TSTP Solution File: SYN036+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN036+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 23:53:13 EDT 2022
% Result : Theorem 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN036+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Sep 5 01:08:44 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 % SZS output start Proof
% 0.19/0.43 tff(big_q_type, type, (
% 0.19/0.43 big_q: $i > $o)).
% 0.19/0.43 tff(tptp_fun_Y1_5_type, type, (
% 0.19/0.43 tptp_fun_Y1_5: $i > $i)).
% 0.19/0.43 tff(tptp_fun_X1_4_type, type, (
% 0.19/0.43 tptp_fun_X1_4: $i)).
% 0.19/0.43 tff(big_p_type, type, (
% 0.19/0.43 big_p: $i > $o)).
% 0.19/0.43 tff(tptp_fun_Y_0_type, type, (
% 0.19/0.43 tptp_fun_Y_0: $i > $i)).
% 0.19/0.43 tff(elem_8_type, type, (
% 0.19/0.43 elem_8: $i)).
% 0.19/0.43 tff(tptp_fun_W_3_type, type, (
% 0.19/0.43 tptp_fun_W_3: $i)).
% 0.19/0.43 tff(tptp_fun_U_2_type, type, (
% 0.19/0.43 tptp_fun_U_2: $i)).
% 0.19/0.43 tff(tptp_fun_X_1_type, type, (
% 0.19/0.43 tptp_fun_X_1: $i)).
% 0.19/0.43 tff(tptp_fun_W1_7_type, type, (
% 0.19/0.43 tptp_fun_W1_7: $i)).
% 0.19/0.43 tff(tptp_fun_U1_6_type, type, (
% 0.19/0.43 tptp_fun_U1_6: $i)).
% 0.19/0.43 tff(1,assumption,(~![Y1: $i] : (big_q(X1!4) <=> big_q(Y1))), introduced(assumption)).
% 0.19/0.43 tff(2,assumption,(~![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))), introduced(assumption)).
% 0.19/0.43 tff(3,assumption,(~big_p(W1!7)), introduced(assumption)).
% 0.19/0.43 tff(4,assumption,(~((~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1))))))) | (~((~((~(big_p(U1!6) | ![W1: $i] : big_p(W1))) | (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))))), introduced(assumption)).
% 0.19/0.43 tff(5,plain,
% 0.19/0.43 (((~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1))))))) | (~((~((~(big_p(U1!6) | ![W1: $i] : big_p(W1))) | (~((~big_p(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_p(W1))) | (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(6,plain,
% 0.19/0.43 ((~((~(big_p(U1!6) | ![W1: $i] : big_p(W1))) | (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[5, 4])).
% 0.19/0.43 tff(7,plain,
% 0.19/0.43 ((~((~((~(big_p(U1!6) | ![W1: $i] : big_p(W1))) | (~((~big_p(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_p(W1))) | (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(8,plain,
% 0.19/0.43 (~((~(big_p(U1!6) | ![W1: $i] : big_p(W1))) | (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[7, 6, 2])).
% 0.19/0.43 tff(9,plain,
% 0.19/0.43 (((~(big_p(U1!6) | ![W1: $i] : big_p(W1))) | (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1))))) | (big_p(U1!6) | ![W1: $i] : big_p(W1))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(10,plain,
% 0.19/0.43 (big_p(U1!6) | ![W1: $i] : big_p(W1)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.19/0.43 tff(11,plain,
% 0.19/0.43 (((~(big_p(U1!6) | ![W1: $i] : big_p(W1))) | (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1))))) | ((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(12,plain,
% 0.19/0.43 ((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[11, 8])).
% 0.19/0.43 tff(13,assumption,((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1))), introduced(assumption)).
% 0.19/0.43 tff(14,assumption,(big_p(W1!7)), introduced(assumption)).
% 0.19/0.43 tff(15,plain,
% 0.19/0.43 ((~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1)))) | (~big_p(W1!7)) | ![U1: $i] : (~big_p(U1))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(16,plain,
% 0.19/0.43 (![U1: $i] : (~big_p(U1))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[15, 14, 13])).
% 0.19/0.43 tff(17,plain,
% 0.19/0.43 ((~![U1: $i] : (~big_p(U1))) | (~big_p(W1!7))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(18,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[17, 14, 16])).
% 0.19/0.43 tff(19,plain,((~big_p(W1!7)) | (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(20,plain,
% 0.19/0.43 (~big_p(W1!7)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[19, 12])).
% 0.19/0.43 tff(21,assumption,(![W1: $i] : big_p(W1)), introduced(assumption)).
% 0.19/0.43 tff(22,plain,
% 0.19/0.43 ((~![W1: $i] : big_p(W1)) | big_p(W1!7)),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(23,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[22, 3, 21])).
% 0.19/0.43 tff(24,plain,(big_p(W1!7) | (~![W1: $i] : big_p(W1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(25,plain,
% 0.19/0.43 (~![W1: $i] : big_p(W1)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[24, 20])).
% 0.19/0.43 tff(26,assumption,(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1)), introduced(assumption)).
% 0.19/0.43 tff(27,assumption,(~![W1: $i] : big_p(W1)), introduced(assumption)).
% 0.19/0.43 tff(28,plain,
% 0.19/0.43 ((~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1))) | ![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(29,plain,
% 0.19/0.43 (![U1: $i] : (~big_p(U1))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[28, 27, 26])).
% 0.19/0.43 tff(30,assumption,(big_p(U1!6) | ![W1: $i] : big_p(W1)), introduced(assumption)).
% 0.19/0.43 tff(31,plain,
% 0.19/0.43 ((~(big_p(U1!6) | ![W1: $i] : big_p(W1))) | big_p(U1!6) | ![W1: $i] : big_p(W1)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(32,plain,
% 0.19/0.43 (big_p(U1!6)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[31, 27, 30])).
% 0.19/0.44 tff(33,plain,
% 0.19/0.44 ((~![U1: $i] : (~big_p(U1))) | (~big_p(U1!6))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(34,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[33, 32, 29])).
% 0.19/0.44 tff(35,plain,(![W1: $i] : big_p(W1) | (~(big_p(U1!6) | ![W1: $i] : big_p(W1))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(36,plain,
% 0.19/0.44 (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[35, 25, 10])).
% 0.19/0.44 tff(37,plain,
% 0.19/0.44 (((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1)))) | (![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(38,plain,
% 0.19/0.44 ((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.19/0.44 tff(39,plain,
% 0.19/0.44 ((~((~((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))) | (~((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(40,plain,
% 0.19/0.44 (~((~((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[39, 38, 2])).
% 0.19/0.44 tff(41,plain,
% 0.19/0.44 (((~((~((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(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_p(W1))) | (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1))))))))) | ((~((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(42,plain,
% 0.19/0.44 ((~((~((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(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_p(W1))) | (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1))))))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.19/0.44 tff(43,plain,
% 0.19/0.44 (((~((~((~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(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_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U)))))))))) | (~((~((~((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(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_p(W1))) | (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1))))))))))) <=> ((~((~((~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(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_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U)))))))))) | (~((~((~((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(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_p(W1))) | (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1)))))))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(44,plain,
% 0.19/0.44 ((~((~((~((~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1))) | (~(big_p(U1!6) | (~big_p(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_p(W1))) | (~(![U1: $i] : (~big_p(U1)) | (~big_p(W1!7)))))))))) <=> (~((~((~((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(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_p(W1))) | (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1))))))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(45,plain,
% 0.19/0.44 ((~((~((~((~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W))) | (~(big_q(U!2) | (~big_q(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_q(W))) | (~(![U: $i] : (~big_q(U)) | (~big_q(W!3)))))))))) <=> (~((~((~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(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_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U))))))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(46,plain,
% 0.19/0.44 (((~((~((~((~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W))) | (~(big_q(U!2) | (~big_q(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_q(W))) | (~(![U: $i] : (~big_q(U)) | (~big_q(W!3)))))))))) | (~((~((~((~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1))) | (~(big_p(U1!6) | (~big_p(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_p(W1))) | (~(![U1: $i] : (~big_p(U1)) | (~big_p(W1!7))))))))))) <=> ((~((~((~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(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_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U)))))))))) | (~((~((~((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(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_p(W1))) | (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1)))))))))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[45, 44])).
% 0.19/0.44 tff(47,plain,
% 0.19/0.44 (((~((~((~((~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W))) | (~(big_q(U!2) | (~big_q(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_q(W))) | (~(![U: $i] : (~big_q(U)) | (~big_q(W!3)))))))))) | (~((~((~((~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1))) | (~(big_p(U1!6) | (~big_p(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_p(W1))) | (~(![U1: $i] : (~big_p(U1)) | (~big_p(W1!7))))))))))) <=> ((~((~((~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(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_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U)))))))))) | (~((~((~((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(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_p(W1))) | (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1)))))))))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[46, 43])).
% 0.19/0.44 tff(48,plain,
% 0.19/0.44 (((~((~((~((~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W))) | (~(big_q(U!2) | (~big_q(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_q(W))) | (~(![U: $i] : (~big_q(U)) | (~big_q(W!3)))))))))) | (~((~((~((~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1))) | (~(big_p(U1!6) | (~big_p(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_p(W1))) | (~(![U1: $i] : (~big_p(U1)) | (~big_p(W1!7))))))))))) <=> ((~((~((~((~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W))) | (~(big_q(U!2) | (~big_q(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_q(W))) | (~(![U: $i] : (~big_q(U)) | (~big_q(W!3)))))))))) | (~((~((~((~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1))) | (~(big_p(U1!6) | (~big_p(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_p(W1))) | (~(![U1: $i] : (~big_p(U1)) | (~big_p(W1!7)))))))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(49,plain,
% 0.19/0.44 ((((((![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W)) & (big_q(U!2) | (~big_q(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_q(W)) & (![U: $i] : (~big_q(U)) | (~big_q(W!3)))))) | ((((![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1)) & (big_p(U1!6) | (~big_p(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_p(W1)) & (![U1: $i] : (~big_p(U1)) | (~big_p(W1!7))))))) <=> ((~((~((~((~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W))) | (~(big_q(U!2) | (~big_q(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_q(W))) | (~(![U: $i] : (~big_q(U)) | (~big_q(W!3)))))))))) | (~((~((~((~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1))) | (~(big_p(U1!6) | (~big_p(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_p(W1))) | (~(![U1: $i] : (~big_p(U1)) | (~big_p(W1!7)))))))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(50,plain,
% 0.19/0.44 (((((![X: $i] : (~(big_p(X) <=> big_p(tptp_fun_Y_0(X)))) | ((![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W)) & (big_q(U!2) | (~big_q(W!3))))) & (![Y: $i] : (big_p(X!1) <=> big_p(Y)) | ((big_q(U!2) | ![W: $i] : big_q(W)) & (![U: $i] : (~big_q(U)) | (~big_q(W!3)))))) | ((![X1: $i] : (~(big_q(X1) <=> big_q(tptp_fun_Y1_5(X1)))) | ((![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1)) & (big_p(U1!6) | (~big_p(W1!7))))) & (![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | ((big_p(U1!6) | ![W1: $i] : big_p(W1)) & (![U1: $i] : (~big_p(U1)) | (~big_p(W1!7))))))) & (((![Y: $i] : (big_p(X!1) <=> big_p(Y)) | ((![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W)) & (big_q(U!2) | (~big_q(W!3))))) & (![X: $i] : (~(big_p(X) <=> big_p(tptp_fun_Y_0(X)))) | ((big_q(U!2) | ![W: $i] : big_q(W)) & (![U: $i] : (~big_q(U)) | (~big_q(W!3)))))) | ((![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | ((![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1)) & (big_p(U1!6) | (~big_p(W1!7))))) & (![X1: $i] : (~(big_q(X1) <=> big_q(tptp_fun_Y1_5(X1)))) | ((big_p(U1!6) | ![W1: $i] : big_p(W1)) & (![U1: $i] : (~big_p(U1)) | (~big_p(W1!7)))))))) <=> ((((((![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W)) & (big_q(U!2) | (~big_q(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_q(W)) & (![U: $i] : (~big_q(U)) | (~big_q(W!3)))))) | ((((![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1)) & (big_p(U1!6) | (~big_p(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_p(W1)) & (![U1: $i] : (~big_p(U1)) | (~big_p(W1!7))))))) & (((![Y: $i] : (big_p(X!1) <=> big_p(Y)) | ((![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W)) & (big_q(U!2) | (~big_q(W!3))))) & (((big_q(U!2) | ![W: $i] : big_q(W)) & (![U: $i] : (~big_q(U)) | (~big_q(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_p(W1)) & (big_p(U1!6) | (~big_p(W1!7))))) & (((big_p(U1!6) | ![W1: $i] : big_p(W1)) & (![U1: $i] : (~big_p(U1)) | (~big_p(W1!7)))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(51,plain,
% 0.19/0.45 ((?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_p(W1))) <=> (?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_p(W1)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(52,plain,
% 0.19/0.45 ((?[U: $i] : big_q(U) <=> ![W: $i] : big_q(W)) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_q(W))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(53,plain,
% 0.19/0.45 ((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(54,plain,
% 0.19/0.45 (((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_q(W))) <=> ((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_q(W)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[53, 52])).
% 0.19/0.45 tff(55,plain,
% 0.19/0.45 ((((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_q(W))) <=> (?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_p(W1)))) <=> (((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_q(W))) <=> (?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_p(W1))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[54, 51])).
% 0.19/0.45 tff(56,plain,
% 0.19/0.45 ((((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_q(W))) <=> (?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_p(W1)))) <=> (((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_q(W))) <=> (?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_p(W1))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(57,plain,
% 0.19/0.45 ((~((?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y)) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_q(W))) <=> (?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_p(W1))))) <=> (((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_q(W))) <=> (?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_p(W1))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(58,plain,
% 0.19/0.45 ((?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y)) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_q(W))) <=> (?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y)) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_q(W)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(59,plain,
% 0.19/0.45 (((?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y)) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_q(W))) <=> (?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_p(W1)))) <=> ((?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y)) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_q(W))) <=> (?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_p(W1))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[58, 51])).
% 0.19/0.45 tff(60,plain,
% 0.19/0.45 ((~((?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y)) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_q(W))) <=> (?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_p(W1))))) <=> (~((?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y)) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_q(W))) <=> (?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_p(W1)))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[59])).
% 0.19/0.45 tff(61,plain,
% 0.19/0.45 ((~((?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y)) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_q(W))) <=> (?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_p(W1))))) <=> (((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_q(W))) <=> (?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_p(W1))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[60, 57])).
% 0.19/0.45 tff(62,axiom,(~((?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y)) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_q(W))) <=> (?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_p(W1))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel34')).
% 0.19/0.45 tff(63,plain,
% 0.19/0.45 (((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_q(W))) <=> (?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_p(W1)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.19/0.45 tff(64,plain,
% 0.19/0.45 (((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_q(W))) <=> (?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_p(W1)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[63, 55])).
% 0.19/0.45 tff(65,plain,
% 0.19/0.45 (((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_q(W))) <=> (?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_p(W1)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[64, 56])).
% 0.19/0.45 tff(66,plain,
% 0.19/0.45 (((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_q(W))) <=> (?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_p(W1)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[65, 55])).
% 0.19/0.45 tff(67,plain,
% 0.19/0.45 (((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_q(W))) <=> (?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_p(W1)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[66, 55])).
% 0.19/0.45 tff(68,plain,
% 0.19/0.45 (((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_q(W))) <=> (?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_p(W1)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[67, 55])).
% 0.19/0.45 tff(69,plain,
% 0.19/0.45 (((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (?[U: $i] : big_q(U) <=> ![W: $i] : big_q(W))) <=> (?[X1: $i] : ![Y1: $i] : (big_q(X1) <=> big_q(Y1)) <=> (?[U1: $i] : big_p(U1) <=> ![W1: $i] : big_p(W1)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[68, 55])).
% 0.19/0.45 tff(70,plain,(
% 0.19/0.45 (((![X: $i] : (~(big_p(X) <=> big_p(tptp_fun_Y_0(X)))) | ((![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W)) & (big_q(U!2) | (~big_q(W!3))))) & (![Y: $i] : (big_p(X!1) <=> big_p(Y)) | ((big_q(U!2) | ![W: $i] : big_q(W)) & (![U: $i] : (~big_q(U)) | (~big_q(W!3)))))) | ((![X1: $i] : (~(big_q(X1) <=> big_q(tptp_fun_Y1_5(X1)))) | ((![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1)) & (big_p(U1!6) | (~big_p(W1!7))))) & (![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | ((big_p(U1!6) | ![W1: $i] : big_p(W1)) & (![U1: $i] : (~big_p(U1)) | (~big_p(W1!7))))))) & (((![Y: $i] : (big_p(X!1) <=> big_p(Y)) | ((![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W)) & (big_q(U!2) | (~big_q(W!3))))) & (![X: $i] : (~(big_p(X) <=> big_p(tptp_fun_Y_0(X)))) | ((big_q(U!2) | ![W: $i] : big_q(W)) & (![U: $i] : (~big_q(U)) | (~big_q(W!3)))))) | ((![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | ((![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1)) & (big_p(U1!6) | (~big_p(W1!7))))) & (![X1: $i] : (~(big_q(X1) <=> big_q(tptp_fun_Y1_5(X1)))) | ((big_p(U1!6) | ![W1: $i] : big_p(W1)) & (![U1: $i] : (~big_p(U1)) | (~big_p(W1!7)))))))),
% 0.19/0.45 inference(skolemize,[status(sab)],[69])).
% 0.19/0.45 tff(71,plain,
% 0.19/0.45 ((((((![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W)) & (big_q(U!2) | (~big_q(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_q(W)) & (![U: $i] : (~big_q(U)) | (~big_q(W!3)))))) | ((((![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1)) & (big_p(U1!6) | (~big_p(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_p(W1)) & (![U1: $i] : (~big_p(U1)) | (~big_p(W1!7))))))) & (((![Y: $i] : (big_p(X!1) <=> big_p(Y)) | ((![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W)) & (big_q(U!2) | (~big_q(W!3))))) & (((big_q(U!2) | ![W: $i] : big_q(W)) & (![U: $i] : (~big_q(U)) | (~big_q(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_p(W1)) & (big_p(U1!6) | (~big_p(W1!7))))) & (((big_p(U1!6) | ![W1: $i] : big_p(W1)) & (![U1: $i] : (~big_p(U1)) | (~big_p(W1!7)))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[70, 50])).
% 0.19/0.45 tff(72,plain,
% 0.19/0.45 (((((![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W)) & (big_q(U!2) | (~big_q(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_q(W)) & (![U: $i] : (~big_q(U)) | (~big_q(W!3)))))) | ((((![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1)) & (big_p(U1!6) | (~big_p(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_p(W1)) & (![U1: $i] : (~big_p(U1)) | (~big_p(W1!7))))))),
% 0.19/0.45 inference(and_elim,[status(thm)],[71])).
% 0.19/0.45 tff(73,plain,
% 0.19/0.45 ((~((~((~((~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W))) | (~(big_q(U!2) | (~big_q(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_q(W))) | (~(![U: $i] : (~big_q(U)) | (~big_q(W!3)))))))))) | (~((~((~((~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1))) | (~(big_p(U1!6) | (~big_p(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_p(W1))) | (~(![U1: $i] : (~big_p(U1)) | (~big_p(W1!7))))))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[72, 49])).
% 0.19/0.45 tff(74,plain,
% 0.19/0.45 ((~((~((~((~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W))) | (~(big_q(U!2) | (~big_q(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_q(W))) | (~(![U: $i] : (~big_q(U)) | (~big_q(W!3)))))))))) | (~((~((~((~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1))) | (~(big_p(U1!6) | (~big_p(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_p(W1))) | (~(![U1: $i] : (~big_p(U1)) | (~big_p(W1!7))))))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[73, 48])).
% 0.19/0.45 tff(75,plain,
% 0.19/0.45 ((~((~((~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(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_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U)))))))))) | (~((~((~((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(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_p(W1))) | (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1))))))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[74, 47])).
% 0.19/0.45 tff(76,plain,
% 0.19/0.45 (~((~((~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(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_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U)))))))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[75, 42])).
% 0.19/0.45 tff(77,plain,
% 0.19/0.45 (((~((~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(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_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U))))))))) | (![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U)))))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(78,plain,
% 0.19/0.45 (![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U))))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.19/0.45 tff(79,plain,
% 0.19/0.45 (big_p(U1!6)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[31, 25, 10])).
% 0.19/0.45 tff(80,assumption,(![Y: $i] : (big_p(X!1) <=> big_p(Y))), introduced(assumption)).
% 0.19/0.45 tff(81,plain,
% 0.19/0.45 ((~![Y: $i] : (big_p(X!1) <=> big_p(Y))) | (big_p(X!1) <=> big_p(W1!7))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(82,plain,
% 0.19/0.45 (big_p(X!1) <=> big_p(W1!7)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.19/0.45 tff(83,plain,
% 0.19/0.45 ((~![Y: $i] : (big_p(X!1) <=> big_p(Y))) | (big_p(X!1) <=> big_p(U1!6))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(84,plain,
% 0.19/0.45 (big_p(X!1) <=> big_p(U1!6)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[83, 80])).
% 0.19/0.45 tff(85,assumption,(big_p(U1!6)), introduced(assumption)).
% 0.19/0.45 tff(86,plain,
% 0.19/0.45 ((~(big_p(X!1) <=> big_p(U1!6))) | big_p(X!1) | (~big_p(U1!6))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(87,plain,
% 0.19/0.45 ((~(big_p(X!1) <=> big_p(U1!6))) | big_p(X!1)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.19/0.45 tff(88,plain,
% 0.19/0.45 (big_p(X!1)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[87, 84])).
% 0.19/0.45 tff(89,plain,
% 0.19/0.45 ((~(big_p(X!1) <=> big_p(W1!7))) | (~big_p(X!1)) | big_p(W1!7)),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(90,plain,
% 0.19/0.45 ((~(big_p(X!1) <=> big_p(W1!7))) | (~big_p(X!1))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[89, 3])).
% 0.19/0.45 tff(91,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[90, 88, 82])).
% 0.19/0.45 tff(92,plain,((~![Y: $i] : (big_p(X!1) <=> big_p(Y))) | big_p(W1!7) | (~big_p(U1!6))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(93,plain,
% 0.19/0.45 (~![Y: $i] : (big_p(X!1) <=> big_p(Y))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[92, 20, 79])).
% 0.19/0.45 tff(94,plain,
% 0.19/0.45 ((~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U)))))))) | ![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U))))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(95,plain,
% 0.19/0.45 (~((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U)))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[94, 93, 78])).
% 0.19/0.45 tff(96,plain,
% 0.19/0.45 (((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U))))) | ((~big_q(W!3)) | ![U: $i] : (~big_q(U)))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(97,plain,
% 0.19/0.45 ((~big_q(W!3)) | ![U: $i] : (~big_q(U))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.19/0.45 tff(98,plain,
% 0.19/0.45 (((~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1))))))) | (~((~((~(big_p(U1!6) | ![W1: $i] : big_p(W1))) | (~((~big_p(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_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1))))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(99,plain,
% 0.19/0.46 (![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[98, 4])).
% 0.19/0.46 tff(100,plain,
% 0.19/0.46 ((~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1))))))) | ![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1)))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(101,plain,
% 0.19/0.46 (![Y1: $i] : (big_q(X1!4) <=> big_q(Y1))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[100, 38, 99])).
% 0.19/0.46 tff(102,assumption,(~(big_q(X1!4) <=> big_q(W!3))), introduced(assumption)).
% 0.19/0.46 tff(103,assumption,(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1))), introduced(assumption)).
% 0.19/0.46 tff(104,plain,
% 0.19/0.46 ((~![Y1: $i] : (big_q(X1!4) <=> big_q(Y1))) | (big_q(X1!4) <=> big_q(W!3))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(105,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[104, 103, 102])).
% 0.19/0.46 tff(106,plain,((big_q(X1!4) <=> big_q(W!3)) | (~![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(107,plain,
% 0.19/0.46 (big_q(X1!4) <=> big_q(W!3)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[106, 101])).
% 0.19/0.46 tff(108,plain,
% 0.19/0.46 (((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U))))) | (big_q(U!2) | ![W: $i] : big_q(W))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(109,plain,
% 0.19/0.46 (big_q(U!2) | ![W: $i] : big_q(W)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[108, 95])).
% 0.19/0.46 tff(110,assumption,(~(big_q(X1!4) <=> big_q(U!2))), introduced(assumption)).
% 0.19/0.46 tff(111,plain,
% 0.19/0.46 ((~![Y1: $i] : (big_q(X1!4) <=> big_q(Y1))) | (big_q(X1!4) <=> big_q(U!2))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(112,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[111, 103, 110])).
% 0.19/0.46 tff(113,plain,((big_q(X1!4) <=> big_q(U!2)) | (~![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(114,plain,
% 0.19/0.46 (big_q(X1!4) <=> big_q(U!2)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[113, 101])).
% 0.19/0.46 tff(115,assumption,(big_q(X1!4) <=> big_q(U!2)), introduced(assumption)).
% 0.19/0.46 tff(116,assumption,(big_q(X1!4) <=> big_q(W!3)), introduced(assumption)).
% 0.19/0.46 tff(117,assumption,(~big_q(W!3)), introduced(assumption)).
% 0.19/0.46 tff(118,plain,
% 0.19/0.46 ((~(big_q(X1!4) <=> big_q(W!3))) | (~big_q(X1!4)) | big_q(W!3)),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(119,plain,
% 0.19/0.46 (~big_q(X1!4)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[118, 117, 116])).
% 0.19/0.46 tff(120,assumption,(big_q(U!2) | ![W: $i] : big_q(W)), introduced(assumption)).
% 0.19/0.46 tff(121,assumption,(![W: $i] : big_q(W)), introduced(assumption)).
% 0.19/0.46 tff(122,plain,
% 0.19/0.46 ((~![W: $i] : big_q(W)) | big_q(W!3)),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(123,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[122, 117, 121])).
% 0.19/0.46 tff(124,plain,((~![W: $i] : big_q(W)) | big_q(W!3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(125,plain,
% 0.19/0.46 (~![W: $i] : big_q(W)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[124, 117])).
% 0.19/0.46 tff(126,plain,
% 0.19/0.46 ((~(big_q(U!2) | ![W: $i] : big_q(W))) | big_q(U!2) | ![W: $i] : big_q(W)),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(127,plain,
% 0.19/0.46 (big_q(U!2)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[126, 125, 120])).
% 0.19/0.46 tff(128,plain,
% 0.19/0.46 ((~(big_q(X1!4) <=> big_q(U!2))) | big_q(X1!4) | (~big_q(U!2))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(129,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[128, 127, 119, 115])).
% 0.19/0.46 tff(130,plain,(big_q(W!3) | (~(big_q(X1!4) <=> big_q(U!2))) | (~(big_q(U!2) | ![W: $i] : big_q(W))) | (~(big_q(X1!4) <=> big_q(W!3)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(131,plain,
% 0.19/0.46 (big_q(W!3)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[130, 114, 109, 107])).
% 0.19/0.46 tff(132,plain,
% 0.19/0.46 ((~((~big_q(W!3)) | ![U: $i] : (~big_q(U)))) | (~big_q(W!3)) | ![U: $i] : (~big_q(U))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(133,plain,
% 0.19/0.46 (![U: $i] : (~big_q(U))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[132, 131, 97])).
% 0.19/0.46 tff(134,plain,
% 0.19/0.46 ((~(big_q(X1!4) <=> big_q(W!3))) | big_q(X1!4) | (~big_q(W!3))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(135,plain,
% 0.19/0.46 (big_q(X1!4)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[134, 131, 107])).
% 0.19/0.46 tff(136,plain,
% 0.19/0.46 ((~(big_q(X1!4) <=> big_q(U!2))) | (~big_q(X1!4)) | big_q(U!2)),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(137,plain,
% 0.19/0.46 (big_q(U!2)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[136, 135, 114])).
% 0.19/0.46 tff(138,plain,
% 0.19/0.46 ((~![U: $i] : (~big_q(U))) | (~big_q(U!2))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(139,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[138, 137, 133])).
% 0.19/0.46 tff(140,plain,(((~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1))))))) | (~((~((~(big_p(U1!6) | ![W1: $i] : big_p(W1))) | (~((~big_p(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,[]))).
% 0.19/0.46 tff(141,plain,
% 0.19/0.46 ((~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1))))))) | (~((~((~(big_p(U1!6) | ![W1: $i] : big_p(W1))) | (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[140, 2])).
% 0.19/0.46 tff(142,plain,
% 0.19/0.46 (((~((~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W))) | (~(big_q(U!2) | (~big_q(W!3)))))))) | (~((~((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~(![U: $i] : (~big_q(U)) | (~big_q(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_p(W1))) | (~(big_p(U1!6) | (~big_p(W1!7)))))))) | (~((~((~(big_p(U1!6) | ![W1: $i] : big_p(W1))) | (~(![U1: $i] : (~big_p(U1)) | (~big_p(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_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W))))))) | (~((~((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(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_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1))))))) | (~((~((~(big_p(U1!6) | ![W1: $i] : big_p(W1))) | (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(143,plain,
% 0.19/0.46 (((~((~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W))) | (~(big_q(U!2) | (~big_q(W!3)))))))) | (~((~((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~(![U: $i] : (~big_q(U)) | (~big_q(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_p(W1))) | (~(big_p(U1!6) | (~big_p(W1!7)))))))) | (~((~((~(big_p(U1!6) | ![W1: $i] : big_p(W1))) | (~(![U1: $i] : (~big_p(U1)) | (~big_p(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_q(W))) | (~(big_q(U!2) | (~big_q(W!3)))))))) | (~((~((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~(![U: $i] : (~big_q(U)) | (~big_q(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_p(W1))) | (~(big_p(U1!6) | (~big_p(W1!7)))))))) | (~((~((~(big_p(U1!6) | ![W1: $i] : big_p(W1))) | (~(![U1: $i] : (~big_p(U1)) | (~big_p(W1!7)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(144,plain,
% 0.19/0.46 ((((![Y: $i] : (big_p(X!1) <=> big_p(Y)) | ((![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W)) & (big_q(U!2) | (~big_q(W!3))))) & (((big_q(U!2) | ![W: $i] : big_q(W)) & (![U: $i] : (~big_q(U)) | (~big_q(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_p(W1)) & (big_p(U1!6) | (~big_p(W1!7))))) & (((big_p(U1!6) | ![W1: $i] : big_p(W1)) & (![U1: $i] : (~big_p(U1)) | (~big_p(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_q(W))) | (~(big_q(U!2) | (~big_q(W!3)))))))) | (~((~((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~(![U: $i] : (~big_q(U)) | (~big_q(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_p(W1))) | (~(big_p(U1!6) | (~big_p(W1!7)))))))) | (~((~((~(big_p(U1!6) | ![W1: $i] : big_p(W1))) | (~(![U1: $i] : (~big_p(U1)) | (~big_p(W1!7)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(145,plain,
% 0.19/0.46 (((![Y: $i] : (big_p(X!1) <=> big_p(Y)) | ((![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W)) & (big_q(U!2) | (~big_q(W!3))))) & (((big_q(U!2) | ![W: $i] : big_q(W)) & (![U: $i] : (~big_q(U)) | (~big_q(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_p(W1)) & (big_p(U1!6) | (~big_p(W1!7))))) & (((big_p(U1!6) | ![W1: $i] : big_p(W1)) & (![U1: $i] : (~big_p(U1)) | (~big_p(W1!7)))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))))),
% 0.19/0.46 inference(and_elim,[status(thm)],[71])).
% 0.19/0.46 tff(146,plain,
% 0.19/0.46 ((~((~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W))) | (~(big_q(U!2) | (~big_q(W!3)))))))) | (~((~((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~(![U: $i] : (~big_q(U)) | (~big_q(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_p(W1))) | (~(big_p(U1!6) | (~big_p(W1!7)))))))) | (~((~((~(big_p(U1!6) | ![W1: $i] : big_p(W1))) | (~(![U1: $i] : (~big_p(U1)) | (~big_p(W1!7)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.19/0.46 tff(147,plain,
% 0.19/0.46 ((~((~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W))) | (~(big_q(U!2) | (~big_q(W!3)))))))) | (~((~((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~(![U: $i] : (~big_q(U)) | (~big_q(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_p(W1))) | (~(big_p(U1!6) | (~big_p(W1!7)))))))) | (~((~((~(big_p(U1!6) | ![W1: $i] : big_p(W1))) | (~(![U1: $i] : (~big_p(U1)) | (~big_p(W1!7)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[146, 143])).
% 0.19/0.46 tff(148,plain,
% 0.19/0.46 ((~((~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W))))))) | (~((~((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(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_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1))))))) | (~((~((~(big_p(U1!6) | ![W1: $i] : big_p(W1))) | (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[147, 142])).
% 0.19/0.46 tff(149,plain,
% 0.19/0.46 (~((~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W))))))) | (~((~((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[148, 141])).
% 0.19/0.46 tff(150,plain,
% 0.19/0.46 (((~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W))))))) | (~((~((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(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_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(151,plain,
% 0.19/0.46 ((~((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[150, 149])).
% 0.19/0.46 tff(152,plain,
% 0.19/0.46 (~![W1: $i] : big_p(W1)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[24, 3])).
% 0.19/0.46 tff(153,plain,
% 0.19/0.46 (((~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W))))))) | (~((~((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(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_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W))))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(154,plain,
% 0.19/0.46 (![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[153, 149])).
% 0.19/0.46 tff(155,plain,
% 0.19/0.46 (~![Y: $i] : (big_p(X!1) <=> big_p(Y))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[92, 85, 3])).
% 0.19/0.46 tff(156,plain,
% 0.19/0.46 ((big_p(U1!6) | ![W1: $i] : big_p(W1)) | (~big_p(U1!6))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(157,plain,
% 0.19/0.46 (big_p(U1!6) | ![W1: $i] : big_p(W1)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[156, 85])).
% 0.19/0.46 tff(158,plain,
% 0.19/0.46 (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[35, 157, 152])).
% 0.19/0.46 tff(159,plain,
% 0.19/0.46 ((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[37, 158])).
% 0.19/0.46 tff(160,plain,
% 0.19/0.46 (~((~((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[39, 159, 2])).
% 0.19/0.46 tff(161,plain,
% 0.19/0.46 ((~((~((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(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_p(W1))) | (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1))))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[41, 160])).
% 0.19/0.46 tff(162,plain,
% 0.19/0.46 (~((~((~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(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_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U)))))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[75, 161])).
% 0.19/0.46 tff(163,plain,
% 0.19/0.46 (![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[77, 162])).
% 0.19/0.46 tff(164,assumption,(~![W: $i] : big_q(W)), introduced(assumption)).
% 0.19/0.46 tff(165,plain,
% 0.19/0.46 ((~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W))))))) | ![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W)))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(166,plain,
% 0.19/0.46 (~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[165, 155, 154])).
% 0.19/0.46 tff(167,plain,
% 0.19/0.46 (((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W)))) | (![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(168,plain,
% 0.19/0.46 (![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[167, 166])).
% 0.19/0.46 tff(169,plain,
% 0.19/0.46 ((~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W))) | ![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W)),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(170,plain,
% 0.19/0.46 (![U: $i] : (~big_q(U))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[169, 168, 164])).
% 0.19/0.46 tff(171,assumption,(![U: $i] : (~big_q(U))), introduced(assumption)).
% 0.19/0.46 tff(172,assumption,(big_q(U!2)), introduced(assumption)).
% 0.19/0.46 tff(173,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[138, 172, 171])).
% 0.19/0.46 tff(174,plain,((~![U: $i] : (~big_q(U))) | (~big_q(U!2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(175,plain,
% 0.19/0.46 (~big_q(U!2)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[174, 170])).
% 0.19/0.46 tff(176,plain,
% 0.19/0.46 (~(big_q(U!2) | ![W: $i] : big_q(W))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[126, 175, 164])).
% 0.19/0.46 tff(177,plain,
% 0.19/0.46 ((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[108, 176])).
% 0.19/0.46 tff(178,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[94, 177, 163, 155])).
% 0.19/0.46 tff(179,plain,((~big_p(U1!6)) | ![W: $i] : big_q(W) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))) | big_p(W1!7)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(180,plain,
% 0.19/0.46 (~big_p(U1!6)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[179, 125, 2, 3])).
% 0.19/0.46 tff(181,assumption,(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W)))))), introduced(assumption)).
% 0.19/0.46 tff(182,assumption,(~big_p(U1!6)), introduced(assumption)).
% 0.19/0.46 tff(183,plain,
% 0.19/0.46 (~(big_p(U1!6) | ![W1: $i] : big_p(W1))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[31, 182, 27])).
% 0.19/0.46 tff(184,plain,
% 0.19/0.46 ((~(big_p(U1!6) | ![W1: $i] : big_p(W1))) | (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[9, 183])).
% 0.19/0.46 tff(185,plain,
% 0.19/0.46 ((~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | ![W1: $i] : big_p(W1))) | (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1)))))))) | ![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | ![W1: $i] : big_p(W1))) | (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1))))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(186,plain,
% 0.19/0.46 (~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | ![W1: $i] : big_p(W1))) | (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1)))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[185, 184, 1])).
% 0.19/0.46 tff(187,plain,
% 0.19/0.46 (((~((~((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(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_p(W1))) | (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1))))))))) | (![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | ![W1: $i] : big_p(W1))) | (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1)))))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(188,plain,
% 0.19/0.46 ((~((~((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(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_p(W1))) | (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1))))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[187, 186])).
% 0.19/0.46 tff(189,plain,
% 0.19/0.46 (~((~((~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(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_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U)))))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[75, 188])).
% 0.19/0.46 tff(190,plain,
% 0.19/0.46 (![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[77, 189])).
% 0.19/0.46 tff(191,assumption,((~((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))), introduced(assumption)).
% 0.19/0.46 tff(192,assumption,((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U))))), introduced(assumption)).
% 0.19/0.46 tff(193,plain,
% 0.19/0.46 ((~((~((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(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_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(194,plain,
% 0.19/0.46 (![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[193, 192, 191])).
% 0.19/0.46 tff(195,plain,
% 0.19/0.46 ((~![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))) | ((~big_p(U1!6)) <=> big_p(tptp_fun_Y_0(U1!6)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(196,plain,
% 0.19/0.46 ((~big_p(U1!6)) <=> big_p(tptp_fun_Y_0(U1!6))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[195, 194])).
% 0.19/0.46 tff(197,plain,
% 0.19/0.46 ((~((~big_p(U1!6)) <=> big_p(tptp_fun_Y_0(U1!6)))) | big_p(U1!6) | big_p(tptp_fun_Y_0(U1!6))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(198,plain,
% 0.19/0.46 ((~((~big_p(U1!6)) <=> big_p(tptp_fun_Y_0(U1!6)))) | big_p(tptp_fun_Y_0(U1!6))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[197, 182])).
% 0.19/0.46 tff(199,plain,
% 0.19/0.46 (big_p(tptp_fun_Y_0(U1!6))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[198, 196])).
% 0.19/0.46 tff(200,assumption,(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U))))))), introduced(assumption)).
% 0.19/0.46 tff(201,plain,
% 0.19/0.46 (![Y: $i] : (big_p(X!1) <=> big_p(Y))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[94, 192, 200])).
% 0.19/0.46 tff(202,plain,
% 0.19/0.46 (big_p(X!1) <=> big_p(U1!6)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[83, 201])).
% 0.19/0.46 tff(203,plain,
% 0.19/0.46 ((~(big_p(X!1) <=> big_p(U1!6))) | (~big_p(X!1)) | big_p(U1!6)),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(204,plain,
% 0.19/0.46 ((~(big_p(X!1) <=> big_p(U1!6))) | (~big_p(X!1))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[203, 182])).
% 0.19/0.46 tff(205,plain,
% 0.19/0.46 (~big_p(X!1)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[204, 202])).
% 0.19/0.46 tff(206,plain,
% 0.19/0.46 ((~(big_p(X!1) <=> big_p(tptp_fun_Y_0(U1!6)))) | big_p(X!1) | (~big_p(tptp_fun_Y_0(U1!6)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(207,plain,
% 0.19/0.46 (~(big_p(X!1) <=> big_p(tptp_fun_Y_0(U1!6)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[206, 205, 199])).
% 0.19/0.46 tff(208,plain,
% 0.19/0.46 ((~![Y: $i] : (big_p(X!1) <=> big_p(Y))) | (big_p(X!1) <=> big_p(tptp_fun_Y_0(U1!6)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(209,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[208, 201, 207])).
% 0.19/0.46 tff(210,plain,((~((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U)))))) | big_p(U1!6) | (~((~((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(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_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U))))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(211,plain,
% 0.19/0.46 (~((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[210, 182, 191, 190])).
% 0.19/0.46 tff(212,plain,
% 0.19/0.46 (big_q(U!2) | ![W: $i] : big_q(W)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[108, 211])).
% 0.19/0.46 tff(213,plain,
% 0.19/0.46 (big_q(U!2)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[126, 212, 164])).
% 0.19/0.46 tff(214,plain,
% 0.19/0.46 (~![U: $i] : (~big_q(U))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[174, 213])).
% 0.19/0.46 tff(215,plain,
% 0.19/0.46 (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[169, 214, 164])).
% 0.19/0.46 tff(216,plain,
% 0.19/0.46 ((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[167, 215])).
% 0.19/0.46 tff(217,plain,
% 0.19/0.47 (![Y: $i] : (big_p(X!1) <=> big_p(Y))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[165, 216, 181])).
% 0.19/0.47 tff(218,plain,
% 0.19/0.47 (big_p(X!1) <=> big_p(U1!6)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[83, 217])).
% 0.19/0.47 tff(219,plain,
% 0.19/0.47 (~big_p(X!1)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[204, 218])).
% 0.19/0.47 tff(220,plain,
% 0.19/0.47 (((~((~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(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_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U))))))))) | ((~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(221,plain,
% 0.19/0.47 ((~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[220, 189])).
% 0.19/0.47 tff(222,plain,
% 0.19/0.47 ((~((~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | (~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(223,plain,
% 0.19/0.47 (![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[222, 216, 221])).
% 0.19/0.47 tff(224,plain,
% 0.19/0.47 ((~big_p(U1!6)) <=> big_p(tptp_fun_Y_0(U1!6))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[195, 223])).
% 0.19/0.47 tff(225,plain,
% 0.19/0.47 (big_p(tptp_fun_Y_0(U1!6))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[198, 224])).
% 0.19/0.47 tff(226,plain,
% 0.19/0.47 (~(big_p(X!1) <=> big_p(tptp_fun_Y_0(U1!6)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[206, 225, 219])).
% 0.19/0.47 tff(227,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[208, 217, 226])).
% 0.19/0.47 tff(228,plain,(big_p(U1!6) | (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W))))))) | ![W: $i] : big_q(W) | (~((~((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(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)) | ![W1: $i] : big_p(W1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(229,plain,
% 0.19/0.47 (![Y1: $i] : (big_q(X1!4) <=> big_q(Y1))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[228, 180, 125, 151, 154, 152])).
% 0.19/0.47 tff(230,plain,
% 0.19/0.47 (big_q(X1!4) <=> big_q(U!2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[113, 229])).
% 0.19/0.47 tff(231,plain,
% 0.19/0.47 (big_q(X1!4) <=> big_q(W!3)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[106, 229])).
% 0.19/0.47 tff(232,plain,
% 0.19/0.47 (~(big_q(U!2) | ![W: $i] : big_q(W))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[130, 231, 117, 230])).
% 0.19/0.47 tff(233,plain,
% 0.19/0.47 ((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[108, 232])).
% 0.19/0.47 tff(234,plain,
% 0.19/0.47 (![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[193, 233, 151])).
% 0.19/0.47 tff(235,plain,
% 0.19/0.47 ((~big_p(U1!6)) <=> big_p(tptp_fun_Y_0(U1!6))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[195, 234])).
% 0.19/0.47 tff(236,plain,
% 0.19/0.47 ((~((~big_p(U1!6)) <=> big_p(tptp_fun_Y_0(U1!6)))) | big_p(tptp_fun_Y_0(U1!6))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[197, 180])).
% 0.19/0.47 tff(237,plain,
% 0.19/0.47 (big_p(tptp_fun_Y_0(U1!6))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[236, 235])).
% 0.19/0.47 tff(238,plain,
% 0.19/0.47 (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U)))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[210, 233, 151, 180])).
% 0.19/0.47 tff(239,plain,
% 0.19/0.47 ((~((~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(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_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U))))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[77, 238])).
% 0.19/0.47 tff(240,plain,
% 0.19/0.47 (~((~((~((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(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_p(W1))) | (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1)))))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[75, 239])).
% 0.19/0.47 tff(241,plain,
% 0.19/0.47 ((~((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[41, 240])).
% 0.19/0.47 tff(242,plain,
% 0.19/0.47 (~((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[39, 241, 2])).
% 0.19/0.47 tff(243,plain,
% 0.19/0.47 (![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[37, 242])).
% 0.19/0.47 tff(244,plain,
% 0.19/0.47 (![U1: $i] : (~big_p(U1))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[28, 243, 152])).
% 0.19/0.47 tff(245,plain,
% 0.19/0.47 ((~![U1: $i] : (~big_p(U1))) | (~big_p(tptp_fun_Y_0(U1!6)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(246,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[245, 244, 237])).
% 0.19/0.47 tff(247,plain,(big_q(W!3) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))) | big_p(W1!7)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(248,plain,
% 0.19/0.47 (big_q(W!3)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[247, 3, 2])).
% 0.19/0.47 tff(249,assumption,(big_q(W!3)), introduced(assumption)).
% 0.19/0.47 tff(250,plain,
% 0.19/0.47 ((~![U: $i] : (~big_q(U))) | (~big_q(W!3))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(251,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[250, 249, 171])).
% 0.19/0.47 tff(252,plain,((~![U: $i] : (~big_q(U))) | (~big_q(W!3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(253,plain,
% 0.19/0.47 (~![U: $i] : (~big_q(U))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[252, 248])).
% 0.19/0.47 tff(254,plain,
% 0.19/0.47 (~((~big_q(W!3)) | ![U: $i] : (~big_q(U)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[132, 253, 248])).
% 0.19/0.47 tff(255,plain,
% 0.19/0.47 ((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[96, 254])).
% 0.19/0.47 tff(256,plain,
% 0.19/0.47 (![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[193, 255, 151])).
% 0.19/0.47 tff(257,plain,
% 0.19/0.47 ((~![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))) | ((~big_p(W1!7)) <=> big_p(tptp_fun_Y_0(W1!7)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(258,plain,
% 0.19/0.47 ((~big_p(W1!7)) <=> big_p(tptp_fun_Y_0(W1!7))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[257, 256])).
% 0.19/0.47 tff(259,plain,
% 0.19/0.47 ((~((~big_p(W1!7)) <=> big_p(tptp_fun_Y_0(W1!7)))) | big_p(W1!7) | big_p(tptp_fun_Y_0(W1!7))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(260,plain,
% 0.19/0.47 ((~((~big_p(W1!7)) <=> big_p(tptp_fun_Y_0(W1!7)))) | big_p(tptp_fun_Y_0(W1!7))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[259, 3])).
% 0.19/0.47 tff(261,plain,
% 0.19/0.47 (big_p(tptp_fun_Y_0(W1!7))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[260, 258])).
% 0.19/0.47 tff(262,assumption,(big_p(tptp_fun_Y_0(W1!7))), introduced(assumption)).
% 0.19/0.47 tff(263,assumption,(![U1: $i] : (~big_p(U1))), introduced(assumption)).
% 0.19/0.47 tff(264,plain,
% 0.19/0.47 ((~![U1: $i] : (~big_p(U1))) | (~big_p(tptp_fun_Y_0(W1!7)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(265,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[264, 263, 262])).
% 0.19/0.47 tff(266,plain,((~![U1: $i] : (~big_p(U1))) | (~big_p(tptp_fun_Y_0(W1!7)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(267,plain,
% 0.19/0.47 (~![U1: $i] : (~big_p(U1))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[266, 261])).
% 0.19/0.47 tff(268,plain,
% 0.19/0.47 (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[28, 267, 152])).
% 0.19/0.47 tff(269,plain,
% 0.19/0.47 ((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[37, 268])).
% 0.19/0.47 tff(270,plain,
% 0.19/0.47 (~((~((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[39, 269, 2])).
% 0.19/0.47 tff(271,plain,
% 0.19/0.47 ((~((~((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(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_p(W1))) | (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1))))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[41, 270])).
% 0.19/0.47 tff(272,plain,
% 0.19/0.47 (~((~((~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(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_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U)))))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[75, 271])).
% 0.19/0.47 tff(273,plain,
% 0.19/0.47 (![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[77, 272])).
% 0.19/0.47 tff(274,plain,
% 0.19/0.47 (big_p(U1!6)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[210, 273, 151, 255])).
% 0.19/0.47 tff(275,plain,
% 0.19/0.47 (![Y: $i] : (big_p(X!1) <=> big_p(Y))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[94, 273, 255])).
% 0.19/0.47 tff(276,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[92, 275, 274, 3])).
% 0.19/0.47 tff(277,plain,(big_p(W1!7) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(278,plain,
% 0.19/0.47 (big_p(W1!7)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[277, 2])).
% 0.19/0.47 tff(279,plain,
% 0.19/0.47 (![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[193, 192, 151])).
% 0.19/0.47 tff(280,plain,
% 0.19/0.47 ((~((~big_p(W1!7)) <=> big_p(tptp_fun_Y_0(W1!7)))) | (~big_p(W1!7)) | (~big_p(tptp_fun_Y_0(W1!7)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(281,plain,
% 0.19/0.47 (~((~big_p(W1!7)) <=> big_p(tptp_fun_Y_0(W1!7)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[280, 14, 262])).
% 0.19/0.47 tff(282,assumption,(![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))), introduced(assumption)).
% 0.19/0.47 tff(283,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[257, 282, 281])).
% 0.19/0.47 tff(284,plain,((~![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))) | (~big_p(W1!7)) | (~big_p(tptp_fun_Y_0(W1!7)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(285,plain,
% 0.19/0.47 (~big_p(tptp_fun_Y_0(W1!7))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[284, 279, 278])).
% 0.19/0.47 tff(286,plain,
% 0.19/0.47 (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[19, 278])).
% 0.19/0.47 tff(287,plain,
% 0.19/0.47 (((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1))) | (~![U1: $i] : (~big_p(U1)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(288,plain,
% 0.19/0.47 (~![U1: $i] : (~big_p(U1))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[287, 286])).
% 0.19/0.47 tff(289,assumption,(~big_p(tptp_fun_Y_0(W1!7))), introduced(assumption)).
% 0.19/0.47 tff(290,plain,
% 0.19/0.47 ((~![W1: $i] : big_p(W1)) | big_p(tptp_fun_Y_0(W1!7))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(291,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[290, 21, 289])).
% 0.19/0.47 tff(292,plain,((~![W1: $i] : big_p(W1)) | big_p(tptp_fun_Y_0(W1!7))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(293,plain,
% 0.19/0.47 (~![W1: $i] : big_p(W1)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[292, 285])).
% 0.19/0.47 tff(294,plain,
% 0.19/0.47 (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[28, 293, 288])).
% 0.19/0.47 tff(295,plain,
% 0.19/0.47 ((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[37, 294])).
% 0.19/0.47 tff(296,plain,
% 0.19/0.47 (~((~((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[39, 295, 2])).
% 0.19/0.47 tff(297,plain,
% 0.19/0.47 ((~((~((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(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_p(W1))) | (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1))))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[41, 296])).
% 0.19/0.47 tff(298,plain,
% 0.19/0.47 (~((~((~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(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_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U)))))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[75, 297])).
% 0.19/0.47 tff(299,plain,
% 0.19/0.47 (![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[77, 298])).
% 0.19/0.47 tff(300,plain,
% 0.19/0.47 (![Y: $i] : (big_p(X!1) <=> big_p(Y))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[94, 299, 192])).
% 0.19/0.47 tff(301,assumption,(~(big_p(X!1) <=> big_p(tptp_fun_Y_0(W1!7)))), introduced(assumption)).
% 0.19/0.47 tff(302,plain,
% 0.19/0.47 ((~![Y: $i] : (big_p(X!1) <=> big_p(Y))) | (big_p(X!1) <=> big_p(tptp_fun_Y_0(W1!7)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(303,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[302, 80, 301])).
% 0.19/0.47 tff(304,plain,((big_p(X!1) <=> big_p(tptp_fun_Y_0(W1!7))) | (~![Y: $i] : (big_p(X!1) <=> big_p(Y)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(305,plain,
% 0.19/0.47 (big_p(X!1) <=> big_p(tptp_fun_Y_0(W1!7))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[304, 300])).
% 0.19/0.47 tff(306,plain,
% 0.19/0.47 ((~(big_p(X!1) <=> big_p(tptp_fun_Y_0(W1!7)))) | (~big_p(X!1)) | big_p(tptp_fun_Y_0(W1!7))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(307,plain,
% 0.19/0.47 (~big_p(X!1)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[306, 305, 285])).
% 0.19/0.47 tff(308,plain,
% 0.19/0.47 ((~(big_p(X!1) <=> big_p(W1!7))) | big_p(X!1) | (~big_p(W1!7))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(309,plain,
% 0.19/0.47 (~(big_p(X!1) <=> big_p(W1!7))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[308, 278, 307])).
% 0.19/0.47 tff(310,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[81, 300, 309])).
% 0.19/0.47 tff(311,plain,((~((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(312,plain,
% 0.19/0.47 (~((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U)))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[311, 2])).
% 0.19/0.47 tff(313,plain,
% 0.19/0.47 ((~big_q(W!3)) | ![U: $i] : (~big_q(U))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[96, 312])).
% 0.19/0.47 tff(314,assumption,((~big_q(W!3)) | ![U: $i] : (~big_q(U))), introduced(assumption)).
% 0.19/0.47 tff(315,plain,
% 0.19/0.47 (~![U: $i] : (~big_q(U))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[252, 249])).
% 0.19/0.47 tff(316,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[132, 315, 249, 314])).
% 0.19/0.47 tff(317,plain,((~big_q(W!3)) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(318,plain,
% 0.19/0.47 (~big_q(W!3)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[317, 313])).
% 0.19/0.47 tff(319,plain,
% 0.19/0.47 (~![W: $i] : big_q(W)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[124, 318])).
% 0.19/0.47 tff(320,assumption,((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W)))), introduced(assumption)).
% 0.19/0.47 tff(321,plain,
% 0.19/0.47 (![Y: $i] : (big_p(X!1) <=> big_p(Y))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[165, 320, 181])).
% 0.19/0.47 tff(322,plain,
% 0.19/0.47 (big_p(X!1) <=> big_p(tptp_fun_Y_0(W1!7))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[304, 321])).
% 0.19/0.47 tff(323,plain,
% 0.19/0.47 (big_p(X!1) <=> big_p(W1!7)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[81, 321])).
% 0.19/0.47 tff(324,plain,
% 0.19/0.47 ((~(big_p(X!1) <=> big_p(W1!7))) | big_p(X!1)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[308, 14])).
% 0.19/0.47 tff(325,plain,
% 0.19/0.47 (big_p(X!1)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[324, 323])).
% 0.19/0.47 tff(326,plain,
% 0.19/0.47 ((~(big_p(X!1) <=> big_p(tptp_fun_Y_0(W1!7)))) | big_p(tptp_fun_Y_0(W1!7))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[306, 325])).
% 0.19/0.47 tff(327,plain,
% 0.19/0.47 (big_p(tptp_fun_Y_0(W1!7))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[326, 322])).
% 0.19/0.47 tff(328,plain,
% 0.19/0.47 (~![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[284, 327, 14])).
% 0.19/0.47 tff(329,plain,
% 0.19/0.47 (~((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U)))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[193, 328, 191])).
% 0.19/0.47 tff(330,plain,
% 0.19/0.47 (big_q(U!2) | ![W: $i] : big_q(W)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[108, 329])).
% 0.19/0.47 tff(331,plain,
% 0.19/0.47 (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[19, 14])).
% 0.19/0.47 tff(332,plain,
% 0.19/0.47 ((~(big_p(U1!6) | ![W1: $i] : big_p(W1))) | (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[11, 331])).
% 0.19/0.47 tff(333,plain,
% 0.19/0.47 (~((~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[222, 328, 320])).
% 0.19/0.47 tff(334,plain,
% 0.19/0.47 ((~((~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(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_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U))))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[220, 333])).
% 0.19/0.47 tff(335,plain,
% 0.19/0.47 (~((~((~((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(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_p(W1))) | (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1)))))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[75, 334])).
% 0.19/0.47 tff(336,plain,
% 0.19/0.47 (![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | ![W1: $i] : big_p(W1))) | (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[187, 335])).
% 0.19/0.47 tff(337,plain,
% 0.19/0.47 (![Y1: $i] : (big_q(X1!4) <=> big_q(Y1))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[185, 336, 332])).
% 0.19/0.47 tff(338,plain,
% 0.19/0.47 (big_q(X1!4) <=> big_q(U!2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[113, 337])).
% 0.19/0.47 tff(339,plain,
% 0.19/0.47 (big_q(X1!4) <=> big_q(W!3)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[106, 337])).
% 0.19/0.47 tff(340,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[130, 339, 338, 330, 117])).
% 0.19/0.47 tff(341,plain,((~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W))))) | big_q(W!3) | (~((~((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))) | (~big_p(W1!7)) | (~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W)))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(342,plain,
% 0.19/0.47 (~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[341, 318, 151, 278, 154])).
% 0.19/0.47 tff(343,plain,
% 0.19/0.47 (![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[167, 342])).
% 0.19/0.47 tff(344,plain,
% 0.19/0.47 (big_q(U!2) | ![W: $i] : big_q(W)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[108, 312])).
% 0.19/0.47 tff(345,plain,
% 0.19/0.47 (big_q(U!2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[126, 319, 344])).
% 0.19/0.47 tff(346,plain,
% 0.19/0.47 (~![U: $i] : (~big_q(U))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[174, 345])).
% 0.19/0.47 tff(347,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[169, 346, 343, 319])).
% 0.19/0.47 tff(348,plain,(![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(349,plain,
% 0.19/0.47 ((~![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))) | ((~big_q(elem!8)) <=> big_q(tptp_fun_Y1_5(elem!8)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(350,plain,
% 0.19/0.47 ((~big_q(elem!8)) <=> big_q(tptp_fun_Y1_5(elem!8))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[349, 348])).
% 0.19/0.47 tff(351,assumption,(big_q(elem!8)), introduced(assumption)).
% 0.19/0.47 tff(352,plain,
% 0.19/0.47 ((~![W: $i] : big_q(W)) | big_q(tptp_fun_Y1_5(elem!8))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(353,plain,
% 0.19/0.47 (big_q(tptp_fun_Y1_5(elem!8))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[352, 121])).
% 0.19/0.47 tff(354,plain,
% 0.19/0.47 ((~((~big_q(elem!8)) <=> big_q(tptp_fun_Y1_5(elem!8)))) | (~big_q(elem!8)) | (~big_q(tptp_fun_Y1_5(elem!8)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(355,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[354, 353, 351, 350])).
% 0.19/0.47 tff(356,plain,((~big_q(elem!8)) | (~![W: $i] : big_q(W))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(357,plain,
% 0.19/0.47 (~big_q(elem!8)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[356, 121])).
% 0.19/0.47 tff(358,plain,
% 0.19/0.47 ((~![W: $i] : big_q(W)) | big_q(elem!8)),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(359,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[358, 121, 357])).
% 0.19/0.47 tff(360,plain,(~![W: $i] : big_q(W)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(361,plain,
% 0.19/0.47 ((~![U: $i] : (~big_q(U))) | (~big_q(elem!8))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(362,plain,
% 0.19/0.47 (~big_q(elem!8)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[361, 171])).
% 0.19/0.47 tff(363,plain,
% 0.19/0.47 ((~![U: $i] : (~big_q(U))) | (~big_q(tptp_fun_Y1_5(elem!8)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(364,plain,
% 0.19/0.47 (~big_q(tptp_fun_Y1_5(elem!8))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[363, 171])).
% 0.19/0.47 tff(365,plain,
% 0.19/0.47 ((~((~big_q(elem!8)) <=> big_q(tptp_fun_Y1_5(elem!8)))) | big_q(elem!8) | big_q(tptp_fun_Y1_5(elem!8))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(366,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[365, 364, 362, 350])).
% 0.19/0.47 tff(367,plain,(~![U: $i] : (~big_q(U))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(368,plain,
% 0.19/0.47 (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[169, 164, 367])).
% 0.19/0.47 tff(369,plain,
% 0.19/0.47 ((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[167, 368])).
% 0.19/0.47 tff(370,plain,
% 0.19/0.47 (![U1: $i] : (~big_p(U1))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[28, 26, 152])).
% 0.19/0.47 tff(371,plain,
% 0.19/0.47 (~big_p(tptp_fun_Y_0(W1!7))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[266, 370])).
% 0.19/0.47 tff(372,plain,
% 0.19/0.47 (~((~big_p(W1!7)) <=> big_p(tptp_fun_Y_0(W1!7)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[259, 3, 371])).
% 0.19/0.47 tff(373,plain,
% 0.19/0.47 (~(big_p(U1!6) | ![W1: $i] : big_p(W1))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[35, 26, 152])).
% 0.19/0.47 tff(374,plain,
% 0.19/0.47 ((~(big_p(U1!6) | ![W1: $i] : big_p(W1))) | (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[9, 373])).
% 0.19/0.47 tff(375,plain,
% 0.19/0.47 (~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | ![W1: $i] : big_p(W1))) | (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1)))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[185, 374, 1])).
% 0.19/0.47 tff(376,plain,
% 0.19/0.47 ((~((~((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(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_p(W1))) | (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1))))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[187, 375])).
% 0.19/0.47 tff(377,plain,
% 0.19/0.47 (~((~((~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(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_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U)))))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[75, 376])).
% 0.19/0.47 tff(378,plain,
% 0.19/0.47 ((~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[220, 377])).
% 0.19/0.47 tff(379,plain,
% 0.19/0.47 (![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[222, 378, 320])).
% 0.19/0.47 tff(380,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[257, 379, 372])).
% 0.19/0.47 tff(381,plain,((~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1))) | big_p(W1!7) | (~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W))))) | ![Y1: $i] : (big_q(X1!4) <=> big_q(Y1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(382,plain,
% 0.19/0.47 (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[381, 1, 3, 369])).
% 0.19/0.47 tff(383,plain,
% 0.19/0.47 ((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[37, 382])).
% 0.19/0.47 tff(384,plain,
% 0.19/0.47 (~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[100, 383, 1])).
% 0.19/0.47 tff(385,plain,
% 0.19/0.47 ((~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1))))))) | (~((~((~(big_p(U1!6) | ![W1: $i] : big_p(W1))) | (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[98, 384])).
% 0.19/0.47 tff(386,plain,
% 0.19/0.47 (~((~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W))))))) | (~((~((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[148, 385])).
% 0.19/0.47 tff(387,plain,
% 0.19/0.47 (![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W)))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[153, 386])).
% 0.19/0.47 tff(388,plain,
% 0.19/0.47 (![Y: $i] : (big_p(X!1) <=> big_p(Y))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[165, 387, 369])).
% 0.19/0.47 tff(389,plain,
% 0.19/0.47 ((~((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[150, 386])).
% 0.19/0.47 tff(390,plain,
% 0.19/0.47 (big_p(U1!6)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[228, 389, 152, 387, 1, 164])).
% 0.19/0.47 tff(391,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[92, 390, 388, 3])).
% 0.19/0.47 tff(392,plain,(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | big_p(W1!7) | ![W: $i] : big_q(W)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(393,plain,
% 0.19/0.47 (![Y1: $i] : (big_q(X1!4) <=> big_q(Y1))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[392, 3, 360])).
% 0.19/0.47 tff(394,plain,
% 0.19/0.47 ((~![Y1: $i] : (big_q(X1!4) <=> big_q(Y1))) | (big_q(X1!4) <=> big_q(elem!8))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(395,plain,
% 0.19/0.47 (big_q(X1!4) <=> big_q(elem!8)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[394, 393])).
% 0.19/0.47 tff(396,plain,
% 0.19/0.47 (![Y1: $i] : (big_q(X1!4) <=> big_q(Y1))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[392, 125, 3])).
% 0.19/0.47 tff(397,plain,
% 0.19/0.47 (big_q(X1!4) <=> big_q(elem!8)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[394, 396])).
% 0.19/0.47 tff(398,plain,
% 0.19/0.47 (((~big_q(W!3)) | ![U: $i] : (~big_q(U))) | big_q(W!3)),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(399,plain,
% 0.19/0.47 ((~big_q(W!3)) | ![U: $i] : (~big_q(U))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[398, 117])).
% 0.19/0.47 tff(400,assumption,(~((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U)))))), introduced(assumption)).
% 0.19/0.47 tff(401,plain,
% 0.19/0.47 (big_q(U!2) | ![W: $i] : big_q(W)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[108, 400])).
% 0.19/0.47 tff(402,plain,
% 0.19/0.47 (((~((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(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_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U)))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(403,plain,
% 0.19/0.47 ((~((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[402, 400])).
% 0.19/0.47 tff(404,plain,
% 0.19/0.47 (big_q(X1!4) <=> big_q(U!2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[113, 103])).
% 0.19/0.47 tff(405,plain,
% 0.19/0.47 (big_q(X1!4) <=> big_q(W!3)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[106, 103])).
% 0.19/0.47 tff(406,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[130, 405, 404, 117, 120])).
% 0.19/0.47 tff(407,plain,((~![Y1: $i] : (big_q(X1!4) <=> big_q(Y1))) | big_q(W!3) | (~(big_q(U!2) | ![W: $i] : big_q(W)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(408,plain,
% 0.19/0.47 (~![Y1: $i] : (big_q(X1!4) <=> big_q(Y1))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[407, 401, 117])).
% 0.19/0.47 tff(409,plain,
% 0.19/0.47 (big_q(U!2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[126, 401, 125])).
% 0.19/0.47 tff(410,plain,
% 0.19/0.47 (~![U: $i] : (~big_q(U))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[174, 409])).
% 0.19/0.47 tff(411,plain,
% 0.19/0.47 (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[169, 410, 125])).
% 0.19/0.47 tff(412,plain,
% 0.19/0.47 ((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[167, 411])).
% 0.19/0.48 tff(413,plain,
% 0.19/0.48 (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[381, 412, 3, 408])).
% 0.19/0.48 tff(414,plain,
% 0.19/0.48 ((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[37, 413])).
% 0.19/0.48 tff(415,plain,
% 0.19/0.48 (~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[100, 414, 408])).
% 0.19/0.48 tff(416,plain,
% 0.19/0.48 ((~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1))))))) | (~((~((~(big_p(U1!6) | ![W1: $i] : big_p(W1))) | (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[98, 415])).
% 0.19/0.48 tff(417,plain,
% 0.19/0.48 (~((~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W))))))) | (~((~((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[148, 416])).
% 0.19/0.48 tff(418,plain,
% 0.19/0.48 (![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W)))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[153, 417])).
% 0.19/0.48 tff(419,plain,
% 0.19/0.48 (![Y1: $i] : (big_q(X1!4) <=> big_q(Y1))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[228, 125, 182, 191, 181, 27])).
% 0.19/0.48 tff(420,plain,
% 0.19/0.48 (big_q(X1!4) <=> big_q(U!2)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[113, 419])).
% 0.19/0.48 tff(421,plain,
% 0.19/0.48 (big_q(X1!4) <=> big_q(W!3)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[106, 419])).
% 0.19/0.48 tff(422,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[130, 421, 420, 120, 117])).
% 0.19/0.48 tff(423,plain,(big_q(W!3) | (~(big_q(U!2) | ![W: $i] : big_q(W))) | big_p(U1!6) | (~((~((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(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_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W))))))) | ![W1: $i] : big_p(W1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(424,plain,
% 0.19/0.48 (big_p(U1!6)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[423, 418, 152, 117, 403, 401])).
% 0.19/0.48 tff(425,plain,
% 0.19/0.48 (![Y: $i] : (big_p(X!1) <=> big_p(Y))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[165, 418, 412])).
% 0.19/0.48 tff(426,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[92, 425, 424, 3])).
% 0.19/0.48 tff(427,plain,(((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U))))) | big_p(W1!7) | big_q(W!3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(428,plain,
% 0.19/0.48 ((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[427, 117, 3])).
% 0.19/0.48 tff(429,plain,
% 0.19/0.48 ((~((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U)))))) | (~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(430,plain,
% 0.19/0.48 (~(big_q(U!2) | ![W: $i] : big_q(W))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[429, 428, 399])).
% 0.19/0.48 tff(431,plain,
% 0.19/0.48 ((big_q(U!2) | ![W: $i] : big_q(W)) | (~big_q(U!2))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(432,plain,
% 0.19/0.48 (~big_q(U!2)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[431, 430])).
% 0.19/0.48 tff(433,plain,
% 0.19/0.48 (big_q(X1!4) <=> big_q(U!2)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[113, 396])).
% 0.19/0.48 tff(434,plain,
% 0.19/0.48 (~big_q(X1!4)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[136, 433, 432])).
% 0.19/0.48 tff(435,plain,
% 0.19/0.48 ((~(big_q(X1!4) <=> big_q(elem!8))) | big_q(X1!4) | (~big_q(elem!8))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(436,plain,
% 0.19/0.48 ((~(big_q(X1!4) <=> big_q(elem!8))) | (~big_q(elem!8))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[435, 434])).
% 0.19/0.48 tff(437,plain,
% 0.19/0.48 (~big_q(elem!8)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[436, 397])).
% 0.19/0.48 tff(438,plain,
% 0.19/0.48 ((~![Y1: $i] : (big_q(X1!4) <=> big_q(Y1))) | (big_q(X1!4) <=> big_q(tptp_fun_Y1_5(elem!8)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(439,plain,
% 0.19/0.48 (big_q(X1!4) <=> big_q(tptp_fun_Y1_5(elem!8))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[438, 396])).
% 0.19/0.48 tff(440,plain,
% 0.19/0.48 ((~(big_q(X1!4) <=> big_q(tptp_fun_Y1_5(elem!8)))) | big_q(X1!4) | (~big_q(tptp_fun_Y1_5(elem!8)))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(441,plain,
% 0.19/0.48 ((~(big_q(X1!4) <=> big_q(tptp_fun_Y1_5(elem!8)))) | (~big_q(tptp_fun_Y1_5(elem!8)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[440, 434])).
% 0.19/0.48 tff(442,plain,
% 0.19/0.48 (~big_q(tptp_fun_Y1_5(elem!8))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[441, 439])).
% 0.19/0.48 tff(443,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[365, 442, 437, 350])).
% 0.19/0.48 tff(444,plain,(big_q(W!3) | big_p(W1!7)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(445,plain,
% 0.19/0.48 (big_q(W!3)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[444, 3])).
% 0.19/0.48 tff(446,plain,
% 0.19/0.48 (big_q(X1!4) <=> big_q(W!3)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[106, 393])).
% 0.19/0.48 tff(447,plain,
% 0.19/0.48 (big_q(X1!4)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[134, 446, 445])).
% 0.19/0.48 tff(448,plain,
% 0.19/0.48 ((~(big_q(X1!4) <=> big_q(elem!8))) | (~big_q(X1!4)) | big_q(elem!8)),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(449,plain,
% 0.19/0.48 ((~(big_q(X1!4) <=> big_q(elem!8))) | big_q(elem!8)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[448, 447])).
% 0.19/0.48 tff(450,plain,
% 0.19/0.48 (big_q(elem!8)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[449, 395])).
% 0.19/0.48 tff(451,plain,
% 0.19/0.48 (big_q(X1!4) <=> big_q(tptp_fun_Y1_5(elem!8))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[438, 393])).
% 0.19/0.48 tff(452,plain,
% 0.19/0.48 ((~(big_q(X1!4) <=> big_q(tptp_fun_Y1_5(elem!8)))) | (~big_q(X1!4)) | big_q(tptp_fun_Y1_5(elem!8))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(453,plain,
% 0.19/0.48 ((~(big_q(X1!4) <=> big_q(tptp_fun_Y1_5(elem!8)))) | big_q(tptp_fun_Y1_5(elem!8))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[452, 447])).
% 0.19/0.48 tff(454,plain,
% 0.19/0.48 (big_q(tptp_fun_Y1_5(elem!8))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[453, 451])).
% 0.19/0.48 tff(455,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[354, 454, 450, 350])).
% 0.19/0.48 tff(456,plain,(big_p(W1!7)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(457,plain,
% 0.19/0.48 (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[19, 456])).
% 0.19/0.48 tff(458,plain,
% 0.19/0.48 ((~(big_p(U1!6) | ![W1: $i] : big_p(W1))) | (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[11, 457])).
% 0.19/0.48 tff(459,plain,
% 0.19/0.48 ((~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | ![W1: $i] : big_p(W1))) | (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1)))))))) | ![Y1: $i] : (big_q(X1!4) <=> big_q(Y1))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[185, 458])).
% 0.19/0.48 tff(460,plain,
% 0.19/0.48 (~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | ![W1: $i] : big_p(W1))) | (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1)))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[459, 1])).
% 0.19/0.48 tff(461,plain,
% 0.19/0.48 ((~((~((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(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_p(W1))) | (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1))))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[187, 460])).
% 0.19/0.48 tff(462,plain,
% 0.19/0.48 (~((~((~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(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_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U)))))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[75, 461])).
% 0.19/0.48 tff(463,plain,
% 0.19/0.48 ((~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[220, 462])).
% 0.19/0.48 tff(464,plain,
% 0.19/0.48 (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[169, 360, 367])).
% 0.19/0.48 tff(465,plain,
% 0.19/0.48 ((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[167, 464])).
% 0.19/0.48 tff(466,plain,
% 0.19/0.48 ((~((~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(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)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[222, 465])).
% 0.19/0.48 tff(467,plain,
% 0.19/0.48 (![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[466, 463])).
% 0.19/0.48 tff(468,plain,
% 0.19/0.48 ((~![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))) | ((~big_p(tptp_fun_Y1_5(tptp_fun_Y1_5(elem!8)))) <=> big_p(tptp_fun_Y_0(tptp_fun_Y1_5(tptp_fun_Y1_5(elem!8)))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(469,plain,
% 0.19/0.48 ((~big_p(tptp_fun_Y1_5(tptp_fun_Y1_5(elem!8)))) <=> big_p(tptp_fun_Y_0(tptp_fun_Y1_5(tptp_fun_Y1_5(elem!8))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[468, 467])).
% 0.19/0.48 tff(470,plain,
% 0.19/0.48 ((~![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))) | (~big_p(tptp_fun_Y_0(W1!7)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[284, 456])).
% 0.19/0.48 tff(471,plain,
% 0.19/0.48 (~big_p(tptp_fun_Y_0(W1!7))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[470, 467])).
% 0.19/0.48 tff(472,plain,
% 0.19/0.48 (~![W1: $i] : big_p(W1)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[292, 471])).
% 0.19/0.48 tff(473,plain,
% 0.19/0.48 (~![U1: $i] : (~big_p(U1))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[287, 457])).
% 0.19/0.48 tff(474,plain,
% 0.19/0.48 ((~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1))) | ![W1: $i] : big_p(W1)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[28, 473])).
% 0.19/0.48 tff(475,plain,
% 0.19/0.48 (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[474, 472])).
% 0.19/0.48 tff(476,plain,
% 0.19/0.48 ((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[37, 475])).
% 0.19/0.48 tff(477,plain,
% 0.19/0.48 (~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[100, 476, 1])).
% 0.19/0.48 tff(478,plain,
% 0.19/0.48 ((~(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1)) | (~((~(big_p(U1!6) | (~big_p(W1!7)))) | (~(![U1: $i] : (~big_p(U1)) | ![W1: $i] : big_p(W1))))))) | (~((~((~(big_p(U1!6) | ![W1: $i] : big_p(W1))) | (~((~big_p(W1!7)) | ![U1: $i] : (~big_p(U1)))))) | ![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[98, 477])).
% 0.19/0.48 tff(479,plain,
% 0.19/0.48 (~((~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W))))))) | (~((~((~(big_q(U!2) | ![W: $i] : big_q(W))) | (~((~big_q(W!3)) | ![U: $i] : (~big_q(U)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[148, 478])).
% 0.19/0.48 tff(480,plain,
% 0.19/0.48 (![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W)))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[153, 479])).
% 0.19/0.48 tff(481,plain,
% 0.19/0.48 ((~(![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_q(U!2) | (~big_q(W!3)))) | (~(![U: $i] : (~big_q(U)) | ![W: $i] : big_q(W))))))) | ![Y: $i] : (big_p(X!1) <=> big_p(Y))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[165, 465])).
% 0.19/0.48 tff(482,plain,
% 0.19/0.48 (![Y: $i] : (big_p(X!1) <=> big_p(Y))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[481, 480])).
% 0.19/0.48 tff(483,plain,
% 0.19/0.48 ((~![Y: $i] : (big_p(X!1) <=> big_p(Y))) | (big_p(X!1) <=> big_p(tptp_fun_Y1_5(tptp_fun_Y1_5(elem!8))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(484,plain,
% 0.19/0.48 (big_p(X!1) <=> big_p(tptp_fun_Y1_5(tptp_fun_Y1_5(elem!8)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[483, 482])).
% 0.19/0.48 tff(485,plain,
% 0.19/0.48 (big_p(X!1) <=> big_p(tptp_fun_Y_0(W1!7))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[304, 482])).
% 0.19/0.48 tff(486,plain,
% 0.19/0.48 (~big_p(X!1)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[306, 485, 471])).
% 0.19/0.48 tff(487,plain,
% 0.19/0.48 ((~(big_p(X!1) <=> big_p(tptp_fun_Y1_5(tptp_fun_Y1_5(elem!8))))) | big_p(X!1) | (~big_p(tptp_fun_Y1_5(tptp_fun_Y1_5(elem!8))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(488,plain,
% 0.19/0.48 ((~(big_p(X!1) <=> big_p(tptp_fun_Y1_5(tptp_fun_Y1_5(elem!8))))) | (~big_p(tptp_fun_Y1_5(tptp_fun_Y1_5(elem!8))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[487, 486])).
% 0.19/0.48 tff(489,plain,
% 0.19/0.48 (~big_p(tptp_fun_Y1_5(tptp_fun_Y1_5(elem!8)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[488, 484])).
% 0.19/0.48 tff(490,plain,
% 0.19/0.48 ((~![Y: $i] : (big_p(X!1) <=> big_p(Y))) | (big_p(X!1) <=> big_p(tptp_fun_Y_0(tptp_fun_Y1_5(tptp_fun_Y1_5(elem!8)))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(491,plain,
% 0.19/0.48 (big_p(X!1) <=> big_p(tptp_fun_Y_0(tptp_fun_Y1_5(tptp_fun_Y1_5(elem!8))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[490, 482])).
% 0.19/0.48 tff(492,plain,
% 0.19/0.48 ((~(big_p(X!1) <=> big_p(tptp_fun_Y_0(tptp_fun_Y1_5(tptp_fun_Y1_5(elem!8)))))) | big_p(X!1) | (~big_p(tptp_fun_Y_0(tptp_fun_Y1_5(tptp_fun_Y1_5(elem!8)))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(493,plain,
% 0.19/0.48 ((~(big_p(X!1) <=> big_p(tptp_fun_Y_0(tptp_fun_Y1_5(tptp_fun_Y1_5(elem!8)))))) | (~big_p(tptp_fun_Y_0(tptp_fun_Y1_5(tptp_fun_Y1_5(elem!8)))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[492, 486])).
% 0.19/0.48 tff(494,plain,
% 0.19/0.48 (~big_p(tptp_fun_Y_0(tptp_fun_Y1_5(tptp_fun_Y1_5(elem!8))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[493, 491])).
% 0.19/0.48 tff(495,plain,
% 0.19/0.48 ((~((~big_p(tptp_fun_Y1_5(tptp_fun_Y1_5(elem!8)))) <=> big_p(tptp_fun_Y_0(tptp_fun_Y1_5(tptp_fun_Y1_5(elem!8)))))) | big_p(tptp_fun_Y1_5(tptp_fun_Y1_5(elem!8))) | big_p(tptp_fun_Y_0(tptp_fun_Y1_5(tptp_fun_Y1_5(elem!8))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(496,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[495, 494, 489, 469])).
% 0.19/0.48 tff(497,plain,(![Y1: $i] : (big_q(X1!4) <=> big_q(Y1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(498,plain,
% 0.19/0.48 ((~![Y1: $i] : (big_q(X1!4) <=> big_q(Y1))) | (big_q(X1!4) <=> big_q(tptp_fun_Y1_5(X1!4)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(499,plain,
% 0.19/0.48 (big_q(X1!4) <=> big_q(tptp_fun_Y1_5(X1!4))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[498, 497])).
% 0.19/0.48 tff(500,assumption,(~big_q(X1!4)), introduced(assumption)).
% 0.19/0.48 tff(501,plain,
% 0.19/0.48 ((~![X1: $i] : ((~big_q(X1)) <=> big_q(tptp_fun_Y1_5(X1)))) | ((~big_q(X1!4)) <=> big_q(tptp_fun_Y1_5(X1!4)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(502,plain,
% 0.19/0.48 ((~big_q(X1!4)) <=> big_q(tptp_fun_Y1_5(X1!4))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[501, 348])).
% 0.19/0.48 tff(503,plain,
% 0.19/0.48 ((~((~big_q(X1!4)) <=> big_q(tptp_fun_Y1_5(X1!4)))) | big_q(X1!4) | big_q(tptp_fun_Y1_5(X1!4))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(504,plain,
% 0.19/0.48 (big_q(tptp_fun_Y1_5(X1!4))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[503, 500, 502])).
% 0.19/0.48 tff(505,plain,
% 0.19/0.48 ((~(big_q(X1!4) <=> big_q(tptp_fun_Y1_5(X1!4)))) | big_q(X1!4) | (~big_q(tptp_fun_Y1_5(X1!4)))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(506,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[505, 504, 500, 499])).
% 0.19/0.48 tff(507,plain,(big_q(X1!4)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(508,plain,
% 0.19/0.48 ((~((~big_q(X1!4)) <=> big_q(tptp_fun_Y1_5(X1!4)))) | (~big_q(X1!4)) | (~big_q(tptp_fun_Y1_5(X1!4)))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(509,plain,
% 0.19/0.48 (~big_q(tptp_fun_Y1_5(X1!4))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[508, 507, 502])).
% 0.19/0.48 tff(510,plain,
% 0.19/0.48 ((~(big_q(X1!4) <=> big_q(tptp_fun_Y1_5(X1!4)))) | (~big_q(X1!4)) | big_q(tptp_fun_Y1_5(X1!4))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(511,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[510, 509, 507, 499])).
% 0.19/0.48 % SZS output end Proof
%------------------------------------------------------------------------------