TSTP Solution File: SYN036+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN036+2 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 23:53:14 EDT 2022
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN036+2 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Sep 5 01:07:53 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.
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(big_p_type, type, (
% 0.20/0.40 big_p: $i > $o)).
% 0.20/0.40 tff(tptp_fun_Y_0_type, type, (
% 0.20/0.40 tptp_fun_Y_0: $i > $i)).
% 0.20/0.40 tff(big_q_type, type, (
% 0.20/0.40 big_q: $i > $o)).
% 0.20/0.40 tff(tptp_fun_W_3_type, type, (
% 0.20/0.40 tptp_fun_W_3: $i)).
% 0.20/0.40 tff(tptp_fun_U_2_type, type, (
% 0.20/0.40 tptp_fun_U_2: $i)).
% 0.20/0.40 tff(tptp_fun_X_1_type, type, (
% 0.20/0.40 tptp_fun_X_1: $i)).
% 0.20/0.40 tff(tptp_fun_Y1_5_type, type, (
% 0.20/0.40 tptp_fun_Y1_5: $i > $i)).
% 0.20/0.40 tff(tptp_fun_W1_7_type, type, (
% 0.20/0.40 tptp_fun_W1_7: $i)).
% 0.20/0.40 tff(tptp_fun_U1_6_type, type, (
% 0.20/0.40 tptp_fun_U1_6: $i)).
% 0.20/0.40 tff(tptp_fun_X1_4_type, type, (
% 0.20/0.40 tptp_fun_X1_4: $i)).
% 0.20/0.40 tff(elem_8_type, type, (
% 0.20/0.40 elem_8: $i)).
% 0.20/0.40 tff(1,assumption,(~big_q(U!2)), introduced(assumption)).
% 0.20/0.40 tff(2,assumption,(~![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))), introduced(assumption)).
% 0.20/0.40 tff(3,assumption,(~![W: $i] : big_p(W)), introduced(assumption)).
% 0.20/0.40 tff(4,assumption,(~((~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))))) | (~((~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))))), introduced(assumption)).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 (((~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))))) | (~((~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))))) | ((~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(6,plain,
% 0.20/0.40 ((~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[5, 4])).
% 0.20/0.40 tff(7,plain,
% 0.20/0.40 ((~((~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))) | (~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 (~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1)))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[7, 6, 2])).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 (((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1))))) | ((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1)))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 ((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.20/0.40 tff(11,plain,
% 0.20/0.40 (((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1))))) | (big_p(U1!6) | ![W1: $i] : big_q(W1))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 (big_p(U1!6) | ![W1: $i] : big_q(W1)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[11, 8])).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 (((~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))))) | (~((~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))))) | (![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(14,plain,
% 0.20/0.40 (![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1)))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[13, 4])).
% 0.20/0.40 tff(15,assumption,((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1))), introduced(assumption)).
% 0.20/0.40 tff(16,assumption,(big_p(U1!6) | ![W1: $i] : big_q(W1)), introduced(assumption)).
% 0.20/0.40 tff(17,assumption,(~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))), introduced(assumption)).
% 0.20/0.41 tff(18,plain,
% 0.20/0.41 (((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1)))) | (![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(19,plain,
% 0.20/0.41 (![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.20/0.41 tff(20,assumption,(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1)), introduced(assumption)).
% 0.20/0.41 tff(21,assumption,(~![W1: $i] : big_q(W1)), introduced(assumption)).
% 0.20/0.41 tff(22,plain,
% 0.20/0.41 ((~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))) | ![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1)),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(23,plain,
% 0.20/0.41 (![U1: $i] : (~big_p(U1))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[22, 21, 20])).
% 0.20/0.41 tff(24,plain,
% 0.20/0.41 ((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | big_p(U1!6) | ![W1: $i] : big_q(W1)),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(25,plain,
% 0.20/0.41 (big_p(U1!6)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[24, 21, 16])).
% 0.20/0.41 tff(26,plain,
% 0.20/0.41 ((~![U1: $i] : (~big_p(U1))) | (~big_p(U1!6))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[26, 25, 23])).
% 0.20/0.41 tff(28,plain,(![W1: $i] : big_q(W1) | (~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 (![W1: $i] : big_q(W1)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[28, 19, 16])).
% 0.20/0.41 tff(30,assumption,(![W1: $i] : big_q(W1)), introduced(assumption)).
% 0.20/0.41 tff(31,assumption,(~big_q(W1!7)), introduced(assumption)).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 ((~![W1: $i] : big_q(W1)) | big_q(W1!7)),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[32, 31, 30])).
% 0.20/0.41 tff(34,plain,(big_q(W1!7) | (~![W1: $i] : big_q(W1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(35,plain,
% 0.20/0.41 (big_q(W1!7)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[34, 29])).
% 0.20/0.41 tff(36,plain,
% 0.20/0.41 ((~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1)))) | (~big_q(W1!7)) | ![U1: $i] : (~big_p(U1))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(37,plain,
% 0.20/0.41 (![U1: $i] : (~big_p(U1))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[36, 35, 15])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 (((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1)))) | (big_p(U1!6) | (~big_q(W1!7)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(39,plain,
% 0.20/0.41 (big_p(U1!6) | (~big_q(W1!7))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[38, 17])).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 ((~(big_p(U1!6) | (~big_q(W1!7)))) | big_p(U1!6) | (~big_q(W1!7))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(41,plain,
% 0.20/0.41 (big_p(U1!6)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[40, 35, 39])).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[26, 41, 37])).
% 0.20/0.41 tff(43,plain,(((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1)))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1)))) | (~(big_p(U1!6) | ![W1: $i] : big_q(W1)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 ((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[43, 10, 12])).
% 0.20/0.41 tff(45,plain,
% 0.20/0.41 ((~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))))) | ![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1)))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(46,plain,
% 0.20/0.41 (![Y1: $i] : (big_q(X1!4) <=> big_q(Y1))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[45, 44, 14])).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 ((~((~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))) | (~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 (~((~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[47, 44, 2])).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 (((~((~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))) | (~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1))))))))) | ((~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(50,plain,
% 0.20/0.41 ((~((~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))) | (~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1))))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 (((~((~((~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))))))) | (~((~((~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))) | (~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1))))))))))) <=> ((~((~((~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))))))) | (~((~((~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))) | (~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1)))))))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(52,plain,
% 0.20/0.41 ((~((~((~((~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))) | (~(big_p(U1!6) | (~big_q(W1!7)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))) | (~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~(![U1: $i] : (~big_p(U1)) | (~big_q(W1!7)))))))))) <=> (~((~((~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))) | (~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1))))))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(53,plain,
% 0.20/0.41 ((~((~((~((~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))) | (~(big_q(U!2) | (~big_p(W!3)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~(![U: $i] : (~big_q(U)) | (~big_p(W!3)))))))))) <=> (~((~((~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U))))))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(54,plain,
% 0.20/0.41 (((~((~((~((~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))) | (~(big_q(U!2) | (~big_p(W!3)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~(![U: $i] : (~big_q(U)) | (~big_p(W!3)))))))))) | (~((~((~((~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))) | (~(big_p(U1!6) | (~big_q(W1!7)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))) | (~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~(![U1: $i] : (~big_p(U1)) | (~big_q(W1!7))))))))))) <=> ((~((~((~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))))))) | (~((~((~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))) | (~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1)))))))))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[53, 52])).
% 0.20/0.41 tff(55,plain,
% 0.20/0.41 (((~((~((~((~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))) | (~(big_q(U!2) | (~big_p(W!3)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~(![U: $i] : (~big_q(U)) | (~big_p(W!3)))))))))) | (~((~((~((~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))) | (~(big_p(U1!6) | (~big_q(W1!7)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))) | (~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~(![U1: $i] : (~big_p(U1)) | (~big_q(W1!7))))))))))) <=> ((~((~((~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))))))) | (~((~((~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))) | (~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1)))))))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[54, 51])).
% 0.20/0.41 tff(56,plain,
% 0.20/0.41 (((~((~((~((~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))) | (~(big_q(U!2) | (~big_p(W!3)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~(![U: $i] : (~big_q(U)) | (~big_p(W!3)))))))))) | (~((~((~((~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))) | (~(big_p(U1!6) | (~big_q(W1!7)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))) | (~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~(![U1: $i] : (~big_p(U1)) | (~big_q(W1!7))))))))))) <=> ((~((~((~((~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))) | (~(big_q(U!2) | (~big_p(W!3)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~(![U: $i] : (~big_q(U)) | (~big_p(W!3)))))))))) | (~((~((~((~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))) | (~(big_p(U1!6) | (~big_q(W1!7)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))) | (~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~(![U1: $i] : (~big_p(U1)) | (~big_q(W1!7)))))))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(57,plain,
% 0.20/0.41 ((((((![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W)) & (big_q(U!2) | (~big_p(W!3)))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))) & (![Y: $i] : (big_p(X!1) <=> big_p(Y)) | ((big_q(U!2) | ![W: $i] : big_p(W)) & (![U: $i] : (~big_q(U)) | (~big_p(W!3)))))) | ((((![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1)) & (big_p(U1!6) | (~big_q(W1!7)))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))) & (![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | ((big_p(U1!6) | ![W1: $i] : big_q(W1)) & (![U1: $i] : (~big_p(U1)) | (~big_q(W1!7))))))) <=> ((~((~((~((~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))) | (~(big_q(U!2) | (~big_p(W!3)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~(![U: $i] : (~big_q(U)) | (~big_p(W!3)))))))))) | (~((~((~((~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))) | (~(big_p(U1!6) | (~big_q(W1!7)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))) | (~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~(![U1: $i] : (~big_p(U1)) | (~big_q(W1!7)))))))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(58,plain,
% 0.20/0.42 (((((![X: $i] : (~(big_p(X) <=> big_p(tptp_fun_Y_0(X)))) | ((![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W)) & (big_q(U!2) | (~big_p(W!3))))) & (![Y: $i] : (big_p(X!1) <=> big_p(Y)) | ((big_q(U!2) | ![W: $i] : big_p(W)) & (![U: $i] : (~big_q(U)) | (~big_p(W!3)))))) | ((![X1: $i] : (~(big_q(X1) <=> big_q(tptp_fun_Y1_5(X1)))) | ((![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1)) & (big_p(U1!6) | (~big_q(W1!7))))) & (![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | ((big_p(U1!6) | ![W1: $i] : big_q(W1)) & (![U1: $i] : (~big_p(U1)) | (~big_q(W1!7))))))) & (((![Y: $i] : (big_p(X!1) <=> big_p(Y)) | ((![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W)) & (big_q(U!2) | (~big_p(W!3))))) & (![X: $i] : (~(big_p(X) <=> big_p(tptp_fun_Y_0(X)))) | ((big_q(U!2) | ![W: $i] : big_p(W)) & (![U: $i] : (~big_q(U)) | (~big_p(W!3)))))) | ((![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | ((![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1)) & (big_p(U1!6) | (~big_q(W1!7))))) & (![X1: $i] : (~(big_q(X1) <=> big_q(tptp_fun_Y1_5(X1)))) | ((big_p(U1!6) | ![W1: $i] : big_q(W1)) & (![U1: $i] : (~big_p(U1)) | (~big_q(W1!7)))))))) <=> ((((((![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W)) & (big_q(U!2) | (~big_p(W!3)))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))) & (![Y: $i] : (big_p(X!1) <=> big_p(Y)) | ((big_q(U!2) | ![W: $i] : big_p(W)) & (![U: $i] : (~big_q(U)) | (~big_p(W!3)))))) | ((((![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1)) & (big_p(U1!6) | (~big_q(W1!7)))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))) & (![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | ((big_p(U1!6) | ![W1: $i] : big_q(W1)) & (![U1: $i] : (~big_p(U1)) | (~big_q(W1!7))))))) & (((![Y: $i] : (big_p(X!1) <=> big_p(Y)) | ((![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W)) & (big_q(U!2) | (~big_p(W!3))))) & (((big_q(U!2) | ![W: $i] : big_p(W)) & (![U: $i] : (~big_q(U)) | (~big_p(W!3)))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | ((![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | ((![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1)) & (big_p(U1!6) | (~big_q(W1!7))))) & (((big_p(U1!6) | ![W1: $i] : big_q(W1)) & (![U1: $i] : (~big_p(U1)) | (~big_q(W1!7)))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(59,plain,
% 0.20/0.42 ((?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_q(W1))) <=> (?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_q(W1)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(60,plain,
% 0.20/0.42 ((?[U: $i] : big_q(U) <=> ![W: $i] : big_p(W)) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_p(W))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(61,plain,
% 0.20/0.42 ((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(62,plain,
% 0.20/0.42 (((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_p(W))) <=> ((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_p(W)))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[61, 60])).
% 0.20/0.42 tff(63,plain,
% 0.20/0.42 ((((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_p(W))) <=> (?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_q(W1)))) <=> (((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_p(W))) <=> (?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_q(W1))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[62, 59])).
% 0.20/0.42 tff(64,plain,
% 0.20/0.42 ((((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_p(W))) <=> (?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_q(W1)))) <=> (((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_p(W))) <=> (?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_q(W1))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(65,plain,
% 0.20/0.42 ((~((?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y)) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_p(W))) <=> (?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_q(W1))))) <=> (((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_p(W))) <=> (?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_q(W1))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(66,plain,
% 0.20/0.42 ((?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y)) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_p(W))) <=> (?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y)) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_p(W)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(67,plain,
% 0.20/0.42 (((?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y)) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_p(W))) <=> (?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_q(W1)))) <=> ((?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y)) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_p(W))) <=> (?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_q(W1))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[66, 59])).
% 0.20/0.42 tff(68,plain,
% 0.20/0.42 ((~((?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y)) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_p(W))) <=> (?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_q(W1))))) <=> (~((?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y)) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_p(W))) <=> (?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_q(W1)))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[67])).
% 0.20/0.42 tff(69,plain,
% 0.20/0.42 ((~((?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y)) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_p(W))) <=> (?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_q(W1))))) <=> (((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_p(W))) <=> (?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_q(W1))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[68, 65])).
% 0.20/0.42 tff(70,axiom,(~((?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y)) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_p(W))) <=> (?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_q(W1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel34')).
% 0.20/0.42 tff(71,plain,
% 0.20/0.42 (((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_p(W))) <=> (?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_q(W1)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.20/0.42 tff(72,plain,
% 0.20/0.42 (((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_p(W))) <=> (?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_q(W1)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[71, 63])).
% 0.20/0.42 tff(73,plain,
% 0.20/0.42 (((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_p(W))) <=> (?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_q(W1)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[72, 64])).
% 0.20/0.42 tff(74,plain,
% 0.20/0.42 (((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_p(W))) <=> (?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_q(W1)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[73, 63])).
% 0.20/0.42 tff(75,plain,
% 0.20/0.42 (((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_p(W))) <=> (?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_q(W1)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[74, 63])).
% 0.20/0.42 tff(76,plain,
% 0.20/0.42 (((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_p(W))) <=> (?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_q(W1)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[75, 63])).
% 0.20/0.42 tff(77,plain,
% 0.20/0.42 (((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_p(W))) <=> (?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_q(W1)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[76, 63])).
% 0.20/0.42 tff(78,plain,(
% 0.20/0.42 (((![X: $i] : (~(big_p(X) <=> big_p(tptp_fun_Y_0(X)))) | ((![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W)) & (big_q(U!2) | (~big_p(W!3))))) & (![Y: $i] : (big_p(X!1) <=> big_p(Y)) | ((big_q(U!2) | ![W: $i] : big_p(W)) & (![U: $i] : (~big_q(U)) | (~big_p(W!3)))))) | ((![X1: $i] : (~(big_q(X1) <=> big_q(tptp_fun_Y1_5(X1)))) | ((![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1)) & (big_p(U1!6) | (~big_q(W1!7))))) & (![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | ((big_p(U1!6) | ![W1: $i] : big_q(W1)) & (![U1: $i] : (~big_p(U1)) | (~big_q(W1!7))))))) & (((![Y: $i] : (big_p(X!1) <=> big_p(Y)) | ((![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W)) & (big_q(U!2) | (~big_p(W!3))))) & (![X: $i] : (~(big_p(X) <=> big_p(tptp_fun_Y_0(X)))) | ((big_q(U!2) | ![W: $i] : big_p(W)) & (![U: $i] : (~big_q(U)) | (~big_p(W!3)))))) | ((![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | ((![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1)) & (big_p(U1!6) | (~big_q(W1!7))))) & (![X1: $i] : (~(big_q(X1) <=> big_q(tptp_fun_Y1_5(X1)))) | ((big_p(U1!6) | ![W1: $i] : big_q(W1)) & (![U1: $i] : (~big_p(U1)) | (~big_q(W1!7)))))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[77])).
% 0.20/0.42 tff(79,plain,
% 0.20/0.42 ((((((![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W)) & (big_q(U!2) | (~big_p(W!3)))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))) & (![Y: $i] : (big_p(X!1) <=> big_p(Y)) | ((big_q(U!2) | ![W: $i] : big_p(W)) & (![U: $i] : (~big_q(U)) | (~big_p(W!3)))))) | ((((![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1)) & (big_p(U1!6) | (~big_q(W1!7)))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))) & (![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | ((big_p(U1!6) | ![W1: $i] : big_q(W1)) & (![U1: $i] : (~big_p(U1)) | (~big_q(W1!7))))))) & (((![Y: $i] : (big_p(X!1) <=> big_p(Y)) | ((![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W)) & (big_q(U!2) | (~big_p(W!3))))) & (((big_q(U!2) | ![W: $i] : big_p(W)) & (![U: $i] : (~big_q(U)) | (~big_p(W!3)))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | ((![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | ((![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1)) & (big_p(U1!6) | (~big_q(W1!7))))) & (((big_p(U1!6) | ![W1: $i] : big_q(W1)) & (![U1: $i] : (~big_p(U1)) | (~big_q(W1!7)))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[78, 58])).
% 0.20/0.42 tff(80,plain,
% 0.20/0.42 (((((![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W)) & (big_q(U!2) | (~big_p(W!3)))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))) & (![Y: $i] : (big_p(X!1) <=> big_p(Y)) | ((big_q(U!2) | ![W: $i] : big_p(W)) & (![U: $i] : (~big_q(U)) | (~big_p(W!3)))))) | ((((![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1)) & (big_p(U1!6) | (~big_q(W1!7)))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))) & (![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | ((big_p(U1!6) | ![W1: $i] : big_q(W1)) & (![U1: $i] : (~big_p(U1)) | (~big_q(W1!7))))))),
% 0.20/0.42 inference(and_elim,[status(thm)],[79])).
% 0.20/0.42 tff(81,plain,
% 0.20/0.42 ((~((~((~((~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))) | (~(big_q(U!2) | (~big_p(W!3)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~(![U: $i] : (~big_q(U)) | (~big_p(W!3)))))))))) | (~((~((~((~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))) | (~(big_p(U1!6) | (~big_q(W1!7)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))) | (~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~(![U1: $i] : (~big_p(U1)) | (~big_q(W1!7))))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[80, 57])).
% 0.20/0.43 tff(82,plain,
% 0.20/0.43 ((~((~((~((~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))) | (~(big_q(U!2) | (~big_p(W!3)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~(![U: $i] : (~big_q(U)) | (~big_p(W!3)))))))))) | (~((~((~((~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))) | (~(big_p(U1!6) | (~big_q(W1!7)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))) | (~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~(![U1: $i] : (~big_p(U1)) | (~big_q(W1!7))))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[81, 56])).
% 0.20/0.43 tff(83,plain,
% 0.20/0.43 ((~((~((~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))))))) | (~((~((~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))) | (~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1))))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[82, 55])).
% 0.20/0.43 tff(84,plain,
% 0.20/0.43 (~((~((~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[83, 50])).
% 0.20/0.43 tff(85,plain,
% 0.20/0.43 (((~((~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U))))))))) | ((~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(86,plain,
% 0.20/0.43 ((~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.20/0.43 tff(87,plain,
% 0.20/0.43 (((~((~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U))))))))) | (![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(88,plain,
% 0.20/0.43 (![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[87, 84])).
% 0.20/0.43 tff(89,assumption,((~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))), introduced(assumption)).
% 0.20/0.43 tff(90,assumption,(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1))), introduced(assumption)).
% 0.20/0.43 tff(91,assumption,(~(big_q(X1!4) <=> big_q(U!2))), introduced(assumption)).
% 0.20/0.43 tff(92,plain,
% 0.20/0.43 ((~![Y1: $i] : (big_q(X1!4) <=> big_q(Y1))) | (big_q(X1!4) <=> big_q(U!2))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(93,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[92, 90, 91])).
% 0.20/0.43 tff(94,plain,((big_q(X1!4) <=> big_q(U!2)) | (~![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(95,plain,
% 0.20/0.43 (big_q(X1!4) <=> big_q(U!2)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[94, 90])).
% 0.20/0.43 tff(96,plain,
% 0.20/0.43 ((~![Y1: $i] : (big_q(X1!4) <=> big_q(Y1))) | (big_q(X1!4) <=> big_q(W1!7))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(97,plain,
% 0.20/0.43 (big_q(X1!4) <=> big_q(W1!7)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[96, 90])).
% 0.20/0.43 tff(98,plain,
% 0.20/0.43 (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[28, 21, 16])).
% 0.20/0.43 tff(99,plain,
% 0.20/0.43 ((![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1)) | (~![U1: $i] : (~big_p(U1)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(100,plain,
% 0.20/0.43 (~![U1: $i] : (~big_p(U1))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.20/0.43 tff(101,plain,
% 0.20/0.43 (~big_q(W1!7)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[36, 100, 15])).
% 0.20/0.43 tff(102,plain,
% 0.20/0.43 ((~(big_q(X1!4) <=> big_q(W1!7))) | (~big_q(X1!4)) | big_q(W1!7)),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(103,plain,
% 0.20/0.43 ((~(big_q(X1!4) <=> big_q(W1!7))) | (~big_q(X1!4))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.20/0.43 tff(104,plain,
% 0.20/0.43 (~big_q(X1!4)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[103, 97])).
% 0.20/0.43 tff(105,plain,
% 0.20/0.43 ((~(big_q(X1!4) <=> big_q(U!2))) | big_q(X1!4) | (~big_q(U!2))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(106,plain,
% 0.20/0.43 (~big_q(U!2)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[105, 104, 95])).
% 0.20/0.43 tff(107,assumption,(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U))))))), introduced(assumption)).
% 0.20/0.43 tff(108,assumption,(~big_p(W!3)), introduced(assumption)).
% 0.20/0.43 tff(109,assumption,(![W: $i] : big_p(W)), introduced(assumption)).
% 0.20/0.43 tff(110,plain,
% 0.20/0.43 ((~![W: $i] : big_p(W)) | big_p(W!3)),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(111,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[110, 108, 109])).
% 0.20/0.43 tff(112,plain,((~![W: $i] : big_p(W)) | big_p(W!3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(113,plain,
% 0.20/0.43 (~![W: $i] : big_p(W)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[112, 108])).
% 0.20/0.43 tff(114,plain,
% 0.20/0.43 ((~(big_q(U!2) | ![W: $i] : big_p(W))) | big_q(U!2) | ![W: $i] : big_p(W)),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(115,plain,
% 0.20/0.43 (~(big_q(U!2) | ![W: $i] : big_p(W))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[114, 113, 1])).
% 0.20/0.43 tff(116,plain,
% 0.20/0.43 (((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U))))) | (big_q(U!2) | ![W: $i] : big_p(W))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(117,plain,
% 0.20/0.43 ((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[116, 115])).
% 0.20/0.43 tff(118,plain,
% 0.20/0.43 ((~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))))) | ![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U))))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(119,plain,
% 0.20/0.43 (![Y: $i] : (big_p(X!1) <=> big_p(Y))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[118, 117, 107])).
% 0.20/0.43 tff(120,plain,
% 0.20/0.43 ((~![Y: $i] : (big_p(X!1) <=> big_p(Y))) | (big_p(X!1) <=> big_p(U1!6))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(121,plain,
% 0.20/0.43 (big_p(X!1) <=> big_p(U1!6)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.20/0.43 tff(122,assumption,(big_p(U1!6)), introduced(assumption)).
% 0.20/0.43 tff(123,plain,
% 0.20/0.43 ((~(big_p(X!1) <=> big_p(U1!6))) | big_p(X!1) | (~big_p(U1!6))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(124,plain,
% 0.20/0.43 ((~(big_p(X!1) <=> big_p(U1!6))) | big_p(X!1)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.20/0.43 tff(125,plain,
% 0.20/0.43 (big_p(X!1)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[124, 121])).
% 0.20/0.43 tff(126,plain,
% 0.20/0.43 ((~(big_p(X!1) <=> big_p(W!3))) | (~big_p(X!1)) | big_p(W!3)),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(127,plain,
% 0.20/0.43 (~(big_p(X!1) <=> big_p(W!3))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[126, 108, 125])).
% 0.20/0.43 tff(128,assumption,(~(big_p(X!1) <=> big_p(W!3))), introduced(assumption)).
% 0.20/0.43 tff(129,assumption,(![Y: $i] : (big_p(X!1) <=> big_p(Y))), introduced(assumption)).
% 0.20/0.43 tff(130,plain,
% 0.20/0.43 ((~![Y: $i] : (big_p(X!1) <=> big_p(Y))) | (big_p(X!1) <=> big_p(W!3))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(131,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[130, 129, 128])).
% 0.20/0.43 tff(132,plain,((big_p(X!1) <=> big_p(W!3)) | (~![Y: $i] : (big_p(X!1) <=> big_p(Y)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(133,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[132, 127, 119])).
% 0.20/0.43 tff(134,plain,(big_p(W!3) | (~big_p(U1!6)) | (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))))) | big_q(U!2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(135,plain,
% 0.20/0.43 (big_p(W!3)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[134, 25, 107, 106])).
% 0.20/0.43 tff(136,plain,
% 0.20/0.43 ((~(big_q(U!2) | (~big_p(W!3)))) | big_q(U!2) | (~big_p(W!3))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(137,plain,
% 0.20/0.43 (~(big_q(U!2) | (~big_p(W!3)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[136, 135, 106])).
% 0.20/0.43 tff(138,plain,
% 0.20/0.43 (((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W)))) | (big_q(U!2) | (~big_p(W!3)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(139,plain,
% 0.20/0.43 ((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.20/0.43 tff(140,plain,
% 0.20/0.43 ((~((~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | (~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(141,plain,
% 0.20/0.43 (![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[140, 139, 89])).
% 0.20/0.43 tff(142,plain,
% 0.20/0.43 ((~![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))) | ((~big_p(U1!6)) <=> big_p(tptp_fun_Y_0(U1!6)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(143,plain,
% 0.20/0.43 ((~big_p(U1!6)) <=> big_p(tptp_fun_Y_0(U1!6))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[142, 141])).
% 0.20/0.43 tff(144,plain,
% 0.20/0.43 ((~((~big_p(U1!6)) <=> big_p(tptp_fun_Y_0(U1!6)))) | (~big_p(U1!6)) | (~big_p(tptp_fun_Y_0(U1!6)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(145,plain,
% 0.20/0.43 ((~((~big_p(U1!6)) <=> big_p(tptp_fun_Y_0(U1!6)))) | (~big_p(tptp_fun_Y_0(U1!6)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[144, 25])).
% 0.20/0.43 tff(146,plain,
% 0.20/0.43 (~big_p(tptp_fun_Y_0(U1!6))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[145, 143])).
% 0.20/0.43 tff(147,assumption,(~big_p(tptp_fun_Y_0(U1!6))), introduced(assumption)).
% 0.20/0.43 tff(148,plain,
% 0.20/0.43 ((~![W: $i] : big_p(W)) | big_p(tptp_fun_Y_0(U1!6))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(149,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[148, 109, 147])).
% 0.20/0.43 tff(150,plain,((~![W: $i] : big_p(W)) | big_p(tptp_fun_Y_0(U1!6))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(151,plain,
% 0.20/0.43 (~![W: $i] : big_p(W)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[150, 146])).
% 0.20/0.43 tff(152,plain,
% 0.20/0.43 (~(big_q(U!2) | ![W: $i] : big_p(W))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[114, 151, 106])).
% 0.20/0.43 tff(153,plain,
% 0.20/0.43 ((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[116, 152])).
% 0.20/0.43 tff(154,plain,
% 0.20/0.43 (![Y: $i] : (big_p(X!1) <=> big_p(Y))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[118, 153, 107])).
% 0.20/0.43 tff(155,plain,
% 0.20/0.43 (big_p(X!1) <=> big_p(W!3)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[132, 154])).
% 0.20/0.43 tff(156,plain,
% 0.20/0.43 ((~(big_p(X!1) <=> big_p(W!3))) | big_p(X!1) | (~big_p(W!3))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(157,plain,
% 0.20/0.43 (big_p(X!1)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[156, 155, 135])).
% 0.20/0.43 tff(158,plain,
% 0.20/0.43 ((~(big_p(X!1) <=> big_p(tptp_fun_Y_0(U1!6)))) | (~big_p(X!1)) | big_p(tptp_fun_Y_0(U1!6))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(159,plain,
% 0.20/0.43 (~(big_p(X!1) <=> big_p(tptp_fun_Y_0(U1!6)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[158, 157, 146])).
% 0.20/0.43 tff(160,plain,
% 0.20/0.43 ((~![Y: $i] : (big_p(X!1) <=> big_p(Y))) | (big_p(X!1) <=> big_p(tptp_fun_Y_0(U1!6)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(161,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[160, 154, 159])).
% 0.20/0.43 tff(162,plain,(![W1: $i] : big_q(W1) | (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))))) | (~((~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | (~![Y1: $i] : (big_q(X1!4) <=> big_q(Y1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1)))) | (~(big_p(U1!6) | ![W1: $i] : big_q(W1)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(163,plain,
% 0.20/0.43 (![W1: $i] : big_q(W1)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[162, 88, 86, 46, 10, 12])).
% 0.20/0.43 tff(164,plain,
% 0.20/0.43 (big_q(W1!7)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[34, 163])).
% 0.20/0.43 tff(165,plain,
% 0.20/0.43 (![U1: $i] : (~big_p(U1))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[36, 164, 10])).
% 0.20/0.43 tff(166,assumption,(big_p(tptp_fun_Y_0(U1!6))), introduced(assumption)).
% 0.20/0.43 tff(167,assumption,(![U1: $i] : (~big_p(U1))), introduced(assumption)).
% 0.20/0.43 tff(168,plain,
% 0.20/0.43 ((~![U1: $i] : (~big_p(U1))) | (~big_p(tptp_fun_Y_0(U1!6)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(169,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[168, 167, 166])).
% 0.20/0.43 tff(170,plain,((~big_p(tptp_fun_Y_0(U1!6))) | (~![U1: $i] : (~big_p(U1)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(171,plain,
% 0.20/0.43 (~big_p(tptp_fun_Y_0(U1!6))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[170, 165])).
% 0.20/0.43 tff(172,plain,
% 0.20/0.43 ((![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1)) | (~![W1: $i] : big_q(W1))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(173,plain,
% 0.20/0.43 (![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[172, 163])).
% 0.20/0.43 tff(174,plain,
% 0.20/0.43 ((~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))) | (~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(175,plain,
% 0.20/0.43 (~(big_p(U1!6) | (~big_q(W1!7)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[174, 173, 44])).
% 0.20/0.43 tff(176,plain,
% 0.20/0.43 ((big_p(U1!6) | (~big_q(W1!7))) | (~big_p(U1!6))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(177,plain,
% 0.20/0.43 (~big_p(U1!6)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[176, 175])).
% 0.20/0.43 tff(178,plain,
% 0.20/0.43 ((~((~big_p(U1!6)) <=> big_p(tptp_fun_Y_0(U1!6)))) | big_p(U1!6) | big_p(tptp_fun_Y_0(U1!6))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(179,plain,
% 0.20/0.43 (~((~big_p(U1!6)) <=> big_p(tptp_fun_Y_0(U1!6)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[178, 177, 171])).
% 0.20/0.43 tff(180,plain,
% 0.20/0.43 (big_q(X1!4) <=> big_q(U!2)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[94, 46])).
% 0.20/0.43 tff(181,plain,
% 0.20/0.43 (big_q(X1!4) <=> big_q(W1!7)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[96, 46])).
% 0.20/0.43 tff(182,plain,
% 0.20/0.43 ((~(big_q(X1!4) <=> big_q(W1!7))) | big_q(X1!4) | (~big_q(W1!7))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(183,plain,
% 0.20/0.43 ((~(big_q(X1!4) <=> big_q(W1!7))) | big_q(X1!4)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[182, 164])).
% 0.20/0.43 tff(184,plain,
% 0.20/0.43 (big_q(X1!4)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[183, 181])).
% 0.20/0.43 tff(185,plain,
% 0.20/0.43 ((~(big_q(X1!4) <=> big_q(U!2))) | (~big_q(X1!4)) | big_q(U!2)),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(186,plain,
% 0.20/0.43 (big_q(U!2)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[185, 184, 180])).
% 0.20/0.43 tff(187,assumption,(![U: $i] : (~big_q(U))), introduced(assumption)).
% 0.20/0.44 tff(188,assumption,(big_q(U!2)), introduced(assumption)).
% 0.20/0.44 tff(189,plain,
% 0.20/0.44 ((~![U: $i] : (~big_q(U))) | (~big_q(U!2))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(190,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[189, 188, 187])).
% 0.20/0.44 tff(191,plain,((~![U: $i] : (~big_q(U))) | (~big_q(U!2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(192,plain,
% 0.20/0.44 (~![U: $i] : (~big_q(U))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[191, 186])).
% 0.20/0.44 tff(193,plain,
% 0.20/0.44 (~![W: $i] : big_p(W)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[150, 171])).
% 0.20/0.44 tff(194,plain,
% 0.20/0.44 ((~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))) | ![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W)),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(195,plain,
% 0.20/0.44 (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[194, 193, 192])).
% 0.20/0.44 tff(196,plain,
% 0.20/0.44 (((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W)))) | (![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(197,plain,
% 0.20/0.44 ((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[196, 195])).
% 0.20/0.44 tff(198,plain,
% 0.20/0.44 (![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[140, 197, 86])).
% 0.20/0.44 tff(199,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[142, 198, 179])).
% 0.20/0.44 tff(200,plain,(((~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))))) | (~((~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(201,plain,
% 0.20/0.44 ((~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))))) | (~((~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[200, 2])).
% 0.20/0.44 tff(202,plain,
% 0.20/0.44 (((~((~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))) | (~(big_q(U!2) | (~big_p(W!3)))))))) | (~((~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~(![U: $i] : (~big_q(U)) | (~big_p(W!3)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))))) | (~((~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))) | (~(big_p(U1!6) | (~big_q(W1!7)))))))) | (~((~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~(![U1: $i] : (~big_p(U1)) | (~big_q(W1!7)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))))))) <=> ((~((~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))))) | (~((~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))))) | (~((~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))))) | (~((~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(203,plain,
% 0.20/0.44 (((~((~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))) | (~(big_q(U!2) | (~big_p(W!3)))))))) | (~((~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~(![U: $i] : (~big_q(U)) | (~big_p(W!3)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))))) | (~((~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))) | (~(big_p(U1!6) | (~big_q(W1!7)))))))) | (~((~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~(![U1: $i] : (~big_p(U1)) | (~big_q(W1!7)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))))))) <=> ((~((~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))) | (~(big_q(U!2) | (~big_p(W!3)))))))) | (~((~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~(![U: $i] : (~big_q(U)) | (~big_p(W!3)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))))) | (~((~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))) | (~(big_p(U1!6) | (~big_q(W1!7)))))))) | (~((~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~(![U1: $i] : (~big_p(U1)) | (~big_q(W1!7)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(204,plain,
% 0.20/0.44 ((((![Y: $i] : (big_p(X!1) <=> big_p(Y)) | ((![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W)) & (big_q(U!2) | (~big_p(W!3))))) & (((big_q(U!2) | ![W: $i] : big_p(W)) & (![U: $i] : (~big_q(U)) | (~big_p(W!3)))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | ((![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | ((![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1)) & (big_p(U1!6) | (~big_q(W1!7))))) & (((big_p(U1!6) | ![W1: $i] : big_q(W1)) & (![U1: $i] : (~big_p(U1)) | (~big_q(W1!7)))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))))) <=> ((~((~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))) | (~(big_q(U!2) | (~big_p(W!3)))))))) | (~((~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~(![U: $i] : (~big_q(U)) | (~big_p(W!3)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))))) | (~((~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))) | (~(big_p(U1!6) | (~big_q(W1!7)))))))) | (~((~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~(![U1: $i] : (~big_p(U1)) | (~big_q(W1!7)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(205,plain,
% 0.20/0.44 (((![Y: $i] : (big_p(X!1) <=> big_p(Y)) | ((![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W)) & (big_q(U!2) | (~big_p(W!3))))) & (((big_q(U!2) | ![W: $i] : big_p(W)) & (![U: $i] : (~big_q(U)) | (~big_p(W!3)))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | ((![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | ((![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1)) & (big_p(U1!6) | (~big_q(W1!7))))) & (((big_p(U1!6) | ![W1: $i] : big_q(W1)) & (![U1: $i] : (~big_p(U1)) | (~big_q(W1!7)))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))))),
% 0.20/0.44 inference(and_elim,[status(thm)],[79])).
% 0.20/0.44 tff(206,plain,
% 0.20/0.44 ((~((~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))) | (~(big_q(U!2) | (~big_p(W!3)))))))) | (~((~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~(![U: $i] : (~big_q(U)) | (~big_p(W!3)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))))) | (~((~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))) | (~(big_p(U1!6) | (~big_q(W1!7)))))))) | (~((~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~(![U1: $i] : (~big_p(U1)) | (~big_q(W1!7)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.20/0.44 tff(207,plain,
% 0.20/0.44 ((~((~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))) | (~(big_q(U!2) | (~big_p(W!3)))))))) | (~((~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~(![U: $i] : (~big_q(U)) | (~big_p(W!3)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))))) | (~((~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))) | (~(big_p(U1!6) | (~big_q(W1!7)))))))) | (~((~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~(![U1: $i] : (~big_p(U1)) | (~big_q(W1!7)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[206, 203])).
% 0.20/0.44 tff(208,plain,
% 0.20/0.44 ((~((~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))))) | (~((~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))))) | (~((~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))))) | (~((~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[207, 202])).
% 0.20/0.44 tff(209,plain,
% 0.20/0.44 (~((~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))))) | (~((~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[208, 201])).
% 0.20/0.44 tff(210,plain,
% 0.20/0.44 (((~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))))) | (~((~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))))) | (![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(211,plain,
% 0.20/0.44 (![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W)))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[210, 209])).
% 0.20/0.44 tff(212,plain,
% 0.20/0.44 (((~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))))) | (~((~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))))) | ((~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(213,plain,
% 0.20/0.44 ((~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[212, 209])).
% 0.20/0.44 tff(214,assumption,(~((~((~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))))))), introduced(assumption)).
% 0.20/0.44 tff(215,plain,
% 0.20/0.44 ((~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[85, 214])).
% 0.20/0.44 tff(216,assumption,((~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))), introduced(assumption)).
% 0.20/0.44 tff(217,plain,
% 0.20/0.44 (![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[87, 214])).
% 0.20/0.44 tff(218,plain,
% 0.20/0.44 (~(big_q(U!2) | ![W: $i] : big_p(W))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[114, 1, 3])).
% 0.20/0.44 tff(219,plain,
% 0.20/0.44 ((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[116, 218])).
% 0.20/0.44 tff(220,plain,
% 0.20/0.44 ((~((~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(221,plain,
% 0.20/0.44 (![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[220, 219, 216])).
% 0.20/0.44 tff(222,plain,
% 0.20/0.44 ((~big_p(U1!6)) <=> big_p(tptp_fun_Y_0(U1!6))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[142, 221])).
% 0.20/0.45 tff(223,plain,
% 0.20/0.45 ((~((~big_p(U1!6)) <=> big_p(tptp_fun_Y_0(U1!6)))) | (~big_p(tptp_fun_Y_0(U1!6)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[144, 122])).
% 0.20/0.45 tff(224,plain,
% 0.20/0.45 (~big_p(tptp_fun_Y_0(U1!6))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[223, 222])).
% 0.20/0.45 tff(225,plain,
% 0.20/0.45 (big_p(W!3)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[134, 1, 122, 107])).
% 0.20/0.45 tff(226,plain,
% 0.20/0.45 (![Y: $i] : (big_p(X!1) <=> big_p(Y))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[118, 219, 107])).
% 0.20/0.45 tff(227,plain,
% 0.20/0.45 (big_p(X!1) <=> big_p(W!3)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[132, 226])).
% 0.20/0.45 tff(228,plain,
% 0.20/0.45 (big_p(X!1)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[156, 227, 225])).
% 0.20/0.45 tff(229,plain,
% 0.20/0.45 (~(big_p(X!1) <=> big_p(tptp_fun_Y_0(U1!6)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[158, 228, 224])).
% 0.20/0.45 tff(230,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[160, 226, 229])).
% 0.20/0.45 tff(231,plain,(big_q(U!2) | (~big_p(U1!6)) | (~((~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))))) | ![W: $i] : big_p(W)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(232,plain,
% 0.20/0.45 (big_q(U!2)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[231, 217, 216, 122, 3])).
% 0.20/0.45 tff(233,plain,
% 0.20/0.45 (~![U: $i] : (~big_q(U))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[191, 232])).
% 0.20/0.45 tff(234,plain,
% 0.20/0.45 (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[194, 233, 3])).
% 0.20/0.45 tff(235,plain,
% 0.20/0.45 ((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[196, 234])).
% 0.20/0.45 tff(236,plain,
% 0.20/0.45 (![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[140, 235, 215])).
% 0.20/0.45 tff(237,plain,
% 0.20/0.45 ((~big_p(U1!6)) <=> big_p(tptp_fun_Y_0(U1!6))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[142, 236])).
% 0.20/0.45 tff(238,plain,
% 0.20/0.45 (~big_p(tptp_fun_Y_0(U1!6))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[223, 237])).
% 0.20/0.45 tff(239,assumption,(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W)))))), introduced(assumption)).
% 0.20/0.45 tff(240,plain,
% 0.20/0.45 ((~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))))) | ![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W)))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(241,plain,
% 0.20/0.45 (![Y: $i] : (big_p(X!1) <=> big_p(Y))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[240, 235, 239])).
% 0.20/0.45 tff(242,plain,
% 0.20/0.45 (big_p(X!1) <=> big_p(U1!6)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[120, 241])).
% 0.20/0.45 tff(243,plain,
% 0.20/0.45 (big_p(X!1)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[124, 242])).
% 0.20/0.45 tff(244,plain,
% 0.20/0.45 (~(big_p(X!1) <=> big_p(tptp_fun_Y_0(U1!6)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[158, 243, 238])).
% 0.20/0.45 tff(245,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[160, 241, 244])).
% 0.20/0.45 tff(246,plain,(((~((~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U))))))))) | (~big_p(U1!6)) | (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))))) | ![W: $i] : big_p(W) | (~((~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(247,plain,
% 0.20/0.45 ((~((~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U))))))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[246, 122, 211, 3, 213])).
% 0.20/0.45 tff(248,plain,
% 0.20/0.45 (~((~((~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))) | (~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1)))))))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[83, 247])).
% 0.20/0.45 tff(249,plain,
% 0.20/0.45 (((~((~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))) | (~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1))))))))) | (![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1)))))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(250,plain,
% 0.20/0.45 (![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1))))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[249, 248])).
% 0.20/0.45 tff(251,plain,
% 0.20/0.45 ((big_p(U1!6) | ![W1: $i] : big_q(W1)) | (~big_p(U1!6))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(252,plain,
% 0.20/0.45 (big_p(U1!6) | ![W1: $i] : big_q(W1)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[251, 122])).
% 0.20/0.45 tff(253,plain,
% 0.20/0.45 ((~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[49, 248])).
% 0.20/0.45 tff(254,plain,
% 0.20/0.45 (~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[47, 253, 2])).
% 0.20/0.45 tff(255,plain,
% 0.20/0.45 (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[43, 254, 252])).
% 0.20/0.45 tff(256,plain,
% 0.20/0.45 ((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[9, 255])).
% 0.20/0.45 tff(257,plain,
% 0.20/0.45 ((~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1)))))))) | ![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1))))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(258,plain,
% 0.20/0.45 (![Y1: $i] : (big_q(X1!4) <=> big_q(Y1))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[257, 256, 250])).
% 0.20/0.45 tff(259,plain,
% 0.20/0.45 (big_q(X1!4) <=> big_q(U!2)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[94, 258])).
% 0.20/0.45 tff(260,plain,
% 0.20/0.45 (big_q(X1!4) <=> big_q(W1!7)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[96, 258])).
% 0.20/0.45 tff(261,plain,
% 0.20/0.45 (((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1))) | big_q(W1!7)),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(262,plain,
% 0.20/0.45 (big_q(W1!7)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[261, 255])).
% 0.20/0.45 tff(263,plain,
% 0.20/0.45 ((~(big_q(X1!4) <=> big_q(W1!7))) | big_q(X1!4)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[182, 262])).
% 0.20/0.45 tff(264,plain,
% 0.20/0.45 (big_q(X1!4)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[263, 260])).
% 0.20/0.45 tff(265,plain,
% 0.20/0.45 (big_q(U!2)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[185, 264, 259])).
% 0.20/0.45 tff(266,plain,
% 0.20/0.45 (~![U: $i] : (~big_q(U))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[191, 265])).
% 0.20/0.45 tff(267,plain,
% 0.20/0.45 (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[194, 266, 3])).
% 0.20/0.45 tff(268,plain,
% 0.20/0.45 ((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[196, 267])).
% 0.20/0.45 tff(269,plain,
% 0.20/0.45 (![Y: $i] : (big_p(X!1) <=> big_p(Y))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[240, 268, 211])).
% 0.20/0.45 tff(270,plain,
% 0.20/0.45 (big_p(X!1) <=> big_p(W!3)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[132, 269])).
% 0.20/0.45 tff(271,plain,
% 0.20/0.45 ((![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U))))))) | (~![Y: $i] : (big_p(X!1) <=> big_p(Y)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(272,plain,
% 0.20/0.45 (![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U))))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[271, 269])).
% 0.20/0.45 tff(273,plain,
% 0.20/0.45 ((~((~((~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))))))) | (~((~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U))))))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(274,plain,
% 0.20/0.45 (~((~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[273, 272, 247])).
% 0.20/0.45 tff(275,plain,
% 0.20/0.45 (((~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))) | (~![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(276,plain,
% 0.20/0.45 (~![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[275, 274])).
% 0.20/0.45 tff(277,plain,
% 0.20/0.45 (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[220, 276, 213])).
% 0.20/0.45 tff(278,plain,
% 0.20/0.45 (((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U))))) | ((~big_p(W!3)) | ![U: $i] : (~big_q(U)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(279,plain,
% 0.20/0.45 ((~big_p(W!3)) | ![U: $i] : (~big_q(U))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[278, 277])).
% 0.20/0.45 tff(280,plain,
% 0.20/0.45 ((~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))) | (~big_p(W!3)) | ![U: $i] : (~big_q(U))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(281,plain,
% 0.20/0.45 (~big_p(W!3)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[280, 279, 266])).
% 0.20/0.45 tff(282,plain,
% 0.20/0.45 (~big_p(X!1)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[126, 281, 270])).
% 0.20/0.45 tff(283,plain,
% 0.20/0.45 (~(big_p(X!1) <=> big_p(U1!6))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[123, 122, 282])).
% 0.20/0.45 tff(284,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[120, 269, 283])).
% 0.20/0.45 tff(285,plain,((~big_p(U1!6)) | ![W: $i] : big_p(W) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(286,plain,
% 0.20/0.45 (~big_p(U1!6)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[285, 3, 2])).
% 0.20/0.45 tff(287,assumption,(~big_p(U1!6)), introduced(assumption)).
% 0.20/0.45 tff(288,assumption,((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U))))), introduced(assumption)).
% 0.20/0.45 tff(289,plain,
% 0.20/0.45 (![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[220, 288, 216])).
% 0.20/0.45 tff(290,plain,
% 0.20/0.45 ((~big_p(U1!6)) <=> big_p(tptp_fun_Y_0(U1!6))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[142, 289])).
% 0.20/0.45 tff(291,plain,
% 0.20/0.45 ((~((~big_p(U1!6)) <=> big_p(tptp_fun_Y_0(U1!6)))) | big_p(tptp_fun_Y_0(U1!6))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[178, 287])).
% 0.20/0.45 tff(292,plain,
% 0.20/0.45 (big_p(tptp_fun_Y_0(U1!6))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[291, 290])).
% 0.20/0.45 tff(293,plain,
% 0.20/0.45 (![Y: $i] : (big_p(X!1) <=> big_p(Y))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[118, 288, 107])).
% 0.20/0.45 tff(294,plain,
% 0.20/0.45 (big_p(X!1) <=> big_p(U1!6)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[120, 293])).
% 0.20/0.45 tff(295,plain,
% 0.20/0.45 ((~(big_p(X!1) <=> big_p(U1!6))) | (~big_p(X!1)) | big_p(U1!6)),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(296,plain,
% 0.20/0.45 ((~(big_p(X!1) <=> big_p(U1!6))) | (~big_p(X!1))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[295, 287])).
% 0.20/0.45 tff(297,plain,
% 0.20/0.45 (~big_p(X!1)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[296, 294])).
% 0.20/0.45 tff(298,plain,
% 0.20/0.45 ((~(big_p(X!1) <=> big_p(tptp_fun_Y_0(U1!6)))) | big_p(X!1) | (~big_p(tptp_fun_Y_0(U1!6)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(299,plain,
% 0.20/0.45 (~(big_p(X!1) <=> big_p(tptp_fun_Y_0(U1!6)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[298, 297, 292])).
% 0.20/0.45 tff(300,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[160, 293, 299])).
% 0.20/0.45 tff(301,plain,((~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))) | big_p(U1!6) | (~((~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U))))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(302,plain,
% 0.20/0.45 (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[301, 217, 216, 287])).
% 0.20/0.45 tff(303,plain,
% 0.20/0.45 (big_q(U!2) | ![W: $i] : big_p(W)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[116, 302])).
% 0.20/0.45 tff(304,plain,
% 0.20/0.45 (big_q(U!2)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[114, 303, 3])).
% 0.20/0.45 tff(305,plain,
% 0.20/0.45 (~![U: $i] : (~big_q(U))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[191, 304])).
% 0.20/0.45 tff(306,plain,
% 0.20/0.45 (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[194, 305, 3])).
% 0.20/0.45 tff(307,plain,
% 0.20/0.45 ((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[196, 306])).
% 0.20/0.45 tff(308,plain,
% 0.20/0.45 (![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[140, 307, 215])).
% 0.20/0.45 tff(309,plain,
% 0.20/0.45 ((~![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))) | ((~big_p(W!3)) <=> big_p(tptp_fun_Y_0(W!3)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(310,plain,
% 0.20/0.45 ((~big_p(W!3)) <=> big_p(tptp_fun_Y_0(W!3))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[309, 308])).
% 0.20/0.45 tff(311,plain,
% 0.20/0.45 ((~big_p(W!3)) | ![U: $i] : (~big_q(U))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[278, 302])).
% 0.20/0.45 tff(312,plain,
% 0.20/0.45 (~big_p(W!3)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[280, 305, 311])).
% 0.20/0.45 tff(313,plain,
% 0.20/0.45 ((~((~big_p(W!3)) <=> big_p(tptp_fun_Y_0(W!3)))) | big_p(W!3) | big_p(tptp_fun_Y_0(W!3))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(314,plain,
% 0.20/0.45 ((~((~big_p(W!3)) <=> big_p(tptp_fun_Y_0(W!3)))) | big_p(tptp_fun_Y_0(W!3))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[313, 312])).
% 0.20/0.45 tff(315,plain,
% 0.20/0.45 (big_p(tptp_fun_Y_0(W!3))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[314, 310])).
% 0.20/0.45 tff(316,plain,
% 0.20/0.45 (![Y: $i] : (big_p(X!1) <=> big_p(Y))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[240, 307, 239])).
% 0.20/0.45 tff(317,plain,
% 0.20/0.45 (big_p(X!1) <=> big_p(W!3)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[132, 316])).
% 0.20/0.45 tff(318,plain,
% 0.20/0.45 (~big_p(X!1)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[126, 317, 312])).
% 0.20/0.45 tff(319,plain,
% 0.20/0.45 ((~(big_p(X!1) <=> big_p(tptp_fun_Y_0(W!3)))) | big_p(X!1) | (~big_p(tptp_fun_Y_0(W!3)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(320,plain,
% 0.20/0.45 (~(big_p(X!1) <=> big_p(tptp_fun_Y_0(W!3)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[319, 318, 315])).
% 0.20/0.45 tff(321,plain,
% 0.20/0.45 ((~![Y: $i] : (big_p(X!1) <=> big_p(Y))) | (big_p(X!1) <=> big_p(tptp_fun_Y_0(W!3)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(322,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[321, 316, 320])).
% 0.20/0.45 tff(323,plain,(((~((~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U))))))))) | (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))))) | ![W: $i] : big_p(W) | (~((~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | big_p(U1!6)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(324,plain,
% 0.20/0.46 ((~((~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U))))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[323, 287, 3, 213, 211])).
% 0.20/0.46 tff(325,plain,
% 0.20/0.46 (~((~((~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))) | (~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1)))))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[83, 324])).
% 0.20/0.46 tff(326,plain,
% 0.20/0.46 ((~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[49, 325])).
% 0.20/0.46 tff(327,plain,
% 0.20/0.46 (~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[47, 326, 2])).
% 0.20/0.46 tff(328,plain,
% 0.20/0.46 (big_p(U1!6) | (~big_q(W1!7))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[38, 327])).
% 0.20/0.46 tff(329,plain,
% 0.20/0.46 (~big_q(W1!7)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[40, 328, 287])).
% 0.20/0.46 tff(330,assumption,(~![U1: $i] : (~big_p(U1))), introduced(assumption)).
% 0.20/0.46 tff(331,plain,
% 0.20/0.46 (![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[18, 327])).
% 0.20/0.46 tff(332,plain,
% 0.20/0.46 (![W1: $i] : big_q(W1)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[22, 331, 330])).
% 0.20/0.46 tff(333,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[34, 332, 329])).
% 0.20/0.46 tff(334,plain,(big_p(U1!6) | ![U1: $i] : (~big_p(U1)) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))) | ![W: $i] : big_p(W)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(335,plain,
% 0.20/0.46 (![U1: $i] : (~big_p(U1))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[334, 286, 2, 3])).
% 0.20/0.46 tff(336,plain,
% 0.20/0.46 (~big_p(tptp_fun_Y_0(U1!6))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[170, 335])).
% 0.20/0.46 tff(337,plain,
% 0.20/0.46 (~((~big_p(U1!6)) <=> big_p(tptp_fun_Y_0(U1!6)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[178, 286, 336])).
% 0.20/0.46 tff(338,plain,
% 0.20/0.46 ((~((~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U))))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[323, 286, 3, 213, 211])).
% 0.20/0.46 tff(339,plain,
% 0.20/0.46 (~((~((~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))) | (~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1)))))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[83, 338])).
% 0.20/0.46 tff(340,plain,
% 0.20/0.46 (![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[249, 339])).
% 0.20/0.46 tff(341,plain,
% 0.20/0.46 (((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1))) | (~![U1: $i] : (~big_p(U1)))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(342,plain,
% 0.20/0.46 ((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[341, 335])).
% 0.20/0.46 tff(343,plain,
% 0.20/0.46 ((~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[49, 339])).
% 0.20/0.46 tff(344,plain,
% 0.20/0.46 (~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[47, 343, 2])).
% 0.20/0.46 tff(345,plain,
% 0.20/0.46 (~(big_p(U1!6) | ![W1: $i] : big_q(W1))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[43, 344, 342])).
% 0.20/0.46 tff(346,plain,
% 0.20/0.46 ((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[11, 345])).
% 0.20/0.46 tff(347,plain,
% 0.20/0.46 (![Y1: $i] : (big_q(X1!4) <=> big_q(Y1))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[257, 346, 340])).
% 0.20/0.46 tff(348,plain,
% 0.20/0.46 (big_q(X1!4) <=> big_q(U!2)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[94, 347])).
% 0.20/0.46 tff(349,plain,
% 0.20/0.46 (big_q(X1!4) <=> big_q(W1!7)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[96, 347])).
% 0.20/0.46 tff(350,plain,
% 0.20/0.46 (big_p(U1!6) | (~big_q(W1!7))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[38, 344])).
% 0.20/0.46 tff(351,plain,
% 0.20/0.46 (~big_q(W1!7)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[40, 350, 286])).
% 0.20/0.46 tff(352,plain,
% 0.20/0.46 ((~(big_q(X1!4) <=> big_q(W1!7))) | (~big_q(X1!4))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[102, 351])).
% 0.20/0.46 tff(353,plain,
% 0.20/0.46 (~big_q(X1!4)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[352, 349])).
% 0.20/0.46 tff(354,plain,
% 0.20/0.46 (~big_q(U!2)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[105, 353, 348])).
% 0.20/0.46 tff(355,plain,
% 0.20/0.46 (~(big_q(U!2) | ![W: $i] : big_p(W))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[114, 354, 3])).
% 0.20/0.46 tff(356,plain,
% 0.20/0.46 ((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[116, 355])).
% 0.20/0.46 tff(357,plain,
% 0.20/0.46 (![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[220, 356, 213])).
% 0.20/0.46 tff(358,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[142, 357, 337])).
% 0.20/0.46 tff(359,plain,(![W: $i] : big_p(W) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(360,plain,
% 0.20/0.46 (![W: $i] : big_p(W)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[359, 2])).
% 0.20/0.46 tff(361,plain,
% 0.20/0.46 (big_p(W!3)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[112, 360])).
% 0.20/0.46 tff(362,plain,
% 0.20/0.46 (big_p(tptp_fun_Y_0(U1!6))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[150, 360])).
% 0.20/0.46 tff(363,plain,
% 0.20/0.46 ((~![W: $i] : big_p(W)) | big_p(U1!6)),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(364,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[363, 109, 287])).
% 0.20/0.46 tff(365,plain,(big_p(U1!6) | (~![W: $i] : big_p(W))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(366,plain,
% 0.20/0.46 (big_p(U1!6)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[365, 360])).
% 0.20/0.46 tff(367,plain,
% 0.20/0.46 (~((~big_p(U1!6)) <=> big_p(tptp_fun_Y_0(U1!6)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[144, 122, 166])).
% 0.20/0.46 tff(368,assumption,(![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))), introduced(assumption)).
% 0.20/0.46 tff(369,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[142, 368, 367])).
% 0.20/0.46 tff(370,plain,((~![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))) | (~big_p(U1!6)) | (~big_p(tptp_fun_Y_0(U1!6)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(371,plain,
% 0.20/0.46 (~![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[370, 366, 362])).
% 0.20/0.46 tff(372,plain,
% 0.20/0.46 (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[220, 371, 213])).
% 0.20/0.46 tff(373,plain,
% 0.20/0.46 ((~big_p(W!3)) | ![U: $i] : (~big_q(U))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[278, 372])).
% 0.20/0.46 tff(374,plain,
% 0.20/0.46 (![U: $i] : (~big_q(U))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[280, 373, 361])).
% 0.20/0.46 tff(375,plain,
% 0.20/0.46 (big_p(U1!6) | ![W1: $i] : big_q(W1)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[251, 366])).
% 0.20/0.46 tff(376,assumption,((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W)))), introduced(assumption)).
% 0.20/0.46 tff(377,assumption,(~![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))), introduced(assumption)).
% 0.20/0.46 tff(378,plain,
% 0.20/0.46 (~((~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[140, 377, 376])).
% 0.20/0.46 tff(379,plain,
% 0.20/0.46 ((~((~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U))))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[85, 378])).
% 0.20/0.46 tff(380,plain,
% 0.20/0.46 (~((~((~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))) | (~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1)))))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[83, 379])).
% 0.20/0.46 tff(381,plain,
% 0.20/0.46 ((~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[49, 380])).
% 0.20/0.46 tff(382,plain,
% 0.20/0.46 (~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[47, 381, 2])).
% 0.20/0.46 tff(383,plain,
% 0.20/0.46 (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[43, 382, 375])).
% 0.20/0.46 tff(384,plain,
% 0.20/0.46 (big_q(W1!7)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[261, 383])).
% 0.20/0.46 tff(385,plain,
% 0.20/0.46 (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[220, 377, 213])).
% 0.20/0.46 tff(386,plain,
% 0.20/0.46 ((~big_p(W!3)) | ![U: $i] : (~big_q(U))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[278, 385])).
% 0.20/0.46 tff(387,plain,
% 0.20/0.46 (![U: $i] : (~big_q(U))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[280, 386, 361])).
% 0.20/0.46 tff(388,plain,
% 0.20/0.46 ((~![U: $i] : (~big_q(U))) | (~big_q(W1!7))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(389,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[388, 387, 384])).
% 0.20/0.46 tff(390,plain,(![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))) | (~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(391,plain,
% 0.20/0.46 (~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[390, 371, 2])).
% 0.20/0.46 tff(392,plain,
% 0.20/0.46 (big_q(U!2) | (~big_p(W!3))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[138, 391])).
% 0.20/0.46 tff(393,plain,
% 0.20/0.46 (big_q(U!2)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[136, 392, 361])).
% 0.20/0.46 tff(394,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[191, 393, 374])).
% 0.20/0.46 tff(395,plain,(![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(396,plain,
% 0.20/0.46 ((~![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))) | ((~big_q(elem!8)) <=> big_q(tptp_fun_Y1_5(elem!8)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(397,plain,
% 0.20/0.46 ((~big_q(elem!8)) <=> big_q(tptp_fun_Y1_5(elem!8))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[396, 395])).
% 0.20/0.46 tff(398,plain,
% 0.20/0.46 ((~![Y1: $i] : (big_q(X1!4) <=> big_q(Y1))) | (big_q(X1!4) <=> big_q(elem!8))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(399,plain,
% 0.20/0.46 (big_q(X1!4) <=> big_q(elem!8)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[398, 90])).
% 0.20/0.46 tff(400,plain,
% 0.20/0.46 (~big_q(X1!4)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[185, 95, 1])).
% 0.20/0.46 tff(401,plain,
% 0.20/0.46 ((~(big_q(X1!4) <=> big_q(elem!8))) | big_q(X1!4) | (~big_q(elem!8))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(402,plain,
% 0.20/0.46 ((~(big_q(X1!4) <=> big_q(elem!8))) | (~big_q(elem!8))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[401, 400])).
% 0.20/0.46 tff(403,plain,
% 0.20/0.46 (~big_q(elem!8)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[402, 399])).
% 0.20/0.46 tff(404,plain,
% 0.20/0.46 ((~![Y1: $i] : (big_q(X1!4) <=> big_q(Y1))) | (big_q(X1!4) <=> big_q(tptp_fun_Y1_5(elem!8)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(405,plain,
% 0.20/0.46 (big_q(X1!4) <=> big_q(tptp_fun_Y1_5(elem!8))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[404, 90])).
% 0.20/0.46 tff(406,plain,
% 0.20/0.46 ((~(big_q(X1!4) <=> big_q(tptp_fun_Y1_5(elem!8)))) | big_q(X1!4) | (~big_q(tptp_fun_Y1_5(elem!8)))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(407,plain,
% 0.20/0.46 ((~(big_q(X1!4) <=> big_q(tptp_fun_Y1_5(elem!8)))) | (~big_q(tptp_fun_Y1_5(elem!8)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[406, 400])).
% 0.20/0.46 tff(408,plain,
% 0.20/0.46 (~big_q(tptp_fun_Y1_5(elem!8))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[407, 405])).
% 0.20/0.46 tff(409,plain,
% 0.20/0.46 ((~((~big_q(elem!8)) <=> big_q(tptp_fun_Y1_5(elem!8)))) | big_q(elem!8) | big_q(tptp_fun_Y1_5(elem!8))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(410,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[409, 408, 403, 397])).
% 0.20/0.46 tff(411,plain,((~![Y1: $i] : (big_q(X1!4) <=> big_q(Y1))) | big_q(U!2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(412,plain,
% 0.20/0.46 (~![Y1: $i] : (big_q(X1!4) <=> big_q(Y1))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[411, 1])).
% 0.20/0.46 tff(413,plain,
% 0.20/0.46 ((~![W1: $i] : big_q(W1)) | big_q(elem!8)),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(414,plain,
% 0.20/0.46 (big_q(elem!8)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[413, 30])).
% 0.20/0.46 tff(415,plain,
% 0.20/0.46 ((~![W1: $i] : big_q(W1)) | big_q(tptp_fun_Y1_5(elem!8))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(416,plain,
% 0.20/0.46 (big_q(tptp_fun_Y1_5(elem!8))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[415, 30])).
% 0.20/0.46 tff(417,plain,
% 0.20/0.46 ((~((~big_q(elem!8)) <=> big_q(tptp_fun_Y1_5(elem!8)))) | (~big_q(elem!8)) | (~big_q(tptp_fun_Y1_5(elem!8)))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(418,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[417, 416, 414, 397])).
% 0.20/0.46 tff(419,plain,(~![W1: $i] : big_q(W1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(420,plain,
% 0.20/0.46 ((~![U: $i] : (~big_q(U))) | (~big_q(elem!8))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(421,plain,
% 0.20/0.46 (~big_q(elem!8)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[420, 187])).
% 0.20/0.46 tff(422,plain,
% 0.20/0.46 ((~![U: $i] : (~big_q(U))) | (~big_q(tptp_fun_Y1_5(elem!8)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(423,plain,
% 0.20/0.46 (~big_q(tptp_fun_Y1_5(elem!8))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[422, 187])).
% 0.20/0.46 tff(424,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[409, 423, 421, 397])).
% 0.20/0.46 tff(425,plain,(~![U: $i] : (~big_q(U))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(426,plain,
% 0.20/0.46 (~![W: $i] : big_p(W)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[365, 287])).
% 0.20/0.46 tff(427,plain,
% 0.20/0.46 (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[194, 426, 425])).
% 0.20/0.46 tff(428,plain,
% 0.20/0.46 ((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[196, 427])).
% 0.20/0.46 tff(429,plain,
% 0.20/0.46 (~(big_p(U1!6) | ![W1: $i] : big_q(W1))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[24, 287, 419])).
% 0.20/0.46 tff(430,plain,
% 0.20/0.46 ((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[11, 429])).
% 0.20/0.46 tff(431,plain,
% 0.20/0.46 (~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1)))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[257, 412, 430])).
% 0.20/0.46 tff(432,plain,
% 0.20/0.46 ((~((~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))) | (~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1))))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[249, 431])).
% 0.20/0.46 tff(433,plain,
% 0.20/0.46 (~((~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[220, 219, 377])).
% 0.20/0.46 tff(434,plain,
% 0.20/0.46 ((~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))))) | (~((~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[212, 433])).
% 0.20/0.46 tff(435,plain,
% 0.20/0.46 (~((~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))))) | (~((~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[208, 434])).
% 0.20/0.46 tff(436,plain,
% 0.20/0.46 (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[194, 3, 425])).
% 0.20/0.46 tff(437,plain,
% 0.20/0.46 ((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[196, 436])).
% 0.20/0.46 tff(438,plain,
% 0.20/0.46 (~((~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[140, 377, 437])).
% 0.20/0.46 tff(439,plain,
% 0.20/0.46 ((~((~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U))))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[85, 438])).
% 0.20/0.46 tff(440,plain,
% 0.20/0.46 (~((~((~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))) | (~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1)))))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[83, 439])).
% 0.20/0.46 tff(441,plain,
% 0.20/0.46 (![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[249, 440])).
% 0.20/0.46 tff(442,plain,
% 0.20/0.46 (~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1)))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[257, 412, 441])).
% 0.20/0.46 tff(443,plain,
% 0.20/0.46 (big_p(U1!6) | ![W1: $i] : big_q(W1)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[11, 442])).
% 0.20/0.46 tff(444,plain,
% 0.20/0.46 ((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[9, 442])).
% 0.20/0.46 tff(445,plain,
% 0.20/0.46 ((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[43, 444, 443])).
% 0.20/0.46 tff(446,plain,
% 0.20/0.46 (~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[45, 445, 412])).
% 0.20/0.46 tff(447,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[13, 446, 435])).
% 0.20/0.46 tff(448,plain,(big_q(U!2) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))) | ![W: $i] : big_p(W)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(449,plain,
% 0.20/0.46 (![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[448, 1, 426])).
% 0.20/0.46 tff(450,plain,
% 0.20/0.46 (((~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))) | (~![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(451,plain,
% 0.20/0.46 ((~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[450, 449])).
% 0.20/0.46 tff(452,plain,
% 0.20/0.46 (~(big_q(U!2) | ![W: $i] : big_p(W))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[114, 1, 426])).
% 0.20/0.46 tff(453,plain,
% 0.20/0.46 ((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[116, 452])).
% 0.20/0.46 tff(454,plain,
% 0.20/0.46 (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[301, 453, 287, 451])).
% 0.20/0.47 tff(455,plain,
% 0.20/0.47 ((~((~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U))))))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[87, 454])).
% 0.20/0.47 tff(456,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[83, 455, 432])).
% 0.20/0.47 tff(457,plain,(big_q(U!2) | big_p(U1!6)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(458,plain,
% 0.20/0.47 (big_q(U!2)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[457, 287])).
% 0.20/0.47 tff(459,plain,
% 0.20/0.47 (big_q(X1!4)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[105, 95, 188])).
% 0.20/0.47 tff(460,plain,
% 0.20/0.47 ((~(big_q(X1!4) <=> big_q(elem!8))) | (~big_q(X1!4)) | big_q(elem!8)),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(461,plain,
% 0.20/0.47 ((~(big_q(X1!4) <=> big_q(elem!8))) | big_q(elem!8)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[460, 459])).
% 0.20/0.47 tff(462,plain,
% 0.20/0.47 (big_q(elem!8)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[461, 399])).
% 0.20/0.47 tff(463,plain,
% 0.20/0.47 ((~(big_q(X1!4) <=> big_q(tptp_fun_Y1_5(elem!8)))) | (~big_q(X1!4)) | big_q(tptp_fun_Y1_5(elem!8))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(464,plain,
% 0.20/0.47 ((~(big_q(X1!4) <=> big_q(tptp_fun_Y1_5(elem!8)))) | big_q(tptp_fun_Y1_5(elem!8))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[463, 459])).
% 0.20/0.47 tff(465,plain,
% 0.20/0.47 (big_q(tptp_fun_Y1_5(elem!8))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[464, 405])).
% 0.20/0.47 tff(466,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[417, 465, 462, 397])).
% 0.20/0.47 tff(467,plain,((~![Y1: $i] : (big_q(X1!4) <=> big_q(Y1))) | (~big_q(U!2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(468,plain,
% 0.20/0.47 (~![Y1: $i] : (big_q(X1!4) <=> big_q(Y1))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[467, 458])).
% 0.20/0.47 tff(469,plain,
% 0.20/0.47 (~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1)))))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[257, 468, 430])).
% 0.20/0.47 tff(470,plain,
% 0.20/0.47 ((~((~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))) | (~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1))))))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[249, 469])).
% 0.20/0.47 tff(471,plain,
% 0.20/0.47 (~((~((~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[83, 470])).
% 0.20/0.47 tff(472,plain,
% 0.20/0.47 ((~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[85, 471])).
% 0.20/0.47 tff(473,plain,
% 0.20/0.47 (![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[140, 472, 428])).
% 0.20/0.47 tff(474,plain,
% 0.20/0.47 ((~big_p(W!3)) <=> big_p(tptp_fun_Y_0(W!3))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[309, 473])).
% 0.20/0.47 tff(475,plain,
% 0.20/0.47 (![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U))))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[87, 471])).
% 0.20/0.47 tff(476,plain,
% 0.20/0.47 ((~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[450, 473])).
% 0.20/0.47 tff(477,plain,
% 0.20/0.47 (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[301, 476, 287, 475])).
% 0.20/0.47 tff(478,plain,
% 0.20/0.47 ((~big_p(W!3)) | ![U: $i] : (~big_q(U))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[278, 477])).
% 0.20/0.47 tff(479,plain,
% 0.20/0.47 (~big_p(W!3)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[280, 478, 425])).
% 0.20/0.47 tff(480,plain,
% 0.20/0.47 ((~((~big_p(W!3)) <=> big_p(tptp_fun_Y_0(W!3)))) | big_p(tptp_fun_Y_0(W!3))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[313, 479])).
% 0.20/0.47 tff(481,plain,
% 0.20/0.47 (big_p(tptp_fun_Y_0(W!3))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[480, 474])).
% 0.20/0.47 tff(482,plain,
% 0.20/0.47 (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[323, 476, 287, 426, 471])).
% 0.20/0.47 tff(483,plain,
% 0.20/0.47 ((~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))))) | (~((~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[210, 482])).
% 0.20/0.47 tff(484,plain,
% 0.20/0.47 (~((~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))))) | (~((~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[208, 483])).
% 0.20/0.47 tff(485,plain,
% 0.20/0.47 (![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1)))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[13, 484])).
% 0.20/0.47 tff(486,plain,
% 0.20/0.47 (~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[45, 485, 468])).
% 0.20/0.47 tff(487,plain,
% 0.20/0.47 (~big_q(W1!7)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[40, 39, 287])).
% 0.20/0.47 tff(488,plain,
% 0.20/0.47 (![W1: $i] : big_q(W1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[22, 19, 330])).
% 0.20/0.47 tff(489,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[34, 488, 487])).
% 0.20/0.47 tff(490,plain,(((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1)))) | ![U1: $i] : (~big_p(U1)) | big_p(U1!6)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(491,plain,
% 0.20/0.47 (![U1: $i] : (~big_p(U1))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[490, 486, 287])).
% 0.20/0.47 tff(492,plain,
% 0.20/0.47 ((~![U1: $i] : (~big_p(U1))) | (~big_p(tptp_fun_Y_0(W!3)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(493,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[492, 491, 481])).
% 0.20/0.47 tff(494,plain,(big_p(U1!6)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(495,plain,
% 0.20/0.47 (big_p(U1!6) | ![W1: $i] : big_q(W1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[251, 494])).
% 0.20/0.47 tff(496,plain,
% 0.20/0.47 (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[28, 495, 419])).
% 0.20/0.47 tff(497,plain,
% 0.20/0.47 ((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[18, 496])).
% 0.20/0.47 tff(498,plain,
% 0.20/0.47 ((~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))))) | ![Y1: $i] : (big_q(X1!4) <=> big_q(Y1))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[45, 497])).
% 0.20/0.47 tff(499,plain,
% 0.20/0.47 (~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[498, 412])).
% 0.20/0.47 tff(500,plain,
% 0.20/0.47 ((~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))))) | (~((~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[13, 499])).
% 0.20/0.47 tff(501,plain,
% 0.20/0.47 (~((~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))))) | (~((~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[208, 500])).
% 0.20/0.47 tff(502,plain,
% 0.20/0.47 ((~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[212, 501])).
% 0.20/0.47 tff(503,plain,
% 0.20/0.47 (![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W)))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[210, 501])).
% 0.20/0.47 tff(504,plain,
% 0.20/0.47 ((~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))) | ![W: $i] : big_p(W)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[194, 425])).
% 0.20/0.47 tff(505,plain,
% 0.20/0.47 (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[504, 3])).
% 0.20/0.47 tff(506,plain,
% 0.20/0.47 ((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[196, 505])).
% 0.20/0.47 tff(507,plain,
% 0.20/0.47 (big_q(U!2) | (~((~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))))) | ![W: $i] : big_p(W)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[231, 494])).
% 0.20/0.47 tff(508,plain,
% 0.20/0.47 (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[507, 3, 502, 1])).
% 0.20/0.47 tff(509,plain,
% 0.20/0.47 (~![Y: $i] : (big_p(X!1) <=> big_p(Y))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[271, 508])).
% 0.20/0.47 tff(510,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[240, 509, 506, 503])).
% 0.20/0.47 tff(511,plain,(![W: $i] : big_p(W) | big_q(U!2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(512,plain,
% 0.20/0.47 (![W: $i] : big_p(W)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[511, 1])).
% 0.20/0.47 tff(513,plain,
% 0.20/0.47 (big_p(tptp_fun_Y_0(U1!6))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[150, 512])).
% 0.20/0.47 tff(514,plain,
% 0.20/0.47 ((~![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))) | (~big_p(tptp_fun_Y_0(U1!6)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[370, 494])).
% 0.20/0.47 tff(515,plain,
% 0.20/0.47 (~![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[514, 513])).
% 0.20/0.47 tff(516,plain,
% 0.20/0.47 (big_p(W!3)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[112, 512])).
% 0.20/0.47 tff(517,plain,
% 0.20/0.47 ((~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))) | (~big_p(W!3))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[280, 425])).
% 0.20/0.47 tff(518,plain,
% 0.20/0.47 (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[517, 516])).
% 0.20/0.47 tff(519,plain,
% 0.20/0.47 ((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[278, 518])).
% 0.20/0.47 tff(520,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[220, 519, 515, 502])).
% 0.20/0.47 tff(521,plain,(big_q(U!2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(522,plain,
% 0.20/0.47 (~![Y1: $i] : (big_q(X1!4) <=> big_q(Y1))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[467, 521])).
% 0.20/0.47 tff(523,plain,
% 0.20/0.47 (~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[498, 522])).
% 0.20/0.47 tff(524,plain,
% 0.20/0.47 ((~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | (~big_q(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_q(W1))))))) | (~((~((~(big_p(U1!6) | ![W1: $i] : big_q(W1))) | (~((~big_q(W1!7)) | ![U1: $i] : (~big_p(U1)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[13, 523])).
% 0.20/0.47 tff(525,plain,
% 0.20/0.47 (~((~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))))) | (~((~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[208, 524])).
% 0.20/0.48 tff(526,plain,
% 0.20/0.48 ((~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[212, 525])).
% 0.20/0.48 tff(527,plain,
% 0.20/0.48 (![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W)))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[210, 525])).
% 0.20/0.48 tff(528,plain,
% 0.20/0.48 (![Y: $i] : (big_p(X!1) <=> big_p(Y))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[240, 506, 527])).
% 0.20/0.48 tff(529,plain,
% 0.20/0.48 (big_p(X!1) <=> big_p(W!3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[132, 528])).
% 0.20/0.48 tff(530,plain,
% 0.20/0.48 (((~((~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U))))))))) | (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))))) | ![W: $i] : big_p(W) | (~((~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[246, 494])).
% 0.20/0.48 tff(531,plain,
% 0.20/0.48 ((~((~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U))))))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[530, 3, 527, 526])).
% 0.20/0.48 tff(532,plain,
% 0.20/0.48 (![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U))))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[271, 528])).
% 0.20/0.48 tff(533,plain,
% 0.20/0.48 (~((~((~(big_q(U!2) | (~big_p(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_p(W))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[273, 532, 531])).
% 0.20/0.48 tff(534,plain,
% 0.20/0.48 (~![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[275, 533])).
% 0.20/0.48 tff(535,plain,
% 0.20/0.48 (~((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[220, 534, 526])).
% 0.20/0.48 tff(536,plain,
% 0.20/0.48 ((~big_p(W!3)) | ![U: $i] : (~big_q(U))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[278, 535])).
% 0.20/0.48 tff(537,plain,
% 0.20/0.48 (~big_p(W!3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[517, 536])).
% 0.20/0.48 tff(538,plain,
% 0.20/0.48 (~big_p(X!1)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[126, 537, 529])).
% 0.20/0.48 tff(539,plain,
% 0.20/0.48 (~(big_p(X!1) <=> big_p(U1!6))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[123, 494, 538])).
% 0.20/0.48 tff(540,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[120, 528, 539])).
% 0.20/0.48 tff(541,plain,(![W: $i] : big_p(W)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(542,plain,
% 0.20/0.48 (big_p(tptp_fun_Y_0(U1!6))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[150, 541])).
% 0.20/0.48 tff(543,plain,
% 0.20/0.48 (~![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[514, 542])).
% 0.20/0.48 tff(544,plain,
% 0.20/0.48 (big_p(W!3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[112, 541])).
% 0.20/0.48 tff(545,plain,
% 0.20/0.48 (~((~big_p(W!3)) | ![U: $i] : (~big_q(U)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[517, 544])).
% 0.20/0.48 tff(546,plain,
% 0.20/0.48 ((~(big_q(U!2) | ![W: $i] : big_p(W))) | (~((~big_p(W!3)) | ![U: $i] : (~big_q(U))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[278, 545])).
% 0.20/0.48 tff(547,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[220, 546, 543, 526])).
% 0.20/0.48 % SZS output end Proof
%------------------------------------------------------------------------------