TSTP Solution File: SYN917+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN917+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 00:01:15 EDT 2022
% Result : Theorem 0.21s 0.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN917+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n029.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Sep 5 09:38:31 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.21/0.41 % SZS status Theorem
% 0.21/0.41 % SZS output start Proof
% 0.21/0.41 tff(p_type, type, (
% 0.21/0.41 p: $i > $o)).
% 0.21/0.41 tff(q_type, type, (
% 0.21/0.41 q: $i > $o)).
% 0.21/0.41 tff(tptp_fun_X_6_type, type, (
% 0.21/0.41 tptp_fun_X_6: $i)).
% 0.21/0.41 tff(tptp_fun_X_8_type, type, (
% 0.21/0.41 tptp_fun_X_8: $i)).
% 0.21/0.41 tff(tptp_fun_X_7_type, type, (
% 0.21/0.41 tptp_fun_X_7: $i)).
% 0.21/0.41 tff(c_type, type, (
% 0.21/0.41 c: $o)).
% 0.21/0.41 tff(tptp_fun_X_18_type, type, (
% 0.21/0.41 tptp_fun_X_18: $i)).
% 0.21/0.41 tff(tptp_fun_X_11_type, type, (
% 0.21/0.41 tptp_fun_X_11: $i)).
% 0.21/0.41 tff(tptp_fun_X_20_type, type, (
% 0.21/0.41 tptp_fun_X_20: $i)).
% 0.21/0.41 tff(tptp_fun_X_16_type, type, (
% 0.21/0.41 tptp_fun_X_16: $i)).
% 0.21/0.41 tff(f_type, type, (
% 0.21/0.41 f: $i > $o)).
% 0.21/0.41 tff(h_type, type, (
% 0.21/0.41 h: $i > $o)).
% 0.21/0.41 tff(g_type, type, (
% 0.21/0.41 g: $i > $o)).
% 0.21/0.41 tff(tptp_fun_X_3_type, type, (
% 0.21/0.41 tptp_fun_X_3: $i)).
% 0.21/0.41 tff(tptp_fun_X_4_type, type, (
% 0.21/0.41 tptp_fun_X_4: $i)).
% 0.21/0.41 tff(tptp_fun_X_9_type, type, (
% 0.21/0.41 tptp_fun_X_9: $i)).
% 0.21/0.41 tff(tptp_fun_X_19_type, type, (
% 0.21/0.41 tptp_fun_X_19: $i)).
% 0.21/0.41 tff(tptp_fun_Y_14_type, type, (
% 0.21/0.41 tptp_fun_Y_14: $i)).
% 0.21/0.41 tff(tptp_fun_Y_0_type, type, (
% 0.21/0.41 tptp_fun_Y_0: $i)).
% 0.21/0.41 tff(tptp_fun_X_17_type, type, (
% 0.21/0.41 tptp_fun_X_17: $i)).
% 0.21/0.41 tff(tptp_fun_X_12_type, type, (
% 0.21/0.41 tptp_fun_X_12: $i)).
% 0.21/0.41 tff(tptp_fun_X_10_type, type, (
% 0.21/0.41 tptp_fun_X_10: $i)).
% 0.21/0.41 tff(tptp_fun_X_21_type, type, (
% 0.21/0.41 tptp_fun_X_21: $i)).
% 0.21/0.41 tff(tptp_fun_Y_5_type, type, (
% 0.21/0.41 tptp_fun_Y_5: $i > $i)).
% 0.21/0.41 tff(r_type, type, (
% 0.21/0.41 r: ( $i * $i ) > $o)).
% 0.21/0.41 tff(tptp_fun_X_2_type, type, (
% 0.21/0.41 tptp_fun_X_2: $i)).
% 0.21/0.41 tff(tptp_fun_Y_1_type, type, (
% 0.21/0.41 tptp_fun_Y_1: $i)).
% 0.21/0.41 tff(tptp_fun_X_13_type, type, (
% 0.21/0.41 tptp_fun_X_13: $i)).
% 0.21/0.41 tff(tptp_fun_Y_15_type, type, (
% 0.21/0.41 tptp_fun_Y_15: $i)).
% 0.21/0.41 tff(1,assumption,(~![X: $i] : p(X)), introduced(assumption)).
% 0.21/0.41 tff(2,plain,
% 0.21/0.41 (((~![X: $i] : p(X)) | (~![X: $i] : q(X))) | ![X: $i] : p(X)),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(3,plain,
% 0.21/0.41 ((~![X: $i] : p(X)) | (~![X: $i] : q(X))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.21/0.41 tff(4,assumption,(~p(X!11)), introduced(assumption)).
% 0.21/0.41 tff(5,assumption,(![X: $i] : p(X)), introduced(assumption)).
% 0.21/0.41 tff(6,plain,
% 0.21/0.41 ((~![X: $i] : p(X)) | p(X!11)),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(7,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[6, 5, 4])).
% 0.21/0.41 tff(8,plain,((~![X: $i] : p(X)) | p(X!11)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(9,plain,
% 0.21/0.41 (~![X: $i] : p(X)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[8, 4])).
% 0.21/0.41 tff(10,plain,
% 0.21/0.41 ((~![X: $i] : p(X)) | (~![X: $i] : q(X))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[2, 9])).
% 0.21/0.41 tff(11,plain,
% 0.21/0.41 (((~p(X!11)) | (~q(X!11))) | p(X!11)),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(12,plain,
% 0.21/0.41 ((~p(X!11)) | (~q(X!11))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[11, 4])).
% 0.21/0.41 tff(13,assumption,(![X: $i] : (~((~p(X)) | (~q(X))))), introduced(assumption)).
% 0.21/0.41 tff(14,plain,
% 0.21/0.41 ((~![X: $i] : (~((~p(X)) | (~q(X))))) | (~((~p(X!11)) | (~q(X!11))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(15,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[14, 13, 12])).
% 0.21/0.41 tff(16,plain,((~![X: $i] : (~((~p(X)) | (~q(X))))) | p(X!11)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(17,plain,
% 0.21/0.41 (~![X: $i] : (~((~p(X)) | (~q(X))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[16, 4])).
% 0.21/0.41 tff(18,plain,
% 0.21/0.41 ((~((~((~![X: $i] : p(X)) | (~![X: $i] : q(X)))) | ![X: $i] : (~((~p(X)) | (~q(X)))))) | (~((~![X: $i] : p(X)) | (~![X: $i] : q(X)))) | ![X: $i] : (~((~p(X)) | (~q(X))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(19,plain,
% 0.21/0.41 (~((~((~![X: $i] : p(X)) | (~![X: $i] : q(X)))) | ![X: $i] : (~((~p(X)) | (~q(X)))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[18, 17, 10])).
% 0.21/0.41 tff(20,plain,
% 0.21/0.41 (((~((~p(X!7)) | (~q(X!8)) | (~p(X!6)) | (~q(X!6)))) | (~((~((~![X: $i] : p(X)) | (~![X: $i] : q(X)))) | ![X: $i] : (~((~p(X)) | (~q(X))))))) | ((~((~![X: $i] : p(X)) | (~![X: $i] : q(X)))) | ![X: $i] : (~((~p(X)) | (~q(X)))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(21,plain,
% 0.21/0.41 ((~((~p(X!7)) | (~q(X!8)) | (~p(X!6)) | (~q(X!6)))) | (~((~((~![X: $i] : p(X)) | (~![X: $i] : q(X)))) | ![X: $i] : (~((~p(X)) | (~q(X))))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.21/0.41 tff(22,assumption,(~c), introduced(assumption)).
% 0.21/0.41 tff(23,plain,
% 0.21/0.41 (((~c) | p(X!20)) | c),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(24,plain,
% 0.21/0.42 ((~c) | p(X!20)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.21/0.42 tff(25,plain,
% 0.21/0.42 (((~c) | p(X!7)) | c),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(26,plain,
% 0.21/0.42 ((~c) | p(X!7)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[25, 22])).
% 0.21/0.42 tff(27,plain,
% 0.21/0.42 ((~((~((~c) | p(X!20))) | (~((~c) | p(X!7))))) | (~((~c) | p(X!20))) | (~((~c) | p(X!7)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(28,plain,
% 0.21/0.42 (~((~((~c) | p(X!20))) | (~((~c) | p(X!7))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[27, 26, 24])).
% 0.21/0.42 tff(29,plain,
% 0.21/0.42 (((~((~((~c) | p(X!20))) | (~((~c) | p(X!7))))) | (~((~c) | ![X: $i] : p(X) | ![X: $i] : ((~c) | p(X))))) | ((~((~c) | p(X!20))) | (~((~c) | p(X!7))))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(30,plain,
% 0.21/0.42 ((~((~((~c) | p(X!20))) | (~((~c) | p(X!7))))) | (~((~c) | ![X: $i] : p(X) | ![X: $i] : ((~c) | p(X))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.21/0.42 tff(31,assumption,(![X: $i] : (p(X) | c)), introduced(assumption)).
% 0.21/0.42 tff(32,plain,
% 0.21/0.42 (((~![X: $i] : (p(X) | c)) | (c | p(X!11))) <=> ((~![X: $i] : (p(X) | c)) | c | p(X!11))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(33,plain,
% 0.21/0.42 ((p(X!11) | c) <=> (c | p(X!11))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(34,plain,
% 0.21/0.42 (((~![X: $i] : (p(X) | c)) | (p(X!11) | c)) <=> ((~![X: $i] : (p(X) | c)) | (c | p(X!11)))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[33])).
% 0.21/0.42 tff(35,plain,
% 0.21/0.42 (((~![X: $i] : (p(X) | c)) | (p(X!11) | c)) <=> ((~![X: $i] : (p(X) | c)) | c | p(X!11))),
% 0.21/0.42 inference(transitivity,[status(thm)],[34, 32])).
% 0.21/0.42 tff(36,plain,
% 0.21/0.42 ((~![X: $i] : (p(X) | c)) | (p(X!11) | c)),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(37,plain,
% 0.21/0.42 ((~![X: $i] : (p(X) | c)) | c | p(X!11)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.21/0.42 tff(38,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[37, 4, 22, 31])).
% 0.21/0.42 tff(39,plain,((~![X: $i] : (p(X) | c)) | p(X!11) | c), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(40,plain,
% 0.21/0.42 (~![X: $i] : (p(X) | c)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[39, 22, 4])).
% 0.21/0.42 tff(41,plain,
% 0.21/0.42 ((~(c | ![X: $i] : p(X) | ![X: $i] : (p(X) | c))) | c | ![X: $i] : p(X) | ![X: $i] : (p(X) | c)),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(42,plain,
% 0.21/0.42 (~(c | ![X: $i] : p(X) | ![X: $i] : (p(X) | c))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[41, 40, 1, 22])).
% 0.21/0.42 tff(43,plain,
% 0.21/0.42 (((~((~(c | p(X!16))) | (~(c | p(X!7))))) | (~(c | ![X: $i] : p(X) | ![X: $i] : (p(X) | c)))) | (c | ![X: $i] : p(X) | ![X: $i] : (p(X) | c))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(44,plain,
% 0.21/0.42 ((~((~(c | p(X!16))) | (~(c | p(X!7))))) | (~(c | ![X: $i] : p(X) | ![X: $i] : (p(X) | c)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.21/0.42 tff(45,assumption,((~((~p(X!7)) | (~q(X!8)) | (~p(X!6)) | (~q(X!6)))) | (~((~((~![X: $i] : p(X)) | (~![X: $i] : q(X)))) | ![X: $i] : (~((~p(X)) | (~q(X))))))), introduced(assumption)).
% 0.21/0.42 tff(46,assumption,(~(q(X!9) | p(X!9) | (~(![X: $i] : p(X) | ![X: $i] : q(X))))), introduced(assumption)).
% 0.21/0.42 tff(47,plain,
% 0.21/0.42 ((q(X!9) | p(X!9) | (~(![X: $i] : p(X) | ![X: $i] : q(X)))) | (![X: $i] : p(X) | ![X: $i] : q(X))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(48,plain,
% 0.21/0.42 (![X: $i] : p(X) | ![X: $i] : q(X)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.21/0.42 tff(49,plain,
% 0.21/0.42 ((~(![X: $i] : p(X) | ![X: $i] : q(X))) | ![X: $i] : p(X) | ![X: $i] : q(X)),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(50,plain,
% 0.21/0.42 (![X: $i] : q(X)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[49, 48, 1])).
% 0.21/0.42 tff(51,plain,
% 0.21/0.42 ((q(X!9) | p(X!9) | (~(![X: $i] : p(X) | ![X: $i] : q(X)))) | (~q(X!9))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(52,plain,
% 0.21/0.42 (~q(X!9)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[51, 46])).
% 0.21/0.42 tff(53,plain,
% 0.21/0.42 ((~![X: $i] : q(X)) | q(X!9)),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(54,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[53, 52, 50])).
% 0.21/0.42 tff(55,plain,((q(X!9) | p(X!9) | (~(![X: $i] : p(X) | ![X: $i] : q(X)))) | ![X: $i] : p(X)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(56,plain,
% 0.21/0.42 (q(X!9) | p(X!9) | (~(![X: $i] : p(X) | ![X: $i] : q(X)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[55, 1])).
% 0.21/0.42 tff(57,plain,
% 0.21/0.42 ((c | (~![X: $i] : p(X))) | ![X: $i] : p(X)),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(58,plain,
% 0.21/0.42 (c | (~![X: $i] : p(X))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[57, 1])).
% 0.21/0.42 tff(59,plain,
% 0.21/0.42 ((c | (~p(X!11))) | p(X!11)),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(60,plain,
% 0.21/0.42 (c | (~p(X!11))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[59, 4])).
% 0.21/0.42 tff(61,assumption,(c | (~p(X!11))), introduced(assumption)).
% 0.21/0.42 tff(62,assumption,(![X: $i] : (~(c | (~p(X))))), introduced(assumption)).
% 0.21/0.42 tff(63,plain,
% 0.21/0.42 ((~![X: $i] : (~(c | (~p(X))))) | (~(c | (~p(X!11))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(64,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[63, 62, 61])).
% 0.21/0.42 tff(65,plain,((~![X: $i] : (~(c | (~p(X))))) | (~(c | (~p(X!11))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(66,plain,
% 0.21/0.42 (~![X: $i] : (~(c | (~p(X))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[65, 60])).
% 0.21/0.42 tff(67,plain,
% 0.21/0.42 ((~(![X: $i] : (~(c | (~p(X)))) | (~(c | (~![X: $i] : p(X)))))) | ![X: $i] : (~(c | (~p(X)))) | (~(c | (~![X: $i] : p(X))))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(68,plain,
% 0.21/0.42 (~(![X: $i] : (~(c | (~p(X)))) | (~(c | (~![X: $i] : p(X)))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[67, 66, 58])).
% 0.21/0.42 tff(69,plain,
% 0.21/0.42 (((~(c | (~p(X!7)) | (~p(X!19)))) | (~(![X: $i] : (~(c | (~p(X)))) | (~(c | (~![X: $i] : p(X))))))) | (![X: $i] : (~(c | (~p(X)))) | (~(c | (~![X: $i] : p(X)))))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(70,plain,
% 0.21/0.42 ((~(c | (~p(X!7)) | (~p(X!19)))) | (~(![X: $i] : (~(c | (~p(X)))) | (~(c | (~![X: $i] : p(X))))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.21/0.42 tff(71,plain,
% 0.21/0.42 (((~![X: $i] : p(X)) | (~![X: $i] : (~p(X)))) | ![X: $i] : p(X)),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(72,plain,
% 0.21/0.42 ((~![X: $i] : p(X)) | (~![X: $i] : (~p(X)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[71, 1])).
% 0.21/0.42 tff(73,plain,
% 0.21/0.42 ((p(Y!14) | (~![X: $i] : p(X))) | ![X: $i] : p(X)),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(74,plain,
% 0.21/0.42 (p(Y!14) | (~![X: $i] : p(X))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[73, 1])).
% 0.21/0.42 tff(75,assumption,(p(Y!14) | (~![X: $i] : p(X))), introduced(assumption)).
% 0.21/0.42 tff(76,assumption,((~((~(c | p(X!16))) | (~(c | p(X!7))))) | (~(c | ![X: $i] : p(X) | ![X: $i] : (p(X) | c)))), introduced(assumption)).
% 0.21/0.42 tff(77,assumption,(~![V: $i] : (h(V) | (~g(V)) | (~f(V)))), introduced(assumption)).
% 0.21/0.42 tff(78,plain,
% 0.21/0.42 (((~((~(g(X!4) | (~f(X!4)))) | (~(h(X!3) | (~f(X!3)) | (~g(X!3)))))) | (~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (~(![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))) | ![V: $i] : (h(V) | (~g(V)) | (~f(V)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(79,plain,
% 0.21/0.42 ((~((~(g(X!4) | (~f(X!4)))) | (~(h(X!3) | (~f(X!3)) | (~g(X!3)))))) | (~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (~(![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.21/0.42 tff(80,assumption,(q(X!9) | p(X!9) | (~(![X: $i] : p(X) | ![X: $i] : q(X)))), introduced(assumption)).
% 0.21/0.42 tff(81,plain,
% 0.21/0.42 (((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (~![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))) | (~(![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))) | ![V: $i] : (h(V) | (~g(V)) | (~f(V)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(82,plain,
% 0.21/0.42 ((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (~![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))) | (~(![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[81, 77])).
% 0.21/0.42 tff(83,assumption,((~(c | (~p(X!7)) | (~p(X!19)))) | (~(![X: $i] : (~(c | (~p(X)))) | (~(c | (~![X: $i] : p(X))))))), introduced(assumption)).
% 0.21/0.42 tff(84,assumption,((~![X: $i] : p(X)) | (~![X: $i] : (~p(X)))), introduced(assumption)).
% 0.21/0.42 tff(85,plain,
% 0.21/0.42 (((~c) | (~p(X!11))) | p(X!11)),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(86,plain,
% 0.21/0.42 ((~c) | (~p(X!11))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[85, 4])).
% 0.21/0.42 tff(87,plain,
% 0.21/0.42 (((~c) | (~p(X!17))) | c),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(88,plain,
% 0.21/0.42 ((~c) | (~p(X!17))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[87, 22])).
% 0.21/0.42 tff(89,plain,
% 0.21/0.42 ((~((~((~c) | (~p(X!17)))) | (~((~c) | (~p(X!11)))))) | (~((~c) | (~p(X!17)))) | (~((~c) | (~p(X!11))))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(90,plain,
% 0.21/0.42 (~((~((~c) | (~p(X!17)))) | (~((~c) | (~p(X!11)))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[89, 88, 86])).
% 0.21/0.42 tff(91,plain,
% 0.21/0.42 (((~((~((~c) | (~p(X!17)))) | (~((~c) | (~p(X!11)))))) | (~((~c) | ![X: $i] : (~p(X)) | ![X: $i] : ((~p(X)) | (~c))))) | ((~((~c) | (~p(X!17)))) | (~((~c) | (~p(X!11)))))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(92,plain,
% 0.21/0.42 ((~((~((~c) | (~p(X!17)))) | (~((~c) | (~p(X!11)))))) | (~((~c) | ![X: $i] : (~p(X)) | ![X: $i] : ((~p(X)) | (~c))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.21/0.42 tff(93,plain,
% 0.21/0.42 (((~c) | (~![X: $i] : (~p(X)))) | c),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(94,plain,
% 0.21/0.42 ((~c) | (~![X: $i] : (~p(X)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[93, 22])).
% 0.21/0.42 tff(95,plain,
% 0.21/0.42 (((~c) | p(X!11)) | c),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(96,plain,
% 0.21/0.42 ((~c) | p(X!11)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[95, 22])).
% 0.21/0.42 tff(97,assumption,(![X: $i] : (~((~c) | p(X)))), introduced(assumption)).
% 0.21/0.42 tff(98,plain,
% 0.21/0.42 ((~![X: $i] : (~((~c) | p(X)))) | (~((~c) | p(X!11)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(99,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[98, 97, 96])).
% 0.21/0.42 tff(100,plain,((~![X: $i] : (~((~c) | p(X)))) | c), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(101,plain,
% 0.21/0.42 (~![X: $i] : (~((~c) | p(X)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[100, 22])).
% 0.21/0.42 tff(102,plain,
% 0.21/0.42 ((~(![X: $i] : (~((~c) | p(X))) | (~((~c) | (~![X: $i] : (~p(X))))))) | ![X: $i] : (~((~c) | p(X))) | (~((~c) | (~![X: $i] : (~p(X)))))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(103,plain,
% 0.21/0.42 (~(![X: $i] : (~((~c) | p(X))) | (~((~c) | (~![X: $i] : (~p(X))))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[102, 101, 94])).
% 0.21/0.42 tff(104,plain,
% 0.21/0.42 (((~((~c) | p(X!11) | p(X!18))) | (~(![X: $i] : (~((~c) | p(X))) | (~((~c) | (~![X: $i] : (~p(X)))))))) | (![X: $i] : (~((~c) | p(X))) | (~((~c) | (~![X: $i] : (~p(X))))))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(105,plain,
% 0.21/0.42 ((~((~c) | p(X!11) | p(X!18))) | (~(![X: $i] : (~((~c) | p(X))) | (~((~c) | (~![X: $i] : (~p(X)))))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.21/0.42 tff(106,assumption,((~((~((~c) | p(X!20))) | (~((~c) | p(X!7))))) | (~((~c) | ![X: $i] : p(X) | ![X: $i] : ((~c) | p(X))))), introduced(assumption)).
% 0.21/0.42 tff(107,assumption,(![X: $i] : (~p(X))), introduced(assumption)).
% 0.21/0.42 tff(108,assumption,(p(X!21)), introduced(assumption)).
% 0.21/0.42 tff(109,plain,
% 0.21/0.42 ((~![X: $i] : (~p(X))) | (~p(X!21))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(110,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[109, 107, 108])).
% 0.21/0.42 tff(111,plain,((~p(X!21)) | (~![X: $i] : (~p(X)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(112,plain,
% 0.21/0.42 (~p(X!21)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[111, 107])).
% 0.21/0.42 tff(113,plain,
% 0.21/0.42 ((c | (~p(X!21))) | p(X!21)),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(114,plain,
% 0.21/0.42 (c | (~p(X!21))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.21/0.42 tff(115,plain,
% 0.21/0.42 ((~((~(c | (~p(X!21)))) | (~(c | (~p(X!11)))))) | (~(c | (~p(X!21)))) | (~(c | (~p(X!11))))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(116,plain,
% 0.21/0.42 (~((~(c | (~p(X!21)))) | (~(c | (~p(X!11)))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[115, 114, 60])).
% 0.21/0.42 tff(117,plain,
% 0.21/0.42 (((~((~(c | (~p(X!21)))) | (~(c | (~p(X!11)))))) | (~(c | ![X: $i] : (~p(X)) | ![X: $i] : (c | (~p(X)))))) | ((~(c | (~p(X!21)))) | (~(c | (~p(X!11)))))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(118,plain,
% 0.21/0.42 ((~((~(c | (~p(X!21)))) | (~(c | (~p(X!11)))))) | (~(c | ![X: $i] : (~p(X)) | ![X: $i] : (c | (~p(X)))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[117, 116])).
% 0.21/0.42 tff(119,assumption,((~((~(g(X!4) | (~f(X!4)))) | (~(h(X!3) | (~f(X!3)) | (~g(X!3)))))) | (~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (~(![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))), introduced(assumption)).
% 0.21/0.42 tff(120,assumption,((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (~![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))) | (~(![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))), introduced(assumption)).
% 0.21/0.42 tff(121,assumption,((~((~((~c) | (~p(X!17)))) | (~((~c) | (~p(X!11)))))) | (~((~c) | ![X: $i] : (~p(X)) | ![X: $i] : ((~p(X)) | (~c))))), introduced(assumption)).
% 0.21/0.42 tff(122,assumption,((~((~c) | p(X!11) | p(X!18))) | (~(![X: $i] : (~((~c) | p(X))) | (~((~c) | (~![X: $i] : (~p(X)))))))), introduced(assumption)).
% 0.21/0.43 tff(123,plain,
% 0.21/0.43 ((p(X!7) | (~p(X!11))) | p(X!11)),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(124,plain,
% 0.21/0.43 (p(X!7) | (~p(X!11))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[123, 4])).
% 0.21/0.43 tff(125,assumption,(![Y: $i] : (~((~p(Y)) | p(X!7)))), introduced(assumption)).
% 0.21/0.43 tff(126,plain,
% 0.21/0.43 (((~![Y: $i] : (~((~p(Y)) | p(X!7)))) | (~(p(X!7) | (~p(X!11))))) <=> ((~![Y: $i] : (~((~p(Y)) | p(X!7)))) | (~(p(X!7) | (~p(X!11)))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(127,plain,
% 0.21/0.43 ((~((~p(X!11)) | p(X!7))) <=> (~(p(X!7) | (~p(X!11))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(128,plain,
% 0.21/0.43 (((~![Y: $i] : (~((~p(Y)) | p(X!7)))) | (~((~p(X!11)) | p(X!7)))) <=> ((~![Y: $i] : (~((~p(Y)) | p(X!7)))) | (~(p(X!7) | (~p(X!11)))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[127])).
% 0.21/0.43 tff(129,plain,
% 0.21/0.43 (((~![Y: $i] : (~((~p(Y)) | p(X!7)))) | (~((~p(X!11)) | p(X!7)))) <=> ((~![Y: $i] : (~((~p(Y)) | p(X!7)))) | (~(p(X!7) | (~p(X!11)))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[128, 126])).
% 0.21/0.43 tff(130,plain,
% 0.21/0.43 ((~![Y: $i] : (~((~p(Y)) | p(X!7)))) | (~((~p(X!11)) | p(X!7)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(131,plain,
% 0.21/0.43 ((~![Y: $i] : (~((~p(Y)) | p(X!7)))) | (~(p(X!7) | (~p(X!11))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.21/0.43 tff(132,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[131, 125, 124])).
% 0.21/0.43 tff(133,plain,((~![Y: $i] : (~((~p(Y)) | p(X!7)))) | p(X!11)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(134,plain,
% 0.21/0.43 (~![Y: $i] : (~((~p(Y)) | p(X!7)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[133, 4])).
% 0.21/0.43 tff(135,plain,
% 0.21/0.43 ((q(X!11) | (~p(X!11)) | p(tptp_fun_Y_5(X!11))) | p(X!11)),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(136,plain,
% 0.21/0.43 (q(X!11) | (~p(X!11)) | p(tptp_fun_Y_5(X!11))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[135, 4])).
% 0.21/0.43 tff(137,assumption,(![X: $i] : (~(q(X) | (~p(X)) | p(tptp_fun_Y_5(X))))), introduced(assumption)).
% 0.21/0.43 tff(138,plain,
% 0.21/0.43 ((~![X: $i] : (~(q(X) | (~p(X)) | p(tptp_fun_Y_5(X))))) | (~(q(X!11) | (~p(X!11)) | p(tptp_fun_Y_5(X!11))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(139,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[138, 137, 136])).
% 0.21/0.43 tff(140,plain,((~![X: $i] : (~(q(X) | (~p(X)) | p(tptp_fun_Y_5(X))))) | p(X!11)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(141,plain,
% 0.21/0.43 (~![X: $i] : (~(q(X) | (~p(X)) | p(tptp_fun_Y_5(X))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[140, 4])).
% 0.21/0.43 tff(142,assumption,(~((~r(X!2, Y!1)) | r(X!2, X!2) | (~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y)))))), introduced(assumption)).
% 0.21/0.43 tff(143,plain,
% 0.21/0.43 (((~r(X!2, Y!1)) | r(X!2, X!2) | (~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y))))) | ![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(144,plain,
% 0.21/0.43 (![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.21/0.43 tff(145,plain,
% 0.21/0.43 (((~r(X!2, Y!1)) | r(X!2, X!2) | (~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y))))) | r(X!2, Y!1)),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(146,plain,
% 0.21/0.43 (r(X!2, Y!1)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[145, 142])).
% 0.21/0.43 tff(147,plain,
% 0.21/0.43 (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(X!2, Y!1)) | r(Y!1, X!2))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(X!2, Y!1)) | r(Y!1, X!2))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(148,plain,
% 0.21/0.43 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(X!2, Y!1)) | r(Y!1, X!2))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(149,plain,
% 0.21/0.43 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(X!2, Y!1)) | r(Y!1, X!2)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.21/0.43 tff(150,plain,
% 0.21/0.43 (r(Y!1, X!2)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[149, 146, 144])).
% 0.21/0.43 tff(151,plain,
% 0.21/0.43 (((~r(X!2, Y!1)) | r(X!2, X!2) | (~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y))))) | ![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y)))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(152,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[151, 142])).
% 0.21/0.43 tff(153,plain,
% 0.21/0.43 (((~r(X!2, Y!1)) | r(X!2, X!2) | (~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y))))) | (~r(X!2, X!2))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(154,plain,
% 0.21/0.43 (~r(X!2, X!2)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[153, 142])).
% 0.21/0.43 tff(155,plain,
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% 0.21/0.43 inference(rewrite,[status(thm)],[])).
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% 0.21/0.43 inference(monotonicity,[status(thm)],[156])).
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% 0.21/0.44 inference(rewrite,[status(thm)],[])).
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% 0.21/0.44 inference(monotonicity,[status(thm)],[200])).
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% 0.21/0.44 inference(monotonicity,[status(thm)],[201])).
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% 0.21/0.44 inference(monotonicity,[status(thm)],[202])).
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% 0.21/0.44 inference(rewrite,[status(thm)],[])).
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% 0.21/0.44 ((~((~r(X!2, Y!1)) | r(X!2, X!2) | (~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y)))))) <=> (~((~r(X!2, Y!1)) | r(X!2, X!2) | (~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
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% 0.21/0.44 inference(rewrite,[status(thm)],[])).
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% 0.21/0.45 inference(rewrite,[status(thm)],[])).
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% 0.21/0.45 ((~![X: $i] : p(X)) <=> (~![X: $i] : p(X))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
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% 0.21/0.45 (((~![X: $i] : p(X)) | (~![X: $i] : (~p(X)))) <=> ((~![X: $i] : p(X)) | (~![X: $i] : (~p(X))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[208, 207])).
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% 0.21/0.45 ((~((~![X: $i] : p(X)) | (~![X: $i] : (~p(X))))) <=> (~((~![X: $i] : p(X)) | (~![X: $i] : (~p(X)))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[209])).
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% 0.21/0.45 ((~((~(![X: $i] : p(X) | ![X: $i] : q(X))) | q(X!9) | p(X!9))) <=> (~(q(X!9) | p(X!9) | (~(![X: $i] : p(X) | ![X: $i] : q(X)))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
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% 0.21/0.45 ((p(Y!14) | (~![X: $i] : p(X))) <=> (p(Y!14) | (~![X: $i] : p(X)))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[208])).
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% 0.21/0.45 ((~(p(Y!14) | (~![X: $i] : p(X)))) <=> (~(p(Y!14) | (~![X: $i] : p(X))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[212])).
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% 0.21/0.45 inference(monotonicity,[status(thm)],[213, 211, 210, 206, 205, 204, 203, 199, 198, 194, 193, 189, 188, 183, 182, 179])).
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% 0.21/0.46 inference(transitivity,[status(thm)],[214, 178])).
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% 0.21/0.46 inference(rewrite,[status(thm)],[])).
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% 0.21/0.46 (((~((~(![X: $i] : p(X) | ![X: $i] : q(X))) | q(X!9) | p(X!9))) | (~(p(Y!14) | (~![X: $i] : p(X)))) | (~((~![X: $i] : p(X)) | (~![X: $i] : (~p(X))))) | (~((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (~![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))) | (~(![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) | (~((~r(X!2, Y!1)) | r(X!2, X!2) | (~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y)))))) | (~((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (~(![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) | (~((~(g(X!4) | (~f(X!4)))) | (~(h(X!3) | (~f(X!3)) | (~g(X!3)))))))) | ![X: $i] : (~(q(X) | (~p(X)) | p(tptp_fun_Y_5(X)))) | (~((~p(X!13)) | (~q(X!13)) | (~(![X: $i] : (~p(X)) | ![X: $i] : (~q(X)))))) | ![Y: $i] : (~((~p(Y)) | p(X!7))) | (~((~((~((~![X: $i] : p(X)) | (~![X: $i] : q(X)))) | ![X: $i] : (~((~p(X)) | (~q(X)))))) | (~((~p(X!7)) | (~q(X!8)) | (~p(X!6)) | (~q(X!6)))))) | (~((~(q(X!10) | p(X!10) | p(X!11) | q(X!12))) | (~(![X: $i] : (~(p(X) | q(X))) | (~((~![X: $i] : (~p(X))) | (~![X: $i] : (~q(X))))))))) | (~(p(Y!15) | (~![Y: $i] : (~p(Y))) | (~p(X!11)))) | (~((~(c | (~p(X!7)) | (~p(X!19)))) | (~(![X: $i] : (~(c | (~p(X)))) | (~(c | (~![X: $i] : p(X)))))))) | (~((~(![X: $i] : p(X) | c | ![X: $i] : (p(X) | c))) | (~((~(c | p(X!16))) | (~(c | p(X!7))))))) | (~((~((~((~c) | (~p(X!17)))) | (~((~c) | (~p(X!11)))))) | (~((~c) | ![X: $i] : (~p(X)) | ![X: $i] : ((~p(X)) | (~c)))))) | (~((~(c | ![X: $i] : (c | (~p(X))) | ![X: $i] : (~p(X)))) | (~((~(c | (~p(X!21)))) | (~(c | (~p(X!11)))))))) | (~((~((~c) | p(X!11) | p(X!18))) | (~(![X: $i] : (~((~c) | p(X))) | (~((~c) | (~![X: $i] : (~p(X))))))))) | (~((~(![X: $i] : p(X) | (~c) | ![X: $i] : ((~c) | p(X)))) | (~((~((~c) | p(X!20))) | (~((~c) | p(X!7)))))))) <=> ((~(p(Y!14) | (~![X: $i] : p(X)))) | ![X: $i] : (~(q(X) | (~p(X)) | p(tptp_fun_Y_5(X)))) | (~((~(![X: $i] : p(X) | ![X: $i] : q(X))) | q(X!9) | p(X!9))) | (~((~![X: $i] : p(X)) | (~![X: $i] : (~p(X))))) | (~((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (~![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))) | (~(![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) | (~((~r(X!2, Y!1)) | r(X!2, X!2) | (~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y)))))) | (~((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (~(![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) | (~((~(g(X!4) | (~f(X!4)))) | (~(h(X!3) | (~f(X!3)) | (~g(X!3)))))))) | (~((~p(X!13)) | (~q(X!13)) | (~(![X: $i] : (~p(X)) | ![X: $i] : (~q(X)))))) | ![Y: $i] : (~((~p(Y)) | p(X!7))) | (~((~((~((~![X: $i] : p(X)) | (~![X: $i] : q(X)))) | ![X: $i] : (~((~p(X)) | (~q(X)))))) | (~((~p(X!7)) | (~q(X!8)) | (~p(X!6)) | (~q(X!6)))))) | (~((~(q(X!10) | p(X!10) | p(X!11) | q(X!12))) | (~(![X: $i] : (~(p(X) | q(X))) | (~((~![X: $i] : (~p(X))) | (~![X: $i] : (~q(X))))))))) | (~(p(Y!15) | (~![Y: $i] : (~p(Y))) | (~p(X!11)))) | (~((~(c | (~p(X!7)) | (~p(X!19)))) | (~(![X: $i] : (~(c | (~p(X)))) | (~(c | (~![X: $i] : p(X)))))))) | (~((~(![X: $i] : p(X) | c | ![X: $i] : (p(X) | c))) | (~((~(c | p(X!16))) | (~(c | p(X!7))))))) | (~((~((~((~c) | (~p(X!17)))) | (~((~c) | (~p(X!11)))))) | (~((~c) | ![X: $i] : (~p(X)) | ![X: $i] : ((~p(X)) | (~c)))))) | (~((~(c | ![X: $i] : (c | (~p(X))) | ![X: $i] : (~p(X)))) | (~((~(c | (~p(X!21)))) | (~(c | (~p(X!11)))))))) | (~((~((~c) | p(X!11) | p(X!18))) | (~(![X: $i] : (~((~c) | p(X))) | (~((~c) | (~![X: $i] : (~p(X))))))))) | (~((~(![X: $i] : p(X) | (~c) | ![X: $i] : ((~c) | p(X)))) | (~((~((~c) | p(X!20))) | (~((~c) | p(X!7))))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
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% 0.21/0.47 (((![X: $i] : p(X) | (~c) | ![X: $i] : ((~c) | p(X))) & ((~((~c) | p(X!20))) | (~((~c) | p(X!7))))) <=> (~((~(![X: $i] : p(X) | (~c) | ![X: $i] : ((~c) | p(X)))) | (~((~((~c) | p(X!20))) | (~((~c) | p(X!7)))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(219,plain,
% 0.21/0.47 (((~((~c) | p(X!20))) | (c & (~p(X!7)))) <=> ((~((~c) | p(X!20))) | (~((~c) | p(X!7))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(220,plain,
% 0.21/0.47 ((![X: $i] : p(X) | (~c) | ![X: $i] : ((~c) | p(X))) <=> (![X: $i] : p(X) | (~c) | ![X: $i] : ((~c) | p(X)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(221,plain,
% 0.21/0.47 (((![X: $i] : p(X) | (~c) | ![X: $i] : ((~c) | p(X))) & ((~((~c) | p(X!20))) | (c & (~p(X!7))))) <=> ((![X: $i] : p(X) | (~c) | ![X: $i] : ((~c) | p(X))) & ((~((~c) | p(X!20))) | (~((~c) | p(X!7)))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[220, 219])).
% 0.21/0.47 tff(222,plain,
% 0.21/0.47 (((![X: $i] : p(X) | (~c) | ![X: $i] : ((~c) | p(X))) & ((~((~c) | p(X!20))) | (c & (~p(X!7))))) <=> (~((~(![X: $i] : p(X) | (~c) | ![X: $i] : ((~c) | p(X)))) | (~((~((~c) | p(X!20))) | (~((~c) | p(X!7)))))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[221, 218])).
% 0.21/0.47 tff(223,plain,
% 0.21/0.47 ((((~c) | p(X!11) | p(X!18)) & (![X: $i] : (~((~c) | p(X))) | (~((~c) | (~![X: $i] : (~p(X))))))) <=> (~((~((~c) | p(X!11) | p(X!18))) | (~(![X: $i] : (~((~c) | p(X))) | (~((~c) | (~![X: $i] : (~p(X)))))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(224,plain,
% 0.21/0.47 ((![X: $i] : (~((~c) | p(X))) | (~((~c) | (~![X: $i] : (~p(X)))))) <=> (![X: $i] : (~((~c) | p(X))) | (~((~c) | (~![X: $i] : (~p(X))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(225,plain,
% 0.21/0.47 ((c & ![X: $i] : (~p(X))) <=> (~((~c) | (~![X: $i] : (~p(X)))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(226,plain,
% 0.21/0.47 ((![X: $i] : (~((~c) | p(X))) | (c & ![X: $i] : (~p(X)))) <=> (![X: $i] : (~((~c) | p(X))) | (~((~c) | (~![X: $i] : (~p(X))))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[225])).
% 0.21/0.47 tff(227,plain,
% 0.21/0.47 ((![X: $i] : (~((~c) | p(X))) | (c & ![X: $i] : (~p(X)))) <=> (![X: $i] : (~((~c) | p(X))) | (~((~c) | (~![X: $i] : (~p(X))))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[226, 224])).
% 0.21/0.47 tff(228,plain,
% 0.21/0.47 ((((~c) | p(X!11) | p(X!18)) & (![X: $i] : (~((~c) | p(X))) | (c & ![X: $i] : (~p(X))))) <=> (((~c) | p(X!11) | p(X!18)) & (![X: $i] : (~((~c) | p(X))) | (~((~c) | (~![X: $i] : (~p(X)))))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[227])).
% 0.21/0.47 tff(229,plain,
% 0.21/0.47 ((((~c) | p(X!11) | p(X!18)) & (![X: $i] : (~((~c) | p(X))) | (c & ![X: $i] : (~p(X))))) <=> (~((~((~c) | p(X!11) | p(X!18))) | (~(![X: $i] : (~((~c) | p(X))) | (~((~c) | (~![X: $i] : (~p(X)))))))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[228, 223])).
% 0.21/0.47 tff(230,plain,
% 0.21/0.47 (((c | ![X: $i] : (c | (~p(X))) | ![X: $i] : (~p(X))) & ((~(c | (~p(X!21)))) | (~(c | (~p(X!11)))))) <=> (~((~(c | ![X: $i] : (c | (~p(X))) | ![X: $i] : (~p(X)))) | (~((~(c | (~p(X!21)))) | (~(c | (~p(X!11))))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(231,plain,
% 0.21/0.47 (((~(c | (~p(X!21)))) | (~(c | (~p(X!11))))) <=> ((~(c | (~p(X!21)))) | (~(c | (~p(X!11)))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(232,plain,
% 0.21/0.47 (((~c) & p(X!11)) <=> (~(c | (~p(X!11))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(233,plain,
% 0.21/0.47 (((~(c | (~p(X!21)))) | ((~c) & p(X!11))) <=> ((~(c | (~p(X!21)))) | (~(c | (~p(X!11)))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[232])).
% 0.21/0.47 tff(234,plain,
% 0.21/0.47 (((~(c | (~p(X!21)))) | ((~c) & p(X!11))) <=> ((~(c | (~p(X!21)))) | (~(c | (~p(X!11)))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[233, 231])).
% 0.21/0.47 tff(235,plain,
% 0.21/0.47 ((c | ![X: $i] : (c | (~p(X))) | ![X: $i] : (~p(X))) <=> (c | ![X: $i] : (c | (~p(X))) | ![X: $i] : (~p(X)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(236,plain,
% 0.21/0.47 (((c | ![X: $i] : (c | (~p(X))) | ![X: $i] : (~p(X))) & ((~(c | (~p(X!21)))) | ((~c) & p(X!11)))) <=> ((c | ![X: $i] : (c | (~p(X))) | ![X: $i] : (~p(X))) & ((~(c | (~p(X!21)))) | (~(c | (~p(X!11))))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[235, 234])).
% 0.21/0.47 tff(237,plain,
% 0.21/0.47 (((c | ![X: $i] : (c | (~p(X))) | ![X: $i] : (~p(X))) & ((~(c | (~p(X!21)))) | ((~c) & p(X!11)))) <=> (~((~(c | ![X: $i] : (c | (~p(X))) | ![X: $i] : (~p(X)))) | (~((~(c | (~p(X!21)))) | (~(c | (~p(X!11))))))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[236, 230])).
% 0.21/0.47 tff(238,plain,
% 0.21/0.47 ((((~((~c) | (~p(X!17)))) | (~((~c) | (~p(X!11))))) & ((~c) | ![X: $i] : (~p(X)) | ![X: $i] : ((~p(X)) | (~c)))) <=> (~((~((~((~c) | (~p(X!17)))) | (~((~c) | (~p(X!11)))))) | (~((~c) | ![X: $i] : (~p(X)) | ![X: $i] : ((~p(X)) | (~c))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
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% 0.21/0.47 inference(rewrite,[status(thm)],[])).
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% 0.21/0.47 inference(rewrite,[status(thm)],[])).
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% 0.21/0.47 ((p(X!11) & c) <=> (~((~c) | (~p(X!11))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
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% 0.21/0.47 inference(rewrite,[status(thm)],[])).
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% 0.21/0.47 inference(monotonicity,[status(thm)],[242, 241])).
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% 0.21/0.47 (((p(X!17) & c) | (p(X!11) & c)) <=> ((~((~c) | (~p(X!17)))) | (~((~c) | (~p(X!11)))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[243, 240])).
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% 0.21/0.47 ((((p(X!17) & c) | (p(X!11) & c)) & ((~c) | ![X: $i] : (~p(X)) | ![X: $i] : (~(p(X) & c)))) <=> (((~((~c) | (~p(X!17)))) | (~((~c) | (~p(X!11))))) & ((~c) | ![X: $i] : (~p(X)) | ![X: $i] : ((~p(X)) | (~c))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[244, 239])).
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% 0.21/0.47 ((((p(X!17) & c) | (p(X!11) & c)) & ((~c) | ![X: $i] : (~p(X)) | ![X: $i] : (~(p(X) & c)))) <=> (~((~((~((~c) | (~p(X!17)))) | (~((~c) | (~p(X!11)))))) | (~((~c) | ![X: $i] : (~p(X)) | ![X: $i] : ((~p(X)) | (~c))))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[245, 238])).
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% 0.21/0.47 inference(rewrite,[status(thm)],[])).
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% 0.21/0.47 (((~(c | p(X!16))) | ((~p(X!7)) & (~c))) <=> ((~(c | p(X!16))) | (~(c | p(X!7))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
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% 0.21/0.47 inference(rewrite,[status(thm)],[])).
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% 0.21/0.47 inference(monotonicity,[status(thm)],[249, 248])).
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% 0.21/0.47 inference(transitivity,[status(thm)],[250, 247])).
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% 0.21/0.47 inference(rewrite,[status(thm)],[])).
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% 0.21/0.47 inference(rewrite,[status(thm)],[])).
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% 0.21/0.47 (((~c) & ![X: $i] : p(X)) <=> (~(c | (~![X: $i] : p(X))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
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% 0.21/0.47 inference(monotonicity,[status(thm)],[254])).
% 0.21/0.47 tff(256,plain,
% 0.21/0.47 ((![X: $i] : (~(c | (~p(X)))) | ((~c) & ![X: $i] : p(X))) <=> (![X: $i] : (~(c | (~p(X)))) | (~(c | (~![X: $i] : p(X)))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[255, 253])).
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% 0.21/0.47 inference(rewrite,[status(thm)],[])).
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% 0.21/0.47 (((c | (~p(X!7)) | (~p(X!19))) & (![X: $i] : (~(c | (~p(X)))) | ((~c) & ![X: $i] : p(X)))) <=> ((c | (~p(X!7)) | (~p(X!19))) & (![X: $i] : (~(c | (~p(X)))) | (~(c | (~![X: $i] : p(X))))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[257, 256])).
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% 0.21/0.47 (((c | (~p(X!7)) | (~p(X!19))) & (![X: $i] : (~(c | (~p(X)))) | ((~c) & ![X: $i] : p(X)))) <=> (~((~(c | (~p(X!7)) | (~p(X!19)))) | (~(![X: $i] : (~(c | (~p(X)))) | (~(c | (~![X: $i] : p(X))))))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[258, 252])).
% 0.21/0.47 tff(260,plain,
% 0.21/0.47 ((![Y: $i] : (~p(Y)) & (~p(Y!15)) & p(X!11)) <=> (~(p(Y!15) | (~![Y: $i] : (~p(Y))) | (~p(X!11))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
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% 0.21/0.47 (((q(X!10) | p(X!10) | p(X!11) | q(X!12)) & (![X: $i] : (~(p(X) | q(X))) | (~((~![X: $i] : (~p(X))) | (~![X: $i] : (~q(X))))))) <=> (~((~(q(X!10) | p(X!10) | p(X!11) | q(X!12))) | (~(![X: $i] : (~(p(X) | q(X))) | (~((~![X: $i] : (~p(X))) | (~![X: $i] : (~q(X)))))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
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% 0.21/0.47 inference(rewrite,[status(thm)],[])).
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% 0.21/0.47 ((![X: $i] : (~p(X)) & ![X: $i] : (~q(X))) <=> (~((~![X: $i] : (~p(X))) | (~![X: $i] : (~q(X)))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
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% 0.21/0.47 ((![X: $i] : (~(p(X) | q(X))) | (![X: $i] : (~p(X)) & ![X: $i] : (~q(X)))) <=> (![X: $i] : (~(p(X) | q(X))) | (~((~![X: $i] : (~p(X))) | (~![X: $i] : (~q(X))))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[263])).
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% 0.21/0.47 ((![X: $i] : (~(p(X) | q(X))) | (![X: $i] : (~p(X)) & ![X: $i] : (~q(X)))) <=> (![X: $i] : (~(p(X) | q(X))) | (~((~![X: $i] : (~p(X))) | (~![X: $i] : (~q(X))))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[264, 262])).
% 0.21/0.47 tff(266,plain,
% 0.21/0.47 ((q(X!10) | p(X!10) | p(X!11) | q(X!12)) <=> (q(X!10) | p(X!10) | p(X!11) | q(X!12))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
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% 0.21/0.47 (((q(X!10) | p(X!10) | p(X!11) | q(X!12)) & (![X: $i] : (~(p(X) | q(X))) | (![X: $i] : (~p(X)) & ![X: $i] : (~q(X))))) <=> ((q(X!10) | p(X!10) | p(X!11) | q(X!12)) & (![X: $i] : (~(p(X) | q(X))) | (~((~![X: $i] : (~p(X))) | (~![X: $i] : (~q(X)))))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[266, 265])).
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% 0.21/0.47 (((q(X!10) | p(X!10) | p(X!11) | q(X!12)) & (![X: $i] : (~(p(X) | q(X))) | (![X: $i] : (~p(X)) & ![X: $i] : (~q(X))))) <=> (~((~(q(X!10) | p(X!10) | p(X!11) | q(X!12))) | (~(![X: $i] : (~(p(X) | q(X))) | (~((~![X: $i] : (~p(X))) | (~![X: $i] : (~q(X)))))))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[267, 261])).
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% 0.21/0.47 inference(rewrite,[status(thm)],[])).
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% 0.21/0.47 ((((~p(X!6)) | (~q(X!6))) | (~p(X!7)) | (~q(X!8))) <=> ((~p(X!7)) | (~q(X!8)) | (~p(X!6)) | (~q(X!6)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
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% 0.21/0.47 ((~(~((~p(X!6)) | (~q(X!6))))) <=> ((~p(X!6)) | (~q(X!6)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(272,plain,
% 0.21/0.47 ((p(X!6) & q(X!6)) <=> (~((~p(X!6)) | (~q(X!6))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
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% 0.21/0.47 ((~(p(X!6) & q(X!6))) <=> (~(~((~p(X!6)) | (~q(X!6)))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[272])).
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% 0.21/0.47 ((~(p(X!6) & q(X!6))) <=> ((~p(X!6)) | (~q(X!6)))),
% 0.21/0.47 inference(transitivity,[status(thm)],[273, 271])).
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% 0.21/0.47 (((~(p(X!6) & q(X!6))) | (~p(X!7)) | (~q(X!8))) <=> (((~p(X!6)) | (~q(X!6))) | (~p(X!7)) | (~q(X!8)))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[274])).
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% 0.21/0.48 (((~(p(X!6) & q(X!6))) | (~p(X!7)) | (~q(X!8))) <=> ((~p(X!7)) | (~q(X!8)) | (~p(X!6)) | (~q(X!6)))),
% 0.21/0.48 inference(transitivity,[status(thm)],[275, 270])).
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% 0.21/0.48 (((![X: $i] : p(X) & ![X: $i] : q(X)) | ![X: $i] : (p(X) & q(X))) <=> ((~((~![X: $i] : p(X)) | (~![X: $i] : q(X)))) | ![X: $i] : (~((~p(X)) | (~q(X)))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(278,plain,
% 0.21/0.48 ((((![X: $i] : p(X) & ![X: $i] : q(X)) | ![X: $i] : (p(X) & q(X))) & ((~(p(X!6) & q(X!6))) | (~p(X!7)) | (~q(X!8)))) <=> (((~((~![X: $i] : p(X)) | (~![X: $i] : q(X)))) | ![X: $i] : (~((~p(X)) | (~q(X))))) & ((~p(X!7)) | (~q(X!8)) | (~p(X!6)) | (~q(X!6))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[277, 276])).
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% 0.21/0.48 inference(transitivity,[status(thm)],[278, 269])).
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% 0.21/0.48 (^[Y: $i] : rewrite((p(Y) & (~p(X!7))) <=> (~((~p(Y)) | p(X!7))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
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% 0.21/0.48 inference(quant_intro,[status(thm)],[280])).
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% 0.21/0.48 inference(rewrite,[status(thm)],[])).
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% 0.21/0.48 ((![X: $i] : (~p(X)) | ![X: $i] : (~q(X))) <=> (![X: $i] : (~p(X)) | ![X: $i] : (~q(X)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
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% 0.21/0.48 ((p(X!13) & q(X!13) & (![X: $i] : (~p(X)) | ![X: $i] : (~q(X)))) <=> (p(X!13) & q(X!13) & (![X: $i] : (~p(X)) | ![X: $i] : (~q(X))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[283])).
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% 0.21/0.48 ((p(X!13) & q(X!13) & (![X: $i] : (~p(X)) | ![X: $i] : (~q(X)))) <=> (~((~p(X!13)) | (~q(X!13)) | (~(![X: $i] : (~p(X)) | ![X: $i] : (~q(X))))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[284, 282])).
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% 0.21/0.48 inference(rewrite,[status(thm)],[])).
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% 0.21/0.48 ((![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))) <=> (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(288,plain,
% 0.21/0.48 (((~(h(X!3) | (~f(X!3)) | (~g(X!3)))) | (~(g(X!4) | (~f(X!4))))) <=> ((~(g(X!4) | (~f(X!4)))) | (~(h(X!3) | (~f(X!3)) | (~g(X!3)))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(289,plain,
% 0.21/0.48 ((f(X!4) & (~g(X!4))) <=> (~(g(X!4) | (~f(X!4))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(290,plain,
% 0.21/0.48 ((~(h(X!3) | (~(f(X!3) & g(X!3))))) <=> (~(h(X!3) | (~f(X!3)) | (~g(X!3))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(291,plain,
% 0.21/0.48 (((~(h(X!3) | (~(f(X!3) & g(X!3))))) | (f(X!4) & (~g(X!4)))) <=> ((~(h(X!3) | (~f(X!3)) | (~g(X!3)))) | (~(g(X!4) | (~f(X!4)))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[290, 289])).
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% 0.21/0.48 (((~(h(X!3) | (~(f(X!3) & g(X!3))))) | (f(X!4) & (~g(X!4)))) <=> ((~(g(X!4) | (~f(X!4)))) | (~(h(X!3) | (~f(X!3)) | (~g(X!3)))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[291, 288])).
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% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(294,plain,
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% 0.21/0.48 inference(quant_intro,[status(thm)],[293])).
% 0.21/0.48 tff(295,plain,
% 0.21/0.48 (^[V: $i] : trans(monotonicity(rewrite((f(V) & g(V) & (~h(V))) <=> (~(h(V) | (~g(V)) | (~f(V))))), ((~(f(V) & g(V) & (~h(V)))) <=> (~(~(h(V) | (~g(V)) | (~f(V))))))), rewrite((~(~(h(V) | (~g(V)) | (~f(V))))) <=> (h(V) | (~g(V)) | (~f(V)))), ((~(f(V) & g(V) & (~h(V)))) <=> (h(V) | (~g(V)) | (~f(V)))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(296,plain,
% 0.21/0.48 (![V: $i] : (~(f(V) & g(V) & (~h(V)))) <=> ![V: $i] : (h(V) | (~g(V)) | (~f(V)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[295])).
% 0.21/0.48 tff(297,plain,
% 0.21/0.48 ((![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & ((~(h(X!3) | (~(f(X!3) & g(X!3))))) | (f(X!4) & (~g(X!4)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) <=> (![V: $i] : (h(V) | (~g(V)) | (~f(V))) & ![R: $i] : (g(R) | (~h(R)) | (~f(R))) & ((~(g(X!4) | (~f(X!4)))) | (~(h(X!3) | (~f(X!3)) | (~g(X!3))))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[296, 294, 292, 287])).
% 0.21/0.48 tff(298,plain,
% 0.21/0.48 ((![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & ((~(h(X!3) | (~(f(X!3) & g(X!3))))) | (f(X!4) & (~g(X!4)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) <=> (~((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (~(![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) | (~((~(g(X!4) | (~f(X!4)))) | (~(h(X!3) | (~f(X!3)) | (~g(X!3))))))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[297, 286])).
% 0.21/0.48 tff(299,plain,
% 0.21/0.48 ((![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y))) & (~((~r(X!2, Y!1)) | r(X!2, X!2)))) <=> (~((~r(X!2, Y!1)) | r(X!2, X!2) | (~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(300,plain,
% 0.21/0.48 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((r(X, Y) & r(Y, Z)) <=> (~((~r(Y, Z)) | (~r(X, Y))))), ((~(r(X, Y) & r(Y, Z))) <=> (~(~((~r(Y, Z)) | (~r(X, Y))))))), rewrite((~(~((~r(Y, Z)) | (~r(X, Y))))) <=> ((~r(Y, Z)) | (~r(X, Y)))), ((~(r(X, Y) & r(Y, Z))) <=> ((~r(Y, Z)) | (~r(X, Y))))), (((~(r(X, Y) & r(Y, Z))) | r(X, Z)) <=> (((~r(Y, Z)) | (~r(X, Y))) | r(X, Z)))), rewrite((((~r(Y, Z)) | (~r(X, Y))) | r(X, Z)) <=> (r(X, Z) | (~r(Y, Z)) | (~r(X, Y)))), (((~(r(X, Y) & r(Y, Z))) | r(X, Z)) <=> (r(X, Z) | (~r(Y, Z)) | (~r(X, Y)))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(301,plain,
% 0.21/0.48 (![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[300])).
% 0.21/0.48 tff(302,plain,
% 0.21/0.48 ((![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)) & (~((~r(X!2, Y!1)) | r(X!2, X!2)))) <=> (![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y))) & (~((~r(X!2, Y!1)) | r(X!2, X!2))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[301])).
% 0.21/0.48 tff(303,plain,
% 0.21/0.48 ((![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)) & (~((~r(X!2, Y!1)) | r(X!2, X!2)))) <=> (~((~r(X!2, Y!1)) | r(X!2, X!2) | (~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y))))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[302, 299])).
% 0.21/0.48 tff(304,plain,
% 0.21/0.48 ((![V: $i] : (h(V) | (~g(V)) | (~f(V))) & ![R: $i] : (g(R) | (~h(R)) | (~f(R))) & ![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0))))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) <=> (~((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (~![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))) | (~(![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(305,plain,
% 0.21/0.48 (^[X: $i] : trans(monotonicity(rewrite((~(h(X) | (~(f(X) & g(X))))) <=> (~(h(X) | (~g(X)) | (~f(X))))), rewrite((f(Y!0) & (~g(Y!0))) <=> (~(g(Y!0) | (~f(Y!0))))), (((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) <=> ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0))))))), rewrite(((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0))))) <=> ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))), (((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) <=> ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(306,plain,
% 0.21/0.48 (![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) <=> ![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[305])).
% 0.21/0.48 tff(307,plain,
% 0.21/0.48 ((![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & ![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) <=> (![V: $i] : (h(V) | (~g(V)) | (~f(V))) & ![R: $i] : (g(R) | (~h(R)) | (~f(R))) & ![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0))))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[296, 294, 306, 287])).
% 0.21/0.48 tff(308,plain,
% 0.21/0.48 ((![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & ![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) <=> (~((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (~![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))) | (~(![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[307, 304])).
% 0.21/0.48 tff(309,plain,
% 0.21/0.48 ((![X: $i] : p(X) & ![X: $i] : (~p(X))) <=> (~((~![X: $i] : p(X)) | (~![X: $i] : (~p(X)))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(310,plain,
% 0.21/0.48 (((~p(Y!14)) & ![X: $i] : p(X)) <=> (~(p(Y!14) | (~![X: $i] : p(X))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(311,plain,
% 0.21/0.48 (((![X: $i] : p(X) | ![X: $i] : q(X)) & (~(p(X!9) | q(X!9)))) <=> (~((~(![X: $i] : p(X) | ![X: $i] : q(X))) | q(X!9) | p(X!9)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(312,plain,
% 0.21/0.48 ((![X: $i] : p(X) | ![X: $i] : q(X)) <=> (![X: $i] : p(X) | ![X: $i] : q(X))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(313,plain,
% 0.21/0.48 (((![X: $i] : p(X) | ![X: $i] : q(X)) & (~(p(X!9) | q(X!9)))) <=> ((![X: $i] : p(X) | ![X: $i] : q(X)) & (~(p(X!9) | q(X!9))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[312])).
% 0.21/0.48 tff(314,plain,
% 0.21/0.48 (((![X: $i] : p(X) | ![X: $i] : q(X)) & (~(p(X!9) | q(X!9)))) <=> (~((~(![X: $i] : p(X) | ![X: $i] : q(X))) | q(X!9) | p(X!9)))),
% 0.21/0.48 inference(transitivity,[status(thm)],[313, 311])).
% 0.21/0.48 tff(315,plain,
% 0.21/0.48 ((((![X: $i] : p(X) | ![X: $i] : q(X)) & (~(p(X!9) | q(X!9)))) | ((~p(Y!14)) & ![X: $i] : p(X)) | (![X: $i] : p(X) & ![X: $i] : (~p(X))) | (![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & ![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) | (![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)) & (~((~r(X!2, Y!1)) | r(X!2, X!2)))) | (![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & ((~(h(X!3) | (~(f(X!3) & g(X!3))))) | (f(X!4) & (~g(X!4)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) | ![X: $i] : (~(q(X) | (~p(X)) | p(tptp_fun_Y_5(X)))) | (p(X!13) & q(X!13) & (![X: $i] : (~p(X)) | ![X: $i] : (~q(X)))) | ![Y: $i] : (p(Y) & (~p(X!7))) | (((![X: $i] : p(X) & ![X: $i] : q(X)) | ![X: $i] : (p(X) & q(X))) & ((~(p(X!6) & q(X!6))) | (~p(X!7)) | (~q(X!8)))) | ((q(X!10) | p(X!10) | p(X!11) | q(X!12)) & (![X: $i] : (~(p(X) | q(X))) | (![X: $i] : (~p(X)) & ![X: $i] : (~q(X))))) | (![Y: $i] : (~p(Y)) & (~p(Y!15)) & p(X!11)) | ((c | (~p(X!7)) | (~p(X!19))) & (![X: $i] : (~(c | (~p(X)))) | ((~c) & ![X: $i] : p(X)))) | ((![X: $i] : p(X) | c | ![X: $i] : (p(X) | c)) & ((~(c | p(X!16))) | ((~p(X!7)) & (~c)))) | (((p(X!17) & c) | (p(X!11) & c)) & ((~c) | ![X: $i] : (~p(X)) | ![X: $i] : (~(p(X) & c)))) | ((c | ![X: $i] : (c | (~p(X))) | ![X: $i] : (~p(X))) & ((~(c | (~p(X!21)))) | ((~c) & p(X!11)))) | (((~c) | p(X!11) | p(X!18)) & (![X: $i] : (~((~c) | p(X))) | (c & ![X: $i] : (~p(X))))) | ((![X: $i] : p(X) | (~c) | ![X: $i] : ((~c) | p(X))) & ((~((~c) | p(X!20))) | (c & (~p(X!7)))))) <=> ((~((~(![X: $i] : p(X) | ![X: $i] : q(X))) | q(X!9) | p(X!9))) | (~(p(Y!14) | (~![X: $i] : p(X)))) | (~((~![X: $i] : p(X)) | (~![X: $i] : (~p(X))))) | (~((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (~![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))) | (~(![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) | (~((~r(X!2, Y!1)) | r(X!2, X!2) | (~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y)))))) | (~((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (~(![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) | (~((~(g(X!4) | (~f(X!4)))) | (~(h(X!3) | (~f(X!3)) | (~g(X!3)))))))) | ![X: $i] : (~(q(X) | (~p(X)) | p(tptp_fun_Y_5(X)))) | (~((~p(X!13)) | (~q(X!13)) | (~(![X: $i] : (~p(X)) | ![X: $i] : (~q(X)))))) | ![Y: $i] : (~((~p(Y)) | p(X!7))) | (~((~((~((~![X: $i] : p(X)) | (~![X: $i] : q(X)))) | ![X: $i] : (~((~p(X)) | (~q(X)))))) | (~((~p(X!7)) | (~q(X!8)) | (~p(X!6)) | (~q(X!6)))))) | (~((~(q(X!10) | p(X!10) | p(X!11) | q(X!12))) | (~(![X: $i] : (~(p(X) | q(X))) | (~((~![X: $i] : (~p(X))) | (~![X: $i] : (~q(X))))))))) | (~(p(Y!15) | (~![Y: $i] : (~p(Y))) | (~p(X!11)))) | (~((~(c | (~p(X!7)) | (~p(X!19)))) | (~(![X: $i] : (~(c | (~p(X)))) | (~(c | (~![X: $i] : p(X)))))))) | (~((~(![X: $i] : p(X) | c | ![X: $i] : (p(X) | c))) | (~((~(c | p(X!16))) | (~(c | p(X!7))))))) | (~((~((~((~c) | (~p(X!17)))) | (~((~c) | (~p(X!11)))))) | (~((~c) | ![X: $i] : (~p(X)) | ![X: $i] : ((~p(X)) | (~c)))))) | (~((~(c | ![X: $i] : (c | (~p(X))) | ![X: $i] : (~p(X)))) | (~((~(c | (~p(X!21)))) | (~(c | (~p(X!11)))))))) | (~((~((~c) | p(X!11) | p(X!18))) | (~(![X: $i] : (~((~c) | p(X))) | (~((~c) | (~![X: $i] : (~p(X))))))))) | (~((~(![X: $i] : p(X) | (~c) | ![X: $i] : ((~c) | p(X)))) | (~((~((~c) | p(X!20))) | (~((~c) | p(X!7))))))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[314, 310, 309, 308, 303, 298, 285, 281, 279, 268, 260, 259, 251, 246, 237, 229, 222])).
% 0.21/0.49 tff(316,plain,
% 0.21/0.49 ((((![X: $i] : p(X) | ![X: $i] : q(X)) & (~(p(X!9) | q(X!9)))) | ((~p(Y!14)) & ![X: $i] : p(X)) | (![X: $i] : p(X) & ![X: $i] : (~p(X))) | (![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & ![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) | (![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)) & (~((~r(X!2, Y!1)) | r(X!2, X!2)))) | (![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & ((~(h(X!3) | (~(f(X!3) & g(X!3))))) | (f(X!4) & (~g(X!4)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) | ![X: $i] : (~(q(X) | (~p(X)) | p(tptp_fun_Y_5(X)))) | (p(X!13) & q(X!13) & (![X: $i] : (~p(X)) | ![X: $i] : (~q(X)))) | ![Y: $i] : (p(Y) & (~p(X!7))) | (((![X: $i] : p(X) & ![X: $i] : q(X)) | ![X: $i] : (p(X) & q(X))) & ((~(p(X!6) & q(X!6))) | (~p(X!7)) | (~q(X!8)))) | ((q(X!10) | p(X!10) | p(X!11) | q(X!12)) & (![X: $i] : (~(p(X) | q(X))) | (![X: $i] : (~p(X)) & ![X: $i] : (~q(X))))) | (![Y: $i] : (~p(Y)) & (~p(Y!15)) & p(X!11)) | ((c | (~p(X!7)) | (~p(X!19))) & (![X: $i] : (~(c | (~p(X)))) | ((~c) & ![X: $i] : p(X)))) | ((![X: $i] : p(X) | c | ![X: $i] : (p(X) | c)) & ((~(c | p(X!16))) | ((~p(X!7)) & (~c)))) | (((p(X!17) & c) | (p(X!11) & c)) & ((~c) | ![X: $i] : (~p(X)) | ![X: $i] : (~(p(X) & c)))) | ((c | ![X: $i] : (c | (~p(X))) | ![X: $i] : (~p(X))) & ((~(c | (~p(X!21)))) | ((~c) & p(X!11)))) | (((~c) | p(X!11) | p(X!18)) & (![X: $i] : (~((~c) | p(X))) | (c & ![X: $i] : (~p(X))))) | ((![X: $i] : p(X) | (~c) | ![X: $i] : ((~c) | p(X))) & ((~((~c) | p(X!20))) | (c & (~p(X!7)))))) <=> ((~(p(Y!14) | (~![X: $i] : p(X)))) | ![X: $i] : (~(q(X) | (~p(X)) | p(tptp_fun_Y_5(X)))) | (~((~(![X: $i] : p(X) | ![X: $i] : q(X))) | q(X!9) | p(X!9))) | (~((~![X: $i] : p(X)) | (~![X: $i] : (~p(X))))) | (~((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (~![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))) | (~(![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) | (~((~r(X!2, Y!1)) | r(X!2, X!2) | (~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y)))))) | (~((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (~(![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) | (~((~(g(X!4) | (~f(X!4)))) | (~(h(X!3) | (~f(X!3)) | (~g(X!3)))))))) | (~((~p(X!13)) | (~q(X!13)) | (~(![X: $i] : (~p(X)) | ![X: $i] : (~q(X)))))) | ![Y: $i] : (~((~p(Y)) | p(X!7))) | (~((~((~((~![X: $i] : p(X)) | (~![X: $i] : q(X)))) | ![X: $i] : (~((~p(X)) | (~q(X)))))) | (~((~p(X!7)) | (~q(X!8)) | (~p(X!6)) | (~q(X!6)))))) | (~((~(q(X!10) | p(X!10) | p(X!11) | q(X!12))) | (~(![X: $i] : (~(p(X) | q(X))) | (~((~![X: $i] : (~p(X))) | (~![X: $i] : (~q(X))))))))) | (~(p(Y!15) | (~![Y: $i] : (~p(Y))) | (~p(X!11)))) | (~((~(c | (~p(X!7)) | (~p(X!19)))) | (~(![X: $i] : (~(c | (~p(X)))) | (~(c | (~![X: $i] : p(X)))))))) | (~((~(![X: $i] : p(X) | c | ![X: $i] : (p(X) | c))) | (~((~(c | p(X!16))) | (~(c | p(X!7))))))) | (~((~((~((~c) | (~p(X!17)))) | (~((~c) | (~p(X!11)))))) | (~((~c) | ![X: $i] : (~p(X)) | ![X: $i] : ((~p(X)) | (~c)))))) | (~((~(c | ![X: $i] : (c | (~p(X))) | ![X: $i] : (~p(X)))) | (~((~(c | (~p(X!21)))) | (~(c | (~p(X!11)))))))) | (~((~((~c) | p(X!11) | p(X!18))) | (~(![X: $i] : (~((~c) | p(X))) | (~((~c) | (~![X: $i] : (~p(X))))))))) | (~((~(![X: $i] : p(X) | (~c) | ![X: $i] : ((~c) | p(X)))) | (~((~((~c) | p(X!20))) | (~((~c) | p(X!7))))))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[315, 217])).
% 0.21/0.49 tff(317,plain,
% 0.21/0.49 (((![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & ![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) | (![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)) & (~((~r(X!2, Y!1)) | r(X!2, X!2)))) | (![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & ((~(h(X!3) | (~(f(X!3) & g(X!3))))) | (f(X!4) & (~g(X!4)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) | ![X: $i] : (~(q(X) | (~p(X)) | p(tptp_fun_Y_5(X)))) | (((![X: $i] : p(X) & ![X: $i] : q(X)) | ![X: $i] : (p(X) & q(X))) & ((~(p(X!6) & q(X!6))) | (~p(X!7)) | (~q(X!8)))) | ((![X: $i] : p(X) | ![X: $i] : q(X)) & (~(p(X!9) | q(X!9)))) | ((q(X!10) | p(X!10) | p(X!11) | q(X!12)) & (![X: $i] : (~(p(X) | q(X))) | (![X: $i] : (~p(X)) & ![X: $i] : (~q(X))))) | ![Y: $i] : (p(Y) & (~p(X!7))) | (p(X!13) & q(X!13) & (![X: $i] : (~p(X)) | ![X: $i] : (~q(X)))) | ((~p(Y!14)) & ![X: $i] : p(X)) | (![X: $i] : p(X) & ![X: $i] : (~p(X))) | (![Y: $i] : (~p(Y)) & (~p(Y!15)) & p(X!11)) | ((![X: $i] : p(X) | c | ![X: $i] : (p(X) | c)) & ((~(c | p(X!16))) | ((~p(X!7)) & (~c)))) | (((p(X!17) & c) | (p(X!11) & c)) & ((~c) | ![X: $i] : (~p(X)) | ![X: $i] : (~(p(X) & c)))) | (((~c) | p(X!11) | p(X!18)) & (![X: $i] : (~((~c) | p(X))) | (c & ![X: $i] : (~p(X))))) | ((c | (~p(X!7)) | (~p(X!19))) & (![X: $i] : (~(c | (~p(X)))) | ((~c) & ![X: $i] : p(X)))) | ((![X: $i] : p(X) | (~c) | ![X: $i] : ((~c) | p(X))) & ((~((~c) | p(X!20))) | (c & (~p(X!7))))) | ((c | ![X: $i] : (c | (~p(X))) | ![X: $i] : (~p(X))) & ((~(c | (~p(X!21)))) | ((~c) & p(X!11))))) <=> (((![X: $i] : p(X) | ![X: $i] : q(X)) & (~(p(X!9) | q(X!9)))) | ((~p(Y!14)) & ![X: $i] : p(X)) | (![X: $i] : p(X) & ![X: $i] : (~p(X))) | (![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & ![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) | (![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)) & (~((~r(X!2, Y!1)) | r(X!2, X!2)))) | (![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & ((~(h(X!3) | (~(f(X!3) & g(X!3))))) | (f(X!4) & (~g(X!4)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) | ![X: $i] : (~(q(X) | (~p(X)) | p(tptp_fun_Y_5(X)))) | (p(X!13) & q(X!13) & (![X: $i] : (~p(X)) | ![X: $i] : (~q(X)))) | ![Y: $i] : (p(Y) & (~p(X!7))) | (((![X: $i] : p(X) & ![X: $i] : q(X)) | ![X: $i] : (p(X) & q(X))) & ((~(p(X!6) & q(X!6))) | (~p(X!7)) | (~q(X!8)))) | ((q(X!10) | p(X!10) | p(X!11) | q(X!12)) & (![X: $i] : (~(p(X) | q(X))) | (![X: $i] : (~p(X)) & ![X: $i] : (~q(X))))) | (![Y: $i] : (~p(Y)) & (~p(Y!15)) & p(X!11)) | ((c | (~p(X!7)) | (~p(X!19))) & (![X: $i] : (~(c | (~p(X)))) | ((~c) & ![X: $i] : p(X)))) | ((![X: $i] : p(X) | c | ![X: $i] : (p(X) | c)) & ((~(c | p(X!16))) | ((~p(X!7)) & (~c)))) | (((p(X!17) & c) | (p(X!11) & c)) & ((~c) | ![X: $i] : (~p(X)) | ![X: $i] : (~(p(X) & c)))) | ((c | ![X: $i] : (c | (~p(X))) | ![X: $i] : (~p(X))) & ((~(c | (~p(X!21)))) | ((~c) & p(X!11)))) | (((~c) | p(X!11) | p(X!18)) & (![X: $i] : (~((~c) | p(X))) | (c & ![X: $i] : (~p(X))))) | ((![X: $i] : p(X) | (~c) | ![X: $i] : ((~c) | p(X))) & ((~((~c) | p(X!20))) | (c & (~p(X!7))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(318,plain,
% 0.21/0.49 (((![X: $i] : (c | (~p(X))) | (c | ![X: $i] : (~p(X)))) & ((~(c | (~p(X!21)))) | ((~c) & p(X!11)))) <=> ((c | ![X: $i] : (c | (~p(X))) | ![X: $i] : (~p(X))) & ((~(c | (~p(X!21)))) | ((~c) & p(X!11))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(319,plain,
% 0.21/0.49 (((![X: $i] : ((~c) | p(X)) | ((~c) | ![X: $i] : p(X))) & ((~((~c) | p(X!20))) | ((~(~c)) & (~p(X!7))))) <=> ((![X: $i] : p(X) | (~c) | ![X: $i] : ((~c) | p(X))) & ((~((~c) | p(X!20))) | (c & (~p(X!7)))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(320,plain,
% 0.21/0.49 ((((c | (~p(X!19))) | (c | (~p(X!7)))) & (![X: $i] : (~(c | (~p(X)))) | ((~c) & ![X: $i] : p(X)))) <=> ((c | (~p(X!7)) | (~p(X!19))) & (![X: $i] : (~(c | (~p(X)))) | ((~c) & ![X: $i] : p(X))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(321,plain,
% 0.21/0.49 (((((~c) | p(X!18)) | ((~c) | p(X!11))) & (![X: $i] : (~((~c) | p(X))) | ((~(~c)) & ![X: $i] : (~p(X))))) <=> (((~c) | p(X!11) | p(X!18)) & (![X: $i] : (~((~c) | p(X))) | (c & ![X: $i] : (~p(X)))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(322,plain,
% 0.21/0.49 ((((p(X!17) & c) | (p(X!11) & c)) & (![X: $i] : (~(p(X) & c)) | (![X: $i] : (~p(X)) | (~c)))) <=> (((p(X!17) & c) | (p(X!11) & c)) & ((~c) | ![X: $i] : (~p(X)) | ![X: $i] : (~(p(X) & c))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(323,plain,
% 0.21/0.49 (((![X: $i] : (p(X) | c) | (![X: $i] : p(X) | c)) & ((~(p(X!16) | c)) | ((~p(X!7)) & (~c)))) <=> ((![X: $i] : p(X) | c | ![X: $i] : (p(X) | c)) & ((~(c | p(X!16))) | ((~p(X!7)) & (~c))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(324,plain,
% 0.21/0.49 ((![Y: $i] : (~p(Y)) & ((~p(Y!15)) & p(X!11))) <=> (![Y: $i] : (~p(Y)) & (~p(Y!15)) & p(X!11))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(325,plain,
% 0.21/0.49 (((p(X!13) & q(X!13)) & (![X: $i] : (~p(X)) | ![X: $i] : (~q(X)))) <=> (p(X!13) & q(X!13) & (![X: $i] : (~p(X)) | ![X: $i] : (~q(X))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(326,plain,
% 0.21/0.49 (^[Y: $i] : rewrite(((~(~p(Y))) & (~p(X!7))) <=> (p(Y) & (~p(X!7))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(327,plain,
% 0.21/0.49 (![Y: $i] : ((~(~p(Y))) & (~p(X!7))) <=> ![Y: $i] : (p(Y) & (~p(X!7)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[326])).
% 0.21/0.49 tff(328,plain,
% 0.21/0.49 ((((p(X!10) | q(X!10)) | (p(X!11) | q(X!12))) & (![X: $i] : (~(p(X) | q(X))) | (![X: $i] : (~p(X)) & ![X: $i] : (~q(X))))) <=> ((q(X!10) | p(X!10) | p(X!11) | q(X!12)) & (![X: $i] : (~(p(X) | q(X))) | (![X: $i] : (~p(X)) & ![X: $i] : (~q(X)))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(329,plain,
% 0.21/0.49 (((![X: $i] : (p(X) & q(X)) | (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(p(X!6) & q(X!6))) | ((~p(X!7)) | (~q(X!8))))) <=> (((![X: $i] : p(X) & ![X: $i] : q(X)) | ![X: $i] : (p(X) & q(X))) & ((~(p(X!6) & q(X!6))) | (~p(X!7)) | (~q(X!8))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(330,plain,
% 0.21/0.49 (^[X: $i] : rewrite((~(q(X) | p(tptp_fun_Y_5(X)) | (~p(X)))) <=> (~(q(X) | (~p(X)) | p(tptp_fun_Y_5(X)))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(331,plain,
% 0.21/0.49 (![X: $i] : (~(q(X) | p(tptp_fun_Y_5(X)) | (~p(X)))) <=> ![X: $i] : (~(q(X) | (~p(X)) | p(tptp_fun_Y_5(X))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[330])).
% 0.21/0.49 tff(332,plain,
% 0.21/0.49 ((![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & (((~(h(X!3) | (~(f(X!3) & g(X!3))))) | (f(X!4) & (~g(X!4)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))) <=> (![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & ((~(h(X!3) | (~(f(X!3) & g(X!3))))) | (f(X!4) & (~g(X!4)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(333,plain,
% 0.21/0.49 ((((~(h(X!3) | (~(f(X!3) & g(X!3))))) | (f(X!4) & (~g(X!4)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) <=> (((~(h(X!3) | (~(f(X!3) & g(X!3))))) | (f(X!4) & (~g(X!4)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[287])).
% 0.21/0.49 tff(334,plain,
% 0.21/0.49 ((![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & (((~(h(X!3) | (~(f(X!3) & g(X!3))))) | (f(X!4) & (~g(X!4)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))) <=> (![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & (((~(h(X!3) | (~(f(X!3) & g(X!3))))) | (f(X!4) & (~g(X!4)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[333])).
% 0.21/0.49 tff(335,plain,
% 0.21/0.49 ((![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & (((~(h(X!3) | (~(f(X!3) & g(X!3))))) | (f(X!4) & (~g(X!4)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))) <=> (![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & ((~(h(X!3) | (~(f(X!3) & g(X!3))))) | (f(X!4) & (~g(X!4)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[334, 332])).
% 0.21/0.49 tff(336,plain,
% 0.21/0.49 (((![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z))) & (~((~r(X!2, Y!1)) | r(X!2, X!2)))) <=> (![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)) & (~((~r(X!2, Y!1)) | r(X!2, X!2))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(337,plain,
% 0.21/0.49 ((![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z))) <=> (![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(338,plain,
% 0.21/0.49 (((![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z))) & (~((~r(X!2, Y!1)) | r(X!2, X!2)))) <=> ((![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z))) & (~((~r(X!2, Y!1)) | r(X!2, X!2))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[337])).
% 0.21/0.49 tff(339,plain,
% 0.21/0.49 (((![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z))) & (~((~r(X!2, Y!1)) | r(X!2, X!2)))) <=> (![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)) & (~((~r(X!2, Y!1)) | r(X!2, X!2))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[338, 336])).
% 0.21/0.49 tff(340,plain,
% 0.21/0.49 ((![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & (![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))) <=> (![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & ![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(341,plain,
% 0.21/0.50 ((![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) <=> (![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(342,plain,
% 0.21/0.50 ((![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & (![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))) <=> (![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & (![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[341])).
% 0.21/0.50 tff(343,plain,
% 0.21/0.50 ((![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & (![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))) <=> (![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & ![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))),
% 0.21/0.50 inference(transitivity,[status(thm)],[342, 340])).
% 0.21/0.50 tff(344,plain,
% 0.21/0.50 (((![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & (![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))) | ((![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z))) & (~((~r(X!2, Y!1)) | r(X!2, X!2)))) | (![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & (((~(h(X!3) | (~(f(X!3) & g(X!3))))) | (f(X!4) & (~g(X!4)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))) | ![X: $i] : (~(q(X) | p(tptp_fun_Y_5(X)) | (~p(X)))) | ((![X: $i] : (p(X) & q(X)) | (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(p(X!6) & q(X!6))) | ((~p(X!7)) | (~q(X!8))))) | ((![X: $i] : p(X) | ![X: $i] : q(X)) & (~(p(X!9) | q(X!9)))) | (((p(X!10) | q(X!10)) | (p(X!11) | q(X!12))) & (![X: $i] : (~(p(X) | q(X))) | (![X: $i] : (~p(X)) & ![X: $i] : (~q(X))))) | ![Y: $i] : ((~(~p(Y))) & (~p(X!7))) | ((p(X!13) & q(X!13)) & (![X: $i] : (~p(X)) | ![X: $i] : (~q(X)))) | ((~p(Y!14)) & ![X: $i] : p(X)) | (![X: $i] : p(X) & ![X: $i] : (~p(X))) | (![Y: $i] : (~p(Y)) & ((~p(Y!15)) & p(X!11))) | ((![X: $i] : (p(X) | c) | (![X: $i] : p(X) | c)) & ((~(p(X!16) | c)) | ((~p(X!7)) & (~c)))) | (((p(X!17) & c) | (p(X!11) & c)) & (![X: $i] : (~(p(X) & c)) | (![X: $i] : (~p(X)) | (~c)))) | ((((~c) | p(X!18)) | ((~c) | p(X!11))) & (![X: $i] : (~((~c) | p(X))) | ((~(~c)) & ![X: $i] : (~p(X))))) | (((c | (~p(X!19))) | (c | (~p(X!7)))) & (![X: $i] : (~(c | (~p(X)))) | ((~c) & ![X: $i] : p(X)))) | ((![X: $i] : ((~c) | p(X)) | ((~c) | ![X: $i] : p(X))) & ((~((~c) | p(X!20))) | ((~(~c)) & (~p(X!7))))) | ((![X: $i] : (c | (~p(X))) | (c | ![X: $i] : (~p(X)))) & ((~(c | (~p(X!21)))) | ((~c) & p(X!11))))) <=> ((![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & ![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) | (![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)) & (~((~r(X!2, Y!1)) | r(X!2, X!2)))) | (![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & ((~(h(X!3) | (~(f(X!3) & g(X!3))))) | (f(X!4) & (~g(X!4)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) | ![X: $i] : (~(q(X) | (~p(X)) | p(tptp_fun_Y_5(X)))) | (((![X: $i] : p(X) & ![X: $i] : q(X)) | ![X: $i] : (p(X) & q(X))) & ((~(p(X!6) & q(X!6))) | (~p(X!7)) | (~q(X!8)))) | ((![X: $i] : p(X) | ![X: $i] : q(X)) & (~(p(X!9) | q(X!9)))) | ((q(X!10) | p(X!10) | p(X!11) | q(X!12)) & (![X: $i] : (~(p(X) | q(X))) | (![X: $i] : (~p(X)) & ![X: $i] : (~q(X))))) | ![Y: $i] : (p(Y) & (~p(X!7))) | (p(X!13) & q(X!13) & (![X: $i] : (~p(X)) | ![X: $i] : (~q(X)))) | ((~p(Y!14)) & ![X: $i] : p(X)) | (![X: $i] : p(X) & ![X: $i] : (~p(X))) | (![Y: $i] : (~p(Y)) & (~p(Y!15)) & p(X!11)) | ((![X: $i] : p(X) | c | ![X: $i] : (p(X) | c)) & ((~(c | p(X!16))) | ((~p(X!7)) & (~c)))) | (((p(X!17) & c) | (p(X!11) & c)) & ((~c) | ![X: $i] : (~p(X)) | ![X: $i] : (~(p(X) & c)))) | (((~c) | p(X!11) | p(X!18)) & (![X: $i] : (~((~c) | p(X))) | (c & ![X: $i] : (~p(X))))) | ((c | (~p(X!7)) | (~p(X!19))) & (![X: $i] : (~(c | (~p(X)))) | ((~c) & ![X: $i] : p(X)))) | ((![X: $i] : p(X) | (~c) | ![X: $i] : ((~c) | p(X))) & ((~((~c) | p(X!20))) | (c & (~p(X!7))))) | ((c | ![X: $i] : (c | (~p(X))) | ![X: $i] : (~p(X))) & ((~(c | (~p(X!21)))) | ((~c) & p(X!11)))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[343, 339, 335, 331, 329, 328, 327, 325, 324, 323, 322, 321, 320, 319, 318])).
% 0.21/0.50 tff(345,plain,
% 0.21/0.50 (((![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & (![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))) | ((![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z))) & (~((~r(X!2, Y!1)) | r(X!2, X!2)))) | (![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & (((~(h(X!3) | (~(f(X!3) & g(X!3))))) | (f(X!4) & (~g(X!4)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))) | ![X: $i] : (~(q(X) | p(tptp_fun_Y_5(X)) | (~p(X)))) | ((![X: $i] : (p(X) & q(X)) | (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(p(X!6) & q(X!6))) | ((~p(X!7)) | (~q(X!8))))) | ((![X: $i] : p(X) | ![X: $i] : q(X)) & (~(p(X!9) | q(X!9)))) | (((p(X!10) | q(X!10)) | (p(X!11) | q(X!12))) & (![X: $i] : (~(p(X) | q(X))) | (![X: $i] : (~p(X)) & ![X: $i] : (~q(X))))) | ![Y: $i] : ((~(~p(Y))) & (~p(X!7))) | ((p(X!13) & q(X!13)) & (![X: $i] : (~p(X)) | ![X: $i] : (~q(X)))) | ((~p(Y!14)) & ![X: $i] : p(X)) | (![X: $i] : p(X) & ![X: $i] : (~p(X))) | (![Y: $i] : (~p(Y)) & ((~p(Y!15)) & p(X!11))) | ((![X: $i] : (p(X) | c) | (![X: $i] : p(X) | c)) & ((~(p(X!16) | c)) | ((~p(X!7)) & (~c)))) | (((p(X!17) & c) | (p(X!11) & c)) & (![X: $i] : (~(p(X) & c)) | (![X: $i] : (~p(X)) | (~c)))) | ((((~c) | p(X!18)) | ((~c) | p(X!11))) & (![X: $i] : (~((~c) | p(X))) | ((~(~c)) & ![X: $i] : (~p(X))))) | (((c | (~p(X!19))) | (c | (~p(X!7)))) & (![X: $i] : (~(c | (~p(X)))) | ((~c) & ![X: $i] : p(X)))) | ((![X: $i] : ((~c) | p(X)) | ((~c) | ![X: $i] : p(X))) & ((~((~c) | p(X!20))) | ((~(~c)) & (~p(X!7))))) | ((![X: $i] : (c | (~p(X))) | (c | ![X: $i] : (~p(X)))) & ((~(c | (~p(X!21)))) | ((~c) & p(X!11))))) <=> (((![X: $i] : p(X) | ![X: $i] : q(X)) & (~(p(X!9) | q(X!9)))) | ((~p(Y!14)) & ![X: $i] : p(X)) | (![X: $i] : p(X) & ![X: $i] : (~p(X))) | (![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & ![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) | (![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)) & (~((~r(X!2, Y!1)) | r(X!2, X!2)))) | (![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & ((~(h(X!3) | (~(f(X!3) & g(X!3))))) | (f(X!4) & (~g(X!4)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) | ![X: $i] : (~(q(X) | (~p(X)) | p(tptp_fun_Y_5(X)))) | (p(X!13) & q(X!13) & (![X: $i] : (~p(X)) | ![X: $i] : (~q(X)))) | ![Y: $i] : (p(Y) & (~p(X!7))) | (((![X: $i] : p(X) & ![X: $i] : q(X)) | ![X: $i] : (p(X) & q(X))) & ((~(p(X!6) & q(X!6))) | (~p(X!7)) | (~q(X!8)))) | ((q(X!10) | p(X!10) | p(X!11) | q(X!12)) & (![X: $i] : (~(p(X) | q(X))) | (![X: $i] : (~p(X)) & ![X: $i] : (~q(X))))) | (![Y: $i] : (~p(Y)) & (~p(Y!15)) & p(X!11)) | ((c | (~p(X!7)) | (~p(X!19))) & (![X: $i] : (~(c | (~p(X)))) | ((~c) & ![X: $i] : p(X)))) | ((![X: $i] : p(X) | c | ![X: $i] : (p(X) | c)) & ((~(c | p(X!16))) | ((~p(X!7)) & (~c)))) | (((p(X!17) & c) | (p(X!11) & c)) & ((~c) | ![X: $i] : (~p(X)) | ![X: $i] : (~(p(X) & c)))) | ((c | ![X: $i] : (c | (~p(X))) | ![X: $i] : (~p(X))) & ((~(c | (~p(X!21)))) | ((~c) & p(X!11)))) | (((~c) | p(X!11) | p(X!18)) & (![X: $i] : (~((~c) | p(X))) | (c & ![X: $i] : (~p(X))))) | ((![X: $i] : p(X) | (~c) | ![X: $i] : ((~c) | p(X))) & ((~((~c) | p(X!20))) | (c & (~p(X!7))))))),
% 0.21/0.50 inference(transitivity,[status(thm)],[344, 317])).
% 0.21/0.50 tff(346,plain,
% 0.21/0.50 (((?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ((~(![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)))) | ![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))) & (?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ?[X: $i] : ![Y: $i] : (q(X) | p(Y) | (~p(X))) & (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(![X: $i] : p(X) | ![X: $i] : q(X))) | ![X: $i] : (p(X) | q(X))) & (?[X: $i] : (p(X) | q(X)) <=> (?[X: $i] : p(X) | ?[X: $i] : q(X))) & ?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X)) & ((~?[X: $i] : (p(X) & q(X))) | (?[X: $i] : p(X) & ?[X: $i] : q(X))) & ![Y: $i] : (p(Y) | (~![X: $i] : p(X))) & ((~![X: $i] : p(X)) | ?[X: $i] : p(X)) & (?[Y: $i] : p(Y) | ![Y: $i] : (p(Y) | (~?[X: $i] : p(X)))) & (![X: $i] : (p(X) | c) <=> (![X: $i] : p(X) | c)) & (?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c)) & (?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))) & (?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))) & (![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))) & (![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X))))) <=> ((?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ((~(![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)))) | ![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))) & (?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ?[X: $i] : ![Y: $i] : (q(X) | p(Y) | (~p(X))) & (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(![X: $i] : p(X) | ![X: $i] : q(X))) | ![X: $i] : (p(X) | q(X))) & (?[X: $i] : (p(X) | q(X)) <=> (?[X: $i] : p(X) | ?[X: $i] : q(X))) & ?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X)) & ((~?[X: $i] : (p(X) & q(X))) | (?[X: $i] : p(X) & ?[X: $i] : q(X))) & ![Y: $i] : (p(Y) | (~![X: $i] : p(X))) & ((~![X: $i] : p(X)) | ?[X: $i] : p(X)) & (?[Y: $i] : p(Y) | ![Y: $i] : (p(Y) | (~?[X: $i] : p(X)))) & (![X: $i] : (p(X) | c) <=> (![X: $i] : p(X) | c)) & (?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c)) & (?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))) & (?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))) & (![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))) & (![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X)))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(347,plain,
% 0.21/0.50 ((~((?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ((~(![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)))) | ![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))) & (?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ?[X: $i] : ![Y: $i] : (q(X) | p(Y) | (~p(X))) & (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(![X: $i] : p(X) | ![X: $i] : q(X))) | ![X: $i] : (p(X) | q(X))) & (?[X: $i] : (p(X) | q(X)) <=> (?[X: $i] : p(X) | ?[X: $i] : q(X))) & ?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X)) & ((~?[X: $i] : (p(X) & q(X))) | (?[X: $i] : p(X) & ?[X: $i] : q(X))) & ![Y: $i] : (p(Y) | (~![X: $i] : p(X))) & ((~![X: $i] : p(X)) | ?[X: $i] : p(X)) & (?[Y: $i] : p(Y) | ![Y: $i] : (p(Y) | (~?[X: $i] : p(X)))) & (![X: $i] : (p(X) | c) <=> (![X: $i] : p(X) | c)) & (?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c)) & (?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))) & (?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))) & (![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))) & (![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X)))))) <=> (~((?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ((~(![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)))) | ![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))) & (?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ?[X: $i] : ![Y: $i] : (q(X) | p(Y) | (~p(X))) & (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(![X: $i] : p(X) | ![X: $i] : q(X))) | ![X: $i] : (p(X) | q(X))) & (?[X: $i] : (p(X) | q(X)) <=> (?[X: $i] : p(X) | ?[X: $i] : q(X))) & ?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X)) & ((~?[X: $i] : (p(X) & q(X))) | (?[X: $i] : p(X) & ?[X: $i] : q(X))) & ![Y: $i] : (p(Y) | (~![X: $i] : p(X))) & ((~![X: $i] : p(X)) | ?[X: $i] : p(X)) & (?[Y: $i] : p(Y) | ![Y: $i] : (p(Y) | (~?[X: $i] : p(X)))) & (![X: $i] : (p(X) | c) <=> (![X: $i] : p(X) | c)) & (?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c)) & (?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))) & (?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))) & (![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))) & (![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X))))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[346])).
% 0.21/0.50 tff(348,plain,
% 0.21/0.50 ((~((?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ((~(![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)))) | ![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))) & (?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ?[X: $i] : ![Y: $i] : (q(X) | (~p(X)) | p(Y)) & (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(![X: $i] : p(X) | ![X: $i] : q(X))) | ![X: $i] : (p(X) | q(X))) & (?[X: $i] : (p(X) | q(X)) <=> (?[X: $i] : p(X) | ?[X: $i] : q(X))) & ?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X)) & ((~?[X: $i] : (p(X) & q(X))) | (?[X: $i] : p(X) & ?[X: $i] : q(X))) & ![Y: $i] : (p(Y) | (~![X: $i] : p(X))) & ((~![X: $i] : p(X)) | ?[X: $i] : p(X)) & (?[Y: $i] : p(Y) | ![Y: $i] : (p(Y) | (~?[X: $i] : p(X)))) & (![X: $i] : (p(X) | c) <=> (![X: $i] : p(X) | c)) & (?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c)) & (?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))) & (?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))) & (![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))) & (![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X)))))) <=> (~((?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ((~(![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)))) | ![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))) & (?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ?[X: $i] : ![Y: $i] : (q(X) | p(Y) | (~p(X))) & (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(![X: $i] : p(X) | ![X: $i] : q(X))) | ![X: $i] : (p(X) | q(X))) & (?[X: $i] : (p(X) | q(X)) <=> (?[X: $i] : p(X) | ?[X: $i] : q(X))) & ?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X)) & ((~?[X: $i] : (p(X) & q(X))) | (?[X: $i] : p(X) & ?[X: $i] : q(X))) & ![Y: $i] : (p(Y) | (~![X: $i] : p(X))) & ((~![X: $i] : p(X)) | ?[X: $i] : p(X)) & (?[Y: $i] : p(Y) | ![Y: $i] : (p(Y) | (~?[X: $i] : p(X)))) & (![X: $i] : (p(X) | c) <=> (![X: $i] : p(X) | c)) & (?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c)) & (?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))) & (?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))) & (![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))) & (![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X))))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(349,plain,
% 0.21/0.51 ((~((?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ((~(![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)))) | ![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))) & (?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ?[X: $i] : ![Y: $i] : (q(X) | (~p(X)) | (~(q(X) | (~p(Y))))) & (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(![X: $i] : p(X) | ![X: $i] : q(X))) | ![X: $i] : (p(X) | q(X))) & (?[X: $i] : (p(X) | q(X)) <=> (?[X: $i] : p(X) | ?[X: $i] : q(X))) & ?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X)) & ((~?[X: $i] : (p(X) & q(X))) | (?[X: $i] : p(X) & ?[X: $i] : q(X))) & ![Y: $i] : (p(Y) | (~![X: $i] : p(X))) & ((~![X: $i] : p(X)) | ?[X: $i] : p(X)) & (?[Y: $i] : p(Y) | ![Y: $i] : (p(Y) | (~?[X: $i] : p(X)))) & (![X: $i] : (p(X) | c) <=> (![X: $i] : p(X) | c)) & (?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c)) & (?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))) & (?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))) & (![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))) & (![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X)))))) <=> (~((?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ((~(![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)))) | ![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))) & (?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ?[X: $i] : ![Y: $i] : (q(X) | (~p(X)) | p(Y)) & (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(![X: $i] : p(X) | ![X: $i] : q(X))) | ![X: $i] : (p(X) | q(X))) & (?[X: $i] : (p(X) | q(X)) <=> (?[X: $i] : p(X) | ?[X: $i] : q(X))) & ?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X)) & ((~?[X: $i] : (p(X) & q(X))) | (?[X: $i] : p(X) & ?[X: $i] : q(X))) & ![Y: $i] : (p(Y) | (~![X: $i] : p(X))) & ((~![X: $i] : p(X)) | ?[X: $i] : p(X)) & (?[Y: $i] : p(Y) | ![Y: $i] : (p(Y) | (~?[X: $i] : p(X)))) & (![X: $i] : (p(X) | c) <=> (![X: $i] : p(X) | c)) & (?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c)) & (?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))) & (?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))) & (![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))) & (![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X))))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(350,plain,
% 0.21/0.51 ((~((?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ((~(![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)))) | ![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))) & (?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ?[X: $i] : ![Y: $i] : (q(X) | (~p(X)) | (~(q(X) | (~p(Y))))) & (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(![X: $i] : p(X) | ![X: $i] : q(X))) | ![X: $i] : (p(X) | q(X))) & (?[X: $i] : (p(X) | q(X)) <=> (?[X: $i] : p(X) | ?[X: $i] : q(X))) & ?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X)) & ((~?[X: $i] : (p(X) & q(X))) | (?[X: $i] : p(X) & ?[X: $i] : q(X))) & ![Y: $i] : (p(Y) | (~![X: $i] : p(X))) & ((~![X: $i] : p(X)) | ?[X: $i] : p(X)) & (?[Y: $i] : p(Y) | ![Y: $i] : (p(Y) | (~?[X: $i] : p(X)))) & (![X: $i] : (p(X) | c) <=> (![X: $i] : p(X) | c)) & (?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c)) & (?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))) & (?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))) & (![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))) & (![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X)))))) <=> (~((?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ((~(![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)))) | ![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))) & (?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ?[X: $i] : ![Y: $i] : (q(X) | (~p(X)) | (~(q(X) | (~p(Y))))) & (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(![X: $i] : p(X) | ![X: $i] : q(X))) | ![X: $i] : (p(X) | q(X))) & (?[X: $i] : (p(X) | q(X)) <=> (?[X: $i] : p(X) | ?[X: $i] : q(X))) & ?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X)) & ((~?[X: $i] : (p(X) & q(X))) | (?[X: $i] : p(X) & ?[X: $i] : q(X))) & ![Y: $i] : (p(Y) | (~![X: $i] : p(X))) & ((~![X: $i] : p(X)) | ?[X: $i] : p(X)) & (?[Y: $i] : p(Y) | ![Y: $i] : (p(Y) | (~?[X: $i] : p(X)))) & (![X: $i] : (p(X) | c) <=> (![X: $i] : p(X) | c)) & (?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c)) & (?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))) & (?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))) & (![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))) & (![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X))))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(351,plain,
% 0.21/0.51 (((?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ((~(![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)))) | ![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))) & (?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ?[X: $i] : ![Y: $i] : (q(X) | (~p(X)) | (~(q(X) | (~p(Y))))) & (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(![X: $i] : p(X) | ![X: $i] : q(X))) | ![X: $i] : (p(X) | q(X))) & (?[X: $i] : (p(X) | q(X)) <=> (?[X: $i] : p(X) | ?[X: $i] : q(X))) & ?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X)) & ((~?[X: $i] : (p(X) & q(X))) | (?[X: $i] : p(X) & ?[X: $i] : q(X))) & ![Y: $i] : (p(Y) | (~![X: $i] : p(X))) & ((~![X: $i] : p(X)) | ?[X: $i] : p(X)) & (?[Y: $i] : p(Y) | ![Y: $i] : (p(Y) | (~?[X: $i] : p(X)))) & (![X: $i] : (p(X) | c) <=> (![X: $i] : p(X) | c)) & (?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c)) & (?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))) & (?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))) & (![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))) & (![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X))))) <=> ((?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ((~(![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)))) | ![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))) & (?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ?[X: $i] : ![Y: $i] : (q(X) | (~p(X)) | (~(q(X) | (~p(Y))))) & (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(![X: $i] : p(X) | ![X: $i] : q(X))) | ![X: $i] : (p(X) | q(X))) & (?[X: $i] : (p(X) | q(X)) <=> (?[X: $i] : p(X) | ?[X: $i] : q(X))) & ?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X)) & ((~?[X: $i] : (p(X) & q(X))) | (?[X: $i] : p(X) & ?[X: $i] : q(X))) & ![Y: $i] : (p(Y) | (~![X: $i] : p(X))) & ((~![X: $i] : p(X)) | ?[X: $i] : p(X)) & (?[Y: $i] : p(Y) | ![Y: $i] : (p(Y) | (~?[X: $i] : p(X)))) & (![X: $i] : (p(X) | c) <=> (![X: $i] : p(X) | c)) & (?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c)) & (?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))) & (?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))) & (![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))) & (![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X)))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(352,plain,
% 0.21/0.51 ((~((?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ((~(![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)))) | ![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))) & (?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ?[X: $i] : ![Y: $i] : (q(X) | (~p(X)) | (~(q(X) | (~p(Y))))) & (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(![X: $i] : p(X) | ![X: $i] : q(X))) | ![X: $i] : (p(X) | q(X))) & (?[X: $i] : (p(X) | q(X)) <=> (?[X: $i] : p(X) | ?[X: $i] : q(X))) & ?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X)) & ((~?[X: $i] : (p(X) & q(X))) | (?[X: $i] : p(X) & ?[X: $i] : q(X))) & ![Y: $i] : (p(Y) | (~![X: $i] : p(X))) & ((~![X: $i] : p(X)) | ?[X: $i] : p(X)) & (?[Y: $i] : p(Y) | ![Y: $i] : (p(Y) | (~?[X: $i] : p(X)))) & (![X: $i] : (p(X) | c) <=> (![X: $i] : p(X) | c)) & (?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c)) & (?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))) & (?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))) & (![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))) & (![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X)))))) <=> (~((?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ((~(![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)))) | ![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))) & (?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ?[X: $i] : ![Y: $i] : (q(X) | (~p(X)) | (~(q(X) | (~p(Y))))) & (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(![X: $i] : p(X) | ![X: $i] : q(X))) | ![X: $i] : (p(X) | q(X))) & (?[X: $i] : (p(X) | q(X)) <=> (?[X: $i] : p(X) | ?[X: $i] : q(X))) & ?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X)) & ((~?[X: $i] : (p(X) & q(X))) | (?[X: $i] : p(X) & ?[X: $i] : q(X))) & ![Y: $i] : (p(Y) | (~![X: $i] : p(X))) & ((~![X: $i] : p(X)) | ?[X: $i] : p(X)) & (?[Y: $i] : p(Y) | ![Y: $i] : (p(Y) | (~?[X: $i] : p(X)))) & (![X: $i] : (p(X) | c) <=> (![X: $i] : p(X) | c)) & (?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c)) & (?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))) & (?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))) & (![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))) & (![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X))))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[351])).
% 0.21/0.52 tff(353,plain,
% 0.21/0.52 ((~(((((((((((((((((((((![X: $i] : (((f(X) & g(X)) => h(X)) => ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (f(W) => g(W)) | ![Z: $i] : (f(Z) => h(Z)))) => (![R: $i] : ((f(R) & h(R)) => g(R)) => ?[V: $i] : ((f(V) & g(V)) & (~h(V))))) & ((![X: $i, Y: $i] : (r(X, Y) => r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((r(X, Y) & r(Y, Z)) => r(X, Z))) => ![X: $i, Y: $i] : (r(X, Y) => r(X, X)))) & (((![X: $i] : ((f(X) & g(X)) => h(X)) => ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (f(W) => g(W)) | ![Z: $i] : (f(Z) => h(Z)))) => (![R: $i] : ((f(R) & h(R)) => g(R)) => ?[V: $i] : ((f(V) & g(V)) & (~h(V)))))) & ?[X: $i] : ![Y: $i] : ((p(Y) => q(X)) => (p(X) => q(X)))) & (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X)))) & ((![X: $i] : p(X) | ![X: $i] : q(X)) => ![X: $i] : (p(X) | q(X)))) & (?[X: $i] : (p(X) | q(X)) <=> (?[X: $i] : p(X) | ?[X: $i] : q(X)))) & ?[Y: $i] : (p(Y) => ![X: $i] : p(X))) & (?[X: $i] : (p(X) & q(X)) => (?[X: $i] : p(X) & ?[X: $i] : q(X)))) & ![Y: $i] : (![X: $i] : p(X) => p(Y))) & (![X: $i] : p(X) => ?[X: $i] : p(X))) & ((~?[Y: $i] : p(Y)) => ![Y: $i] : (?[X: $i] : p(X) => p(Y)))) & (![X: $i] : (p(X) | c) <=> (![X: $i] : p(X) | c))) & (?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c))) & (?[X: $i] : c <=> c)) & (![X: $i] : c <=> c)) & (?[X: $i] : (c => p(X)) <=> (c => ?[X: $i] : p(X)))) & (?[X: $i] : (p(X) => c) <=> (![X: $i] : p(X) => c))) & (![X: $i] : (c => p(X)) <=> (c => ![X: $i] : p(X)))) & (![X: $i] : (p(X) => c) <=> (?[X: $i] : p(X) => c)))) <=> (~((?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ((~(![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)))) | ![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))) & (?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ?[X: $i] : ![Y: $i] : (q(X) | (~p(X)) | (~(q(X) | (~p(Y))))) & (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(![X: $i] : p(X) | ![X: $i] : q(X))) | ![X: $i] : (p(X) | q(X))) & (?[X: $i] : (p(X) | q(X)) <=> (?[X: $i] : p(X) | ?[X: $i] : q(X))) & ?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X)) & ((~?[X: $i] : (p(X) & q(X))) | (?[X: $i] : p(X) & ?[X: $i] : q(X))) & ![Y: $i] : (p(Y) | (~![X: $i] : p(X))) & ((~![X: $i] : p(X)) | ?[X: $i] : p(X)) & (?[Y: $i] : p(Y) | ![Y: $i] : (p(Y) | (~?[X: $i] : p(X)))) & (![X: $i] : (p(X) | c) <=> (![X: $i] : p(X) | c)) & (?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c)) & (?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))) & (?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))) & (![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))) & (![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X))))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(354,axiom,(~(((((((((((((((((((((![X: $i] : (((f(X) & g(X)) => h(X)) => ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (f(W) => g(W)) | ![Z: $i] : (f(Z) => h(Z)))) => (![R: $i] : ((f(R) & h(R)) => g(R)) => ?[V: $i] : ((f(V) & g(V)) & (~h(V))))) & ((![X: $i, Y: $i] : (r(X, Y) => r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((r(X, Y) & r(Y, Z)) => r(X, Z))) => ![X: $i, Y: $i] : (r(X, Y) => r(X, X)))) & (((![X: $i] : ((f(X) & g(X)) => h(X)) => ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (f(W) => g(W)) | ![Z: $i] : (f(Z) => h(Z)))) => (![R: $i] : ((f(R) & h(R)) => g(R)) => ?[V: $i] : ((f(V) & g(V)) & (~h(V)))))) & ?[X: $i] : ![Y: $i] : ((p(Y) => q(X)) => (p(X) => q(X)))) & (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X)))) & ((![X: $i] : p(X) | ![X: $i] : q(X)) => ![X: $i] : (p(X) | q(X)))) & (?[X: $i] : (p(X) | q(X)) <=> (?[X: $i] : p(X) | ?[X: $i] : q(X)))) & ?[Y: $i] : (p(Y) => ![X: $i] : p(X))) & (?[X: $i] : (p(X) & q(X)) => (?[X: $i] : p(X) & ?[X: $i] : q(X)))) & ![Y: $i] : (![X: $i] : p(X) => p(Y))) & (![X: $i] : p(X) => ?[X: $i] : p(X))) & ((~?[Y: $i] : p(Y)) => ![Y: $i] : (?[X: $i] : p(X) => p(Y)))) & (![X: $i] : (p(X) | c) <=> (![X: $i] : p(X) | c))) & (?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c))) & (?[X: $i] : c <=> c)) & (![X: $i] : c <=> c)) & (?[X: $i] : (c => p(X)) <=> (c => ?[X: $i] : p(X)))) & (?[X: $i] : (p(X) => c) <=> (![X: $i] : p(X) => c))) & (![X: $i] : (c => p(X)) <=> (c => ![X: $i] : p(X)))) & (![X: $i] : (p(X) => c) <=> (?[X: $i] : p(X) => c)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.21/0.52 tff(355,plain,
% 0.21/0.52 (~((?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ((~(![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)))) | ![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))) & (?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ?[X: $i] : ![Y: $i] : (q(X) | (~p(X)) | (~(q(X) | (~p(Y))))) & (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(![X: $i] : p(X) | ![X: $i] : q(X))) | ![X: $i] : (p(X) | q(X))) & (?[X: $i] : (p(X) | q(X)) <=> (?[X: $i] : p(X) | ?[X: $i] : q(X))) & ?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X)) & ((~?[X: $i] : (p(X) & q(X))) | (?[X: $i] : p(X) & ?[X: $i] : q(X))) & ![Y: $i] : (p(Y) | (~![X: $i] : p(X))) & ((~![X: $i] : p(X)) | ?[X: $i] : p(X)) & (?[Y: $i] : p(Y) | ![Y: $i] : (p(Y) | (~?[X: $i] : p(X)))) & (![X: $i] : (p(X) | c) <=> (![X: $i] : p(X) | c)) & (?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c)) & (?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))) & (?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))) & (![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))) & (![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X)))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[354, 353])).
% 0.21/0.52 tff(356,plain,
% 0.21/0.52 (~((?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ((~(![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)))) | ![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))) & (?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ?[X: $i] : ![Y: $i] : (q(X) | (~p(X)) | (~(q(X) | (~p(Y))))) & (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(![X: $i] : p(X) | ![X: $i] : q(X))) | ![X: $i] : (p(X) | q(X))) & (?[X: $i] : (p(X) | q(X)) <=> (?[X: $i] : p(X) | ?[X: $i] : q(X))) & ?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X)) & ((~?[X: $i] : (p(X) & q(X))) | (?[X: $i] : p(X) & ?[X: $i] : q(X))) & ![Y: $i] : (p(Y) | (~![X: $i] : p(X))) & ((~![X: $i] : p(X)) | ?[X: $i] : p(X)) & (?[Y: $i] : p(Y) | ![Y: $i] : (p(Y) | (~?[X: $i] : p(X)))) & (![X: $i] : (p(X) | c) <=> (![X: $i] : p(X) | c)) & (?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c)) & (?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))) & (?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))) & (![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))) & (![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X)))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[355, 352])).
% 0.21/0.52 tff(357,plain,
% 0.21/0.52 (~((?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ((~(![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)))) | ![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))) & (?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ?[X: $i] : ![Y: $i] : (q(X) | (~p(X)) | (~(q(X) | (~p(Y))))) & (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(![X: $i] : p(X) | ![X: $i] : q(X))) | ![X: $i] : (p(X) | q(X))) & (?[X: $i] : (p(X) | q(X)) <=> (?[X: $i] : p(X) | ?[X: $i] : q(X))) & ?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X)) & ((~?[X: $i] : (p(X) & q(X))) | (?[X: $i] : p(X) & ?[X: $i] : q(X))) & ![Y: $i] : (p(Y) | (~![X: $i] : p(X))) & ((~![X: $i] : p(X)) | ?[X: $i] : p(X)) & (?[Y: $i] : p(Y) | ![Y: $i] : (p(Y) | (~?[X: $i] : p(X)))) & (![X: $i] : (p(X) | c) <=> (![X: $i] : p(X) | c)) & (?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c)) & (?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))) & (?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))) & (![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))) & (![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X)))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[356, 350])).
% 0.21/0.52 tff(358,plain,
% 0.21/0.52 (~((?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ((~(![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)))) | ![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))) & (?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ?[X: $i] : ![Y: $i] : (q(X) | (~p(X)) | p(Y)) & (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(![X: $i] : p(X) | ![X: $i] : q(X))) | ![X: $i] : (p(X) | q(X))) & (?[X: $i] : (p(X) | q(X)) <=> (?[X: $i] : p(X) | ?[X: $i] : q(X))) & ?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X)) & ((~?[X: $i] : (p(X) & q(X))) | (?[X: $i] : p(X) & ?[X: $i] : q(X))) & ![Y: $i] : (p(Y) | (~![X: $i] : p(X))) & ((~![X: $i] : p(X)) | ?[X: $i] : p(X)) & (?[Y: $i] : p(Y) | ![Y: $i] : (p(Y) | (~?[X: $i] : p(X)))) & (![X: $i] : (p(X) | c) <=> (![X: $i] : p(X) | c)) & (?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c)) & (?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))) & (?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))) & (![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))) & (![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X)))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[357, 349])).
% 0.21/0.52 tff(359,plain,
% 0.21/0.52 (~((?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ((~(![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)))) | ![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))) & (?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ?[X: $i] : ![Y: $i] : (q(X) | p(Y) | (~p(X))) & (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(![X: $i] : p(X) | ![X: $i] : q(X))) | ![X: $i] : (p(X) | q(X))) & (?[X: $i] : (p(X) | q(X)) <=> (?[X: $i] : p(X) | ?[X: $i] : q(X))) & ?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X)) & ((~?[X: $i] : (p(X) & q(X))) | (?[X: $i] : p(X) & ?[X: $i] : q(X))) & ![Y: $i] : (p(Y) | (~![X: $i] : p(X))) & ((~![X: $i] : p(X)) | ?[X: $i] : p(X)) & (?[Y: $i] : p(Y) | ![Y: $i] : (p(Y) | (~?[X: $i] : p(X)))) & (![X: $i] : (p(X) | c) <=> (![X: $i] : p(X) | c)) & (?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c)) & (?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))) & (?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))) & (![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))) & (![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X)))))),
% 0.42/0.55 inference(modus_ponens,[status(thm)],[358, 348])).
% 0.42/0.55 tff(360,plain,
% 0.42/0.55 (~((?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ((~(![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)))) | ![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))) & (?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ?[X: $i] : ![Y: $i] : (q(X) | p(Y) | (~p(X))) & (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(![X: $i] : p(X) | ![X: $i] : q(X))) | ![X: $i] : (p(X) | q(X))) & (?[X: $i] : (p(X) | q(X)) <=> (?[X: $i] : p(X) | ?[X: $i] : q(X))) & ?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X)) & ((~?[X: $i] : (p(X) & q(X))) | (?[X: $i] : p(X) & ?[X: $i] : q(X))) & ![Y: $i] : (p(Y) | (~![X: $i] : p(X))) & ((~![X: $i] : p(X)) | ?[X: $i] : p(X)) & (?[Y: $i] : p(Y) | ![Y: $i] : (p(Y) | (~?[X: $i] : p(X)))) & (![X: $i] : (p(X) | c) <=> (![X: $i] : p(X) | c)) & (?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c)) & (?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))) & (?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))) & (![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))) & (![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X)))))),
% 0.42/0.55 inference(modus_ponens,[status(thm)],[359, 347])).
% 0.42/0.55 tff(361,plain,
% 0.42/0.55 (~((?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ((~(![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)))) | ![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))) & (?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ?[X: $i] : ![Y: $i] : (q(X) | p(Y) | (~p(X))) & (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(![X: $i] : p(X) | ![X: $i] : q(X))) | ![X: $i] : (p(X) | q(X))) & (?[X: $i] : (p(X) | q(X)) <=> (?[X: $i] : p(X) | ?[X: $i] : q(X))) & ?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X)) & ((~?[X: $i] : (p(X) & q(X))) | (?[X: $i] : p(X) & ?[X: $i] : q(X))) & ![Y: $i] : (p(Y) | (~![X: $i] : p(X))) & ((~![X: $i] : p(X)) | ?[X: $i] : p(X)) & (?[Y: $i] : p(Y) | ![Y: $i] : (p(Y) | (~?[X: $i] : p(X)))) & (![X: $i] : (p(X) | c) <=> (![X: $i] : p(X) | c)) & (?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c)) & (?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))) & (?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))) & (![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))) & (![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X)))))),
% 0.42/0.55 inference(modus_ponens,[status(thm)],[360, 347])).
% 0.42/0.55 unexpected number of arguments: (let ((a!1 (proof-bind (lambda ((V $i))
% 0.42/0.55 (let ((a!1 (not (and (f V) (g V) (not (h V))))))
% 0.42/0.55 (refl (~ a!1 a!1))))))
% 0.42/0.55 (a!2 (exists ((V $i)) (and (f V) (g V) (not (h V)))))
% 0.42/0.55 (a!3 (forall ((V $i)) (not (and (f V) (g V) (not (h V))))))
% 0.42/0.55 (a!4 (proof-bind (lambda ((R $i))
% 0.42/0.55 (let ((a!1 (or (g R) (not (and (f R) (h R))))))
% 0.42/0.55 (refl (~ a!1 a!1))))))
% 0.42/0.55 (a!5 (forall ((R $i)) (or (g R) (not (and (f R) (h R))))))
% 0.42/0.55 (a!7 (lambda ((X $i))
% 0.42/0.55 (let ((a!1 (or (h X) (not (and (f X) (g X)))))
% 0.42/0.55 (a!2 (exists ((Y $i)) (and (f Y) (not (g Y))))))
% 0.42/0.55 (let ((a!3 (~ a!2 (and (f Y!0) (not (g Y!0)))))
% 0.42/0.55 (a!4 (or (not a!1) (and (f Y!0) (not (g Y!0))))))
% 0.42/0.55 (monotonicity (refl (~ (not a!1) (not a!1)))
% 0.42/0.55 (sk a!3)
% 0.42/0.55 (~ (or (not a!1) a!2) a!4))))))
% 0.42/0.55 (a!8 (forall ((X $i))
% 0.42/0.55 (let ((a!1 (or (h X) (not (and (f X) (g X)))))
% 0.42/0.55 (a!2 (exists ((Y $i)) (and (f Y) (not (g Y))))))
% 0.42/0.55 (or (not a!1) a!2))))
% 0.42/0.55 (a!9 (forall ((X $i))
% 0.42/0.55 (let ((a!1 (or (h X) (not (and (f X) (g X))))))
% 0.42/0.55 (or (not a!1) (and (f Y!0) (not (g Y!0)))))))
% 0.42/0.55 (a!10 (forall ((W $i)) (or (g W) (not (f W)))))
% 0.42/0.55 (a!12 (forall ((Z $i)) (or (h Z) (not (f Z)))))
% 0.42/0.55 (a!21 (forall ((X $i) (Y $i)) (or (not (r X Y)) (r Y X))))
% 0.42/0.55 (a!23 (proof-bind (lambda ((X $i) (Y $i) (Z $i))
% 0.42/0.55 (let ((a!1 (or (not (and (r X Y) (r Y Z))) (r X Z))))
% 0.42/0.55 (refl (~ a!1 a!1))))))
% 0.42/0.55 (a!24 (forall ((X $i) (Y $i) (Z $i))
% 0.42/0.55 (or (not (and (r X Y) (r Y Z))) (r X Z))))
% 0.42/0.55 (a!27 (forall ((X $i) (Y $i)) (or (not (r X Y)) (r X X))))
% 0.42/0.55 (a!28 (not (or (not (r X!2 Y!1)) (r X!2 X!2))))
% 0.42/0.55 (a!31 (forall ((X $i)) (or (h X) (not (and (f X) (g X))))))
% 0.42/0.55 (a!32 (or (h X!3) (not (and (f X!3) (g X!3)))))
% 0.42/0.55 (a!33 (exists ((X $i)) (and (f X) (not (g X)))))
% 0.42/0.55 (a!42 (lambda ((X $i))
% 0.42/0.55 (let ((a!1 (forall ((Y $i)) (or (q X) (p Y) (not (p X)))))
% 0.42/0.55 (a!2 (not (or (q X) (p (Y!5 X)) (not (p X))))))
% 0.42/0.55 (sk (~ (not a!1) a!2)))))
% 0.42/0.55 (a!43 (exists ((X $i)) (forall ((Y $i)) (or (q X) (p Y) (not (p X))))))
% 0.42/0.55 (a!44 (forall ((X $i)) (not (or (q X) (p (Y!5 X)) (not (p X))))))
% 0.42/0.55 (a!45 (lambda ((X $i)) (refl (~ (and (p X) (q X)) (and (p X) (q X))))))
% 0.42/0.55 (a!46 (forall ((X $i)) (and (p X) (q X))))
% 0.42/0.55 (a!48 (lambda ((X $i)) (refl (~ (p X) (p X)))))
% 0.42/0.55 (a!49 (forall ((X $i)) (p X)))
% 0.42/0.55 (a!50 (lambda ((X $i)) (refl (~ (q X) (q X)))))
% 0.42/0.55 (a!51 (forall ((X $i)) (q X)))
% 0.42/0.55 (a!55 (or (not (and (p X!6) (q X!6))) (or (not (p X!7)) (not (q X!8)))))
% 0.42/0.55 (a!60 (forall ((X $i)) (or (p X) (q X))))
% 0.42/0.55 (a!64 (exists ((X $i)) (or (p X) (q X))))
% 0.42/0.55 (a!66 (forall ((X $i)) (not (or (p X) (q X)))))
% 0.42/0.55 (a!68 (exists ((X $i)) (p X)))
% 0.42/0.55 (a!69 (exists ((X $i)) (q X)))
% 0.42/0.55 (a!71 (lambda ((X $i)) (refl (~ (not (p X)) (not (p X))))))
% 0.42/0.55 (a!72 (forall ((X $i)) (not (p X))))
% 0.42/0.55 (a!73 (lambda ((X $i)) (refl (~ (not (q X)) (not (q X))))))
% 0.42/0.55 (a!74 (forall ((X $i)) (not (q X))))
% 0.42/0.55 (a!78 (proof-bind (lambda ((Y $i))
% 0.42/0.55 (let ((a!1 (~ (not (not (p Y))) (not (not (p Y)))))
% 0.42/0.55 (a!2 (forall ((X $i)) (p X)))
% 0.42/0.55 (a!5 (and (not (not (p Y))) (not (p X!7)))))
% 0.42/0.55 (let ((a!3 (sk (~ (not a!2) (not (p X!7)))))
% 0.42/0.55 (a!4 (not (or (not (p Y)) a!2))))
% 0.42/0.55 (nnf-neg (refl a!1) a!3 (~ a!4 a!5)))))))
% 0.42/0.55 (a!79 (exists ((Y $i))
% 0.42/0.55 (let ((a!1 (forall ((X $i)) (p X))))
% 0.42/0.55 (or (not (p Y)) a!1))))
% 0.42/0.55 (a!80 (forall ((Y $i)) (and (not (not (p Y))) (not (p X!7)))))
% 0.42/0.55 (a!81 (exists ((X $i)) (and (p X) (q X))))
% 0.42/0.55 (a!86 (forall ((Y $i))
% 0.42/0.55 (let ((a!1 (forall ((X $i)) (p X))))
% 0.42/0.55 (or (p Y) (not a!1)))))
% 0.42/0.55 (a!88 (refl (~ (not (p Y!14)) (not (p Y!14)))))
% 0.42/0.55 (a!94 (lambda ((Y $i)) (refl (~ (not (p Y)) (not (p Y))))))
% 0.42/0.55 (a!95 (exists ((Y $i)) (p Y)))
% 0.42/0.55 (a!96 (forall ((Y $i)) (not (p Y))))
% 0.42/0.55 (a!97 (forall ((Y $i))
% 0.42/0.55 (let ((a!1 (exists ((X $i)) (p X))))
% 0.42/0.55 (or (p Y) (not a!1)))))
% 0.42/0.55 (a!99 (refl (~ (not (p Y!15)) (not (p Y!15)))))
% 0.42/0.55 (a!105 (lambda ((X $i)) (refl (~ (or (p X) c) (or (p X) c)))))
% 0.42/0.55 (a!106 (forall ((X $i)) (or (p X) c)))
% 0.42/0.55 (a!110 (or (not (or (p X!16) c)) (and (not (p X!7)) (not c))))
% 0.42/0.55 (a!113 (exists ((X $i)) (and (p X) c)))
% 0.42/0.55 (a!115 (forall ((X $i)) (not (and (p X) c))))
% 0.42/0.55 (a!121 (exists ((X $i)) (or (not c) (p X))))
% 0.42/0.55 (a!123 (forall ((X $i)) (not (or (not c) (p X)))))
% 0.42/0.55 (a!126 (refl (~ (not (not c)) (not (not c)))))
% 0.42/0.55 (a!132 (exists ((X $i)) (or c (not (p X)))))
% 0.42/0.55 (a!134 (proof-bind (lambda ((X $i))
% 0.42/0.55 (let ((a!1 (not (or c (not (p X))))))
% 0.42/0.55 (refl (~ a!1 a!1))))))
% 0.42/0.55 (a!135 (forall ((X $i)) (not (or c (not (p X))))))
% 0.42/0.55 (a!140 (or (or c (not (p X!19))) (or c (not (p X!7)))))
% 0.42/0.55 (a!143 (lambda ((X $i)) (refl (~ (or (not c) (p X)) (or (not c) (p X))))))
% 0.42/0.55 (a!144 (forall ((X $i)) (or (not c) (p X))))
% 0.42/0.55 (a!149 (or (not (or (not c) (p X!20))) (and (not (not c)) (not (p X!7)))))
% 0.42/0.55 (a!151 (forall ((X $i)) (or c (not (p X)))))
% 0.42/0.55 (a!153 (not (or c (not (p X!21))))))
% 0.42/0.55 (let ((a!6 (nnf-neg (nnf-pos a!4 (~ a!5 a!5)) (~ (not (not a!5)) a!5)))
% 0.42/0.55 (a!11 (nnf-pos (proof-bind (lambda ((W $i))
% 0.42/0.55 (let ((a!1 (~ (or (g W) (not (f W)))
% 0.42/0.55 (or (g W) (not (f W))))))
% 0.42/0.55 (refl a!1))))
% 0.42/0.55 (~ a!10 a!10)))
% 0.42/0.55 (a!13 (nnf-pos (proof-bind (lambda ((Z $i))
% 0.42/0.55 (let ((a!1 (~ (or (h Z) (not (f Z)))
% 0.42/0.55 (or (h Z) (not (f Z))))))
% 0.42/0.55 (refl a!1))))
% 0.42/0.55 (~ a!12 a!12)))
% 0.42/0.55 (a!16 (not (not (and a!8 (or a!10 a!12)))))
% 0.42/0.55 (a!18 (or a!2 (not a!5) (not (and a!8 (or a!10 a!12)))))
% 0.42/0.55 (a!22 (nnf-pos (proof-bind (lambda ((X $i) (Y $i))
% 0.42/0.55 (let ((a!1 (~ (or (not (r X Y)) (r Y X))
% 0.42/0.55 (or (not (r X Y)) (r Y X)))))
% 0.42/0.55 (refl a!1))))
% 0.42/0.55 (~ a!21 a!21)))
% 0.42/0.55 (a!25 (~ (not (not (and a!21 a!24))) (and a!21 a!24)))
% 0.42/0.55 (a!29 (not (or (not (and a!21 a!24)) a!27)))
% 0.42/0.55 (a!34 (~ a!33 (and (f X!4) (not (g X!4)))))
% 0.42/0.55 (a!35 (or (not a!32) (and (f X!4) (not (g X!4)))))
% 0.42/0.55 (a!38 (not (and (or (not a!31) a!33) (or a!10 a!12))))
% 0.42/0.55 (a!47 (~ (not a!46) (not (and (p X!6) (q X!6)))))
% 0.42/0.55 (a!52 (sk (~ (not a!49) (not (p X!7)))))
% 0.42/0.55 (a!53 (sk (~ (not a!51) (not (q X!8)))))
% 0.42/0.55 (a!54 (~ (not (and a!49 a!51)) (or (not (p X!7)) (not (q X!8)))))
% 0.42/0.55 (a!56 (~ (not (= a!46 (and a!49 a!51)))
% 0.42/0.55 (and (or a!46 (and a!49 a!51)) a!55)))
% 0.42/0.55 (a!58 (~ (not (not (or a!49 a!51))) (or a!49 a!51)))
% 0.42/0.55 (a!61 (~ (not a!60) (not (or (p X!9) (q X!9)))))
% 0.42/0.55 (a!62 (not (or (not (or a!49 a!51)) a!60)))
% 0.42/0.55 (a!63 (and (or a!49 a!51) (not (or (p X!9) (q X!9)))))
% 0.42/0.55 (a!65 (sk (~ a!64 (or (p X!10) (q X!10)))))
% 0.42/0.55 (a!67 (nnf-neg (proof-bind (lambda ((X $i))
% 0.42/0.55 (let ((a!1 (~ (not (or (p X) (q X)))
% 0.42/0.55 (not (or (p X) (q X))))))
% 0.42/0.55 (refl a!1))))
% 0.42/0.55 (~ (not a!64) a!66)))
% 0.42/0.55 (a!70 (monotonicity (sk (~ a!68 (p X!11)))
% 0.42/0.55 (sk (~ a!69 (q X!12)))
% 0.42/0.55 (~ (or a!68 a!69) (or (p X!11) (q X!12)))))
% 0.42/0.55 (a!75 (nnf-neg (nnf-neg (proof-bind a!71) (~ (not a!68) a!72))
% 0.42/0.55 (nnf-neg (proof-bind a!73) (~ (not a!69) a!74))
% 0.42/0.55 (~ (not (or a!68 a!69)) (and a!72 a!74))))
% 0.42/0.55 (a!76 (and (or (or (p X!10) (q X!10)) (or (p X!11) (q X!12)))
% 0.42/0.55 (or a!66 (and a!72 a!74))))
% 0.42/0.55 (a!82 (sk (~ a!81 (and (p X!13) (q X!13)))))
% 0.42/0.55 (a!84 (nnf-neg (nnf-neg (proof-bind a!71) (~ (not a!68) a!72))
% 0.42/0.55 (nnf-neg (proof-bind a!73) (~ (not a!69) a!74))
% 0.42/0.55 (~ (not (and a!68 a!69)) (or a!72 a!74))))
% 0.42/0.55 (a!85 (~ (not (or (not a!81) (and a!68 a!69)))
% 0.42/0.55 (and (and (p X!13) (q X!13)) (or a!72 a!74))))
% 0.42/0.55 (a!87 (~ (not a!86) (not (or (p Y!14) (not a!49)))))
% 0.42/0.55 (a!89 (nnf-neg (nnf-pos (proof-bind a!48) (~ a!49 a!49))
% 0.42/0.55 (~ (not (not a!49)) a!49)))
% 0.42/0.55 (a!90 (~ (not (or (p Y!14) (not a!49))) (and (not (p Y!14)) a!49)))
% 0.42/0.55 (a!91 (~ (not a!86) (and (not (p Y!14)) a!49)))
% 0.42/0.55 (a!92 (~ (not (or (not a!49) a!68)) (and a!49 a!72)))
% 0.42/0.55 (a!98 (~ (not a!97) (not (or (p Y!15) (not a!68)))))
% 0.42/0.55 (a!100 (nnf-neg (sk (~ a!68 (p X!11))) (~ (not (not a!68)) (p X!11))))
% 0.42/0.55 (a!101 (~ (not (or (p Y!15) (not a!68))) (and (not (p Y!15)) (p X!11))))
% 0.42/0.55 (a!102 (~ (not a!97) (and (not (p Y!15)) (p X!11))))
% 0.42/0.55 (a!103 (and a!96 (and (not (p Y!15)) (p X!11))))
% 0.42/0.55 (a!107 (~ (not a!106) (not (or (p X!16) c))))
% 0.42/0.55 (a!108 (~ (not (or a!49 c)) (and (not (p X!7)) (not c))))
% 0.42/0.55 (a!111 (~ (not (= a!106 (or a!49 c))) (and (or a!106 (or a!49 c)) a!110)))
% 0.42/0.55 (a!114 (sk (~ a!113 (and (p X!17) c))))
% 0.42/0.55 (a!116 (nnf-neg (proof-bind (lambda ((X $i))
% 0.42/0.55 (let ((a!1 (~ (not (and (p X) c))
% 0.42/0.55 (not (and (p X) c)))))
% 0.42/0.55 (refl a!1))))
% 0.42/0.55 (~ (not a!113) a!115)))
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% 0.42/0.55 (~ (and a!68 c) (and (p X!11) c))))
% 0.42/0.55 (a!118 (nnf-neg (nnf-neg (proof-bind a!71) (~ (not a!68) a!72))
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% 0.42/0.55 (a!119 (and (or (and (p X!17) c) (and (p X!11) c))
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% 0.42/0.55 (a!122 (sk (~ a!121 (or (not c) (p X!18)))))
% 0.42/0.55 (a!124 (nnf-neg (proof-bind (lambda ((X $i))
% 0.42/0.55 (let ((a!1 (~ (not (or (not c) (p X)))
% 0.42/0.55 (not (or (not c) (p X))))))
% 0.42/0.55 (refl a!1))))
% 0.42/0.55 (~ (not a!121) a!123)))
% 0.42/0.55 (a!125 (monotonicity (refl (~ (not c) (not c)))
% 0.42/0.55 (sk (~ a!68 (p X!11)))
% 0.42/0.55 (~ (or (not c) a!68) (or (not c) (p X!11)))))
% 0.42/0.55 (a!127 (~ (not (or (not c) a!68)) (and (not (not c)) a!72)))
% 0.42/0.55 (a!129 (not (= a!121 (or (not c) a!68))))
% 0.42/0.55 (a!130 (or a!123 (and (not (not c)) a!72)))
% 0.42/0.55 (a!133 (~ a!132 (or c (not (p X!19)))))
% 0.42/0.55 (a!136 (~ (or c (not a!49)) (or c (not (p X!7)))))
% 0.42/0.55 (a!137 (~ (not (or c (not a!49))) (and (not c) a!49)))
% 0.42/0.55 (a!139 (not (= a!132 (or c (not a!49)))))
% 0.42/0.55 (a!141 (and a!140 (or a!135 (and (not c) a!49))))
% 0.42/0.55 (a!145 (~ (not a!144) (not (or (not c) (p X!20)))))
% 0.42/0.55 (a!146 (monotonicity (refl (~ (not c) (not c)))
% 0.42/0.55 (nnf-pos (proof-bind a!48) (~ a!49 a!49))
% 0.42/0.55 (~ (or (not c) a!49) (or (not c) a!49))))
% 0.42/0.55 (a!147 (~ (not (or (not c) a!49)) (and (not (not c)) (not (p X!7)))))
% 0.42/0.55 (a!148 (not (= a!144 (or (not c) a!49))))
% 0.42/0.55 (a!150 (and (or a!144 (or (not c) a!49)) a!149))
% 0.42/0.55 (a!152 (nnf-pos (proof-bind (lambda ((X $i))
% 0.42/0.55 (let ((a!1 (~ (or c (not (p X)))
% 0.42/0.55 (or c (not (p X))))))
% 0.42/0.55 (refl a!1))))
% 0.42/0.55 (~ a!151 a!151)))
% 0.42/0.55 (a!154 (monotonicity (refl (~ c c))
% 0.42/0.55 (nnf-neg (proof-bind a!71) (~ (not a!68) a!72))
% 0.42/0.55 (~ (or c (not a!68)) (or c a!72))))
% 0.42/0.55 (a!155 (~ (not (or c (not a!68))) (and (not c) (p X!11))))
% 0.42/0.55 (a!157 (not (= a!151 (or c (not a!68)))))
% 0.42/0.55 (a!158 (and (or a!151 (or c a!72)) (or a!153 (and (not c) (p X!11))))))
% 0.42/0.55 (let ((a!14 (monotonicity a!11 a!13 (~ (or a!10 a!12) (or a!10 a!12))))
% 0.42/0.55 (a!19 (~ (not a!18) (and a!3 a!5 (and a!9 (or a!10 a!12)))))
% 0.42/0.55 (a!26 (nnf-neg (monotonicity a!22
% 0.42/0.55 (nnf-pos a!23 (~ a!24 a!24))
% 0.42/0.55 (~ (and a!21 a!24) (and a!21 a!24)))
% 0.42/0.55 a!25))
% 0.42/0.55 (a!36 (monotonicity (sk (~ (not a!31) (not a!32)))
% 0.42/0.55 (sk a!34)
% 0.42/0.55 (~ (or (not a!31) a!33) a!35)))
% 0.42/0.55 (a!37 (~ (and (or (not a!31) a!33) (or a!10 a!12))
% 0.42/0.55 (and a!35 (or a!10 a!12))))
% 0.42/0.55 (a!40 (~ (not (or a!2 (not a!5) a!38))
% 0.42/0.55 (and a!3 a!5 (and a!35 (or a!10 a!12)))))
% 0.42/0.55 (a!57 (nnf-neg (nnf-pos (proof-bind a!45) (~ a!46 a!46))
% 0.42/0.55 (sk a!47)
% 0.42/0.55 (monotonicity (nnf-pos (proof-bind a!48) (~ a!49 a!49))
% 0.42/0.55 (nnf-pos (proof-bind a!50) (~ a!51 a!51))
% 0.42/0.55 (~ (and a!49 a!51) (and a!49 a!51)))
% 0.42/0.55 (nnf-neg a!52 a!53 a!54)
% 0.42/0.55 a!56))
% 0.42/0.55 (a!59 (nnf-neg (monotonicity (nnf-pos (proof-bind a!48) (~ a!49 a!49))
% 0.42/0.55 (nnf-pos (proof-bind a!50) (~ a!51 a!51))
% 0.42/0.55 (~ (or a!49 a!51) (or a!49 a!51)))
% 0.42/0.55 a!58))
% 0.42/0.55 (a!77 (~ (not (= a!64 (or a!68 a!69))) a!76))
% 0.42/0.55 (a!83 (nnf-neg a!82 (~ (not (not a!81)) (and (p X!13) (q X!13)))))
% 0.42/0.55 (a!93 (nnf-neg a!89 (nnf-neg (proof-bind a!71) (~ (not a!68) a!72)) a!92))
% 0.42/0.55 (a!104 (nnf-neg (nnf-neg (proof-bind a!94) (~ (not a!95) a!96))
% 0.42/0.55 (trans (sk a!98) (nnf-neg a!99 a!100 a!101) a!102)
% 0.42/0.55 (~ (not (or a!95 a!97)) a!103)))
% 0.42/0.55 (a!109 (nnf-neg a!52 (refl (~ (not c) (not c))) a!108))
% 0.42/0.55 (a!120 (~ (not (= a!113 (and a!68 c))) a!119))
% 0.42/0.55 (a!128 (nnf-neg a!126
% 0.42/0.55 (nnf-neg (proof-bind a!71) (~ (not a!68) a!72))
% 0.42/0.55 a!127))
% 0.42/0.55 (a!131 (and (or (or (not c) (p X!18)) (or (not c) (p X!11))) a!130))
% 0.42/0.55 (a!138 (nnf-neg (refl (~ (not c) (not c))) a!89 a!137))
% 0.42/0.55 (a!156 (nnf-neg (refl (~ (not c) (not c))) a!100 a!155))
% 0.42/0.55 (a!160 (and a!18
% 0.42/0.55 (or (not (and a!21 a!24)) a!27)
% 0.42/0.55 (or a!2 (not a!5) a!38)
% 0.42/0.55 a!43
% 0.42/0.55 (= a!46 (and a!49 a!51))
% 0.42/0.55 (or (not (or a!49 a!51)) a!60)
% 0.42/0.55 (= a!64 (or a!68 a!69))
% 0.42/0.55 a!79
% 0.42/0.55 (or (not a!81) (and a!68 a!69))
% 0.42/0.55 a!86
% 0.42/0.55 (or (not a!49) a!68)
% 0.42/0.55 (or a!95 a!97)
% 0.42/0.55 (= a!106 (or a!49 c))
% 0.42/0.55 (= a!113 (and a!68 c))
% 0.42/0.55 (= a!121 (or (not c) a!68))
% 0.42/0.55 (= a!132 (or c (not a!49)))
% 0.42/0.55 (= a!144 (or (not c) a!49))
% 0.42/0.55 (= a!151 (or c (not a!68))))))
% 0.42/0.55 (let ((a!15 (monotonicity (nnf-pos (proof-bind a!7) (~ a!8 a!9))
% 0.42/0.55 a!14
% 0.42/0.55 (~ (and a!8 (or a!10 a!12)) (and a!9 (or a!10 a!12)))))
% 0.42/0.55 (a!30 (nnf-neg a!26
% 0.42/0.55 (sk (~ (not a!27) a!28))
% 0.42/0.55 (~ a!29 (and (and a!21 a!24) a!28))))
% 0.42/0.55 (a!39 (nnf-neg (monotonicity a!36 a!14 a!37)
% 0.42/0.55 (~ (not a!38) (and a!35 (or a!10 a!12)))))
% 0.42/0.55 (a!112 (nnf-neg (nnf-pos (proof-bind a!105) (~ a!106 a!106))
% 0.42/0.55 (sk a!107)
% 0.42/0.55 (monotonicity (nnf-pos (proof-bind a!48) (~ a!49 a!49))
% 0.42/0.55 (refl (~ c c))
% 0.42/0.55 (~ (or a!49 c) (or a!49 c)))
% 0.42/0.55 a!109
% 0.42/0.55 a!111))
% 0.42/0.55 (a!142 (nnf-neg (sk a!133)
% 0.42/0.55 (nnf-neg a!134 (~ (not a!132) a!135))
% 0.42/0.55 (monotonicity (refl (~ c c)) a!52 a!136)
% 0.42/0.55 a!138
% 0.42/0.55 (~ a!139 a!141)))
% 0.42/0.55 (a!159 (nnf-neg a!152
% 0.42/0.55 (sk (~ (not a!151) a!153))
% 0.42/0.55 a!154
% 0.42/0.55 a!156
% 0.42/0.55 (~ a!157 a!158)))
% 0.42/0.55 (a!161 (or (and a!3 a!5 (and a!9 (or a!10 a!12)))
% 0.42/0.55 (and (and a!21 a!24) a!28)
% 0.42/0.55 (and a!3 a!5 (and a!35 (or a!10 a!12)))
% 0.42/0.55 a!44
% 0.42/0.55 (and (or a!46 (and a!49 a!51)) a!55)
% 0.42/0.55 a!63
% 0.42/0.55 a!76
% 0.42/0.55 a!80
% 0.42/0.55 (and (and (p X!13) (q X!13)) (or a!72 a!74))
% 0.42/0.55 (and (not (p Y!14)) a!49)
% 0.42/0.55 (and a!49 a!72)
% 0.42/0.55 a!103
% 0.42/0.55 (and (or a!106 (or a!49 c)) a!110)
% 0.42/0.55 a!119
% 0.42/0.55 a!131
% 0.42/0.55 a!141
% 0.42/0.55 a!150
% 0.42/0.55 a!158)))
% 0.42/0.55 (let ((a!17 (nnf-neg a!15 (~ a!16 (and a!9 (or a!10 a!12)))))
% 0.42/0.55 (a!41 (nnf-neg (nnf-neg a!1 (~ (not a!2) a!3)) a!6 a!39 a!40)))
% 0.42/0.55 (let ((a!20 (nnf-neg (nnf-neg a!1 (~ (not a!2) a!3)) a!6 a!17 a!19)))
% 0.42/0.55 (nnf-neg a!20
% 0.42/0.55 a!30
% 0.42/0.55 a!41
% 0.42/0.55 (nnf-neg (proof-bind a!42) (~ (not a!43) a!44))
% 0.42/0.55 a!57
% 0.42/0.55 (nnf-neg a!59 (sk a!61) (~ a!62 a!63))
% 0.42/0.55 (nnf-neg a!65 a!67 a!70 a!75 a!77)
% 0.42/0.55 (nnf-neg a!78 (~ (not a!79) a!80))
% 0.42/0.55 (nnf-neg a!83 a!84 a!85)
% 0.42/0.55 (trans (sk a!87) (nnf-neg a!88 a!89 a!90) a!91)
% 0.42/0.55 a!93
% 0.42/0.55 a!104
% 0.42/0.55 a!112
% 0.42/0.55 (nnf-neg a!114 a!116 a!117 a!118 a!120)
% 0.42/0.55 (nnf-neg a!122 a!124 a!125 a!128 (~ a!129 a!131))
% 0.42/0.55 a!142
% 0.42/0.55 (nnf-neg (nnf-pos (proof-bind a!143) (~ a!144 a!144))
% 0.42/0.55 (sk a!145)
% 0.42/0.55 a!146
% 0.42/0.55 (nnf-neg a!126 a!52 a!147)
% 0.42/0.55 (~ a!148 a!150))
% 0.42/0.55 a!159
% 0.42/0.55 (~ (not a!160) a!161))))))))
% 0.42/0.55 Proof display could not be completed: unexpected number of arguments
%------------------------------------------------------------------------------