TSTP Solution File: SYN067+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN067+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 : Thu Sep 29 23:53:30 EDT 2022
% Result : Theorem 4.16s 2.97s
% Output : Proof 4.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN067+1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 01:32:26 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 4.16/2.97 % SZS status Theorem
% 4.16/2.97 % SZS output start Proof
% 4.16/2.97 tff(big_r_type, type, (
% 4.16/2.97 big_r: ( $i * $i ) > $o)).
% 4.16/2.97 tff(tptp_fun_X1_8_type, type, (
% 4.16/2.97 tptp_fun_X1_8: $i)).
% 4.16/2.97 tff(big_p_type, type, (
% 4.16/2.97 big_p: $i > $o)).
% 4.16/2.97 tff(tptp_fun_Z_3_type, type, (
% 4.16/2.97 tptp_fun_Z_3: $i > $i)).
% 4.16/2.97 tff(tptp_fun_W_2_type, type, (
% 4.16/2.97 tptp_fun_W_2: $i > $i)).
% 4.16/2.97 tff(tptp_fun_Y1_9_type, type, (
% 4.16/2.97 tptp_fun_Y1_9: $i)).
% 4.16/2.97 tff(a_type, type, (
% 4.16/2.97 a: $i)).
% 4.16/2.97 tff(tptp_fun_X_0_type, type, (
% 4.16/2.97 tptp_fun_X_0: $i)).
% 4.16/2.97 tff(tptp_fun_Y_1_type, type, (
% 4.16/2.97 tptp_fun_Y_1: $i)).
% 4.16/2.97 tff(tptp_fun_Z2_7_type, type, (
% 4.16/2.97 tptp_fun_Z2_7: $i > $i)).
% 4.16/2.97 tff(tptp_fun_W2_6_type, type, (
% 4.16/2.97 tptp_fun_W2_6: $i > $i)).
% 4.16/2.97 tff(tptp_fun_W1_4_type, type, (
% 4.16/2.97 tptp_fun_W1_4: $i > $i)).
% 4.16/2.97 tff(tptp_fun_Z1_5_type, type, (
% 4.16/2.97 tptp_fun_Z1_5: $i > $i)).
% 4.16/2.97 tff(1,assumption,(~((~big_p(tptp_fun_Z_3(X1!8))) | (~big_r(X1!8, tptp_fun_W_2(X1!8))) | (~big_r(tptp_fun_W_2(X1!8), tptp_fun_Z_3(X1!8))))), introduced(assumption)).
% 4.16/2.97 tff(2,plain,
% 4.16/2.97 (((~big_p(tptp_fun_Z_3(X1!8))) | (~big_r(X1!8, tptp_fun_W_2(X1!8))) | (~big_r(tptp_fun_W_2(X1!8), tptp_fun_Z_3(X1!8)))) | big_r(tptp_fun_W_2(X1!8), tptp_fun_Z_3(X1!8))),
% 4.16/2.97 inference(tautology,[status(thm)],[])).
% 4.16/2.97 tff(3,plain,
% 4.16/2.97 (big_r(tptp_fun_W_2(X1!8), tptp_fun_Z_3(X1!8))),
% 4.16/2.97 inference(unit_resolution,[status(thm)],[2, 1])).
% 4.16/2.97 tff(4,plain,
% 4.16/2.97 (((~big_p(tptp_fun_Z_3(X1!8))) | (~big_r(X1!8, tptp_fun_W_2(X1!8))) | (~big_r(tptp_fun_W_2(X1!8), tptp_fun_Z_3(X1!8)))) | big_r(X1!8, tptp_fun_W_2(X1!8))),
% 4.16/2.97 inference(tautology,[status(thm)],[])).
% 4.16/2.97 tff(5,plain,
% 4.16/2.97 (big_r(X1!8, tptp_fun_W_2(X1!8))),
% 4.16/2.97 inference(unit_resolution,[status(thm)],[4, 1])).
% 4.16/2.97 tff(6,plain,
% 4.16/2.97 (((~big_p(tptp_fun_Z_3(X1!8))) | (~big_r(X1!8, tptp_fun_W_2(X1!8))) | (~big_r(tptp_fun_W_2(X1!8), tptp_fun_Z_3(X1!8)))) | big_p(tptp_fun_Z_3(X1!8))),
% 4.16/2.97 inference(tautology,[status(thm)],[])).
% 4.16/2.97 tff(7,plain,
% 4.16/2.97 (big_p(tptp_fun_Z_3(X1!8))),
% 4.16/2.97 inference(unit_resolution,[status(thm)],[6, 1])).
% 4.16/2.97 tff(8,assumption,(![X1: $i] : (~((~((~big_p(a)) | big_p(X1) | (~((~big_r(tptp_fun_W1_4(X1), tptp_fun_Z1_5(X1))) | (~big_p(tptp_fun_Z1_5(X1))) | (~big_r(X1, tptp_fun_W1_4(X1))))))) | (~((~big_p(a)) | (~((~big_p(tptp_fun_Z2_7(X1))) | (~big_r(X1, tptp_fun_W2_6(X1))) | (~big_r(tptp_fun_W2_6(X1), tptp_fun_Z2_7(X1))))) | ![Y1: $i] : ((~big_p(Y1)) | (~big_r(X1, Y1)))))))), introduced(assumption)).
% 4.16/2.97 tff(9,plain,
% 4.16/2.97 ((~![X1: $i] : (~((~((~big_p(a)) | big_p(X1) | (~((~big_r(tptp_fun_W1_4(X1), tptp_fun_Z1_5(X1))) | (~big_p(tptp_fun_Z1_5(X1))) | (~big_r(X1, tptp_fun_W1_4(X1))))))) | (~((~big_p(a)) | (~((~big_p(tptp_fun_Z2_7(X1))) | (~big_r(X1, tptp_fun_W2_6(X1))) | (~big_r(tptp_fun_W2_6(X1), tptp_fun_Z2_7(X1))))) | ![Y1: $i] : ((~big_p(Y1)) | (~big_r(X1, Y1)))))))) | (~((~((~big_p(a)) | big_p(X!0) | (~((~big_r(tptp_fun_W1_4(X!0), tptp_fun_Z1_5(X!0))) | (~big_p(tptp_fun_Z1_5(X!0))) | (~big_r(X!0, tptp_fun_W1_4(X!0))))))) | (~((~big_p(a)) | (~((~big_p(tptp_fun_Z2_7(X!0))) | (~big_r(X!0, tptp_fun_W2_6(X!0))) | (~big_r(tptp_fun_W2_6(X!0), tptp_fun_Z2_7(X!0))))) | ![Y1: $i] : ((~big_p(Y1)) | (~big_r(X!0, Y1)))))))),
% 4.16/2.97 inference(quant_inst,[status(thm)],[])).
% 4.16/2.97 tff(10,plain,
% 4.16/2.97 (~((~((~big_p(a)) | big_p(X!0) | (~((~big_r(tptp_fun_W1_4(X!0), tptp_fun_Z1_5(X!0))) | (~big_p(tptp_fun_Z1_5(X!0))) | (~big_r(X!0, tptp_fun_W1_4(X!0))))))) | (~((~big_p(a)) | (~((~big_p(tptp_fun_Z2_7(X!0))) | (~big_r(X!0, tptp_fun_W2_6(X!0))) | (~big_r(tptp_fun_W2_6(X!0), tptp_fun_Z2_7(X!0))))) | ![Y1: $i] : ((~big_p(Y1)) | (~big_r(X!0, Y1))))))),
% 4.16/2.97 inference(unit_resolution,[status(thm)],[9, 8])).
% 4.16/2.97 tff(11,plain,
% 4.16/2.97 (((~((~big_p(a)) | big_p(X!0) | (~((~big_r(tptp_fun_W1_4(X!0), tptp_fun_Z1_5(X!0))) | (~big_p(tptp_fun_Z1_5(X!0))) | (~big_r(X!0, tptp_fun_W1_4(X!0))))))) | (~((~big_p(a)) | (~((~big_p(tptp_fun_Z2_7(X!0))) | (~big_r(X!0, tptp_fun_W2_6(X!0))) | (~big_r(tptp_fun_W2_6(X!0), tptp_fun_Z2_7(X!0))))) | ![Y1: $i] : ((~big_p(Y1)) | (~big_r(X!0, Y1)))))) | ((~big_p(a)) | (~((~big_p(tptp_fun_Z2_7(X!0))) | (~big_r(X!0, tptp_fun_W2_6(X!0))) | (~big_r(tptp_fun_W2_6(X!0), tptp_fun_Z2_7(X!0))))) | ![Y1: $i] : ((~big_p(Y1)) | (~big_r(X!0, Y1))))),
% 4.16/2.97 inference(tautology,[status(thm)],[])).
% 4.16/2.97 tff(12,plain,
% 4.16/2.97 ((~big_p(a)) | (~((~big_p(tptp_fun_Z2_7(X!0))) | (~big_r(X!0, tptp_fun_W2_6(X!0))) | (~big_r(tptp_fun_W2_6(X!0), tptp_fun_Z2_7(X!0))))) | ![Y1: $i] : ((~big_p(Y1)) | (~big_r(X!0, Y1)))),
% 4.16/2.97 inference(unit_resolution,[status(thm)],[11, 10])).
% 4.16/2.97 tff(13,plain,
% 4.16/2.97 ((~![X1: $i] : (~((~((~big_p(a)) | big_p(X1) | (~((~big_r(tptp_fun_W1_4(X1), tptp_fun_Z1_5(X1))) | (~big_p(tptp_fun_Z1_5(X1))) | (~big_r(X1, tptp_fun_W1_4(X1))))))) | (~((~big_p(a)) | (~((~big_p(tptp_fun_Z2_7(X1))) | (~big_r(X1, tptp_fun_W2_6(X1))) | (~big_r(tptp_fun_W2_6(X1), tptp_fun_Z2_7(X1))))) | ![Y1: $i] : ((~big_p(Y1)) | (~big_r(X1, Y1)))))))) | (~((~((~big_p(a)) | big_p(X1!8) | (~((~big_r(tptp_fun_W1_4(X1!8), tptp_fun_Z1_5(X1!8))) | (~big_p(tptp_fun_Z1_5(X1!8))) | (~big_r(X1!8, tptp_fun_W1_4(X1!8))))))) | (~((~big_p(a)) | (~((~big_p(tptp_fun_Z2_7(X1!8))) | (~big_r(X1!8, tptp_fun_W2_6(X1!8))) | (~big_r(tptp_fun_W2_6(X1!8), tptp_fun_Z2_7(X1!8))))) | ![Y1: $i] : ((~big_p(Y1)) | (~big_r(X1!8, Y1)))))))),
% 4.16/2.97 inference(quant_inst,[status(thm)],[])).
% 4.16/2.97 tff(14,plain,
% 4.16/2.97 (~((~((~big_p(a)) | big_p(X1!8) | (~((~big_r(tptp_fun_W1_4(X1!8), tptp_fun_Z1_5(X1!8))) | (~big_p(tptp_fun_Z1_5(X1!8))) | (~big_r(X1!8, tptp_fun_W1_4(X1!8))))))) | (~((~big_p(a)) | (~((~big_p(tptp_fun_Z2_7(X1!8))) | (~big_r(X1!8, tptp_fun_W2_6(X1!8))) | (~big_r(tptp_fun_W2_6(X1!8), tptp_fun_Z2_7(X1!8))))) | ![Y1: $i] : ((~big_p(Y1)) | (~big_r(X1!8, Y1))))))),
% 4.16/2.97 inference(unit_resolution,[status(thm)],[13, 8])).
% 4.16/2.97 tff(15,plain,
% 4.16/2.97 (((~((~big_p(a)) | big_p(X1!8) | (~((~big_r(tptp_fun_W1_4(X1!8), tptp_fun_Z1_5(X1!8))) | (~big_p(tptp_fun_Z1_5(X1!8))) | (~big_r(X1!8, tptp_fun_W1_4(X1!8))))))) | (~((~big_p(a)) | (~((~big_p(tptp_fun_Z2_7(X1!8))) | (~big_r(X1!8, tptp_fun_W2_6(X1!8))) | (~big_r(tptp_fun_W2_6(X1!8), tptp_fun_Z2_7(X1!8))))) | ![Y1: $i] : ((~big_p(Y1)) | (~big_r(X1!8, Y1)))))) | ((~big_p(a)) | (~((~big_p(tptp_fun_Z2_7(X1!8))) | (~big_r(X1!8, tptp_fun_W2_6(X1!8))) | (~big_r(tptp_fun_W2_6(X1!8), tptp_fun_Z2_7(X1!8))))) | ![Y1: $i] : ((~big_p(Y1)) | (~big_r(X1!8, Y1))))),
% 4.16/2.97 inference(tautology,[status(thm)],[])).
% 4.16/2.97 tff(16,plain,
% 4.16/2.97 ((~big_p(a)) | (~((~big_p(tptp_fun_Z2_7(X1!8))) | (~big_r(X1!8, tptp_fun_W2_6(X1!8))) | (~big_r(tptp_fun_W2_6(X1!8), tptp_fun_Z2_7(X1!8))))) | ![Y1: $i] : ((~big_p(Y1)) | (~big_r(X1!8, Y1)))),
% 4.16/2.97 inference(unit_resolution,[status(thm)],[15, 14])).
% 4.16/2.97 tff(17,assumption,((~big_p(a)) | (~((~big_p(tptp_fun_Z2_7(X1!8))) | (~big_r(X1!8, tptp_fun_W2_6(X1!8))) | (~big_r(tptp_fun_W2_6(X1!8), tptp_fun_Z2_7(X1!8))))) | ![Y1: $i] : ((~big_p(Y1)) | (~big_r(X1!8, Y1)))), introduced(assumption)).
% 4.16/2.97 tff(18,assumption,(~((~big_p(a)) | (~big_p(Y1!9)) | (~big_r(X1!8, Y1!9)) | (~![Z2: $i, W2: $i] : ((~big_p(Z2)) | (~big_r(X1!8, W2)) | (~big_r(W2, Z2)))))), introduced(assumption)).
% 4.16/2.97 tff(19,plain,
% 4.16/2.97 (((~big_p(a)) | (~big_p(Y1!9)) | (~big_r(X1!8, Y1!9)) | (~![Z2: $i, W2: $i] : ((~big_p(Z2)) | (~big_r(X1!8, W2)) | (~big_r(W2, Z2))))) | ![Z2: $i, W2: $i] : ((~big_p(Z2)) | (~big_r(X1!8, W2)) | (~big_r(W2, Z2)))),
% 4.16/2.97 inference(tautology,[status(thm)],[])).
% 4.16/2.97 tff(20,plain,
% 4.16/2.97 (![Z2: $i, W2: $i] : ((~big_p(Z2)) | (~big_r(X1!8, W2)) | (~big_r(W2, Z2)))),
% 4.16/2.97 inference(unit_resolution,[status(thm)],[19, 18])).
% 4.16/2.97 tff(21,assumption,(~((~big_p(tptp_fun_Z2_7(X1!8))) | (~big_r(X1!8, tptp_fun_W2_6(X1!8))) | (~big_r(tptp_fun_W2_6(X1!8), tptp_fun_Z2_7(X1!8))))), introduced(assumption)).
% 4.16/2.97 tff(22,plain,
% 4.16/2.97 (((~big_p(tptp_fun_Z2_7(X1!8))) | (~big_r(X1!8, tptp_fun_W2_6(X1!8))) | (~big_r(tptp_fun_W2_6(X1!8), tptp_fun_Z2_7(X1!8)))) | big_r(tptp_fun_W2_6(X1!8), tptp_fun_Z2_7(X1!8))),
% 4.16/2.97 inference(tautology,[status(thm)],[])).
% 4.16/2.97 tff(23,plain,
% 4.16/2.97 (big_r(tptp_fun_W2_6(X1!8), tptp_fun_Z2_7(X1!8))),
% 4.16/2.97 inference(unit_resolution,[status(thm)],[22, 21])).
% 4.16/2.97 tff(24,plain,
% 4.16/2.97 (((~big_p(tptp_fun_Z2_7(X1!8))) | (~big_r(X1!8, tptp_fun_W2_6(X1!8))) | (~big_r(tptp_fun_W2_6(X1!8), tptp_fun_Z2_7(X1!8)))) | big_r(X1!8, tptp_fun_W2_6(X1!8))),
% 4.16/2.97 inference(tautology,[status(thm)],[])).
% 4.16/2.97 tff(25,plain,
% 4.16/2.97 (big_r(X1!8, tptp_fun_W2_6(X1!8))),
% 4.16/2.97 inference(unit_resolution,[status(thm)],[24, 21])).
% 4.16/2.97 tff(26,plain,
% 4.16/2.97 (((~big_p(tptp_fun_Z2_7(X1!8))) | (~big_r(X1!8, tptp_fun_W2_6(X1!8))) | (~big_r(tptp_fun_W2_6(X1!8), tptp_fun_Z2_7(X1!8)))) | big_p(tptp_fun_Z2_7(X1!8))),
% 4.16/2.97 inference(tautology,[status(thm)],[])).
% 4.16/2.97 tff(27,plain,
% 4.16/2.97 (big_p(tptp_fun_Z2_7(X1!8))),
% 4.16/2.97 inference(unit_resolution,[status(thm)],[26, 21])).
% 4.16/2.97 tff(28,assumption,(![Z2: $i, W2: $i] : ((~big_p(Z2)) | (~big_r(X1!8, W2)) | (~big_r(W2, Z2)))), introduced(assumption)).
% 4.16/2.97 tff(29,plain,
% 4.16/2.97 (((~![Z2: $i, W2: $i] : ((~big_p(Z2)) | (~big_r(X1!8, W2)) | (~big_r(W2, Z2)))) | ((~big_p(tptp_fun_Z2_7(X1!8))) | (~big_r(X1!8, tptp_fun_W2_6(X1!8))) | (~big_r(tptp_fun_W2_6(X1!8), tptp_fun_Z2_7(X1!8))))) <=> ((~![Z2: $i, W2: $i] : ((~big_p(Z2)) | (~big_r(X1!8, W2)) | (~big_r(W2, Z2)))) | (~big_p(tptp_fun_Z2_7(X1!8))) | (~big_r(X1!8, tptp_fun_W2_6(X1!8))) | (~big_r(tptp_fun_W2_6(X1!8), tptp_fun_Z2_7(X1!8))))),
% 4.16/2.97 inference(rewrite,[status(thm)],[])).
% 4.16/2.97 tff(30,plain,
% 4.16/2.97 ((~![Z2: $i, W2: $i] : ((~big_p(Z2)) | (~big_r(X1!8, W2)) | (~big_r(W2, Z2)))) | ((~big_p(tptp_fun_Z2_7(X1!8))) | (~big_r(X1!8, tptp_fun_W2_6(X1!8))) | (~big_r(tptp_fun_W2_6(X1!8), tptp_fun_Z2_7(X1!8))))),
% 4.16/2.97 inference(quant_inst,[status(thm)],[])).
% 4.16/2.97 tff(31,plain,
% 4.16/2.97 ((~![Z2: $i, W2: $i] : ((~big_p(Z2)) | (~big_r(X1!8, W2)) | (~big_r(W2, Z2)))) | (~big_p(tptp_fun_Z2_7(X1!8))) | (~big_r(X1!8, tptp_fun_W2_6(X1!8))) | (~big_r(tptp_fun_W2_6(X1!8), tptp_fun_Z2_7(X1!8)))),
% 4.16/2.97 inference(modus_ponens,[status(thm)],[30, 29])).
% 4.16/2.97 tff(32,plain,
% 4.16/2.97 ($false),
% 4.16/2.97 inference(unit_resolution,[status(thm)],[31, 28, 27, 25, 23])).
% 4.16/2.97 tff(33,plain,(((~big_p(tptp_fun_Z2_7(X1!8))) | (~big_r(X1!8, tptp_fun_W2_6(X1!8))) | (~big_r(tptp_fun_W2_6(X1!8), tptp_fun_Z2_7(X1!8)))) | (~![Z2: $i, W2: $i] : ((~big_p(Z2)) | (~big_r(X1!8, W2)) | (~big_r(W2, Z2))))), inference(lemma,lemma(discharge,[]))).
% 4.16/2.97 tff(34,plain,
% 4.16/2.97 ((~big_p(tptp_fun_Z2_7(X1!8))) | (~big_r(X1!8, tptp_fun_W2_6(X1!8))) | (~big_r(tptp_fun_W2_6(X1!8), tptp_fun_Z2_7(X1!8)))),
% 4.16/2.97 inference(unit_resolution,[status(thm)],[33, 20])).
% 4.16/2.97 tff(35,assumption,(~big_p(a)), introduced(assumption)).
% 4.16/2.97 tff(36,plain,
% 4.16/2.97 (((~big_p(a)) | (~((~big_p(X!0)) | (~((~big_p(Y!1)) | (~big_r(X!0, Y!1)))))) | (~![Z: $i, W: $i] : ((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z))))) | big_p(a)),
% 4.16/2.97 inference(tautology,[status(thm)],[])).
% 4.16/2.97 tff(37,plain,
% 4.16/2.97 ((~big_p(a)) | (~((~big_p(X!0)) | (~((~big_p(Y!1)) | (~big_r(X!0, Y!1)))))) | (~![Z: $i, W: $i] : ((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z))))),
% 4.16/2.97 inference(unit_resolution,[status(thm)],[36, 35])).
% 4.16/2.97 tff(38,plain,
% 4.16/2.97 (((~big_p(a)) | (~big_p(Y1!9)) | (~big_r(X1!8, Y1!9)) | (~![Z2: $i, W2: $i] : ((~big_p(Z2)) | (~big_r(X1!8, W2)) | (~big_r(W2, Z2))))) | big_p(a)),
% 4.16/2.97 inference(tautology,[status(thm)],[])).
% 4.16/2.97 tff(39,plain,
% 4.16/2.97 ((~big_p(a)) | (~big_p(Y1!9)) | (~big_r(X1!8, Y1!9)) | (~![Z2: $i, W2: $i] : ((~big_p(Z2)) | (~big_r(X1!8, W2)) | (~big_r(W2, Z2))))),
% 4.16/2.97 inference(unit_resolution,[status(thm)],[38, 35])).
% 4.16/2.97 tff(40,assumption,(~((~big_p(a)) | big_p(X1!8) | (~![Z1: $i, W1: $i] : ((~big_p(Z1)) | (~big_r(X1!8, W1)) | (~big_r(W1, Z1)))))), introduced(assumption)).
% 4.16/2.97 tff(41,plain,
% 4.16/2.97 (((~big_p(a)) | big_p(X1!8) | (~![Z1: $i, W1: $i] : ((~big_p(Z1)) | (~big_r(X1!8, W1)) | (~big_r(W1, Z1))))) | (~big_p(X1!8))),
% 4.16/2.97 inference(tautology,[status(thm)],[])).
% 4.16/2.97 tff(42,plain,
% 4.16/2.97 (~big_p(X1!8)),
% 4.16/2.97 inference(unit_resolution,[status(thm)],[41, 40])).
% 4.16/2.97 tff(43,plain,
% 4.16/2.97 (((~big_p(a)) | big_p(X1!8) | (~![Z1: $i, W1: $i] : ((~big_p(Z1)) | (~big_r(X1!8, W1)) | (~big_r(W1, Z1))))) | ![Z1: $i, W1: $i] : ((~big_p(Z1)) | (~big_r(X1!8, W1)) | (~big_r(W1, Z1)))),
% 4.16/2.97 inference(tautology,[status(thm)],[])).
% 4.16/2.97 tff(44,plain,
% 4.16/2.97 (![Z1: $i, W1: $i] : ((~big_p(Z1)) | (~big_r(X1!8, W1)) | (~big_r(W1, Z1)))),
% 4.16/2.97 inference(unit_resolution,[status(thm)],[43, 40])).
% 4.16/2.97 tff(45,assumption,(![Z1: $i, W1: $i] : ((~big_p(Z1)) | (~big_r(X1!8, W1)) | (~big_r(W1, Z1)))), introduced(assumption)).
% 4.16/2.97 tff(46,plain,
% 4.16/2.97 (((~![Z1: $i, W1: $i] : ((~big_p(Z1)) | (~big_r(X1!8, W1)) | (~big_r(W1, Z1)))) | ((~big_p(tptp_fun_Z_3(X1!8))) | (~big_r(X1!8, tptp_fun_W_2(X1!8))) | (~big_r(tptp_fun_W_2(X1!8), tptp_fun_Z_3(X1!8))))) <=> ((~![Z1: $i, W1: $i] : ((~big_p(Z1)) | (~big_r(X1!8, W1)) | (~big_r(W1, Z1)))) | (~big_p(tptp_fun_Z_3(X1!8))) | (~big_r(X1!8, tptp_fun_W_2(X1!8))) | (~big_r(tptp_fun_W_2(X1!8), tptp_fun_Z_3(X1!8))))),
% 4.16/2.97 inference(rewrite,[status(thm)],[])).
% 4.16/2.97 tff(47,plain,
% 4.16/2.97 ((~![Z1: $i, W1: $i] : ((~big_p(Z1)) | (~big_r(X1!8, W1)) | (~big_r(W1, Z1)))) | ((~big_p(tptp_fun_Z_3(X1!8))) | (~big_r(X1!8, tptp_fun_W_2(X1!8))) | (~big_r(tptp_fun_W_2(X1!8), tptp_fun_Z_3(X1!8))))),
% 4.16/2.97 inference(quant_inst,[status(thm)],[])).
% 4.16/2.97 tff(48,plain,
% 4.16/2.97 ((~![Z1: $i, W1: $i] : ((~big_p(Z1)) | (~big_r(X1!8, W1)) | (~big_r(W1, Z1)))) | (~big_p(tptp_fun_Z_3(X1!8))) | (~big_r(X1!8, tptp_fun_W_2(X1!8))) | (~big_r(tptp_fun_W_2(X1!8), tptp_fun_Z_3(X1!8)))),
% 4.16/2.97 inference(modus_ponens,[status(thm)],[47, 46])).
% 4.16/2.97 tff(49,plain,
% 4.16/2.97 ($false),
% 4.16/2.97 inference(unit_resolution,[status(thm)],[48, 45, 7, 5, 3])).
% 4.16/2.97 tff(50,plain,(((~big_p(tptp_fun_Z_3(X1!8))) | (~big_r(X1!8, tptp_fun_W_2(X1!8))) | (~big_r(tptp_fun_W_2(X1!8), tptp_fun_Z_3(X1!8)))) | (~![Z1: $i, W1: $i] : ((~big_p(Z1)) | (~big_r(X1!8, W1)) | (~big_r(W1, Z1))))), inference(lemma,lemma(discharge,[]))).
% 4.16/2.97 tff(51,plain,
% 4.16/2.97 ((~big_p(tptp_fun_Z_3(X1!8))) | (~big_r(X1!8, tptp_fun_W_2(X1!8))) | (~big_r(tptp_fun_W_2(X1!8), tptp_fun_Z_3(X1!8)))),
% 4.16/2.97 inference(unit_resolution,[status(thm)],[50, 44])).
% 4.16/2.97 tff(52,plain,
% 4.16/2.97 (((~big_p(a)) | big_p(X1!8) | (~![Z1: $i, W1: $i] : ((~big_p(Z1)) | (~big_r(X1!8, W1)) | (~big_r(W1, Z1))))) | big_p(a)),
% 4.16/2.97 inference(tautology,[status(thm)],[])).
% 4.16/2.97 tff(53,plain,
% 4.16/2.97 (big_p(a)),
% 4.16/2.97 inference(unit_resolution,[status(thm)],[52, 40])).
% 4.16/2.97 tff(54,assumption,(~big_p(X1!8)), introduced(assumption)).
% 4.16/2.97 tff(55,plain,
% 4.16/2.97 (((~big_p(X1!8)) | (~![Y: $i] : ((~big_p(Y)) | (~big_r(X1!8, Y))))) | big_p(X1!8)),
% 4.16/2.97 inference(tautology,[status(thm)],[])).
% 4.16/2.97 tff(56,plain,
% 4.16/2.97 ((~big_p(X1!8)) | (~![Y: $i] : ((~big_p(Y)) | (~big_r(X1!8, Y))))),
% 4.16/2.97 inference(unit_resolution,[status(thm)],[55, 54])).
% 4.16/2.97 tff(57,assumption,((~big_p(tptp_fun_Z_3(X1!8))) | (~big_r(X1!8, tptp_fun_W_2(X1!8))) | (~big_r(tptp_fun_W_2(X1!8), tptp_fun_Z_3(X1!8)))), introduced(assumption)).
% 4.16/2.97 tff(58,assumption,(big_p(a)), introduced(assumption)).
% 4.16/2.97 tff(59,assumption,(![X: $i] : ((~big_p(a)) | (~((~big_p(tptp_fun_Z_3(X))) | (~big_r(X, tptp_fun_W_2(X))) | (~big_r(tptp_fun_W_2(X), tptp_fun_Z_3(X))))) | (~((~big_p(X)) | (~![Y: $i] : ((~big_p(Y)) | (~big_r(X, Y)))))))), introduced(assumption)).
% 4.16/2.97 tff(60,plain,
% 4.16/2.97 (((~![X: $i] : ((~big_p(a)) | (~((~big_p(tptp_fun_Z_3(X))) | (~big_r(X, tptp_fun_W_2(X))) | (~big_r(tptp_fun_W_2(X), tptp_fun_Z_3(X))))) | (~((~big_p(X)) | (~![Y: $i] : ((~big_p(Y)) | (~big_r(X, Y)))))))) | ((~big_p(a)) | (~((~big_p(tptp_fun_Z_3(X1!8))) | (~big_r(X1!8, tptp_fun_W_2(X1!8))) | (~big_r(tptp_fun_W_2(X1!8), tptp_fun_Z_3(X1!8))))) | (~((~big_p(X1!8)) | (~![Y: $i] : ((~big_p(Y)) | (~big_r(X1!8, Y)))))))) <=> ((~![X: $i] : ((~big_p(a)) | (~((~big_p(tptp_fun_Z_3(X))) | (~big_r(X, tptp_fun_W_2(X))) | (~big_r(tptp_fun_W_2(X), tptp_fun_Z_3(X))))) | (~((~big_p(X)) | (~![Y: $i] : ((~big_p(Y)) | (~big_r(X, Y)))))))) | (~big_p(a)) | (~((~big_p(tptp_fun_Z_3(X1!8))) | (~big_r(X1!8, tptp_fun_W_2(X1!8))) | (~big_r(tptp_fun_W_2(X1!8), tptp_fun_Z_3(X1!8))))) | (~((~big_p(X1!8)) | (~![Y: $i] : ((~big_p(Y)) | (~big_r(X1!8, Y)))))))),
% 4.16/2.97 inference(rewrite,[status(thm)],[])).
% 4.16/2.97 tff(61,plain,
% 4.16/2.97 ((~![X: $i] : ((~big_p(a)) | (~((~big_p(tptp_fun_Z_3(X))) | (~big_r(X, tptp_fun_W_2(X))) | (~big_r(tptp_fun_W_2(X), tptp_fun_Z_3(X))))) | (~((~big_p(X)) | (~![Y: $i] : ((~big_p(Y)) | (~big_r(X, Y)))))))) | ((~big_p(a)) | (~((~big_p(tptp_fun_Z_3(X1!8))) | (~big_r(X1!8, tptp_fun_W_2(X1!8))) | (~big_r(tptp_fun_W_2(X1!8), tptp_fun_Z_3(X1!8))))) | (~((~big_p(X1!8)) | (~![Y: $i] : ((~big_p(Y)) | (~big_r(X1!8, Y)))))))),
% 4.16/2.97 inference(quant_inst,[status(thm)],[])).
% 4.16/2.97 tff(62,plain,
% 4.16/2.97 ((~![X: $i] : ((~big_p(a)) | (~((~big_p(tptp_fun_Z_3(X))) | (~big_r(X, tptp_fun_W_2(X))) | (~big_r(tptp_fun_W_2(X), tptp_fun_Z_3(X))))) | (~((~big_p(X)) | (~![Y: $i] : ((~big_p(Y)) | (~big_r(X, Y)))))))) | (~big_p(a)) | (~((~big_p(tptp_fun_Z_3(X1!8))) | (~big_r(X1!8, tptp_fun_W_2(X1!8))) | (~big_r(tptp_fun_W_2(X1!8), tptp_fun_Z_3(X1!8))))) | (~((~big_p(X1!8)) | (~![Y: $i] : ((~big_p(Y)) | (~big_r(X1!8, Y))))))),
% 4.16/2.97 inference(modus_ponens,[status(thm)],[61, 60])).
% 4.16/2.97 tff(63,plain,
% 4.16/2.97 ($false),
% 4.16/2.97 inference(unit_resolution,[status(thm)],[62, 59, 58, 57, 56])).
% 4.16/2.97 tff(64,plain,((~![X: $i] : ((~big_p(a)) | (~((~big_p(tptp_fun_Z_3(X))) | (~big_r(X, tptp_fun_W_2(X))) | (~big_r(tptp_fun_W_2(X), tptp_fun_Z_3(X))))) | (~((~big_p(X)) | (~![Y: $i] : ((~big_p(Y)) | (~big_r(X, Y)))))))) | (~big_p(a)) | (~((~big_p(tptp_fun_Z_3(X1!8))) | (~big_r(X1!8, tptp_fun_W_2(X1!8))) | (~big_r(tptp_fun_W_2(X1!8), tptp_fun_Z_3(X1!8))))) | big_p(X1!8)), inference(lemma,lemma(discharge,[]))).
% 4.16/2.97 tff(65,plain,
% 4.16/2.97 (~![X: $i] : ((~big_p(a)) | (~((~big_p(tptp_fun_Z_3(X))) | (~big_r(X, tptp_fun_W_2(X))) | (~big_r(tptp_fun_W_2(X), tptp_fun_Z_3(X))))) | (~((~big_p(X)) | (~![Y: $i] : ((~big_p(Y)) | (~big_r(X, Y)))))))),
% 4.16/2.97 inference(unit_resolution,[status(thm)],[64, 53, 51, 42])).
% 4.16/2.97 tff(66,plain,
% 4.16/2.97 ((![X: $i] : ((~big_p(a)) | (~((~big_p(tptp_fun_Z_3(X))) | (~big_r(X, tptp_fun_W_2(X))) | (~big_r(tptp_fun_W_2(X), tptp_fun_Z_3(X))))) | (~((~big_p(X)) | (~![Y: $i] : ((~big_p(Y)) | (~big_r(X, Y))))))) | ![X1: $i] : (~((~((~big_p(a)) | big_p(X1) | (~((~big_r(tptp_fun_W1_4(X1), tptp_fun_Z1_5(X1))) | (~big_p(tptp_fun_Z1_5(X1))) | (~big_r(X1, tptp_fun_W1_4(X1))))))) | (~((~big_p(a)) | ![Y1: $i] : ((~big_p(Y1)) | (~big_r(X1, Y1))) | (~((~big_p(tptp_fun_Z2_7(X1))) | (~big_r(X1, tptp_fun_W2_6(X1))) | (~big_r(tptp_fun_W2_6(X1), tptp_fun_Z2_7(X1)))))))))) <=> (![X: $i] : ((~big_p(a)) | (~((~big_p(tptp_fun_Z_3(X))) | (~big_r(X, tptp_fun_W_2(X))) | (~big_r(tptp_fun_W_2(X), tptp_fun_Z_3(X))))) | (~((~big_p(X)) | (~![Y: $i] : ((~big_p(Y)) | (~big_r(X, Y))))))) | ![X1: $i] : (~((~((~big_p(a)) | big_p(X1) | (~((~big_r(tptp_fun_W1_4(X1), tptp_fun_Z1_5(X1))) | (~big_p(tptp_fun_Z1_5(X1))) | (~big_r(X1, tptp_fun_W1_4(X1))))))) | (~((~big_p(a)) | (~((~big_p(tptp_fun_Z2_7(X1))) | (~big_r(X1, tptp_fun_W2_6(X1))) | (~big_r(tptp_fun_W2_6(X1), tptp_fun_Z2_7(X1))))) | ![Y1: $i] : ((~big_p(Y1)) | (~big_r(X1, Y1))))))))),
% 4.16/2.97 inference(rewrite,[status(thm)],[])).
% 4.16/2.97 tff(67,plain,
% 4.16/2.97 ((![X: $i] : ((~big_p(a)) | (~((~big_p(tptp_fun_Z_3(X))) | (~big_r(X, tptp_fun_W_2(X))) | (~big_r(tptp_fun_W_2(X), tptp_fun_Z_3(X))))) | (~((~big_p(X)) | (~![Y: $i] : ((~big_p(Y)) | (~big_r(X, Y))))))) | ![X1: $i] : (~((~((~big_p(a)) | big_p(X1) | (~((~big_r(tptp_fun_W1_4(X1), tptp_fun_Z1_5(X1))) | (~big_p(tptp_fun_Z1_5(X1))) | (~big_r(X1, tptp_fun_W1_4(X1))))))) | (~((~big_p(a)) | ![Y1: $i] : ((~big_p(Y1)) | (~big_r(X1, Y1))) | (~((~big_p(tptp_fun_Z2_7(X1))) | (~big_r(X1, tptp_fun_W2_6(X1))) | (~big_r(tptp_fun_W2_6(X1), tptp_fun_Z2_7(X1)))))))))) <=> (![X: $i] : ((~big_p(a)) | (~((~big_p(tptp_fun_Z_3(X))) | (~big_r(X, tptp_fun_W_2(X))) | (~big_r(tptp_fun_W_2(X), tptp_fun_Z_3(X))))) | (~((~big_p(X)) | (~![Y: $i] : ((~big_p(Y)) | (~big_r(X, Y))))))) | ![X1: $i] : (~((~((~big_p(a)) | big_p(X1) | (~((~big_r(tptp_fun_W1_4(X1), tptp_fun_Z1_5(X1))) | (~big_p(tptp_fun_Z1_5(X1))) | (~big_r(X1, tptp_fun_W1_4(X1))))))) | (~((~big_p(a)) | ![Y1: $i] : ((~big_p(Y1)) | (~big_r(X1, Y1))) | (~((~big_p(tptp_fun_Z2_7(X1))) | (~big_r(X1, tptp_fun_W2_6(X1))) | (~big_r(tptp_fun_W2_6(X1), tptp_fun_Z2_7(X1))))))))))),
% 4.16/2.97 inference(rewrite,[status(thm)],[])).
% 4.16/2.97 tff(68,plain,
% 4.16/2.97 ((![X: $i] : ((~big_p(a)) | (big_p(tptp_fun_Z_3(X)) & big_r(X, tptp_fun_W_2(X)) & big_r(tptp_fun_W_2(X), tptp_fun_Z_3(X))) | (big_p(X) & ![Y: $i] : (~(big_p(Y) & big_r(X, Y))))) | ![X1: $i] : (((~big_p(a)) | big_p(X1) | (big_p(tptp_fun_Z1_5(X1)) & big_r(X1, tptp_fun_W1_4(X1)) & big_r(tptp_fun_W1_4(X1), tptp_fun_Z1_5(X1)))) & ((~big_p(a)) | ![Y1: $i] : (~(big_p(Y1) & big_r(X1, Y1))) | (big_p(tptp_fun_Z2_7(X1)) & big_r(X1, tptp_fun_W2_6(X1)) & big_r(tptp_fun_W2_6(X1), tptp_fun_Z2_7(X1)))))) <=> (![X: $i] : ((~big_p(a)) | (~((~big_p(tptp_fun_Z_3(X))) | (~big_r(X, tptp_fun_W_2(X))) | (~big_r(tptp_fun_W_2(X), tptp_fun_Z_3(X))))) | (~((~big_p(X)) | (~![Y: $i] : ((~big_p(Y)) | (~big_r(X, Y))))))) | ![X1: $i] : (~((~((~big_p(a)) | big_p(X1) | (~((~big_r(tptp_fun_W1_4(X1), tptp_fun_Z1_5(X1))) | (~big_p(tptp_fun_Z1_5(X1))) | (~big_r(X1, tptp_fun_W1_4(X1))))))) | (~((~big_p(a)) | ![Y1: $i] : ((~big_p(Y1)) | (~big_r(X1, Y1))) | (~((~big_p(tptp_fun_Z2_7(X1))) | (~big_r(X1, tptp_fun_W2_6(X1))) | (~big_r(tptp_fun_W2_6(X1), tptp_fun_Z2_7(X1))))))))))),
% 4.16/2.97 inference(rewrite,[status(thm)],[])).
% 4.16/2.97 tff(69,plain,
% 4.16/2.97 (((![X: $i] : (((~big_p(a)) | ((~(~big_p(X))) & ![Y: $i] : (~(big_p(Y) & big_r(X, Y))))) | (big_p(tptp_fun_Z_3(X)) & big_r(X, tptp_fun_W_2(X)) & big_r(tptp_fun_W_2(X), tptp_fun_Z_3(X)))) | ![X1: $i] : (((~big_p(a)) | big_p(X1) | (big_p(tptp_fun_Z1_5(X1)) & big_r(X1, tptp_fun_W1_4(X1)) & big_r(tptp_fun_W1_4(X1), tptp_fun_Z1_5(X1)))) & ((~big_p(a)) | ![Y1: $i] : (~(big_p(Y1) & big_r(X1, Y1))) | (big_p(tptp_fun_Z2_7(X1)) & big_r(X1, tptp_fun_W2_6(X1)) & big_r(tptp_fun_W2_6(X1), tptp_fun_Z2_7(X1)))))) & (((big_p(a) & ((~big_p(X!0)) | (big_p(Y!1) & big_r(X!0, Y!1)))) & ![Z: $i, W: $i] : (~(big_p(Z) & big_r(X!0, W) & big_r(W, Z)))) | (((~(~big_p(a))) & (~big_p(X1!8)) & ![Z1: $i, W1: $i] : (~(big_p(Z1) & big_r(X1!8, W1) & big_r(W1, Z1)))) | ((~(~big_p(a))) & (big_p(Y1!9) & big_r(X1!8, Y1!9)) & ![Z2: $i, W2: $i] : (~(big_p(Z2) & big_r(X1!8, W2) & big_r(W2, Z2))))))) <=> ((![X: $i] : ((~big_p(a)) | (big_p(tptp_fun_Z_3(X)) & big_r(X, tptp_fun_W_2(X)) & big_r(tptp_fun_W_2(X), tptp_fun_Z_3(X))) | (big_p(X) & ![Y: $i] : (~(big_p(Y) & big_r(X, Y))))) | ![X1: $i] : (((~big_p(a)) | big_p(X1) | (big_p(tptp_fun_Z1_5(X1)) & big_r(X1, tptp_fun_W1_4(X1)) & big_r(tptp_fun_W1_4(X1), tptp_fun_Z1_5(X1)))) & ((~big_p(a)) | ![Y1: $i] : (~(big_p(Y1) & big_r(X1, Y1))) | (big_p(tptp_fun_Z2_7(X1)) & big_r(X1, tptp_fun_W2_6(X1)) & big_r(tptp_fun_W2_6(X1), tptp_fun_Z2_7(X1)))))) & ((big_p(a) & ((~big_p(X!0)) | (big_p(Y!1) & big_r(X!0, Y!1))) & ![Z: $i, W: $i] : (~(big_p(Z) & big_r(X!0, W) & big_r(W, Z)))) | (big_p(a) & (~big_p(X1!8)) & ![Z1: $i, W1: $i] : (~(big_p(Z1) & big_r(X1!8, W1) & big_r(W1, Z1)))) | (big_p(a) & big_p(Y1!9) & big_r(X1!8, Y1!9) & ![Z2: $i, W2: $i] : (~(big_p(Z2) & big_r(X1!8, W2) & big_r(W2, Z2))))))),
% 4.16/2.97 inference(rewrite,[status(thm)],[])).
% 4.16/2.97 tff(70,plain,
% 4.16/2.97 (((~![X: $i] : ((~(big_p(a) & ((~big_p(X)) | ?[Y: $i] : (big_p(Y) & big_r(X, Y))))) | ?[Z: $i, W: $i] : (big_p(Z) & big_r(X, W) & big_r(W, Z)))) <=> ![X1: $i] : (((~big_p(a)) | big_p(X1) | ?[Z1: $i, W1: $i] : (big_p(Z1) & big_r(X1, W1) & big_r(W1, Z1))) & ((~big_p(a)) | (~?[Y1: $i] : (big_p(Y1) & big_r(X1, Y1))) | ?[Z2: $i, W2: $i] : (big_p(Z2) & big_r(X1, W2) & big_r(W2, Z2))))) <=> ((~![X: $i] : ((~(big_p(a) & ((~big_p(X)) | ?[Y: $i] : (big_p(Y) & big_r(X, Y))))) | ?[Z: $i, W: $i] : (big_p(Z) & big_r(X, W) & big_r(W, Z)))) <=> ![X1: $i] : (((~big_p(a)) | big_p(X1) | ?[Z1: $i, W1: $i] : (big_p(Z1) & big_r(X1, W1) & big_r(W1, Z1))) & ((~big_p(a)) | (~?[Y1: $i] : (big_p(Y1) & big_r(X1, Y1))) | ?[Z2: $i, W2: $i] : (big_p(Z2) & big_r(X1, W2) & big_r(W2, Z2)))))),
% 4.16/2.97 inference(rewrite,[status(thm)],[])).
% 4.16/2.97 tff(71,plain,
% 4.16/2.97 ((~(![X: $i] : ((~(big_p(a) & ((~big_p(X)) | ?[Y: $i] : (big_p(Y) & big_r(X, Y))))) | ?[Z: $i, W: $i] : (big_p(Z) & big_r(X, W) & big_r(W, Z))) <=> ![X1: $i] : (((~big_p(a)) | big_p(X1) | ?[Z1: $i, W1: $i] : (big_p(Z1) & big_r(X1, W1) & big_r(W1, Z1))) & ((~big_p(a)) | (~?[Y1: $i] : (big_p(Y1) & big_r(X1, Y1))) | ?[Z2: $i, W2: $i] : (big_p(Z2) & big_r(X1, W2) & big_r(W2, Z2)))))) <=> ((~![X: $i] : ((~(big_p(a) & ((~big_p(X)) | ?[Y: $i] : (big_p(Y) & big_r(X, Y))))) | ?[Z: $i, W: $i] : (big_p(Z) & big_r(X, W) & big_r(W, Z)))) <=> ![X1: $i] : (((~big_p(a)) | big_p(X1) | ?[Z1: $i, W1: $i] : (big_p(Z1) & big_r(X1, W1) & big_r(W1, Z1))) & ((~big_p(a)) | (~?[Y1: $i] : (big_p(Y1) & big_r(X1, Y1))) | ?[Z2: $i, W2: $i] : (big_p(Z2) & big_r(X1, W2) & big_r(W2, Z2)))))),
% 4.16/2.97 inference(rewrite,[status(thm)],[])).
% 4.16/2.97 tff(72,plain,
% 4.16/2.97 ((![X: $i] : ((big_p(a) & (big_p(X) => ?[Y: $i] : (big_p(Y) & big_r(X, Y)))) => ?[Z: $i, W: $i] : ((big_p(Z) & big_r(X, W)) & big_r(W, Z))) <=> ![X1: $i] : ((((~big_p(a)) | big_p(X1)) | ?[Z1: $i, W1: $i] : ((big_p(Z1) & big_r(X1, W1)) & big_r(W1, Z1))) & (((~big_p(a)) | (~?[Y1: $i] : (big_p(Y1) & big_r(X1, Y1)))) | ?[Z2: $i, W2: $i] : ((big_p(Z2) & big_r(X1, W2)) & big_r(W2, Z2))))) <=> (![X: $i] : ((~(big_p(a) & ((~big_p(X)) | ?[Y: $i] : (big_p(Y) & big_r(X, Y))))) | ?[Z: $i, W: $i] : (big_p(Z) & big_r(X, W) & big_r(W, Z))) <=> ![X1: $i] : (((~big_p(a)) | big_p(X1) | ?[Z1: $i, W1: $i] : (big_p(Z1) & big_r(X1, W1) & big_r(W1, Z1))) & ((~big_p(a)) | (~?[Y1: $i] : (big_p(Y1) & big_r(X1, Y1))) | ?[Z2: $i, W2: $i] : (big_p(Z2) & big_r(X1, W2) & big_r(W2, Z2)))))),
% 4.16/2.98 inference(rewrite,[status(thm)],[])).
% 4.16/2.98 tff(73,plain,
% 4.16/2.98 ((~(![X: $i] : ((big_p(a) & (big_p(X) => ?[Y: $i] : (big_p(Y) & big_r(X, Y)))) => ?[Z: $i, W: $i] : ((big_p(Z) & big_r(X, W)) & big_r(W, Z))) <=> ![X1: $i] : ((((~big_p(a)) | big_p(X1)) | ?[Z1: $i, W1: $i] : ((big_p(Z1) & big_r(X1, W1)) & big_r(W1, Z1))) & (((~big_p(a)) | (~?[Y1: $i] : (big_p(Y1) & big_r(X1, Y1)))) | ?[Z2: $i, W2: $i] : ((big_p(Z2) & big_r(X1, W2)) & big_r(W2, Z2)))))) <=> (~(![X: $i] : ((~(big_p(a) & ((~big_p(X)) | ?[Y: $i] : (big_p(Y) & big_r(X, Y))))) | ?[Z: $i, W: $i] : (big_p(Z) & big_r(X, W) & big_r(W, Z))) <=> ![X1: $i] : (((~big_p(a)) | big_p(X1) | ?[Z1: $i, W1: $i] : (big_p(Z1) & big_r(X1, W1) & big_r(W1, Z1))) & ((~big_p(a)) | (~?[Y1: $i] : (big_p(Y1) & big_r(X1, Y1))) | ?[Z2: $i, W2: $i] : (big_p(Z2) & big_r(X1, W2) & big_r(W2, Z2))))))),
% 4.16/2.98 inference(monotonicity,[status(thm)],[72])).
% 4.16/2.98 tff(74,plain,
% 4.16/2.98 ((~(![X: $i] : ((big_p(a) & (big_p(X) => ?[Y: $i] : (big_p(Y) & big_r(X, Y)))) => ?[Z: $i, W: $i] : ((big_p(Z) & big_r(X, W)) & big_r(W, Z))) <=> ![X1: $i] : ((((~big_p(a)) | big_p(X1)) | ?[Z1: $i, W1: $i] : ((big_p(Z1) & big_r(X1, W1)) & big_r(W1, Z1))) & (((~big_p(a)) | (~?[Y1: $i] : (big_p(Y1) & big_r(X1, Y1)))) | ?[Z2: $i, W2: $i] : ((big_p(Z2) & big_r(X1, W2)) & big_r(W2, Z2)))))) <=> ((~![X: $i] : ((~(big_p(a) & ((~big_p(X)) | ?[Y: $i] : (big_p(Y) & big_r(X, Y))))) | ?[Z: $i, W: $i] : (big_p(Z) & big_r(X, W) & big_r(W, Z)))) <=> ![X1: $i] : (((~big_p(a)) | big_p(X1) | ?[Z1: $i, W1: $i] : (big_p(Z1) & big_r(X1, W1) & big_r(W1, Z1))) & ((~big_p(a)) | (~?[Y1: $i] : (big_p(Y1) & big_r(X1, Y1))) | ?[Z2: $i, W2: $i] : (big_p(Z2) & big_r(X1, W2) & big_r(W2, Z2)))))),
% 4.16/2.98 inference(transitivity,[status(thm)],[73, 71])).
% 4.16/2.98 tff(75,axiom,(~(![X: $i] : ((big_p(a) & (big_p(X) => ?[Y: $i] : (big_p(Y) & big_r(X, Y)))) => ?[Z: $i, W: $i] : ((big_p(Z) & big_r(X, W)) & big_r(W, Z))) <=> ![X1: $i] : ((((~big_p(a)) | big_p(X1)) | ?[Z1: $i, W1: $i] : ((big_p(Z1) & big_r(X1, W1)) & big_r(W1, Z1))) & (((~big_p(a)) | (~?[Y1: $i] : (big_p(Y1) & big_r(X1, Y1)))) | ?[Z2: $i, W2: $i] : ((big_p(Z2) & big_r(X1, W2)) & big_r(W2, Z2)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel38')).
% 4.16/2.98 tff(76,plain,
% 4.16/2.98 ((~![X: $i] : ((~(big_p(a) & ((~big_p(X)) | ?[Y: $i] : (big_p(Y) & big_r(X, Y))))) | ?[Z: $i, W: $i] : (big_p(Z) & big_r(X, W) & big_r(W, Z)))) <=> ![X1: $i] : (((~big_p(a)) | big_p(X1) | ?[Z1: $i, W1: $i] : (big_p(Z1) & big_r(X1, W1) & big_r(W1, Z1))) & ((~big_p(a)) | (~?[Y1: $i] : (big_p(Y1) & big_r(X1, Y1))) | ?[Z2: $i, W2: $i] : (big_p(Z2) & big_r(X1, W2) & big_r(W2, Z2))))),
% 4.16/2.98 inference(modus_ponens,[status(thm)],[75, 74])).
% 4.16/2.98 tff(77,plain,
% 4.16/2.98 ((~![X: $i] : ((~(big_p(a) & ((~big_p(X)) | ?[Y: $i] : (big_p(Y) & big_r(X, Y))))) | ?[Z: $i, W: $i] : (big_p(Z) & big_r(X, W) & big_r(W, Z)))) <=> ![X1: $i] : (((~big_p(a)) | big_p(X1) | ?[Z1: $i, W1: $i] : (big_p(Z1) & big_r(X1, W1) & big_r(W1, Z1))) & ((~big_p(a)) | (~?[Y1: $i] : (big_p(Y1) & big_r(X1, Y1))) | ?[Z2: $i, W2: $i] : (big_p(Z2) & big_r(X1, W2) & big_r(W2, Z2))))),
% 4.16/2.98 inference(modus_ponens,[status(thm)],[76, 70])).
% 4.16/2.98 tff(78,plain,
% 4.16/2.98 ((~![X: $i] : ((~(big_p(a) & ((~big_p(X)) | ?[Y: $i] : (big_p(Y) & big_r(X, Y))))) | ?[Z: $i, W: $i] : (big_p(Z) & big_r(X, W) & big_r(W, Z)))) <=> ![X1: $i] : (((~big_p(a)) | big_p(X1) | ?[Z1: $i, W1: $i] : (big_p(Z1) & big_r(X1, W1) & big_r(W1, Z1))) & ((~big_p(a)) | (~?[Y1: $i] : (big_p(Y1) & big_r(X1, Y1))) | ?[Z2: $i, W2: $i] : (big_p(Z2) & big_r(X1, W2) & big_r(W2, Z2))))),
% 4.16/2.98 inference(modus_ponens,[status(thm)],[77, 70])).
% 4.16/2.98 tff(79,plain,
% 4.16/2.98 ((~![X: $i] : ((~(big_p(a) & ((~big_p(X)) | ?[Y: $i] : (big_p(Y) & big_r(X, Y))))) | ?[Z: $i, W: $i] : (big_p(Z) & big_r(X, W) & big_r(W, Z)))) <=> ![X1: $i] : (((~big_p(a)) | big_p(X1) | ?[Z1: $i, W1: $i] : (big_p(Z1) & big_r(X1, W1) & big_r(W1, Z1))) & ((~big_p(a)) | (~?[Y1: $i] : (big_p(Y1) & big_r(X1, Y1))) | ?[Z2: $i, W2: $i] : (big_p(Z2) & big_r(X1, W2) & big_r(W2, Z2))))),
% 4.16/2.98 inference(modus_ponens,[status(thm)],[78, 70])).
% 4.16/2.98 tff(80,plain,
% 4.16/2.98 ((~![X: $i] : ((~(big_p(a) & ((~big_p(X)) | ?[Y: $i] : (big_p(Y) & big_r(X, Y))))) | ?[Z: $i, W: $i] : (big_p(Z) & big_r(X, W) & big_r(W, Z)))) <=> ![X1: $i] : (((~big_p(a)) | big_p(X1) | ?[Z1: $i, W1: $i] : (big_p(Z1) & big_r(X1, W1) & big_r(W1, Z1))) & ((~big_p(a)) | (~?[Y1: $i] : (big_p(Y1) & big_r(X1, Y1))) | ?[Z2: $i, W2: $i] : (big_p(Z2) & big_r(X1, W2) & big_r(W2, Z2))))),
% 4.16/2.98 inference(modus_ponens,[status(thm)],[79, 70])).
% 4.16/2.98 tff(81,plain,
% 4.16/2.98 ((~![X: $i] : ((~(big_p(a) & ((~big_p(X)) | ?[Y: $i] : (big_p(Y) & big_r(X, Y))))) | ?[Z: $i, W: $i] : (big_p(Z) & big_r(X, W) & big_r(W, Z)))) <=> ![X1: $i] : (((~big_p(a)) | big_p(X1) | ?[Z1: $i, W1: $i] : (big_p(Z1) & big_r(X1, W1) & big_r(W1, Z1))) & ((~big_p(a)) | (~?[Y1: $i] : (big_p(Y1) & big_r(X1, Y1))) | ?[Z2: $i, W2: $i] : (big_p(Z2) & big_r(X1, W2) & big_r(W2, Z2))))),
% 4.16/2.98 inference(modus_ponens,[status(thm)],[80, 70])).
% 4.16/2.98 tff(82,plain,
% 4.16/2.98 ((~![X: $i] : ((~(big_p(a) & ((~big_p(X)) | ?[Y: $i] : (big_p(Y) & big_r(X, Y))))) | ?[Z: $i, W: $i] : (big_p(Z) & big_r(X, W) & big_r(W, Z)))) <=> ![X1: $i] : (((~big_p(a)) | big_p(X1) | ?[Z1: $i, W1: $i] : (big_p(Z1) & big_r(X1, W1) & big_r(W1, Z1))) & ((~big_p(a)) | (~?[Y1: $i] : (big_p(Y1) & big_r(X1, Y1))) | ?[Z2: $i, W2: $i] : (big_p(Z2) & big_r(X1, W2) & big_r(W2, Z2))))),
% 4.16/2.98 inference(modus_ponens,[status(thm)],[81, 70])).
% 4.16/2.98 tff(83,plain,(
% 4.16/2.98 (![X: $i] : (((~big_p(a)) | ((~(~big_p(X))) & ![Y: $i] : (~(big_p(Y) & big_r(X, Y))))) | (big_p(tptp_fun_Z_3(X)) & big_r(X, tptp_fun_W_2(X)) & big_r(tptp_fun_W_2(X), tptp_fun_Z_3(X)))) | ![X1: $i] : (((~big_p(a)) | big_p(X1) | (big_p(tptp_fun_Z1_5(X1)) & big_r(X1, tptp_fun_W1_4(X1)) & big_r(tptp_fun_W1_4(X1), tptp_fun_Z1_5(X1)))) & ((~big_p(a)) | ![Y1: $i] : (~(big_p(Y1) & big_r(X1, Y1))) | (big_p(tptp_fun_Z2_7(X1)) & big_r(X1, tptp_fun_W2_6(X1)) & big_r(tptp_fun_W2_6(X1), tptp_fun_Z2_7(X1)))))) & (((big_p(a) & ((~big_p(X!0)) | (big_p(Y!1) & big_r(X!0, Y!1)))) & ![Z: $i, W: $i] : (~(big_p(Z) & big_r(X!0, W) & big_r(W, Z)))) | (((~(~big_p(a))) & (~big_p(X1!8)) & ![Z1: $i, W1: $i] : (~(big_p(Z1) & big_r(X1!8, W1) & big_r(W1, Z1)))) | ((~(~big_p(a))) & (big_p(Y1!9) & big_r(X1!8, Y1!9)) & ![Z2: $i, W2: $i] : (~(big_p(Z2) & big_r(X1!8, W2) & big_r(W2, Z2))))))),
% 4.16/2.98 inference(skolemize,[status(sab)],[82])).
% 4.16/2.98 tff(84,plain,
% 4.16/2.98 ((![X: $i] : ((~big_p(a)) | (big_p(tptp_fun_Z_3(X)) & big_r(X, tptp_fun_W_2(X)) & big_r(tptp_fun_W_2(X), tptp_fun_Z_3(X))) | (big_p(X) & ![Y: $i] : (~(big_p(Y) & big_r(X, Y))))) | ![X1: $i] : (((~big_p(a)) | big_p(X1) | (big_p(tptp_fun_Z1_5(X1)) & big_r(X1, tptp_fun_W1_4(X1)) & big_r(tptp_fun_W1_4(X1), tptp_fun_Z1_5(X1)))) & ((~big_p(a)) | ![Y1: $i] : (~(big_p(Y1) & big_r(X1, Y1))) | (big_p(tptp_fun_Z2_7(X1)) & big_r(X1, tptp_fun_W2_6(X1)) & big_r(tptp_fun_W2_6(X1), tptp_fun_Z2_7(X1)))))) & ((big_p(a) & ((~big_p(X!0)) | (big_p(Y!1) & big_r(X!0, Y!1))) & ![Z: $i, W: $i] : (~(big_p(Z) & big_r(X!0, W) & big_r(W, Z)))) | (big_p(a) & (~big_p(X1!8)) & ![Z1: $i, W1: $i] : (~(big_p(Z1) & big_r(X1!8, W1) & big_r(W1, Z1)))) | (big_p(a) & big_p(Y1!9) & big_r(X1!8, Y1!9) & ![Z2: $i, W2: $i] : (~(big_p(Z2) & big_r(X1!8, W2) & big_r(W2, Z2)))))),
% 4.16/2.98 inference(modus_ponens,[status(thm)],[83, 69])).
% 4.16/2.98 tff(85,plain,
% 4.16/2.98 (![X: $i] : ((~big_p(a)) | (big_p(tptp_fun_Z_3(X)) & big_r(X, tptp_fun_W_2(X)) & big_r(tptp_fun_W_2(X), tptp_fun_Z_3(X))) | (big_p(X) & ![Y: $i] : (~(big_p(Y) & big_r(X, Y))))) | ![X1: $i] : (((~big_p(a)) | big_p(X1) | (big_p(tptp_fun_Z1_5(X1)) & big_r(X1, tptp_fun_W1_4(X1)) & big_r(tptp_fun_W1_4(X1), tptp_fun_Z1_5(X1)))) & ((~big_p(a)) | ![Y1: $i] : (~(big_p(Y1) & big_r(X1, Y1))) | (big_p(tptp_fun_Z2_7(X1)) & big_r(X1, tptp_fun_W2_6(X1)) & big_r(tptp_fun_W2_6(X1), tptp_fun_Z2_7(X1)))))),
% 4.16/2.98 inference(and_elim,[status(thm)],[84])).
% 4.16/2.98 tff(86,plain,
% 4.16/2.98 (![X: $i] : ((~big_p(a)) | (~((~big_p(tptp_fun_Z_3(X))) | (~big_r(X, tptp_fun_W_2(X))) | (~big_r(tptp_fun_W_2(X), tptp_fun_Z_3(X))))) | (~((~big_p(X)) | (~![Y: $i] : ((~big_p(Y)) | (~big_r(X, Y))))))) | ![X1: $i] : (~((~((~big_p(a)) | big_p(X1) | (~((~big_r(tptp_fun_W1_4(X1), tptp_fun_Z1_5(X1))) | (~big_p(tptp_fun_Z1_5(X1))) | (~big_r(X1, tptp_fun_W1_4(X1))))))) | (~((~big_p(a)) | ![Y1: $i] : ((~big_p(Y1)) | (~big_r(X1, Y1))) | (~((~big_p(tptp_fun_Z2_7(X1))) | (~big_r(X1, tptp_fun_W2_6(X1))) | (~big_r(tptp_fun_W2_6(X1), tptp_fun_Z2_7(X1)))))))))),
% 4.16/2.98 inference(modus_ponens,[status(thm)],[85, 68])).
% 4.16/2.98 tff(87,plain,
% 4.16/2.98 (![X: $i] : ((~big_p(a)) | (~((~big_p(tptp_fun_Z_3(X))) | (~big_r(X, tptp_fun_W_2(X))) | (~big_r(tptp_fun_W_2(X), tptp_fun_Z_3(X))))) | (~((~big_p(X)) | (~![Y: $i] : ((~big_p(Y)) | (~big_r(X, Y))))))) | ![X1: $i] : (~((~((~big_p(a)) | big_p(X1) | (~((~big_r(tptp_fun_W1_4(X1), tptp_fun_Z1_5(X1))) | (~big_p(tptp_fun_Z1_5(X1))) | (~big_r(X1, tptp_fun_W1_4(X1))))))) | (~((~big_p(a)) | ![Y1: $i] : ((~big_p(Y1)) | (~big_r(X1, Y1))) | (~((~big_p(tptp_fun_Z2_7(X1))) | (~big_r(X1, tptp_fun_W2_6(X1))) | (~big_r(tptp_fun_W2_6(X1), tptp_fun_Z2_7(X1)))))))))),
% 4.16/2.98 inference(modus_ponens,[status(thm)],[86, 67])).
% 4.16/2.98 tff(88,plain,
% 4.16/2.98 (![X: $i] : ((~big_p(a)) | (~((~big_p(tptp_fun_Z_3(X))) | (~big_r(X, tptp_fun_W_2(X))) | (~big_r(tptp_fun_W_2(X), tptp_fun_Z_3(X))))) | (~((~big_p(X)) | (~![Y: $i] : ((~big_p(Y)) | (~big_r(X, Y))))))) | ![X1: $i] : (~((~((~big_p(a)) | big_p(X1) | (~((~big_r(tptp_fun_W1_4(X1), tptp_fun_Z1_5(X1))) | (~big_p(tptp_fun_Z1_5(X1))) | (~big_r(X1, tptp_fun_W1_4(X1))))))) | (~((~big_p(a)) | (~((~big_p(tptp_fun_Z2_7(X1))) | (~big_r(X1, tptp_fun_W2_6(X1))) | (~big_r(tptp_fun_W2_6(X1), tptp_fun_Z2_7(X1))))) | ![Y1: $i] : ((~big_p(Y1)) | (~big_r(X1, Y1)))))))),
% 4.16/2.98 inference(modus_ponens,[status(thm)],[87, 66])).
% 4.16/2.98 tff(89,plain,
% 4.16/2.98 (![X1: $i] : (~((~((~big_p(a)) | big_p(X1) | (~((~big_r(tptp_fun_W1_4(X1), tptp_fun_Z1_5(X1))) | (~big_p(tptp_fun_Z1_5(X1))) | (~big_r(X1, tptp_fun_W1_4(X1))))))) | (~((~big_p(a)) | (~((~big_p(tptp_fun_Z2_7(X1))) | (~big_r(X1, tptp_fun_W2_6(X1))) | (~big_r(tptp_fun_W2_6(X1), tptp_fun_Z2_7(X1))))) | ![Y1: $i] : ((~big_p(Y1)) | (~big_r(X1, Y1)))))))),
% 4.16/2.98 inference(unit_resolution,[status(thm)],[88, 65])).
% 4.16/2.98 tff(90,plain,
% 4.16/2.98 (~((~((~big_p(a)) | big_p(X1!8) | (~((~big_r(tptp_fun_W1_4(X1!8), tptp_fun_Z1_5(X1!8))) | (~big_p(tptp_fun_Z1_5(X1!8))) | (~big_r(X1!8, tptp_fun_W1_4(X1!8))))))) | (~((~big_p(a)) | (~((~big_p(tptp_fun_Z2_7(X1!8))) | (~big_r(X1!8, tptp_fun_W2_6(X1!8))) | (~big_r(tptp_fun_W2_6(X1!8), tptp_fun_Z2_7(X1!8))))) | ![Y1: $i] : ((~big_p(Y1)) | (~big_r(X1!8, Y1))))))),
% 4.16/2.98 inference(unit_resolution,[status(thm)],[13, 89])).
% 4.16/2.98 tff(91,plain,
% 4.16/2.98 (((~((~big_p(a)) | big_p(X1!8) | (~((~big_r(tptp_fun_W1_4(X1!8), tptp_fun_Z1_5(X1!8))) | (~big_p(tptp_fun_Z1_5(X1!8))) | (~big_r(X1!8, tptp_fun_W1_4(X1!8))))))) | (~((~big_p(a)) | (~((~big_p(tptp_fun_Z2_7(X1!8))) | (~big_r(X1!8, tptp_fun_W2_6(X1!8))) | (~big_r(tptp_fun_W2_6(X1!8), tptp_fun_Z2_7(X1!8))))) | ![Y1: $i] : ((~big_p(Y1)) | (~big_r(X1!8, Y1)))))) | ((~big_p(a)) | big_p(X1!8) | (~((~big_r(tptp_fun_W1_4(X1!8), tptp_fun_Z1_5(X1!8))) | (~big_p(tptp_fun_Z1_5(X1!8))) | (~big_r(X1!8, tptp_fun_W1_4(X1!8))))))),
% 4.16/2.98 inference(tautology,[status(thm)],[])).
% 4.16/2.98 tff(92,plain,
% 4.16/2.98 ((~big_p(a)) | big_p(X1!8) | (~((~big_r(tptp_fun_W1_4(X1!8), tptp_fun_Z1_5(X1!8))) | (~big_p(tptp_fun_Z1_5(X1!8))) | (~big_r(X1!8, tptp_fun_W1_4(X1!8)))))),
% 4.16/2.98 inference(unit_resolution,[status(thm)],[91, 90])).
% 4.16/2.98 tff(93,plain,
% 4.16/2.98 ((~((~big_p(a)) | big_p(X1!8) | (~((~big_r(tptp_fun_W1_4(X1!8), tptp_fun_Z1_5(X1!8))) | (~big_p(tptp_fun_Z1_5(X1!8))) | (~big_r(X1!8, tptp_fun_W1_4(X1!8))))))) | (~big_p(a)) | big_p(X1!8) | (~((~big_r(tptp_fun_W1_4(X1!8), tptp_fun_Z1_5(X1!8))) | (~big_p(tptp_fun_Z1_5(X1!8))) | (~big_r(X1!8, tptp_fun_W1_4(X1!8)))))),
% 4.16/2.98 inference(tautology,[status(thm)],[])).
% 4.16/2.98 tff(94,plain,
% 4.16/2.98 ((~((~big_p(a)) | big_p(X1!8) | (~((~big_r(tptp_fun_W1_4(X1!8), tptp_fun_Z1_5(X1!8))) | (~big_p(tptp_fun_Z1_5(X1!8))) | (~big_r(X1!8, tptp_fun_W1_4(X1!8))))))) | (~((~big_r(tptp_fun_W1_4(X1!8), tptp_fun_Z1_5(X1!8))) | (~big_p(tptp_fun_Z1_5(X1!8))) | (~big_r(X1!8, tptp_fun_W1_4(X1!8)))))),
% 4.16/2.98 inference(unit_resolution,[status(thm)],[93, 53, 42])).
% 4.16/2.98 tff(95,plain,
% 4.16/2.98 (~((~big_r(tptp_fun_W1_4(X1!8), tptp_fun_Z1_5(X1!8))) | (~big_p(tptp_fun_Z1_5(X1!8))) | (~big_r(X1!8, tptp_fun_W1_4(X1!8))))),
% 4.16/2.98 inference(unit_resolution,[status(thm)],[94, 92])).
% 4.16/2.98 tff(96,plain,
% 4.16/2.98 (((~big_r(tptp_fun_W1_4(X1!8), tptp_fun_Z1_5(X1!8))) | (~big_p(tptp_fun_Z1_5(X1!8))) | (~big_r(X1!8, tptp_fun_W1_4(X1!8)))) | big_r(X1!8, tptp_fun_W1_4(X1!8))),
% 4.16/2.98 inference(tautology,[status(thm)],[])).
% 4.16/2.98 tff(97,plain,
% 4.16/2.98 (big_r(X1!8, tptp_fun_W1_4(X1!8))),
% 4.16/2.98 inference(unit_resolution,[status(thm)],[96, 95])).
% 4.16/2.98 tff(98,plain,
% 4.16/2.98 (((~big_r(tptp_fun_W1_4(X1!8), tptp_fun_Z1_5(X1!8))) | (~big_p(tptp_fun_Z1_5(X1!8))) | (~big_r(X1!8, tptp_fun_W1_4(X1!8)))) | big_p(tptp_fun_Z1_5(X1!8))),
% 4.16/2.98 inference(tautology,[status(thm)],[])).
% 4.16/2.98 tff(99,plain,
% 4.16/2.98 (big_p(tptp_fun_Z1_5(X1!8))),
% 4.16/2.98 inference(unit_resolution,[status(thm)],[98, 95])).
% 4.16/2.98 tff(100,plain,
% 4.16/2.98 (((~big_r(tptp_fun_W1_4(X1!8), tptp_fun_Z1_5(X1!8))) | (~big_p(tptp_fun_Z1_5(X1!8))) | (~big_r(X1!8, tptp_fun_W1_4(X1!8)))) | big_r(tptp_fun_W1_4(X1!8), tptp_fun_Z1_5(X1!8))),
% 4.16/2.98 inference(tautology,[status(thm)],[])).
% 4.16/2.98 tff(101,plain,
% 4.16/2.98 (big_r(tptp_fun_W1_4(X1!8), tptp_fun_Z1_5(X1!8))),
% 4.16/2.98 inference(unit_resolution,[status(thm)],[100, 95])).
% 4.16/2.98 tff(102,plain,
% 4.16/2.98 (((~![Z1: $i, W1: $i] : ((~big_p(Z1)) | (~big_r(X1!8, W1)) | (~big_r(W1, Z1)))) | ((~big_p(tptp_fun_Z1_5(X1!8))) | (~big_r(X1!8, tptp_fun_W1_4(X1!8))) | (~big_r(tptp_fun_W1_4(X1!8), tptp_fun_Z1_5(X1!8))))) <=> ((~![Z1: $i, W1: $i] : ((~big_p(Z1)) | (~big_r(X1!8, W1)) | (~big_r(W1, Z1)))) | (~big_p(tptp_fun_Z1_5(X1!8))) | (~big_r(X1!8, tptp_fun_W1_4(X1!8))) | (~big_r(tptp_fun_W1_4(X1!8), tptp_fun_Z1_5(X1!8))))),
% 4.16/2.98 inference(rewrite,[status(thm)],[])).
% 4.16/2.98 tff(103,plain,
% 4.16/2.98 ((~![Z1: $i, W1: $i] : ((~big_p(Z1)) | (~big_r(X1!8, W1)) | (~big_r(W1, Z1)))) | ((~big_p(tptp_fun_Z1_5(X1!8))) | (~big_r(X1!8, tptp_fun_W1_4(X1!8))) | (~big_r(tptp_fun_W1_4(X1!8), tptp_fun_Z1_5(X1!8))))),
% 4.16/2.98 inference(quant_inst,[status(thm)],[])).
% 4.16/2.98 tff(104,plain,
% 4.16/2.98 ((~![Z1: $i, W1: $i] : ((~big_p(Z1)) | (~big_r(X1!8, W1)) | (~big_r(W1, Z1)))) | (~big_p(tptp_fun_Z1_5(X1!8))) | (~big_r(X1!8, tptp_fun_W1_4(X1!8))) | (~big_r(tptp_fun_W1_4(X1!8), tptp_fun_Z1_5(X1!8)))),
% 4.16/2.98 inference(modus_ponens,[status(thm)],[103, 102])).
% 4.16/2.98 tff(105,plain,
% 4.16/2.98 ($false),
% 4.16/2.98 inference(unit_resolution,[status(thm)],[104, 44, 101, 99, 97])).
% 4.16/2.98 tff(106,plain,((~big_p(a)) | big_p(X1!8) | (~![Z1: $i, W1: $i] : ((~big_p(Z1)) | (~big_r(X1!8, W1)) | (~big_r(W1, Z1))))), inference(lemma,lemma(discharge,[]))).
% 4.16/2.98 tff(107,plain,
% 4.16/2.98 (((~((~big_p(a)) | (~((~big_p(X!0)) | (~((~big_p(Y!1)) | (~big_r(X!0, Y!1)))))) | (~![Z: $i, W: $i] : ((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z)))))) | (~((~big_p(a)) | big_p(X1!8) | (~![Z1: $i, W1: $i] : ((~big_p(Z1)) | (~big_r(X1!8, W1)) | (~big_r(W1, Z1)))))) | (~((~big_p(a)) | (~big_p(Y1!9)) | (~big_r(X1!8, Y1!9)) | (~![Z2: $i, W2: $i] : ((~big_p(Z2)) | (~big_r(X1!8, W2)) | (~big_r(W2, Z2))))))) <=> ((~((~big_p(a)) | (~((~big_p(X!0)) | (~((~big_p(Y!1)) | (~big_r(X!0, Y!1)))))) | (~![Z: $i, W: $i] : ((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z)))))) | (~((~big_p(a)) | big_p(X1!8) | (~![Z1: $i, W1: $i] : ((~big_p(Z1)) | (~big_r(X1!8, W1)) | (~big_r(W1, Z1)))))) | (~((~big_p(a)) | (~big_p(Y1!9)) | (~big_r(X1!8, Y1!9)) | (~![Z2: $i, W2: $i] : ((~big_p(Z2)) | (~big_r(X1!8, W2)) | (~big_r(W2, Z2)))))))),
% 4.16/2.98 inference(rewrite,[status(thm)],[])).
% 4.16/2.98 tff(108,plain,
% 4.16/2.98 (((~((~big_p(a)) | (~((~big_p(X!0)) | (~((~big_p(Y!1)) | (~big_r(X!0, Y!1)))))) | (~![Z: $i, W: $i] : ((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z)))))) | (~((~big_p(a)) | big_p(X1!8) | (~![Z1: $i, W1: $i] : ((~big_p(Z1)) | (~big_r(X1!8, W1)) | (~big_r(W1, Z1)))))) | (~((~big_p(a)) | (~big_p(Y1!9)) | (~big_r(X1!8, Y1!9)) | (~![Z2: $i, W2: $i] : ((~big_p(Z2)) | (~big_r(X1!8, W2)) | (~big_r(W2, Z2))))))) <=> ((~((~big_p(a)) | (~((~big_p(X!0)) | (~((~big_p(Y!1)) | (~big_r(X!0, Y!1)))))) | (~![Z: $i, W: $i] : ((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z)))))) | (~((~big_p(a)) | big_p(X1!8) | (~![Z1: $i, W1: $i] : ((~big_p(Z1)) | (~big_r(X1!8, W1)) | (~big_r(W1, Z1)))))) | (~((~big_p(a)) | (~big_p(Y1!9)) | (~big_r(X1!8, Y1!9)) | (~![Z2: $i, W2: $i] : ((~big_p(Z2)) | (~big_r(X1!8, W2)) | (~big_r(W2, Z2)))))))),
% 4.16/2.98 inference(rewrite,[status(thm)],[])).
% 4.16/2.98 tff(109,plain,
% 4.16/2.98 ((big_p(a) & big_p(Y1!9) & big_r(X1!8, Y1!9) & ![Z2: $i, W2: $i] : ((~big_p(Z2)) | (~big_r(X1!8, W2)) | (~big_r(W2, Z2)))) <=> (~((~big_p(a)) | (~big_p(Y1!9)) | (~big_r(X1!8, Y1!9)) | (~![Z2: $i, W2: $i] : ((~big_p(Z2)) | (~big_r(X1!8, W2)) | (~big_r(W2, Z2))))))),
% 4.16/2.98 inference(rewrite,[status(thm)],[])).
% 4.16/2.98 tff(110,plain,
% 4.16/2.98 (^[Z2: $i, W2: $i] : trans(monotonicity(rewrite((big_p(Z2) & big_r(X1!8, W2) & big_r(W2, Z2)) <=> (~((~big_p(Z2)) | (~big_r(X1!8, W2)) | (~big_r(W2, Z2))))), ((~(big_p(Z2) & big_r(X1!8, W2) & big_r(W2, Z2))) <=> (~(~((~big_p(Z2)) | (~big_r(X1!8, W2)) | (~big_r(W2, Z2))))))), rewrite((~(~((~big_p(Z2)) | (~big_r(X1!8, W2)) | (~big_r(W2, Z2))))) <=> ((~big_p(Z2)) | (~big_r(X1!8, W2)) | (~big_r(W2, Z2)))), ((~(big_p(Z2) & big_r(X1!8, W2) & big_r(W2, Z2))) <=> ((~big_p(Z2)) | (~big_r(X1!8, W2)) | (~big_r(W2, Z2)))))),
% 4.16/2.98 inference(bind,[status(th)],[])).
% 4.16/2.98 tff(111,plain,
% 4.16/2.98 (![Z2: $i, W2: $i] : (~(big_p(Z2) & big_r(X1!8, W2) & big_r(W2, Z2))) <=> ![Z2: $i, W2: $i] : ((~big_p(Z2)) | (~big_r(X1!8, W2)) | (~big_r(W2, Z2)))),
% 4.16/2.98 inference(quant_intro,[status(thm)],[110])).
% 4.16/2.98 tff(112,plain,
% 4.16/2.98 ((big_p(a) & big_p(Y1!9) & big_r(X1!8, Y1!9) & ![Z2: $i, W2: $i] : (~(big_p(Z2) & big_r(X1!8, W2) & big_r(W2, Z2)))) <=> (big_p(a) & big_p(Y1!9) & big_r(X1!8, Y1!9) & ![Z2: $i, W2: $i] : ((~big_p(Z2)) | (~big_r(X1!8, W2)) | (~big_r(W2, Z2))))),
% 4.16/2.98 inference(monotonicity,[status(thm)],[111])).
% 4.16/2.98 tff(113,plain,
% 4.16/2.98 ((big_p(a) & big_p(Y1!9) & big_r(X1!8, Y1!9) & ![Z2: $i, W2: $i] : (~(big_p(Z2) & big_r(X1!8, W2) & big_r(W2, Z2)))) <=> (~((~big_p(a)) | (~big_p(Y1!9)) | (~big_r(X1!8, Y1!9)) | (~![Z2: $i, W2: $i] : ((~big_p(Z2)) | (~big_r(X1!8, W2)) | (~big_r(W2, Z2))))))),
% 4.16/2.98 inference(transitivity,[status(thm)],[112, 109])).
% 4.16/2.98 tff(114,plain,
% 4.16/2.98 ((big_p(a) & (~big_p(X1!8)) & ![Z1: $i, W1: $i] : ((~big_p(Z1)) | (~big_r(X1!8, W1)) | (~big_r(W1, Z1)))) <=> (~((~big_p(a)) | big_p(X1!8) | (~![Z1: $i, W1: $i] : ((~big_p(Z1)) | (~big_r(X1!8, W1)) | (~big_r(W1, Z1))))))),
% 4.16/2.98 inference(rewrite,[status(thm)],[])).
% 4.16/2.98 tff(115,plain,
% 4.16/2.98 (^[Z1: $i, W1: $i] : trans(monotonicity(rewrite((big_p(Z1) & big_r(X1!8, W1) & big_r(W1, Z1)) <=> (~((~big_p(Z1)) | (~big_r(X1!8, W1)) | (~big_r(W1, Z1))))), ((~(big_p(Z1) & big_r(X1!8, W1) & big_r(W1, Z1))) <=> (~(~((~big_p(Z1)) | (~big_r(X1!8, W1)) | (~big_r(W1, Z1))))))), rewrite((~(~((~big_p(Z1)) | (~big_r(X1!8, W1)) | (~big_r(W1, Z1))))) <=> ((~big_p(Z1)) | (~big_r(X1!8, W1)) | (~big_r(W1, Z1)))), ((~(big_p(Z1) & big_r(X1!8, W1) & big_r(W1, Z1))) <=> ((~big_p(Z1)) | (~big_r(X1!8, W1)) | (~big_r(W1, Z1)))))),
% 4.16/2.98 inference(bind,[status(th)],[])).
% 4.16/2.98 tff(116,plain,
% 4.16/2.98 (![Z1: $i, W1: $i] : (~(big_p(Z1) & big_r(X1!8, W1) & big_r(W1, Z1))) <=> ![Z1: $i, W1: $i] : ((~big_p(Z1)) | (~big_r(X1!8, W1)) | (~big_r(W1, Z1)))),
% 4.16/2.98 inference(quant_intro,[status(thm)],[115])).
% 4.16/2.98 tff(117,plain,
% 4.16/2.98 ((big_p(a) & (~big_p(X1!8)) & ![Z1: $i, W1: $i] : (~(big_p(Z1) & big_r(X1!8, W1) & big_r(W1, Z1)))) <=> (big_p(a) & (~big_p(X1!8)) & ![Z1: $i, W1: $i] : ((~big_p(Z1)) | (~big_r(X1!8, W1)) | (~big_r(W1, Z1))))),
% 4.16/2.98 inference(monotonicity,[status(thm)],[116])).
% 4.16/2.98 tff(118,plain,
% 4.16/2.98 ((big_p(a) & (~big_p(X1!8)) & ![Z1: $i, W1: $i] : (~(big_p(Z1) & big_r(X1!8, W1) & big_r(W1, Z1)))) <=> (~((~big_p(a)) | big_p(X1!8) | (~![Z1: $i, W1: $i] : ((~big_p(Z1)) | (~big_r(X1!8, W1)) | (~big_r(W1, Z1))))))),
% 4.16/2.98 inference(transitivity,[status(thm)],[117, 114])).
% 4.16/2.98 tff(119,plain,
% 4.16/2.98 ((big_p(a) & ((~big_p(X!0)) | (~((~big_p(Y!1)) | (~big_r(X!0, Y!1))))) & ![Z: $i, W: $i] : ((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z)))) <=> (~((~big_p(a)) | (~((~big_p(X!0)) | (~((~big_p(Y!1)) | (~big_r(X!0, Y!1)))))) | (~![Z: $i, W: $i] : ((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z))))))),
% 4.16/2.98 inference(rewrite,[status(thm)],[])).
% 4.16/2.98 tff(120,plain,
% 4.16/2.98 (^[Z: $i, W: $i] : trans(monotonicity(rewrite((big_p(Z) & big_r(X!0, W) & big_r(W, Z)) <=> (~((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z))))), ((~(big_p(Z) & big_r(X!0, W) & big_r(W, Z))) <=> (~(~((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z))))))), rewrite((~(~((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z))))) <=> ((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z)))), ((~(big_p(Z) & big_r(X!0, W) & big_r(W, Z))) <=> ((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z)))))),
% 4.16/2.98 inference(bind,[status(th)],[])).
% 4.16/2.98 tff(121,plain,
% 4.16/2.98 (![Z: $i, W: $i] : (~(big_p(Z) & big_r(X!0, W) & big_r(W, Z))) <=> ![Z: $i, W: $i] : ((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z)))),
% 4.16/2.98 inference(quant_intro,[status(thm)],[120])).
% 4.16/2.98 tff(122,plain,
% 4.16/2.98 (((~big_p(X!0)) | (big_p(Y!1) & big_r(X!0, Y!1))) <=> ((~big_p(X!0)) | (~((~big_p(Y!1)) | (~big_r(X!0, Y!1)))))),
% 4.16/2.98 inference(rewrite,[status(thm)],[])).
% 4.16/2.98 tff(123,plain,
% 4.16/2.98 ((big_p(a) & ((~big_p(X!0)) | (big_p(Y!1) & big_r(X!0, Y!1))) & ![Z: $i, W: $i] : (~(big_p(Z) & big_r(X!0, W) & big_r(W, Z)))) <=> (big_p(a) & ((~big_p(X!0)) | (~((~big_p(Y!1)) | (~big_r(X!0, Y!1))))) & ![Z: $i, W: $i] : ((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z))))),
% 4.16/2.98 inference(monotonicity,[status(thm)],[122, 121])).
% 4.16/2.98 tff(124,plain,
% 4.16/2.98 ((big_p(a) & ((~big_p(X!0)) | (big_p(Y!1) & big_r(X!0, Y!1))) & ![Z: $i, W: $i] : (~(big_p(Z) & big_r(X!0, W) & big_r(W, Z)))) <=> (~((~big_p(a)) | (~((~big_p(X!0)) | (~((~big_p(Y!1)) | (~big_r(X!0, Y!1)))))) | (~![Z: $i, W: $i] : ((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z))))))),
% 4.16/2.98 inference(transitivity,[status(thm)],[123, 119])).
% 4.16/2.98 tff(125,plain,
% 4.16/2.98 (((big_p(a) & ((~big_p(X!0)) | (big_p(Y!1) & big_r(X!0, Y!1))) & ![Z: $i, W: $i] : (~(big_p(Z) & big_r(X!0, W) & big_r(W, Z)))) | (big_p(a) & (~big_p(X1!8)) & ![Z1: $i, W1: $i] : (~(big_p(Z1) & big_r(X1!8, W1) & big_r(W1, Z1)))) | (big_p(a) & big_p(Y1!9) & big_r(X1!8, Y1!9) & ![Z2: $i, W2: $i] : (~(big_p(Z2) & big_r(X1!8, W2) & big_r(W2, Z2))))) <=> ((~((~big_p(a)) | (~((~big_p(X!0)) | (~((~big_p(Y!1)) | (~big_r(X!0, Y!1)))))) | (~![Z: $i, W: $i] : ((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z)))))) | (~((~big_p(a)) | big_p(X1!8) | (~![Z1: $i, W1: $i] : ((~big_p(Z1)) | (~big_r(X1!8, W1)) | (~big_r(W1, Z1)))))) | (~((~big_p(a)) | (~big_p(Y1!9)) | (~big_r(X1!8, Y1!9)) | (~![Z2: $i, W2: $i] : ((~big_p(Z2)) | (~big_r(X1!8, W2)) | (~big_r(W2, Z2)))))))),
% 4.16/2.98 inference(monotonicity,[status(thm)],[124, 118, 113])).
% 4.16/2.98 tff(126,plain,
% 4.16/2.98 (((big_p(a) & ((~big_p(X!0)) | (big_p(Y!1) & big_r(X!0, Y!1))) & ![Z: $i, W: $i] : (~(big_p(Z) & big_r(X!0, W) & big_r(W, Z)))) | (big_p(a) & (~big_p(X1!8)) & ![Z1: $i, W1: $i] : (~(big_p(Z1) & big_r(X1!8, W1) & big_r(W1, Z1)))) | (big_p(a) & big_p(Y1!9) & big_r(X1!8, Y1!9) & ![Z2: $i, W2: $i] : (~(big_p(Z2) & big_r(X1!8, W2) & big_r(W2, Z2))))) <=> ((~((~big_p(a)) | (~((~big_p(X!0)) | (~((~big_p(Y!1)) | (~big_r(X!0, Y!1)))))) | (~![Z: $i, W: $i] : ((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z)))))) | (~((~big_p(a)) | big_p(X1!8) | (~![Z1: $i, W1: $i] : ((~big_p(Z1)) | (~big_r(X1!8, W1)) | (~big_r(W1, Z1)))))) | (~((~big_p(a)) | (~big_p(Y1!9)) | (~big_r(X1!8, Y1!9)) | (~![Z2: $i, W2: $i] : ((~big_p(Z2)) | (~big_r(X1!8, W2)) | (~big_r(W2, Z2)))))))),
% 4.16/2.98 inference(transitivity,[status(thm)],[125, 108])).
% 4.16/2.98 tff(127,plain,
% 4.16/2.98 ((big_p(a) & ((~big_p(X!0)) | (big_p(Y!1) & big_r(X!0, Y!1))) & ![Z: $i, W: $i] : (~(big_p(Z) & big_r(X!0, W) & big_r(W, Z)))) | (big_p(a) & (~big_p(X1!8)) & ![Z1: $i, W1: $i] : (~(big_p(Z1) & big_r(X1!8, W1) & big_r(W1, Z1)))) | (big_p(a) & big_p(Y1!9) & big_r(X1!8, Y1!9) & ![Z2: $i, W2: $i] : (~(big_p(Z2) & big_r(X1!8, W2) & big_r(W2, Z2))))),
% 4.16/2.98 inference(and_elim,[status(thm)],[84])).
% 4.16/2.98 tff(128,plain,
% 4.16/2.98 ((~((~big_p(a)) | (~((~big_p(X!0)) | (~((~big_p(Y!1)) | (~big_r(X!0, Y!1)))))) | (~![Z: $i, W: $i] : ((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z)))))) | (~((~big_p(a)) | big_p(X1!8) | (~![Z1: $i, W1: $i] : ((~big_p(Z1)) | (~big_r(X1!8, W1)) | (~big_r(W1, Z1)))))) | (~((~big_p(a)) | (~big_p(Y1!9)) | (~big_r(X1!8, Y1!9)) | (~![Z2: $i, W2: $i] : ((~big_p(Z2)) | (~big_r(X1!8, W2)) | (~big_r(W2, Z2))))))),
% 4.16/2.98 inference(modus_ponens,[status(thm)],[127, 126])).
% 4.16/2.98 tff(129,plain,
% 4.16/2.98 ((~((~big_p(a)) | (~((~big_p(X!0)) | (~((~big_p(Y!1)) | (~big_r(X!0, Y!1)))))) | (~![Z: $i, W: $i] : ((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z)))))) | (~((~big_p(a)) | big_p(X1!8) | (~![Z1: $i, W1: $i] : ((~big_p(Z1)) | (~big_r(X1!8, W1)) | (~big_r(W1, Z1)))))) | (~((~big_p(a)) | (~big_p(Y1!9)) | (~big_r(X1!8, Y1!9)) | (~![Z2: $i, W2: $i] : ((~big_p(Z2)) | (~big_r(X1!8, W2)) | (~big_r(W2, Z2))))))),
% 4.16/2.98 inference(modus_ponens,[status(thm)],[128, 107])).
% 4.16/2.98 tff(130,plain,
% 4.16/2.98 ((~((~big_p(a)) | (~((~big_p(X!0)) | (~((~big_p(Y!1)) | (~big_r(X!0, Y!1)))))) | (~![Z: $i, W: $i] : ((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z)))))) | (~((~big_p(a)) | (~big_p(Y1!9)) | (~big_r(X1!8, Y1!9)) | (~![Z2: $i, W2: $i] : ((~big_p(Z2)) | (~big_r(X1!8, W2)) | (~big_r(W2, Z2))))))),
% 4.16/2.98 inference(unit_resolution,[status(thm)],[129, 106])).
% 4.16/2.98 tff(131,plain,
% 4.16/2.98 ($false),
% 4.16/2.98 inference(unit_resolution,[status(thm)],[130, 39, 37])).
% 4.16/2.98 tff(132,plain,(big_p(a)), inference(lemma,lemma(discharge,[]))).
% 4.16/2.98 tff(133,plain,
% 4.16/2.98 ((~((~big_p(a)) | (~((~big_p(tptp_fun_Z2_7(X1!8))) | (~big_r(X1!8, tptp_fun_W2_6(X1!8))) | (~big_r(tptp_fun_W2_6(X1!8), tptp_fun_Z2_7(X1!8))))) | ![Y1: $i] : ((~big_p(Y1)) | (~big_r(X1!8, Y1))))) | (~big_p(a)) | (~((~big_p(tptp_fun_Z2_7(X1!8))) | (~big_r(X1!8, tptp_fun_W2_6(X1!8))) | (~big_r(tptp_fun_W2_6(X1!8), tptp_fun_Z2_7(X1!8))))) | ![Y1: $i] : ((~big_p(Y1)) | (~big_r(X1!8, Y1)))),
% 4.16/2.98 inference(tautology,[status(thm)],[])).
% 4.16/2.98 tff(134,plain,
% 4.16/2.98 ((~((~big_p(a)) | (~((~big_p(tptp_fun_Z2_7(X1!8))) | (~big_r(X1!8, tptp_fun_W2_6(X1!8))) | (~big_r(tptp_fun_W2_6(X1!8), tptp_fun_Z2_7(X1!8))))) | ![Y1: $i] : ((~big_p(Y1)) | (~big_r(X1!8, Y1))))) | (~((~big_p(tptp_fun_Z2_7(X1!8))) | (~big_r(X1!8, tptp_fun_W2_6(X1!8))) | (~big_r(tptp_fun_W2_6(X1!8), tptp_fun_Z2_7(X1!8))))) | ![Y1: $i] : ((~big_p(Y1)) | (~big_r(X1!8, Y1)))),
% 4.16/2.98 inference(unit_resolution,[status(thm)],[133, 132])).
% 4.16/2.98 tff(135,plain,
% 4.16/2.98 (![Y1: $i] : ((~big_p(Y1)) | (~big_r(X1!8, Y1)))),
% 4.16/2.98 inference(unit_resolution,[status(thm)],[134, 34, 17])).
% 4.16/2.98 tff(136,plain,
% 4.16/2.98 (((~big_p(a)) | (~big_p(Y1!9)) | (~big_r(X1!8, Y1!9)) | (~![Z2: $i, W2: $i] : ((~big_p(Z2)) | (~big_r(X1!8, W2)) | (~big_r(W2, Z2))))) | big_r(X1!8, Y1!9)),
% 4.16/2.98 inference(tautology,[status(thm)],[])).
% 4.16/2.98 tff(137,plain,
% 4.16/2.98 (big_r(X1!8, Y1!9)),
% 4.16/2.98 inference(unit_resolution,[status(thm)],[136, 18])).
% 4.16/2.98 tff(138,plain,
% 4.16/2.98 (((~big_p(a)) | (~big_p(Y1!9)) | (~big_r(X1!8, Y1!9)) | (~![Z2: $i, W2: $i] : ((~big_p(Z2)) | (~big_r(X1!8, W2)) | (~big_r(W2, Z2))))) | big_p(Y1!9)),
% 4.16/2.98 inference(tautology,[status(thm)],[])).
% 4.16/2.98 tff(139,plain,
% 4.16/2.98 (big_p(Y1!9)),
% 4.16/2.98 inference(unit_resolution,[status(thm)],[138, 18])).
% 4.16/2.98 tff(140,plain,
% 4.16/2.98 (((~![Y1: $i] : ((~big_p(Y1)) | (~big_r(X1!8, Y1)))) | ((~big_p(Y1!9)) | (~big_r(X1!8, Y1!9)))) <=> ((~![Y1: $i] : ((~big_p(Y1)) | (~big_r(X1!8, Y1)))) | (~big_p(Y1!9)) | (~big_r(X1!8, Y1!9)))),
% 4.16/2.98 inference(rewrite,[status(thm)],[])).
% 4.16/2.98 tff(141,plain,
% 4.16/2.98 ((~![Y1: $i] : ((~big_p(Y1)) | (~big_r(X1!8, Y1)))) | ((~big_p(Y1!9)) | (~big_r(X1!8, Y1!9)))),
% 4.16/2.98 inference(quant_inst,[status(thm)],[])).
% 4.16/2.98 tff(142,plain,
% 4.16/2.98 ((~![Y1: $i] : ((~big_p(Y1)) | (~big_r(X1!8, Y1)))) | (~big_p(Y1!9)) | (~big_r(X1!8, Y1!9))),
% 4.16/2.98 inference(modus_ponens,[status(thm)],[141, 140])).
% 4.16/2.98 tff(143,plain,
% 4.16/2.98 ($false),
% 4.16/2.98 inference(unit_resolution,[status(thm)],[142, 139, 137, 135])).
% 4.16/2.98 tff(144,plain,(((~big_p(a)) | (~big_p(Y1!9)) | (~big_r(X1!8, Y1!9)) | (~![Z2: $i, W2: $i] : ((~big_p(Z2)) | (~big_r(X1!8, W2)) | (~big_r(W2, Z2))))) | (~((~big_p(a)) | (~((~big_p(tptp_fun_Z2_7(X1!8))) | (~big_r(X1!8, tptp_fun_W2_6(X1!8))) | (~big_r(tptp_fun_W2_6(X1!8), tptp_fun_Z2_7(X1!8))))) | ![Y1: $i] : ((~big_p(Y1)) | (~big_r(X1!8, Y1)))))), inference(lemma,lemma(discharge,[]))).
% 4.16/2.98 tff(145,plain,
% 4.16/2.98 ((~big_p(a)) | (~big_p(Y1!9)) | (~big_r(X1!8, Y1!9)) | (~![Z2: $i, W2: $i] : ((~big_p(Z2)) | (~big_r(X1!8, W2)) | (~big_r(W2, Z2))))),
% 4.16/2.98 inference(unit_resolution,[status(thm)],[144, 16])).
% 4.16/2.98 tff(146,plain,
% 4.16/2.98 (~((~big_p(a)) | (~((~big_p(X!0)) | (~((~big_p(Y!1)) | (~big_r(X!0, Y!1)))))) | (~![Z: $i, W: $i] : ((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z)))))),
% 4.16/2.98 inference(unit_resolution,[status(thm)],[130, 145])).
% 4.16/2.98 tff(147,plain,
% 4.16/2.98 (((~((~big_p(a)) | big_p(X!0) | (~((~big_r(tptp_fun_W1_4(X!0), tptp_fun_Z1_5(X!0))) | (~big_p(tptp_fun_Z1_5(X!0))) | (~big_r(X!0, tptp_fun_W1_4(X!0))))))) | (~((~big_p(a)) | (~((~big_p(tptp_fun_Z2_7(X!0))) | (~big_r(X!0, tptp_fun_W2_6(X!0))) | (~big_r(tptp_fun_W2_6(X!0), tptp_fun_Z2_7(X!0))))) | ![Y1: $i] : ((~big_p(Y1)) | (~big_r(X!0, Y1)))))) | ((~big_p(a)) | big_p(X!0) | (~((~big_r(tptp_fun_W1_4(X!0), tptp_fun_Z1_5(X!0))) | (~big_p(tptp_fun_Z1_5(X!0))) | (~big_r(X!0, tptp_fun_W1_4(X!0))))))),
% 4.16/2.98 inference(tautology,[status(thm)],[])).
% 4.16/2.98 tff(148,plain,
% 4.16/2.98 ((~big_p(a)) | big_p(X!0) | (~((~big_r(tptp_fun_W1_4(X!0), tptp_fun_Z1_5(X!0))) | (~big_p(tptp_fun_Z1_5(X!0))) | (~big_r(X!0, tptp_fun_W1_4(X!0)))))),
% 4.16/2.98 inference(unit_resolution,[status(thm)],[147, 10])).
% 4.16/2.98 tff(149,assumption,((~big_p(Y!1)) | (~big_r(X!0, Y!1))), introduced(assumption)).
% 4.16/2.98 tff(150,assumption,(~((~big_p(a)) | (~((~big_p(X!0)) | (~((~big_p(Y!1)) | (~big_r(X!0, Y!1)))))) | (~![Z: $i, W: $i] : ((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z)))))), introduced(assumption)).
% 4.16/2.98 tff(151,plain,
% 4.16/2.98 (((~big_p(a)) | (~((~big_p(X!0)) | (~((~big_p(Y!1)) | (~big_r(X!0, Y!1)))))) | (~![Z: $i, W: $i] : ((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z))))) | ((~big_p(X!0)) | (~((~big_p(Y!1)) | (~big_r(X!0, Y!1)))))),
% 4.16/2.98 inference(tautology,[status(thm)],[])).
% 4.16/2.98 tff(152,plain,
% 4.16/2.98 ((~big_p(X!0)) | (~((~big_p(Y!1)) | (~big_r(X!0, Y!1))))),
% 4.16/2.98 inference(unit_resolution,[status(thm)],[151, 150])).
% 4.16/2.98 tff(153,plain,
% 4.16/2.98 ((~((~big_p(X!0)) | (~((~big_p(Y!1)) | (~big_r(X!0, Y!1)))))) | (~big_p(X!0)) | (~((~big_p(Y!1)) | (~big_r(X!0, Y!1))))),
% 4.16/2.98 inference(tautology,[status(thm)],[])).
% 4.16/2.98 tff(154,plain,
% 4.16/2.98 (~big_p(X!0)),
% 4.16/2.98 inference(unit_resolution,[status(thm)],[153, 152, 149])).
% 4.16/2.98 tff(155,plain,
% 4.16/2.98 ((~((~big_p(a)) | big_p(X!0) | (~((~big_r(tptp_fun_W1_4(X!0), tptp_fun_Z1_5(X!0))) | (~big_p(tptp_fun_Z1_5(X!0))) | (~big_r(X!0, tptp_fun_W1_4(X!0))))))) | (~big_p(a)) | big_p(X!0) | (~((~big_r(tptp_fun_W1_4(X!0), tptp_fun_Z1_5(X!0))) | (~big_p(tptp_fun_Z1_5(X!0))) | (~big_r(X!0, tptp_fun_W1_4(X!0)))))),
% 4.16/2.98 inference(tautology,[status(thm)],[])).
% 4.16/2.98 tff(156,plain,
% 4.16/2.98 ((~((~big_p(a)) | big_p(X!0) | (~((~big_r(tptp_fun_W1_4(X!0), tptp_fun_Z1_5(X!0))) | (~big_p(tptp_fun_Z1_5(X!0))) | (~big_r(X!0, tptp_fun_W1_4(X!0))))))) | (~((~big_r(tptp_fun_W1_4(X!0), tptp_fun_Z1_5(X!0))) | (~big_p(tptp_fun_Z1_5(X!0))) | (~big_r(X!0, tptp_fun_W1_4(X!0)))))),
% 4.16/2.98 inference(unit_resolution,[status(thm)],[155, 132, 154])).
% 4.16/2.98 tff(157,plain,
% 4.16/2.98 (~((~big_r(tptp_fun_W1_4(X!0), tptp_fun_Z1_5(X!0))) | (~big_p(tptp_fun_Z1_5(X!0))) | (~big_r(X!0, tptp_fun_W1_4(X!0))))),
% 4.16/2.98 inference(unit_resolution,[status(thm)],[156, 148])).
% 4.16/2.98 tff(158,plain,
% 4.16/2.98 (((~big_r(tptp_fun_W1_4(X!0), tptp_fun_Z1_5(X!0))) | (~big_p(tptp_fun_Z1_5(X!0))) | (~big_r(X!0, tptp_fun_W1_4(X!0)))) | big_r(X!0, tptp_fun_W1_4(X!0))),
% 4.16/2.98 inference(tautology,[status(thm)],[])).
% 4.16/2.98 tff(159,plain,
% 4.16/2.98 (big_r(X!0, tptp_fun_W1_4(X!0))),
% 4.16/2.98 inference(unit_resolution,[status(thm)],[158, 157])).
% 4.16/2.98 tff(160,plain,
% 4.16/2.98 (((~big_r(tptp_fun_W1_4(X!0), tptp_fun_Z1_5(X!0))) | (~big_p(tptp_fun_Z1_5(X!0))) | (~big_r(X!0, tptp_fun_W1_4(X!0)))) | big_p(tptp_fun_Z1_5(X!0))),
% 4.16/2.98 inference(tautology,[status(thm)],[])).
% 4.16/2.98 tff(161,plain,
% 4.16/2.98 (big_p(tptp_fun_Z1_5(X!0))),
% 4.16/2.98 inference(unit_resolution,[status(thm)],[160, 157])).
% 4.16/2.98 tff(162,plain,
% 4.16/2.98 (((~big_r(tptp_fun_W1_4(X!0), tptp_fun_Z1_5(X!0))) | (~big_p(tptp_fun_Z1_5(X!0))) | (~big_r(X!0, tptp_fun_W1_4(X!0)))) | big_r(tptp_fun_W1_4(X!0), tptp_fun_Z1_5(X!0))),
% 4.16/2.98 inference(tautology,[status(thm)],[])).
% 4.16/2.98 tff(163,plain,
% 4.16/2.98 (big_r(tptp_fun_W1_4(X!0), tptp_fun_Z1_5(X!0))),
% 4.16/2.98 inference(unit_resolution,[status(thm)],[162, 157])).
% 4.16/2.98 tff(164,plain,
% 4.16/2.98 (((~big_p(a)) | (~((~big_p(X!0)) | (~((~big_p(Y!1)) | (~big_r(X!0, Y!1)))))) | (~![Z: $i, W: $i] : ((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z))))) | ![Z: $i, W: $i] : ((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z)))),
% 4.30/2.99 inference(tautology,[status(thm)],[])).
% 4.30/2.99 tff(165,plain,
% 4.30/2.99 (![Z: $i, W: $i] : ((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z)))),
% 4.30/2.99 inference(unit_resolution,[status(thm)],[164, 150])).
% 4.30/2.99 tff(166,plain,
% 4.30/2.99 (((~![Z: $i, W: $i] : ((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z)))) | ((~big_p(tptp_fun_Z1_5(X!0))) | (~big_r(X!0, tptp_fun_W1_4(X!0))) | (~big_r(tptp_fun_W1_4(X!0), tptp_fun_Z1_5(X!0))))) <=> ((~![Z: $i, W: $i] : ((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z)))) | (~big_p(tptp_fun_Z1_5(X!0))) | (~big_r(X!0, tptp_fun_W1_4(X!0))) | (~big_r(tptp_fun_W1_4(X!0), tptp_fun_Z1_5(X!0))))),
% 4.30/2.99 inference(rewrite,[status(thm)],[])).
% 4.30/2.99 tff(167,plain,
% 4.30/2.99 ((~![Z: $i, W: $i] : ((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z)))) | ((~big_p(tptp_fun_Z1_5(X!0))) | (~big_r(X!0, tptp_fun_W1_4(X!0))) | (~big_r(tptp_fun_W1_4(X!0), tptp_fun_Z1_5(X!0))))),
% 4.30/2.99 inference(quant_inst,[status(thm)],[])).
% 4.30/2.99 tff(168,plain,
% 4.30/2.99 ((~![Z: $i, W: $i] : ((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z)))) | (~big_p(tptp_fun_Z1_5(X!0))) | (~big_r(X!0, tptp_fun_W1_4(X!0))) | (~big_r(tptp_fun_W1_4(X!0), tptp_fun_Z1_5(X!0)))),
% 4.30/2.99 inference(modus_ponens,[status(thm)],[167, 166])).
% 4.30/2.99 tff(169,plain,
% 4.30/2.99 ($false),
% 4.30/2.99 inference(unit_resolution,[status(thm)],[168, 165, 163, 161, 159])).
% 4.30/2.99 tff(170,plain,(((~big_p(a)) | (~((~big_p(X!0)) | (~((~big_p(Y!1)) | (~big_r(X!0, Y!1)))))) | (~![Z: $i, W: $i] : ((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z))))) | (~![X1: $i] : (~((~((~big_p(a)) | big_p(X1) | (~((~big_r(tptp_fun_W1_4(X1), tptp_fun_Z1_5(X1))) | (~big_p(tptp_fun_Z1_5(X1))) | (~big_r(X1, tptp_fun_W1_4(X1))))))) | (~((~big_p(a)) | (~((~big_p(tptp_fun_Z2_7(X1))) | (~big_r(X1, tptp_fun_W2_6(X1))) | (~big_r(tptp_fun_W2_6(X1), tptp_fun_Z2_7(X1))))) | ![Y1: $i] : ((~big_p(Y1)) | (~big_r(X1, Y1)))))))) | (~((~big_p(Y!1)) | (~big_r(X!0, Y!1))))), inference(lemma,lemma(discharge,[]))).
% 4.30/2.99 tff(171,plain,
% 4.30/2.99 (~((~big_p(Y!1)) | (~big_r(X!0, Y!1)))),
% 4.30/2.99 inference(unit_resolution,[status(thm)],[170, 146, 8])).
% 4.30/2.99 tff(172,plain,
% 4.30/2.99 (((~big_p(Y!1)) | (~big_r(X!0, Y!1))) | big_r(X!0, Y!1)),
% 4.30/2.99 inference(tautology,[status(thm)],[])).
% 4.30/2.99 tff(173,plain,
% 4.30/2.99 (big_r(X!0, Y!1)),
% 4.30/2.99 inference(unit_resolution,[status(thm)],[172, 171])).
% 4.30/2.99 tff(174,plain,
% 4.30/2.99 (((~big_p(Y!1)) | (~big_r(X!0, Y!1))) | big_p(Y!1)),
% 4.30/2.99 inference(tautology,[status(thm)],[])).
% 4.30/2.99 tff(175,plain,
% 4.30/2.99 (big_p(Y!1)),
% 4.30/2.99 inference(unit_resolution,[status(thm)],[174, 171])).
% 4.30/2.99 tff(176,assumption,(![Y1: $i] : ((~big_p(Y1)) | (~big_r(X!0, Y1)))), introduced(assumption)).
% 4.30/2.99 tff(177,assumption,(big_r(X!0, Y!1)), introduced(assumption)).
% 4.30/2.99 tff(178,assumption,(big_p(Y!1)), introduced(assumption)).
% 4.30/2.99 tff(179,plain,
% 4.30/2.99 (((~![Y1: $i] : ((~big_p(Y1)) | (~big_r(X!0, Y1)))) | ((~big_p(Y!1)) | (~big_r(X!0, Y!1)))) <=> ((~![Y1: $i] : ((~big_p(Y1)) | (~big_r(X!0, Y1)))) | (~big_p(Y!1)) | (~big_r(X!0, Y!1)))),
% 4.30/2.99 inference(rewrite,[status(thm)],[])).
% 4.30/2.99 tff(180,plain,
% 4.30/2.99 ((~![Y1: $i] : ((~big_p(Y1)) | (~big_r(X!0, Y1)))) | ((~big_p(Y!1)) | (~big_r(X!0, Y!1)))),
% 4.30/2.99 inference(quant_inst,[status(thm)],[])).
% 4.30/2.99 tff(181,plain,
% 4.30/2.99 ((~![Y1: $i] : ((~big_p(Y1)) | (~big_r(X!0, Y1)))) | (~big_p(Y!1)) | (~big_r(X!0, Y!1))),
% 4.30/2.99 inference(modus_ponens,[status(thm)],[180, 179])).
% 4.30/2.99 tff(182,plain,
% 4.30/2.99 ($false),
% 4.30/2.99 inference(unit_resolution,[status(thm)],[181, 178, 177, 176])).
% 4.30/2.99 tff(183,plain,((~![Y1: $i] : ((~big_p(Y1)) | (~big_r(X!0, Y1)))) | (~big_p(Y!1)) | (~big_r(X!0, Y!1))), inference(lemma,lemma(discharge,[]))).
% 4.30/2.99 tff(184,plain,
% 4.30/2.99 (~![Y1: $i] : ((~big_p(Y1)) | (~big_r(X!0, Y1)))),
% 4.30/2.99 inference(unit_resolution,[status(thm)],[183, 175, 173])).
% 4.30/2.99 tff(185,plain,
% 4.30/2.99 ((~((~big_p(a)) | (~((~big_p(tptp_fun_Z2_7(X!0))) | (~big_r(X!0, tptp_fun_W2_6(X!0))) | (~big_r(tptp_fun_W2_6(X!0), tptp_fun_Z2_7(X!0))))) | ![Y1: $i] : ((~big_p(Y1)) | (~big_r(X!0, Y1))))) | (~big_p(a)) | (~((~big_p(tptp_fun_Z2_7(X!0))) | (~big_r(X!0, tptp_fun_W2_6(X!0))) | (~big_r(tptp_fun_W2_6(X!0), tptp_fun_Z2_7(X!0))))) | ![Y1: $i] : ((~big_p(Y1)) | (~big_r(X!0, Y1)))),
% 4.30/2.99 inference(tautology,[status(thm)],[])).
% 4.30/2.99 tff(186,plain,
% 4.30/2.99 ((~((~big_p(a)) | (~((~big_p(tptp_fun_Z2_7(X!0))) | (~big_r(X!0, tptp_fun_W2_6(X!0))) | (~big_r(tptp_fun_W2_6(X!0), tptp_fun_Z2_7(X!0))))) | ![Y1: $i] : ((~big_p(Y1)) | (~big_r(X!0, Y1))))) | (~((~big_p(tptp_fun_Z2_7(X!0))) | (~big_r(X!0, tptp_fun_W2_6(X!0))) | (~big_r(tptp_fun_W2_6(X!0), tptp_fun_Z2_7(X!0))))) | ![Y1: $i] : ((~big_p(Y1)) | (~big_r(X!0, Y1)))),
% 4.30/2.99 inference(unit_resolution,[status(thm)],[185, 132])).
% 4.30/2.99 tff(187,plain,
% 4.30/2.99 (~((~big_p(tptp_fun_Z2_7(X!0))) | (~big_r(X!0, tptp_fun_W2_6(X!0))) | (~big_r(tptp_fun_W2_6(X!0), tptp_fun_Z2_7(X!0))))),
% 4.30/2.99 inference(unit_resolution,[status(thm)],[186, 184, 12])).
% 4.30/2.99 tff(188,plain,
% 4.30/2.99 (((~big_p(tptp_fun_Z2_7(X!0))) | (~big_r(X!0, tptp_fun_W2_6(X!0))) | (~big_r(tptp_fun_W2_6(X!0), tptp_fun_Z2_7(X!0)))) | big_r(tptp_fun_W2_6(X!0), tptp_fun_Z2_7(X!0))),
% 4.30/2.99 inference(tautology,[status(thm)],[])).
% 4.30/2.99 tff(189,plain,
% 4.30/2.99 (big_r(tptp_fun_W2_6(X!0), tptp_fun_Z2_7(X!0))),
% 4.30/2.99 inference(unit_resolution,[status(thm)],[188, 187])).
% 4.30/2.99 tff(190,plain,
% 4.30/2.99 (((~big_p(tptp_fun_Z2_7(X!0))) | (~big_r(X!0, tptp_fun_W2_6(X!0))) | (~big_r(tptp_fun_W2_6(X!0), tptp_fun_Z2_7(X!0)))) | big_r(X!0, tptp_fun_W2_6(X!0))),
% 4.30/2.99 inference(tautology,[status(thm)],[])).
% 4.30/2.99 tff(191,plain,
% 4.30/2.99 (big_r(X!0, tptp_fun_W2_6(X!0))),
% 4.30/2.99 inference(unit_resolution,[status(thm)],[190, 187])).
% 4.30/2.99 tff(192,plain,
% 4.30/2.99 (((~big_p(tptp_fun_Z2_7(X!0))) | (~big_r(X!0, tptp_fun_W2_6(X!0))) | (~big_r(tptp_fun_W2_6(X!0), tptp_fun_Z2_7(X!0)))) | big_p(tptp_fun_Z2_7(X!0))),
% 4.30/2.99 inference(tautology,[status(thm)],[])).
% 4.30/2.99 tff(193,plain,
% 4.30/2.99 (big_p(tptp_fun_Z2_7(X!0))),
% 4.30/2.99 inference(unit_resolution,[status(thm)],[192, 187])).
% 4.30/2.99 tff(194,plain,
% 4.30/2.99 (![Z: $i, W: $i] : ((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z)))),
% 4.30/2.99 inference(unit_resolution,[status(thm)],[164, 146])).
% 4.30/2.99 tff(195,plain,
% 4.30/2.99 (((~![Z: $i, W: $i] : ((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z)))) | ((~big_p(tptp_fun_Z2_7(X!0))) | (~big_r(X!0, tptp_fun_W2_6(X!0))) | (~big_r(tptp_fun_W2_6(X!0), tptp_fun_Z2_7(X!0))))) <=> ((~![Z: $i, W: $i] : ((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z)))) | (~big_p(tptp_fun_Z2_7(X!0))) | (~big_r(X!0, tptp_fun_W2_6(X!0))) | (~big_r(tptp_fun_W2_6(X!0), tptp_fun_Z2_7(X!0))))),
% 4.30/2.99 inference(rewrite,[status(thm)],[])).
% 4.30/2.99 tff(196,plain,
% 4.30/2.99 ((~![Z: $i, W: $i] : ((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z)))) | ((~big_p(tptp_fun_Z2_7(X!0))) | (~big_r(X!0, tptp_fun_W2_6(X!0))) | (~big_r(tptp_fun_W2_6(X!0), tptp_fun_Z2_7(X!0))))),
% 4.30/2.99 inference(quant_inst,[status(thm)],[])).
% 4.30/2.99 tff(197,plain,
% 4.30/2.99 ((~![Z: $i, W: $i] : ((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z)))) | (~big_p(tptp_fun_Z2_7(X!0))) | (~big_r(X!0, tptp_fun_W2_6(X!0))) | (~big_r(tptp_fun_W2_6(X!0), tptp_fun_Z2_7(X!0)))),
% 4.30/2.99 inference(modus_ponens,[status(thm)],[196, 195])).
% 4.30/2.99 tff(198,plain,
% 4.30/2.99 ($false),
% 4.30/2.99 inference(unit_resolution,[status(thm)],[197, 194, 193, 191, 189])).
% 4.30/2.99 tff(199,plain,(~![X1: $i] : (~((~((~big_p(a)) | big_p(X1) | (~((~big_r(tptp_fun_W1_4(X1), tptp_fun_Z1_5(X1))) | (~big_p(tptp_fun_Z1_5(X1))) | (~big_r(X1, tptp_fun_W1_4(X1))))))) | (~((~big_p(a)) | (~((~big_p(tptp_fun_Z2_7(X1))) | (~big_r(X1, tptp_fun_W2_6(X1))) | (~big_r(tptp_fun_W2_6(X1), tptp_fun_Z2_7(X1))))) | ![Y1: $i] : ((~big_p(Y1)) | (~big_r(X1, Y1)))))))), inference(lemma,lemma(discharge,[]))).
% 4.30/2.99 tff(200,plain,
% 4.30/2.99 (![X: $i] : ((~big_p(a)) | (~((~big_p(tptp_fun_Z_3(X))) | (~big_r(X, tptp_fun_W_2(X))) | (~big_r(tptp_fun_W_2(X), tptp_fun_Z_3(X))))) | (~((~big_p(X)) | (~![Y: $i] : ((~big_p(Y)) | (~big_r(X, Y)))))))),
% 4.30/2.99 inference(unit_resolution,[status(thm)],[88, 199])).
% 4.30/2.99 tff(201,assumption,(~((~big_p(tptp_fun_Z_3(X!0))) | (~big_r(X!0, tptp_fun_W_2(X!0))) | (~big_r(tptp_fun_W_2(X!0), tptp_fun_Z_3(X!0))))), introduced(assumption)).
% 4.30/2.99 tff(202,plain,
% 4.30/2.99 (((~big_p(tptp_fun_Z_3(X!0))) | (~big_r(X!0, tptp_fun_W_2(X!0))) | (~big_r(tptp_fun_W_2(X!0), tptp_fun_Z_3(X!0)))) | big_r(tptp_fun_W_2(X!0), tptp_fun_Z_3(X!0))),
% 4.30/2.99 inference(tautology,[status(thm)],[])).
% 4.30/2.99 tff(203,plain,
% 4.30/2.99 (big_r(tptp_fun_W_2(X!0), tptp_fun_Z_3(X!0))),
% 4.30/2.99 inference(unit_resolution,[status(thm)],[202, 201])).
% 4.30/2.99 tff(204,plain,
% 4.30/2.99 (((~big_p(tptp_fun_Z_3(X!0))) | (~big_r(X!0, tptp_fun_W_2(X!0))) | (~big_r(tptp_fun_W_2(X!0), tptp_fun_Z_3(X!0)))) | big_r(X!0, tptp_fun_W_2(X!0))),
% 4.30/2.99 inference(tautology,[status(thm)],[])).
% 4.30/2.99 tff(205,plain,
% 4.30/2.99 (big_r(X!0, tptp_fun_W_2(X!0))),
% 4.30/2.99 inference(unit_resolution,[status(thm)],[204, 201])).
% 4.30/2.99 tff(206,plain,
% 4.30/2.99 (((~big_p(tptp_fun_Z_3(X!0))) | (~big_r(X!0, tptp_fun_W_2(X!0))) | (~big_r(tptp_fun_W_2(X!0), tptp_fun_Z_3(X!0)))) | big_p(tptp_fun_Z_3(X!0))),
% 4.30/2.99 inference(tautology,[status(thm)],[])).
% 4.30/2.99 tff(207,plain,
% 4.30/2.99 (big_p(tptp_fun_Z_3(X!0))),
% 4.30/2.99 inference(unit_resolution,[status(thm)],[206, 201])).
% 4.30/2.99 tff(208,assumption,(![Z: $i, W: $i] : ((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z)))), introduced(assumption)).
% 4.30/2.99 tff(209,plain,
% 4.30/2.99 (((~![Z: $i, W: $i] : ((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z)))) | ((~big_p(tptp_fun_Z_3(X!0))) | (~big_r(X!0, tptp_fun_W_2(X!0))) | (~big_r(tptp_fun_W_2(X!0), tptp_fun_Z_3(X!0))))) <=> ((~![Z: $i, W: $i] : ((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z)))) | (~big_p(tptp_fun_Z_3(X!0))) | (~big_r(X!0, tptp_fun_W_2(X!0))) | (~big_r(tptp_fun_W_2(X!0), tptp_fun_Z_3(X!0))))),
% 4.30/2.99 inference(rewrite,[status(thm)],[])).
% 4.30/2.99 tff(210,plain,
% 4.30/2.99 ((~![Z: $i, W: $i] : ((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z)))) | ((~big_p(tptp_fun_Z_3(X!0))) | (~big_r(X!0, tptp_fun_W_2(X!0))) | (~big_r(tptp_fun_W_2(X!0), tptp_fun_Z_3(X!0))))),
% 4.30/2.99 inference(quant_inst,[status(thm)],[])).
% 4.30/2.99 tff(211,plain,
% 4.30/2.99 ((~![Z: $i, W: $i] : ((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z)))) | (~big_p(tptp_fun_Z_3(X!0))) | (~big_r(X!0, tptp_fun_W_2(X!0))) | (~big_r(tptp_fun_W_2(X!0), tptp_fun_Z_3(X!0)))),
% 4.30/2.99 inference(modus_ponens,[status(thm)],[210, 209])).
% 4.30/2.99 tff(212,plain,
% 4.30/2.99 ($false),
% 4.30/2.99 inference(unit_resolution,[status(thm)],[211, 208, 207, 205, 203])).
% 4.30/2.99 tff(213,plain,(((~big_p(tptp_fun_Z_3(X!0))) | (~big_r(X!0, tptp_fun_W_2(X!0))) | (~big_r(tptp_fun_W_2(X!0), tptp_fun_Z_3(X!0)))) | (~![Z: $i, W: $i] : ((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z))))), inference(lemma,lemma(discharge,[]))).
% 4.30/2.99 tff(214,plain,
% 4.30/2.99 ((~big_p(tptp_fun_Z_3(X!0))) | (~big_r(X!0, tptp_fun_W_2(X!0))) | (~big_r(tptp_fun_W_2(X!0), tptp_fun_Z_3(X!0)))),
% 4.30/2.99 inference(unit_resolution,[status(thm)],[213, 165])).
% 4.30/2.99 tff(215,assumption,((~big_p(X!0)) | (~![Y: $i] : ((~big_p(Y)) | (~big_r(X!0, Y))))), introduced(assumption)).
% 4.30/2.99 tff(216,assumption,((~big_p(tptp_fun_Z_3(X!0))) | (~big_r(X!0, tptp_fun_W_2(X!0))) | (~big_r(tptp_fun_W_2(X!0), tptp_fun_Z_3(X!0)))), introduced(assumption)).
% 4.30/2.99 tff(217,plain,
% 4.30/2.99 (((~![X: $i] : ((~big_p(a)) | (~((~big_p(tptp_fun_Z_3(X))) | (~big_r(X, tptp_fun_W_2(X))) | (~big_r(tptp_fun_W_2(X), tptp_fun_Z_3(X))))) | (~((~big_p(X)) | (~![Y: $i] : ((~big_p(Y)) | (~big_r(X, Y)))))))) | ((~big_p(a)) | (~((~big_p(tptp_fun_Z_3(X!0))) | (~big_r(X!0, tptp_fun_W_2(X!0))) | (~big_r(tptp_fun_W_2(X!0), tptp_fun_Z_3(X!0))))) | (~((~big_p(X!0)) | (~![Y: $i] : ((~big_p(Y)) | (~big_r(X!0, Y)))))))) <=> ((~![X: $i] : ((~big_p(a)) | (~((~big_p(tptp_fun_Z_3(X))) | (~big_r(X, tptp_fun_W_2(X))) | (~big_r(tptp_fun_W_2(X), tptp_fun_Z_3(X))))) | (~((~big_p(X)) | (~![Y: $i] : ((~big_p(Y)) | (~big_r(X, Y)))))))) | (~big_p(a)) | (~((~big_p(tptp_fun_Z_3(X!0))) | (~big_r(X!0, tptp_fun_W_2(X!0))) | (~big_r(tptp_fun_W_2(X!0), tptp_fun_Z_3(X!0))))) | (~((~big_p(X!0)) | (~![Y: $i] : ((~big_p(Y)) | (~big_r(X!0, Y)))))))),
% 4.30/2.99 inference(rewrite,[status(thm)],[])).
% 4.30/2.99 tff(218,plain,
% 4.30/2.99 ((~![X: $i] : ((~big_p(a)) | (~((~big_p(tptp_fun_Z_3(X))) | (~big_r(X, tptp_fun_W_2(X))) | (~big_r(tptp_fun_W_2(X), tptp_fun_Z_3(X))))) | (~((~big_p(X)) | (~![Y: $i] : ((~big_p(Y)) | (~big_r(X, Y)))))))) | ((~big_p(a)) | (~((~big_p(tptp_fun_Z_3(X!0))) | (~big_r(X!0, tptp_fun_W_2(X!0))) | (~big_r(tptp_fun_W_2(X!0), tptp_fun_Z_3(X!0))))) | (~((~big_p(X!0)) | (~![Y: $i] : ((~big_p(Y)) | (~big_r(X!0, Y)))))))),
% 4.30/2.99 inference(quant_inst,[status(thm)],[])).
% 4.30/2.99 tff(219,plain,
% 4.30/2.99 ((~![X: $i] : ((~big_p(a)) | (~((~big_p(tptp_fun_Z_3(X))) | (~big_r(X, tptp_fun_W_2(X))) | (~big_r(tptp_fun_W_2(X), tptp_fun_Z_3(X))))) | (~((~big_p(X)) | (~![Y: $i] : ((~big_p(Y)) | (~big_r(X, Y)))))))) | (~big_p(a)) | (~((~big_p(tptp_fun_Z_3(X!0))) | (~big_r(X!0, tptp_fun_W_2(X!0))) | (~big_r(tptp_fun_W_2(X!0), tptp_fun_Z_3(X!0))))) | (~((~big_p(X!0)) | (~![Y: $i] : ((~big_p(Y)) | (~big_r(X!0, Y))))))),
% 4.30/2.99 inference(modus_ponens,[status(thm)],[218, 217])).
% 4.30/2.99 tff(220,plain,
% 4.30/2.99 ($false),
% 4.30/2.99 inference(unit_resolution,[status(thm)],[219, 59, 132, 216, 215])).
% 4.30/2.99 tff(221,plain,((~((~big_p(X!0)) | (~![Y: $i] : ((~big_p(Y)) | (~big_r(X!0, Y)))))) | (~![X: $i] : ((~big_p(a)) | (~((~big_p(tptp_fun_Z_3(X))) | (~big_r(X, tptp_fun_W_2(X))) | (~big_r(tptp_fun_W_2(X), tptp_fun_Z_3(X))))) | (~((~big_p(X)) | (~![Y: $i] : ((~big_p(Y)) | (~big_r(X, Y)))))))) | (~((~big_p(tptp_fun_Z_3(X!0))) | (~big_r(X!0, tptp_fun_W_2(X!0))) | (~big_r(tptp_fun_W_2(X!0), tptp_fun_Z_3(X!0)))))), inference(lemma,lemma(discharge,[]))).
% 4.30/2.99 tff(222,plain,
% 4.30/2.99 (~((~big_p(X!0)) | (~![Y: $i] : ((~big_p(Y)) | (~big_r(X!0, Y)))))),
% 4.30/2.99 inference(unit_resolution,[status(thm)],[221, 214, 59])).
% 4.30/2.99 tff(223,plain,
% 4.30/2.99 (((~big_p(X!0)) | (~![Y: $i] : ((~big_p(Y)) | (~big_r(X!0, Y))))) | ![Y: $i] : ((~big_p(Y)) | (~big_r(X!0, Y)))),
% 4.30/2.99 inference(tautology,[status(thm)],[])).
% 4.30/2.99 tff(224,plain,
% 4.30/2.99 (![Y: $i] : ((~big_p(Y)) | (~big_r(X!0, Y)))),
% 4.30/2.99 inference(unit_resolution,[status(thm)],[223, 222])).
% 4.30/2.99 tff(225,plain,
% 4.30/2.99 (((~big_p(X!0)) | (~![Y: $i] : ((~big_p(Y)) | (~big_r(X!0, Y))))) | big_p(X!0)),
% 4.30/2.99 inference(tautology,[status(thm)],[])).
% 4.30/2.99 tff(226,plain,
% 4.30/2.99 (big_p(X!0)),
% 4.30/2.99 inference(unit_resolution,[status(thm)],[225, 222])).
% 4.30/2.99 tff(227,plain,
% 4.30/2.99 (~((~big_p(Y!1)) | (~big_r(X!0, Y!1)))),
% 4.30/2.99 inference(unit_resolution,[status(thm)],[153, 226, 152])).
% 4.30/2.99 tff(228,plain,
% 4.30/2.99 (big_r(X!0, Y!1)),
% 4.30/2.99 inference(unit_resolution,[status(thm)],[172, 227])).
% 4.30/2.99 tff(229,plain,
% 4.30/2.99 (big_p(Y!1)),
% 4.30/2.99 inference(unit_resolution,[status(thm)],[174, 227])).
% 4.30/2.99 tff(230,plain,
% 4.30/2.99 (((~![Y: $i] : ((~big_p(Y)) | (~big_r(X!0, Y)))) | ((~big_p(Y!1)) | (~big_r(X!0, Y!1)))) <=> ((~![Y: $i] : ((~big_p(Y)) | (~big_r(X!0, Y)))) | (~big_p(Y!1)) | (~big_r(X!0, Y!1)))),
% 4.30/2.99 inference(rewrite,[status(thm)],[])).
% 4.30/2.99 tff(231,plain,
% 4.30/2.99 ((~![Y: $i] : ((~big_p(Y)) | (~big_r(X!0, Y)))) | ((~big_p(Y!1)) | (~big_r(X!0, Y!1)))),
% 4.30/2.99 inference(quant_inst,[status(thm)],[])).
% 4.30/2.99 tff(232,plain,
% 4.30/2.99 ((~![Y: $i] : ((~big_p(Y)) | (~big_r(X!0, Y)))) | (~big_p(Y!1)) | (~big_r(X!0, Y!1))),
% 4.30/2.99 inference(modus_ponens,[status(thm)],[231, 230])).
% 4.30/2.99 tff(233,plain,
% 4.30/2.99 ($false),
% 4.30/2.99 inference(unit_resolution,[status(thm)],[232, 229, 228, 224])).
% 4.30/2.99 tff(234,plain,(((~big_p(a)) | (~((~big_p(X!0)) | (~((~big_p(Y!1)) | (~big_r(X!0, Y!1)))))) | (~![Z: $i, W: $i] : ((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z))))) | (~![X: $i] : ((~big_p(a)) | (~((~big_p(tptp_fun_Z_3(X))) | (~big_r(X, tptp_fun_W_2(X))) | (~big_r(tptp_fun_W_2(X), tptp_fun_Z_3(X))))) | (~((~big_p(X)) | (~![Y: $i] : ((~big_p(Y)) | (~big_r(X, Y))))))))), inference(lemma,lemma(discharge,[]))).
% 4.30/2.99 tff(235,plain,
% 4.30/2.99 ((~big_p(a)) | (~((~big_p(X!0)) | (~((~big_p(Y!1)) | (~big_r(X!0, Y!1)))))) | (~![Z: $i, W: $i] : ((~big_p(Z)) | (~big_r(X!0, W)) | (~big_r(W, Z))))),
% 4.30/2.99 inference(unit_resolution,[status(thm)],[234, 200])).
% 4.30/2.99 tff(236,plain,
% 4.30/2.99 (~((~big_p(a)) | (~big_p(Y1!9)) | (~big_r(X1!8, Y1!9)) | (~![Z2: $i, W2: $i] : ((~big_p(Z2)) | (~big_r(X1!8, W2)) | (~big_r(W2, Z2)))))),
% 4.30/2.99 inference(unit_resolution,[status(thm)],[130, 235])).
% 4.30/2.99 tff(237,plain,
% 4.30/2.99 (![Z2: $i, W2: $i] : ((~big_p(Z2)) | (~big_r(X1!8, W2)) | (~big_r(W2, Z2)))),
% 4.30/2.99 inference(unit_resolution,[status(thm)],[19, 236])).
% 4.30/2.99 tff(238,plain,
% 4.30/2.99 (((~![Z2: $i, W2: $i] : ((~big_p(Z2)) | (~big_r(X1!8, W2)) | (~big_r(W2, Z2)))) | ((~big_p(tptp_fun_Z_3(X1!8))) | (~big_r(X1!8, tptp_fun_W_2(X1!8))) | (~big_r(tptp_fun_W_2(X1!8), tptp_fun_Z_3(X1!8))))) <=> ((~![Z2: $i, W2: $i] : ((~big_p(Z2)) | (~big_r(X1!8, W2)) | (~big_r(W2, Z2)))) | (~big_p(tptp_fun_Z_3(X1!8))) | (~big_r(X1!8, tptp_fun_W_2(X1!8))) | (~big_r(tptp_fun_W_2(X1!8), tptp_fun_Z_3(X1!8))))),
% 4.30/2.99 inference(rewrite,[status(thm)],[])).
% 4.30/2.99 tff(239,plain,
% 4.30/2.99 ((~![Z2: $i, W2: $i] : ((~big_p(Z2)) | (~big_r(X1!8, W2)) | (~big_r(W2, Z2)))) | ((~big_p(tptp_fun_Z_3(X1!8))) | (~big_r(X1!8, tptp_fun_W_2(X1!8))) | (~big_r(tptp_fun_W_2(X1!8), tptp_fun_Z_3(X1!8))))),
% 4.30/2.99 inference(quant_inst,[status(thm)],[])).
% 4.30/2.99 tff(240,plain,
% 4.30/2.99 ((~![Z2: $i, W2: $i] : ((~big_p(Z2)) | (~big_r(X1!8, W2)) | (~big_r(W2, Z2)))) | (~big_p(tptp_fun_Z_3(X1!8))) | (~big_r(X1!8, tptp_fun_W_2(X1!8))) | (~big_r(tptp_fun_W_2(X1!8), tptp_fun_Z_3(X1!8)))),
% 4.30/2.99 inference(modus_ponens,[status(thm)],[239, 238])).
% 4.30/2.99 tff(241,plain,
% 4.30/2.99 ($false),
% 4.30/2.99 inference(unit_resolution,[status(thm)],[240, 237, 7, 5, 3])).
% 4.30/2.99 tff(242,plain,((~big_p(tptp_fun_Z_3(X1!8))) | (~big_r(X1!8, tptp_fun_W_2(X1!8))) | (~big_r(tptp_fun_W_2(X1!8), tptp_fun_Z_3(X1!8)))), inference(lemma,lemma(discharge,[]))).
% 4.30/2.99 tff(243,plain,
% 4.30/2.99 ((~![X: $i] : ((~big_p(a)) | (~((~big_p(tptp_fun_Z_3(X))) | (~big_r(X, tptp_fun_W_2(X))) | (~big_r(tptp_fun_W_2(X), tptp_fun_Z_3(X))))) | (~((~big_p(X)) | (~![Y: $i] : ((~big_p(Y)) | (~big_r(X, Y)))))))) | (~((~big_p(tptp_fun_Z_3(X1!8))) | (~big_r(X1!8, tptp_fun_W_2(X1!8))) | (~big_r(tptp_fun_W_2(X1!8), tptp_fun_Z_3(X1!8))))) | (~((~big_p(X1!8)) | (~![Y: $i] : ((~big_p(Y)) | (~big_r(X1!8, Y))))))),
% 4.30/2.99 inference(unit_resolution,[status(thm)],[62, 132])).
% 4.30/2.99 tff(244,plain,
% 4.30/2.99 ((~((~big_p(tptp_fun_Z_3(X1!8))) | (~big_r(X1!8, tptp_fun_W_2(X1!8))) | (~big_r(tptp_fun_W_2(X1!8), tptp_fun_Z_3(X1!8))))) | (~((~big_p(X1!8)) | (~![Y: $i] : ((~big_p(Y)) | (~big_r(X1!8, Y))))))),
% 4.30/2.99 inference(unit_resolution,[status(thm)],[243, 200])).
% 4.30/2.99 tff(245,plain,
% 4.30/2.99 (~((~big_p(X1!8)) | (~![Y: $i] : ((~big_p(Y)) | (~big_r(X1!8, Y)))))),
% 4.30/2.99 inference(unit_resolution,[status(thm)],[244, 242])).
% 4.30/2.99 tff(246,plain,
% 4.30/2.99 (((~big_p(X1!8)) | (~![Y: $i] : ((~big_p(Y)) | (~big_r(X1!8, Y))))) | ![Y: $i] : ((~big_p(Y)) | (~big_r(X1!8, Y)))),
% 4.30/2.99 inference(tautology,[status(thm)],[])).
% 4.30/2.99 tff(247,plain,
% 4.30/2.99 (![Y: $i] : ((~big_p(Y)) | (~big_r(X1!8, Y)))),
% 4.30/2.99 inference(unit_resolution,[status(thm)],[246, 245])).
% 4.30/2.99 tff(248,plain,
% 4.30/2.99 (big_r(X1!8, Y1!9)),
% 4.30/2.99 inference(unit_resolution,[status(thm)],[136, 236])).
% 4.30/2.99 tff(249,plain,
% 4.30/2.99 (big_p(Y1!9)),
% 4.30/2.99 inference(unit_resolution,[status(thm)],[138, 236])).
% 4.30/2.99 tff(250,plain,
% 4.30/2.99 (((~![Y: $i] : ((~big_p(Y)) | (~big_r(X1!8, Y)))) | ((~big_p(Y1!9)) | (~big_r(X1!8, Y1!9)))) <=> ((~![Y: $i] : ((~big_p(Y)) | (~big_r(X1!8, Y)))) | (~big_p(Y1!9)) | (~big_r(X1!8, Y1!9)))),
% 4.30/2.99 inference(rewrite,[status(thm)],[])).
% 4.30/2.99 tff(251,plain,
% 4.30/2.99 ((~![Y: $i] : ((~big_p(Y)) | (~big_r(X1!8, Y)))) | ((~big_p(Y1!9)) | (~big_r(X1!8, Y1!9)))),
% 4.30/2.99 inference(quant_inst,[status(thm)],[])).
% 4.30/2.99 tff(252,plain,
% 4.30/2.99 ((~![Y: $i] : ((~big_p(Y)) | (~big_r(X1!8, Y)))) | (~big_p(Y1!9)) | (~big_r(X1!8, Y1!9))),
% 4.30/2.99 inference(modus_ponens,[status(thm)],[251, 250])).
% 4.30/2.99 tff(253,plain,
% 4.30/2.99 ($false),
% 4.30/2.99 inference(unit_resolution,[status(thm)],[252, 249, 248, 247])).
% 4.30/2.99 % SZS output end Proof
%------------------------------------------------------------------------------