i] : ![Y: $i] : p(X, Y)) | ![Y: $i] : ?[X: $i] : p(X, Y)) & ((~?[X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & ((~![X: $i, Y: $i] : p(X, Y)) | ![X: $i] : p(X, X)) & ![A: $i] : (q1(A) | (~(k!0 & ![X: $i] : (p1(X) & q1(X))))) & ((~(a0 & b0)) | (a0 <=> b0)) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q1(X)) | p(X, A)) & q1(A) & q1(B) & ((~r1(Y)) | p(B, Y)) & r1(A) & r1(B) & ((~s1(A)) | p(X, Y)) & s1(A))) | p(A, B)) & ![B: $i] : ((~![Y: $i] : ((~(r1(Y) | (~r1(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))) & ((~(![X: $i] : (q1(X) | (~p1(X))) & ?[Y: $i] : (r1(Y) | (~q1(Y))))) | ?[Z: $i] : (r1(Z) | (~p1(Z)))))),
% 0.56/0.67 inference(modus_ponens,[status(thm)],[1055, 1042])).
% 0.56/0.67 tff(1057,plain,
% 0.56/0.67 (~(![C: $i, B: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B) & r1(C))) & q1(X))) & ![B: $i, C: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ![B: $i, C: $i] : ((~q1(f(B))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ((~(![X: $i] : (c(X) | b(X) | (~a1(X))) & (~![X: $i] : (b(X) | (~a1(X)))))) | ?[X: $i] : (a1(X) & c(X))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A) & e(A) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A, Y)))))) & ![A: $i, B: $i, C: $i] : ((~(s1(A) & s1(B) & r(B, C) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p1(X) & q(X, Y))) & ((~![X: $i] : p1(X)) | ![A: $i, B: $i] : (p1(A) & p1(B))) & ((~(![X: $i] : p1(X) & ?[Y: $i] : q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (p1(X) & q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)) & ![A: $i, B: $i] : ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & ((~![X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & (![X: $i] : q1(X) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) & ![A: $i, B: $i] : ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & (?[X: $i] : b(X) | (~![X: $i] : (b(X) | (~a1(X)))) | (~?[X: $i] : a1(X))) & (?[X: $i] : b(X) | (~![X: $i] : a1(X)) | (~?[X: $i] : (b(X) | (~a1(X))))) & (~?[Y: $i] : ![X: $i] : (a(X, Y) <=> (~a(X, X)))) & ((~(?[X: $i] : a1(X) & ![X: $i] : b(X))) | ?[X: $i] : (a1(X) & b(X))) & ((~?[X: $i] : b(X)) | ?[X: $i] : (a1(X) | b(X))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y)) & ![A: $i, B: $i] : ((~![X: $i] : p1(X)) | (p1(A) & p1(B))) & ((~![X: $i] : p1(X)) | (![X: $i] : p1(X) & ![Y: $i] : p1(Y))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y)) & ((~?[X: $i] : p1(X)) | ?[Z: $i] : p1(Z)) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))) & ((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) & ?[X: $i] : ![Y: $i] : (p1(Y) | (~p1(X))) & ![B: $i] : (q1(B) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | (~(![X: $i] : (q1(X) | (~p1(X))) & r1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (r1(B) | (~p1(A)) | (~(r1(Y) | (~p1(X))))) & ?[Y: $i] : (p1(Y) | (~?[X: $i] : p1(X))) & ((~?[X: $i] : ![Y: $i] : p(X, Y)) | ![Y: $i] : ?[X: $i] : p(X, Y)) & ((~?[X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & ((~![X: $i, Y: $i] : p(X, Y)) | ![X: $i] : p(X, X)) & ![A: $i] : (q1(A) | (~(k!0 & ![X: $i] : (p1(X) & q1(X))))) & ((~(a0 & b0)) | (a0 <=> b0)) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q1(X)) | p(X, A)) & q1(A) & q1(B) & ((~r1(Y)) | p(B, Y)) & r1(A) & r1(B) & ((~s1(A)) | p(X, Y)) & s1(A))) | p(A, B)) & ![B: $i] : ((~![Y: $i] : ((~(r1(Y) | (~r1(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))) & ((~(![X: $i] : (q1(X) | (~p1(X))) & ?[Y: $i] : (r1(Y) | (~q1(Y))))) | ?[Z: $i] : (r1(Z) | (~p1(Z)))))),
% 0.56/0.67 inference(modus_ponens,[status(thm)],[1056, 1042])).
% 0.56/0.67 tff(1058,plain,
% 0.56/0.67 (~(![C: $i, B: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B) & r1(C))) & q1(X))) & ![B: $i, C: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ![B: $i, C: $i] : ((~q1(f(B))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ((~(![X: $i] : (c(X) | b(X) | (~a1(X))) & (~![X: $i] : (b(X) | (~a1(X)))))) | ?[X: $i] : (a1(X) & c(X))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A) & e(A) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A, Y)))))) & ![A: $i, B: $i, C: $i] : ((~(s1(A) & s1(B) & r(B, C) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p1(X) & q(X, Y))) & ((~![X: $i] : p1(X)) | ![A: $i, B: $i] : (p1(A) & p1(B))) & ((~(![X: $i] : p1(X) & ?[Y: $i] : q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (p1(X) & q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)) & ![A: $i, B: $i] : ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & ((~![X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & (![X: $i] : q1(X) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) & ![A: $i, B: $i] : ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & (?[X: $i] : b(X) | (~![X: $i] : (b(X) | (~a1(X)))) | (~?[X: $i] : a1(X))) & (?[X: $i] : b(X) | (~![X: $i] : a1(X)) | (~?[X: $i] : (b(X) | (~a1(X))))) & (~?[Y: $i] : ![X: $i] : (a(X, Y) <=> (~a(X, X)))) & ((~(?[X: $i] : a1(X) & ![X: $i] : b(X))) | ?[X: $i] : (a1(X) & b(X))) & ((~?[X: $i] : b(X)) | ?[X: $i] : (a1(X) | b(X))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y)) & ![A: $i, B: $i] : ((~![X: $i] : p1(X)) | (p1(A) & p1(B))) & ((~![X: $i] : p1(X)) | (![X: $i] : p1(X) & ![Y: $i] : p1(Y))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y)) & ((~?[X: $i] : p1(X)) | ?[Z: $i] : p1(Z)) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))) & ((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) & ?[X: $i] : ![Y: $i] : (p1(Y) | (~p1(X))) & ![B: $i] : (q1(B) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | (~(![X: $i] : (q1(X) | (~p1(X))) & r1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (r1(B) | (~p1(A)) | (~(r1(Y) | (~p1(X))))) & ?[Y: $i] : (p1(Y) | (~?[X: $i] : p1(X))) & ((~?[X: $i] : ![Y: $i] : p(X, Y)) | ![Y: $i] : ?[X: $i] : p(X, Y)) & ((~?[X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & ((~![X: $i, Y: $i] : p(X, Y)) | ![X: $i] : p(X, X)) & ![A: $i] : (q1(A) | (~(k!0 & ![X: $i] : (p1(X) & q1(X))))) & ((~(a0 & b0)) | (a0 <=> b0)) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q1(X)) | p(X, A)) & q1(A) & q1(B) & ((~r1(Y)) | p(B, Y)) & r1(A) & r1(B) & ((~s1(A)) | p(X, Y)) & s1(A))) | p(A, B)) & ![B: $i] : ((~![Y: $i] : ((~(r1(Y) | (~r1(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))) & ((~(![X: $i] : (q1(X) | (~p1(X))) & ?[Y: $i] : (r1(Y) | (~q1(Y))))) | ?[Z: $i] : (r1(Z) | (~p1(Z)))))),
% 0.62/0.75 inference(modus_ponens,[status(thm)],[1057, 1042])).
% 0.62/0.75 unexpected number of arguments: (let ((a!1 (forall ((C $i) (B $i))
% 0.62/0.75 (let ((a!1 (forall ((Z $i)) (q1 (f Z))))
% 0.62/0.75 (a!2 (exists ((X $i) (Y $i))
% 0.62/0.75 (let ((a!1 (or (p1 X) (not (p1 (f Y))))))
% 0.62/0.75 (and a!1
% 0.62/0.75 (or (not (r1 Y)) (and (r1 B) (r1 C)))
% 0.62/0.75 (q1 X))))))
% 0.62/0.75 (or (not a!1) a!2))))
% 0.62/0.75 (a!2 (forall ((Z $i)) (q1 (f Z))))
% 0.62/0.75 (a!3 (exists ((X $i) (Y $i))
% 0.62/0.75 (let ((a!1 (or (p1 X) (not (p1 (f Y))))))
% 0.62/0.75 (and a!1 (or (not (r1 Y)) (and (r1 B!1) (r1 C!2))) (q1 X)))))
% 0.62/0.75 (a!5 (lambda ((Z $i)) (refl (~ (q1 (f Z)) (q1 (f Z))))))
% 0.62/0.75 (a!7 (lambda ((X $i) (Y $i))
% 0.62/0.75 (let ((a!1 (or (p1 X) (not (p1 (f Y))))))
% 0.62/0.75 (let ((a!2 (and a!1
% 0.62/0.75 (or (not (r1 Y)) (and (r1 B!1) (r1 C!2)))
% 0.62/0.75 (q1 X))))
% 0.62/0.75 (refl (~ (not a!2) (not a!2)))))))
% 0.62/0.75 (a!8 (forall ((X $i) (Y $i))
% 0.62/0.75 (let ((a!1 (or (p1 X) (not (p1 (f Y))))))
% 0.62/0.75 (let ((a!2 (and a!1
% 0.62/0.75 (or (not (r1 Y)) (and (r1 B!1) (r1 C!2)))
% 0.62/0.75 (q1 X))))
% 0.62/0.75 (not a!2)))))
% 0.62/0.75 (a!11 (forall ((B $i) (C $i))
% 0.62/0.75 (let ((a!1 (forall ((Z $i)) (q1 (f Z))))
% 0.62/0.75 (a!2 (exists ((X $i) (Y $i))
% 0.62/0.75 (let ((a!1 (and (p1 X)
% 0.62/0.75 (or (not (r1 Y)) (and (r1 B) (r1 C))))))
% 0.62/0.75 (let ((a!2 (or (not (p1 (f Y))) a!1)))
% 0.62/0.75 (and a!2 (q1 X)))))))
% 0.62/0.75 (or (not a!1) a!2))))
% 0.62/0.75 (a!12 (exists ((X $i) (Y $i))
% 0.62/0.75 (let ((a!1 (and (p1 X) (or (not (r1 Y)) (and (r1 B!4) (r1 C!3))))))
% 0.62/0.75 (let ((a!2 (or (not (p1 (f Y))) a!1)))
% 0.62/0.75 (and a!2 (q1 X))))))
% 0.62/0.75 (a!14 (forall ((X $i) (Y $i))
% 0.62/0.75 (let ((a!1 (and (p1 X) (or (not (r1 Y)) (and (r1 B!4) (r1 C!3))))))
% 0.62/0.75 (let ((a!2 (or (not (p1 (f Y))) a!1)))
% 0.62/0.75 (not (and a!2 (q1 X)))))))
% 0.62/0.75 (a!17 (forall ((B $i) (C $i))
% 0.62/0.75 (let ((a!1 (exists ((X $i) (Y $i))
% 0.62/0.75 (let ((a!1 (and (p1 X)
% 0.62/0.75 (or (not (r1 Y)) (and (r1 B) (r1 C))))))
% 0.62/0.75 (let ((a!2 (or (not (p1 (f Y))) a!1)))
% 0.62/0.75 (and a!2 (q1 X)))))))
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% 0.62/0.75 (a!45 (~ (not a!40) (not (or (not a!43) a!44))))
% 0.62/0.75 (a!48 (monotonicity (refl (~ (s1 A!11) (s1 A!11)))
% 0.62/0.75 (refl (~ (s1 B!10) (s1 B!10)))
% 0.62/0.75 (refl (~ (r B!10 C!9) (r B!10 C!9)))
% 0.62/0.75 a!46
% 0.62/0.75 a!47
% 0.62/0.75 (~ a!43 a!43)))
% 0.62/0.75 (a!52 (~ (not (or (not a!43) a!44)) (and a!43 a!50)))
% 0.62/0.75 (a!59 (~ (not (or (not a!54) a!56)) a!58))
% 0.62/0.75 (a!67 (~ a!66 (and (and a!54 (q1 Y!14)) a!65)))
% 0.62/0.75 (a!72 (nnf-neg a!71 (~ (not (not a!69)) a!70)))
% 0.62/0.75 (a!83 (nnf-neg a!78 (nnf-neg (proof-bind a!79) (~ (not a!80) a!81)) a!82))
% 0.62/0.75 (a!89 (nnf-neg a!88 (~ (not (not a!85)) a!85)))
% 0.62/0.75 (a!98 (nnf-neg a!55 (nnf-neg (proof-bind a!94) (~ (not a!95) a!96)) a!97))
% 0.62/0.75 (a!103 (nnf-neg a!102 (~ (not (not a!101)) a!101)))
% 0.62/0.75 (a!110 (nnf-neg a!109 (~ (not (not a!106)) a!106)))
% 0.62/0.75 (a!119 (nnf-neg a!118 (~ (not (not a!26)) a!26)))
% 0.62/0.75 (a!131 (~ (not (or a!116 (not a!125) (not a!127))) a!130))
% 0.62/0.75 (a!136 (nnf-neg (trans (sk (~ a!133 a!134)) a!135 (~ a!133 a!134))
% 0.62/0.75 (~ (not (not a!133)) a!134)))
% 0.62/0.75 (a!145 (~ a!144 (and (and (a1 X!23) a!138) a!142)))
% 0.62/0.75 (a!158 (nnf-neg (sk (~ a!151 (a X!28 Y!27)))
% 0.62/0.75 (nnf-neg (proof-bind a!152) (~ (not a!151) a!153))
% 0.62/0.75 (sk (~ a!154 (a X!29 Y!30)))
% 0.62/0.75 (nnf-neg (proof-bind a!155) (~ (not a!154) a!156))
% 0.62/0.75 (~ (not (= a!151 a!154)) a!157)))
% 0.62/0.75 (a!163 (trans (sk (~ (not a!159) a!160))
% 0.62/0.75 (nnf-neg a!55 (refl a!161) (~ a!160 a!162))
% 0.62/0.75 (~ (not a!159) a!162)))
% 0.62/0.75 (a!169 (~ (not (or (not a!54) (and a!54 a!165))) a!168))
% 0.62/0.75 (a!174 (nnf-neg (sk (~ a!170 (p1 X!35)))
% 0.62/0.75 (nnf-neg (proof-bind a!171) (~ (not a!170) a!172))
% 0.62/0.75 (sk (~ a!95 (p1 Y!36)))
% 0.62/0.75 (nnf-neg (proof-bind a!94) (~ (not a!95) a!96))
% 0.62/0.75 a!173))
% 0.62/0.75 (a!180 (nnf-neg a!175
% 0.62/0.75 (nnf-neg (proof-bind a!176) (~ (not a!177) a!178))
% 0.62/0.75 a!179))
% 0.62/0.75 (a!191 (nnf-neg a!187 (sk (~ (not a!188) a!189)) a!190))
% 0.62/0.75 (a!200 (nnf-neg a!199 (~ (not (not a!196)) a!196)))
% 0.62/0.75 (a!201 (monotonicity a!102
% 0.62/0.75 (refl (~ (r1 B!42) (r1 B!42)))
% 0.62/0.75 (~ (and a!101 (r1 B!42)) (and a!101 (r1 B!42)))))
% 0.62/0.75 (a!204 (~ (not a!197) (and (not (q1 B!42)) a!196 (and a!101 (r1 B!42)))))
% 0.62/0.75 (a!225 (nnf-neg a!218
% 0.62/0.75 (trans (sk a!220)
% 0.62/0.75 (nnf-neg (proof-bind a!221) a!223)
% 0.62/0.75 (~ (not a!219) a!222))
% 0.62/0.75 a!224))
% 0.62/0.75 (a!227 (nnf-neg a!175
% 0.62/0.75 (nnf-neg (proof-bind a!94) (~ (not a!95) a!96))
% 0.62/0.75 a!226))
% 0.62/0.75 (a!240 (nnf-neg (monotonicity (refl (~ k!0 k!0))
% 0.62/0.75 (nnf-pos (proof-bind a!238) (~ a!235 a!235))
% 0.62/0.75 (~ (and k!0 a!235) (and k!0 a!235)))
% 0.62/0.75 a!239))
% 0.62/0.75 (a!241 (~ a!236 (and (not (q1 A!48)) (and k!0 a!235))))
% 0.62/0.75 (a!249 (trans (sk (~ (not a!245) a!246)) a!248 (~ (not a!245) a!247)))
% 0.62/0.75 (a!255 (nnf-neg a!254 (~ (not (not a!251)) a!251)))
% 0.62/0.75 (a!262 (~ (not (not (and a!101 a!259))) a!261))
% 0.62/0.75 (a!269 (and a!1
% 0.62/0.75 a!11
% 0.62/0.75 a!17
% 0.62/0.75 a!33
% 0.62/0.75 a!35
% 0.62/0.75 a!40
% 0.62/0.75 (or (not a!54) a!56)
% 0.62/0.75 (or (not (and a!54 a!60)) a!64)
% 0.62/0.75 (or (not a!69) a!64)
% 0.62/0.75 (or (not a!76) a!80)
% 0.62/0.75 a!84
% 0.62/0.75 (or (not a!54) a!95)
% 0.62/0.75 (or a!99 (not a!54) (not a!101))
% 0.62/0.75 a!105
% 0.62/0.75 (or a!116 (not a!26) (not a!120))
% 0.62/0.75 (or a!116 (not a!125) (not a!127))
% 0.62/0.75 (not a!133)
% 0.62/0.75 (or (not (and a!120 a!138)) a!141)
% 0.62/0.75 (or (not a!116) a!147)
% 0.62/0.75 (= a!151 a!154)
% 0.62/0.75 a!159
% 0.62/0.75 (or (not a!54) (and a!54 a!165))
% 0.62/0.75 (= a!170 a!95)
% 0.62/0.75 (or (not a!170) a!177)
% 0.62/0.75 a!182
% 0.62/0.75 (or (not a!185) a!188)
% 0.62/0.75 a!193
% 0.62/0.75 a!195
% 0.62/0.75 a!207
% 0.62/0.75 a!212
% 0.62/0.75 (or (not a!215) a!219)
% 0.62/0.75 (or (not a!170) a!95)
% 0.62/0.75 (or (not a!229) a!231)
% 0.62/0.75 a!234
% 0.62/0.75 (or (not (and a0 b0)) (= a0 b0))
% 0.62/0.75 a!245
% 0.62/0.75 a!250
% 0.62/0.75 (or (not (and a!101 a!259)) a!265)))
% 0.62/0.75 (a!270 (or (and a!2 a!8)
% 0.62/0.75 (and a!2 a!14)
% 0.62/0.75 (and a!20 a!21)
% 0.62/0.75 (and (and a!24 a!27) a!31)
% 0.62/0.75 a!38
% 0.62/0.75 (and a!43 a!50)
% 0.62/0.75 a!58
% 0.62/0.75 (and (and a!54 (q1 Y!14)) a!65)
% 0.62/0.75 (and a!70 a!65)
% 0.62/0.75 (and a!77 a!81)
% 0.62/0.75 (and a!85 a!91)
% 0.62/0.75 (and a!54 a!96)
% 0.62/0.75 (and (not (q1 X!20)) a!54 a!101)
% 0.62/0.75 (and a!106 a!112)
% 0.62/0.75 (and a!117 a!26 (a1 X!23))
% 0.62/0.75 a!130
% 0.62/0.75 a!134
% 0.62/0.75 (and (and (a1 X!23) a!138) a!142)
% 0.62/0.75 (and (b X!26) a!148)
% 0.62/0.75 a!157
% 0.62/0.75 a!162
% 0.62/0.75 a!168
% 0.62/0.75 (and (or (p1 X!35) (p1 Y!36)) (or a!172 a!96))
% 0.62/0.75 (and (p1 X!35) a!178)
% 0.62/0.75 a!183
% 0.62/0.75 (and a!186 a!189)
% 0.62/0.75 a!194
% 0.62/0.75 (and (not (q1 B!42)) a!196 (and a!101 (r1 B!42)))
% 0.62/0.75 a!210
% 0.62/0.75 a!213
% 0.62/0.75 (and a!216 a!222)
% 0.62/0.75 (and (p1 X!35) a!96)
% 0.62/0.75 (and a!229 (not (p X!47 X!47)))
% 0.62/0.75 (and (not (q1 A!48)) (and k!0 a!235))
% 0.62/0.75 a!244
% 0.62/0.75 a!247
% 0.62/0.75 (and a!251 a!256)
% 0.62/0.75 (and a!261 a!266))))
% 0.62/0.75 (let ((a!34 (nnf-neg (nnf-neg a!28 (~ a!29 (and a!24 a!27)))
% 0.62/0.75 a!32
% 0.62/0.75 (~ (not a!33) (and (and a!24 a!27) a!31))))
% 0.62/0.75 (a!49 (nnf-neg a!48 (~ (not (not a!43)) a!43)))
% 0.62/0.75 (a!68 (nnf-neg (nnf-neg a!61 a!62)
% 0.62/0.75 (nnf-neg (proof-bind a!63) (~ (not a!64) a!65))
% 0.62/0.75 a!67))
% 0.62/0.75 (a!74 (nnf-neg a!72 (nnf-neg (proof-bind a!63) (~ (not a!64) a!65)) a!73))
% 0.62/0.75 (a!93 (nnf-neg a!89 (nnf-neg (proof-bind a!90) (~ (not a!86) a!91)) a!92))
% 0.62/0.75 (a!114 (nnf-neg a!110
% 0.62/0.75 (nnf-neg (proof-bind a!111) (~ (not a!107) a!112))
% 0.62/0.75 a!113))
% 0.62/0.75 (a!123 (nnf-neg (nnf-neg (proof-bind a!115) (~ (not a!116) a!117))
% 0.62/0.75 a!119
% 0.62/0.75 a!121
% 0.62/0.75 a!122))
% 0.62/0.75 (a!132 (nnf-neg (nnf-neg (proof-bind a!115) (~ (not a!116) a!117))
% 0.62/0.75 a!126
% 0.62/0.75 (nnf-neg (sk a!128) a!129)
% 0.62/0.75 a!131))
% 0.62/0.75 (a!203 (nnf-neg a!201 (~ a!202 (and a!101 (r1 B!42)))))
% 0.62/0.75 (a!243 (trans (sk (~ (not a!234) a!236))
% 0.62/0.75 (nnf-neg a!237 a!240 a!241)
% 0.62/0.75 a!242))
% 0.62/0.75 (a!263 (nnf-neg (monotonicity a!102
% 0.62/0.75 (sk a!260)
% 0.62/0.75 (~ (and a!101 a!259) a!261))
% 0.62/0.75 a!262)))
% 0.62/0.75 (let ((a!206 (trans (sk (~ (not a!195) (not a!197)))
% 0.62/0.75 (nnf-neg a!198 a!200 a!203 a!204)
% 0.62/0.75 a!205))
% 0.62/0.75 (a!268 (nnf-neg a!263
% 0.62/0.75 (nnf-neg a!264 (~ (not a!265) a!266))
% 0.62/0.75 (~ a!267 (and a!261 a!266)))))
% 0.62/0.75 (nnf-neg (trans (sk a!4) a!10 (~ (not a!1) (and a!2 a!8)))
% 0.62/0.75 (trans (sk a!13)
% 0.62/0.75 (nnf-neg a!6 a!15 a!16)
% 0.62/0.75 (~ (not a!11) (and a!2 a!14)))
% 0.62/0.75 a!23
% 0.62/0.75 a!34
% 0.62/0.75 a!39
% 0.62/0.75 (trans (sk a!45)
% 0.62/0.75 (nnf-neg a!49 a!51 a!52)
% 0.62/0.75 (~ (not a!40) (and a!43 a!50)))
% 0.62/0.75 (nnf-neg a!55 (sk a!57) a!59)
% 0.62/0.75 a!68
% 0.62/0.75 a!74
% 0.62/0.75 a!83
% 0.62/0.75 (trans (sk a!87) a!93 (~ (not a!84) (and a!85 a!91)))
% 0.62/0.75 a!98
% 0.62/0.75 (nnf-neg a!100 a!55 a!103 a!104)
% 0.62/0.75 (trans (sk a!108) a!114 (~ (not a!105) (and a!106 a!112)))
% 0.62/0.75 a!123
% 0.62/0.75 a!132
% 0.62/0.75 a!136
% 0.62/0.75 (nnf-neg (nnf-neg a!139 a!140) a!143 a!145)
% 0.62/0.75 (nnf-neg a!146 a!149 a!150)
% 0.62/0.75 a!158
% 0.62/0.75 a!163
% 0.62/0.75 (nnf-neg a!55 (nnf-neg a!164 a!166 a!167) a!169)
% 0.62/0.75 a!174
% 0.62/0.75 a!180
% 0.62/0.75 (nnf-neg (proof-bind a!181) (~ (not a!182) a!183))
% 0.62/0.75 a!191
% 0.62/0.75 (nnf-neg (proof-bind a!192) (~ (not a!193) a!194))
% 0.62/0.75 a!206
% 0.62/0.75 a!211
% 0.62/0.75 a!214
% 0.62/0.75 a!225
% 0.62/0.75 a!227
% 0.62/0.75 (nnf-neg a!230 a!232 a!233)
% 0.62/0.75 a!243
% 0.62/0.75 (refl (~ a!244 a!244))
% 0.62/0.75 a!249
% 0.62/0.75 (trans (sk a!253)
% 0.62/0.75 (nnf-neg a!255 a!257 a!258)
% 0.62/0.75 (~ (not a!250) (and a!251 a!256)))
% 0.62/0.75 a!268
% 0.62/0.75 (~ (not a!269) a!270)))))))
% 0.62/0.75 Proof display could not be completed: unexpected number of arguments
%------------------------------------------------------------------------------