TSTP Solution File: LCL654+1.001 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL654+1.001 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 : Sun Sep 18 04:57:27 EDT 2022
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL654+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Sep 1 23:08:02 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(r1_type, type, (
% 0.13/0.40 r1: ( $i * $i ) > $o)).
% 0.13/0.40 tff(tptp_fun_X_7_type, type, (
% 0.13/0.40 tptp_fun_X_7: $i)).
% 0.13/0.40 tff(p1_type, type, (
% 0.13/0.40 p1: $i > $o)).
% 0.13/0.40 tff(tptp_fun_X_4_type, type, (
% 0.13/0.40 tptp_fun_X_4: $i > $i)).
% 0.13/0.40 tff(tptp_fun_Y_2_type, type, (
% 0.13/0.40 tptp_fun_Y_2: $i > $i)).
% 0.13/0.40 tff(tptp_fun_Y_6_type, type, (
% 0.13/0.40 tptp_fun_Y_6: $i)).
% 0.13/0.40 tff(tptp_fun_Y_3_type, type, (
% 0.13/0.40 tptp_fun_Y_3: $i > $i)).
% 0.13/0.40 tff(tptp_fun_Y_8_type, type, (
% 0.13/0.40 tptp_fun_Y_8: $i)).
% 0.13/0.40 tff(tptp_fun_X_0_type, type, (
% 0.13/0.40 tptp_fun_X_0: $i)).
% 0.13/0.40 tff(tptp_fun_X_5_type, type, (
% 0.13/0.40 tptp_fun_X_5: $i > $i)).
% 0.13/0.40 tff(tptp_fun_Y_1_type, type, (
% 0.13/0.40 tptp_fun_Y_1: $i > $i)).
% 0.13/0.40 tff(1,assumption,(~(p1(tptp_fun_X_4(tptp_fun_Y_2(X!7))) | (~r1(tptp_fun_Y_2(X!7), tptp_fun_X_4(tptp_fun_Y_2(X!7)))))), introduced(assumption)).
% 0.13/0.40 tff(2,plain,
% 0.13/0.40 ((p1(tptp_fun_X_4(tptp_fun_Y_2(X!7))) | (~r1(tptp_fun_Y_2(X!7), tptp_fun_X_4(tptp_fun_Y_2(X!7))))) | r1(tptp_fun_Y_2(X!7), tptp_fun_X_4(tptp_fun_Y_2(X!7)))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(3,plain,
% 0.13/0.40 (r1(tptp_fun_Y_2(X!7), tptp_fun_X_4(tptp_fun_Y_2(X!7)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.13/0.40 tff(4,plain,
% 0.13/0.40 ((p1(tptp_fun_X_4(tptp_fun_Y_2(X!7))) | (~r1(tptp_fun_Y_2(X!7), tptp_fun_X_4(tptp_fun_Y_2(X!7))))) | (~p1(tptp_fun_X_4(tptp_fun_Y_2(X!7))))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(5,plain,
% 0.13/0.40 (~p1(tptp_fun_X_4(tptp_fun_Y_2(X!7)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.13/0.40 tff(6,assumption,(~(p1(tptp_fun_Y_3(Y!6)) | (~r1(Y!6, tptp_fun_Y_3(Y!6))))), introduced(assumption)).
% 0.13/0.40 tff(7,plain,
% 0.13/0.40 ((p1(tptp_fun_Y_3(Y!6)) | (~r1(Y!6, tptp_fun_Y_3(Y!6)))) | r1(Y!6, tptp_fun_Y_3(Y!6))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(8,plain,
% 0.13/0.40 (r1(Y!6, tptp_fun_Y_3(Y!6))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[7, 6])).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 ((p1(tptp_fun_Y_3(Y!6)) | (~r1(Y!6, tptp_fun_Y_3(Y!6)))) | (~p1(tptp_fun_Y_3(Y!6)))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 (~p1(tptp_fun_Y_3(Y!6))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[9, 6])).
% 0.13/0.40 tff(11,plain,
% 0.13/0.40 (^[X: $i] : refl((p1(X) | (~r1(Y!6, X))) <=> (p1(X) | (~r1(Y!6, X))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(12,plain,
% 0.13/0.40 (![X: $i] : (p1(X) | (~r1(Y!6, X))) <=> ![X: $i] : (p1(X) | (~r1(Y!6, X)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[11])).
% 0.13/0.40 tff(13,plain,
% 0.13/0.40 ((![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_2(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_5(Y))) & (r1(X!0, Y!6) & ![X: $i] : (p1(X) | (~r1(Y!6, X))) & r1(Y!6, X!7) & (~(p1(Y!8) | (~r1(X!7, Y!8)))))) <=> (![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_2(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_5(Y))) & r1(X!0, Y!6) & ![X: $i] : (p1(X) | (~r1(Y!6, X))) & r1(Y!6, X!7) & (~(p1(Y!8) | (~r1(X!7, Y!8)))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(14,plain,
% 0.13/0.40 ((r1(X!0, Y!6) & ![X: $i] : (p1(X) | (~r1(Y!6, X))) & (r1(Y!6, X!7) & (~(p1(Y!8) | (~r1(X!7, Y!8)))))) <=> (r1(X!0, Y!6) & ![X: $i] : (p1(X) | (~r1(Y!6, X))) & r1(Y!6, X!7) & (~(p1(Y!8) | (~r1(X!7, Y!8)))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(15,plain,
% 0.13/0.40 (((~(~r1(Y!6, X!7))) & (~(p1(Y!8) | (~r1(X!7, Y!8))))) <=> (r1(Y!6, X!7) & (~(p1(Y!8) | (~r1(X!7, Y!8)))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(16,plain,
% 0.13/0.40 ((~(~r1(X!0, Y!6))) <=> r1(X!0, Y!6)),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(17,plain,
% 0.13/0.40 (((~(~r1(X!0, Y!6))) & ![X: $i] : (p1(X) | (~r1(Y!6, X))) & ((~(~r1(Y!6, X!7))) & (~(p1(Y!8) | (~r1(X!7, Y!8)))))) <=> (r1(X!0, Y!6) & ![X: $i] : (p1(X) | (~r1(Y!6, X))) & (r1(Y!6, X!7) & (~(p1(Y!8) | (~r1(X!7, Y!8))))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[16, 15])).
% 0.13/0.40 tff(18,plain,
% 0.13/0.40 (((~(~r1(X!0, Y!6))) & ![X: $i] : (p1(X) | (~r1(Y!6, X))) & ((~(~r1(Y!6, X!7))) & (~(p1(Y!8) | (~r1(X!7, Y!8)))))) <=> (r1(X!0, Y!6) & ![X: $i] : (p1(X) | (~r1(Y!6, X))) & r1(Y!6, X!7) & (~(p1(Y!8) | (~r1(X!7, Y!8)))))),
% 0.13/0.40 inference(transitivity,[status(thm)],[17, 14])).
% 0.13/0.40 tff(19,plain,
% 0.13/0.40 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | (~(~r1(Y, tptp_fun_X_5(Y))))) <=> ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_5(Y))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(20,plain,
% 0.13/0.40 (![Y: $i] : ((~r1(X!0, Y)) | (~(~r1(Y, tptp_fun_X_5(Y))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_5(Y)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[19])).
% 0.13/0.40 tff(21,plain,
% 0.13/0.40 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(22,plain,
% 0.13/0.40 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[21])).
% 0.13/0.40 tff(23,plain,
% 0.13/0.40 (^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : rewrite(((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_2(X)))) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))) <=> ((~r1(Y, X)) | (r1(X, tptp_fun_Y_2(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))))), (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_2(X)))) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))) <=> ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_2(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))))), ((![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_2(X)))) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))) <=> (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_2(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))))), rewrite((![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_2(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))) <=> (![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_2(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))))), ((![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_2(X)))) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))) <=> (![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_2(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X)))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_2(X)))) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_2(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_2(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_2(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_2(X)))) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_2(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(24,plain,
% 0.13/0.40 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_2(X)))) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_2(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[23])).
% 0.13/0.40 tff(25,plain,
% 0.13/0.40 (^[Y: $i] : trans(monotonicity(rewrite((![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~p1(Y))) <=> ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~p1(Y)))) <=> ((~r1(X!0, Y)) | ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))))))), rewrite(((~r1(X!0, Y)) | ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))))) <=> ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~p1(Y)))) <=> ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(26,plain,
% 0.13/0.40 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~p1(Y)))) <=> ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[25])).
% 0.13/0.40 tff(27,plain,
% 0.13/0.40 ((![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~p1(Y)))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_2(X)))) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | (~(~r1(Y, tptp_fun_X_5(Y))))) & ((~(~r1(X!0, Y!6))) & ![X: $i] : (p1(X) | (~r1(Y!6, X))) & ((~(~r1(Y!6, X!7))) & (~(p1(Y!8) | (~r1(X!7, Y!8))))))) <=> (![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_2(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_5(Y))) & (r1(X!0, Y!6) & ![X: $i] : (p1(X) | (~r1(Y!6, X))) & r1(Y!6, X!7) & (~(p1(Y!8) | (~r1(X!7, Y!8))))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[26, 24, 22, 20, 18])).
% 0.20/0.40 tff(28,plain,
% 0.20/0.40 ((![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~p1(Y)))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_2(X)))) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | (~(~r1(Y, tptp_fun_X_5(Y))))) & ((~(~r1(X!0, Y!6))) & ![X: $i] : (p1(X) | (~r1(Y!6, X))) & ((~(~r1(Y!6, X!7))) & (~(p1(Y!8) | (~r1(X!7, Y!8))))))) <=> (![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_2(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_5(Y))) & r1(X!0, Y!6) & ![X: $i] : (p1(X) | (~r1(Y!6, X))) & r1(Y!6, X!7) & (~(p1(Y!8) | (~r1(X!7, Y!8)))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[27, 13])).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 (?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) <=> ?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 ((~(~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) <=> ?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(31,plain,
% 0.20/0.41 ((~?[X: $i] : (~(((((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) <=> (~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 ((~(~?[X: $i] : (~(((((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) <=> (~(~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[31])).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 ((~(~?[X: $i] : (~(((((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) <=> ?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[32, 30])).
% 0.20/0.41 tff(34,axiom,(~(~?[X: $i] : (~(((((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','main')).
% 0.20/0.41 tff(35,plain,
% 0.20/0.41 (?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.20/0.41 tff(36,plain,
% 0.20/0.41 (?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[35, 29])).
% 0.20/0.41 tff(37,plain,
% 0.20/0.41 (![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_2(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_5(Y))) & r1(X!0, Y!6) & ![X: $i] : (p1(X) | (~r1(Y!6, X))) & r1(Y!6, X!7) & (~(p1(Y!8) | (~r1(X!7, Y!8))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[36, 28])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 (![X: $i] : (p1(X) | (~r1(Y!6, X)))),
% 0.20/0.41 inference(and_elim,[status(thm)],[37])).
% 0.20/0.41 tff(39,plain,
% 0.20/0.41 (![X: $i] : (p1(X) | (~r1(Y!6, X)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[38, 12])).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 (((~![X: $i] : (p1(X) | (~r1(Y!6, X)))) | (p1(tptp_fun_Y_3(Y!6)) | (~r1(Y!6, tptp_fun_Y_3(Y!6))))) <=> ((~![X: $i] : (p1(X) | (~r1(Y!6, X)))) | p1(tptp_fun_Y_3(Y!6)) | (~r1(Y!6, tptp_fun_Y_3(Y!6))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(41,plain,
% 0.20/0.41 ((~![X: $i] : (p1(X) | (~r1(Y!6, X)))) | (p1(tptp_fun_Y_3(Y!6)) | (~r1(Y!6, tptp_fun_Y_3(Y!6))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 ((~![X: $i] : (p1(X) | (~r1(Y!6, X)))) | p1(tptp_fun_Y_3(Y!6)) | (~r1(Y!6, tptp_fun_Y_3(Y!6)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.20/0.41 tff(43,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[42, 39, 10, 8])).
% 0.20/0.41 tff(44,plain,(p1(tptp_fun_Y_3(Y!6)) | (~r1(Y!6, tptp_fun_Y_3(Y!6)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(45,assumption,(~r1(Y!6, Y!6)), introduced(assumption)).
% 0.20/0.41 tff(46,plain,
% 0.20/0.41 (^[X: $i] : refl(r1(X, X) <=> r1(X, X))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 0.20/0.41 inference(quant_intro,[status(thm)],[46])).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(49,axiom,(![X: $i] : r1(X, X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','reflexivity')).
% 0.20/0.41 tff(50,plain,
% 0.20/0.41 (![X: $i] : r1(X, X)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.20/0.41 tff(51,plain,(
% 0.20/0.41 ![X: $i] : r1(X, X)),
% 0.20/0.41 inference(skolemize,[status(sab)],[50])).
% 0.20/0.41 tff(52,plain,
% 0.20/0.41 (![X: $i] : r1(X, X)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.20/0.41 tff(53,plain,
% 0.20/0.41 ((~![X: $i] : r1(X, X)) | r1(Y!6, Y!6)),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(54,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[53, 52, 45])).
% 0.20/0.41 tff(55,plain,(r1(Y!6, Y!6)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(56,assumption,(![X: $i] : ((~r1(Y!6, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))), introduced(assumption)).
% 0.20/0.41 tff(57,plain,
% 0.20/0.41 (((~![X: $i] : ((~r1(Y!6, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))) | ((~r1(Y!6, Y!6)) | (~(p1(tptp_fun_Y_3(Y!6)) | (~r1(Y!6, tptp_fun_Y_3(Y!6))))))) <=> ((~![X: $i] : ((~r1(Y!6, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))) | (~r1(Y!6, Y!6)) | (~(p1(tptp_fun_Y_3(Y!6)) | (~r1(Y!6, tptp_fun_Y_3(Y!6))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(58,plain,
% 0.20/0.41 ((~![X: $i] : ((~r1(Y!6, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))) | ((~r1(Y!6, Y!6)) | (~(p1(tptp_fun_Y_3(Y!6)) | (~r1(Y!6, tptp_fun_Y_3(Y!6))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(59,plain,
% 0.20/0.41 ((~![X: $i] : ((~r1(Y!6, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))) | (~r1(Y!6, Y!6)) | (~(p1(tptp_fun_Y_3(Y!6)) | (~r1(Y!6, tptp_fun_Y_3(Y!6)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.20/0.41 tff(60,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[59, 56, 55, 44])).
% 0.20/0.41 tff(61,plain,(~![X: $i] : ((~r1(Y!6, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(62,plain,
% 0.20/0.41 (r1(X!0, Y!6)),
% 0.20/0.41 inference(and_elim,[status(thm)],[37])).
% 0.20/0.41 tff(63,plain,
% 0.20/0.41 (^[Y: $i] : refl(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X)))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X)))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(64,plain,
% 0.20/0.41 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X)))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[63])).
% 0.20/0.41 tff(65,plain,
% 0.20/0.41 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X)))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X)))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(66,plain,
% 0.20/0.42 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X)))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[65])).
% 0.20/0.42 tff(67,plain,
% 0.20/0.42 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X)))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[66, 64])).
% 0.20/0.42 tff(68,plain,
% 0.20/0.42 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_2(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X)))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(69,plain,
% 0.20/0.42 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_2(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[68])).
% 0.20/0.42 tff(70,plain,
% 0.20/0.42 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_2(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))))),
% 0.20/0.42 inference(and_elim,[status(thm)],[37])).
% 0.20/0.42 tff(71,plain,
% 0.20/0.42 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.20/0.42 tff(72,plain,
% 0.20/0.42 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.20/0.42 tff(73,plain,
% 0.20/0.42 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))))))) | ((~r1(X!0, Y!6)) | ![X: $i] : ((~r1(Y!6, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y!6, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))))))) | (~r1(X!0, Y!6)) | ![X: $i] : ((~r1(Y!6, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y!6, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(74,plain,
% 0.20/0.42 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))))))) | ((~r1(X!0, Y!6)) | ![X: $i] : ((~r1(Y!6, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y!6, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(75,plain,
% 0.20/0.42 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))))))) | (~r1(X!0, Y!6)) | ![X: $i] : ((~r1(Y!6, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y!6, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.20/0.42 tff(76,plain,
% 0.20/0.42 (![X: $i] : ((~r1(Y!6, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y!6, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X)))))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[75, 72, 62])).
% 0.20/0.42 tff(77,plain,
% 0.20/0.42 (![X: $i] : ((~r1(Y!6, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X)))))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[76, 61])).
% 0.20/0.42 tff(78,plain,
% 0.20/0.42 (r1(Y!6, X!7)),
% 0.20/0.42 inference(and_elim,[status(thm)],[37])).
% 0.20/0.42 tff(79,plain,
% 0.20/0.42 (((~![X: $i] : ((~r1(Y!6, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X)))))))) | ((~r1(Y!6, X!7)) | (~((~r1(X!7, tptp_fun_Y_2(X!7))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X!7), X)))))))) <=> ((~![X: $i] : ((~r1(Y!6, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X)))))))) | (~r1(Y!6, X!7)) | (~((~r1(X!7, tptp_fun_Y_2(X!7))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X!7), X)))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(80,plain,
% 0.20/0.42 ((~![X: $i] : ((~r1(Y!6, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X)))))))) | ((~r1(Y!6, X!7)) | (~((~r1(X!7, tptp_fun_Y_2(X!7))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X!7), X)))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(81,plain,
% 0.20/0.42 ((~![X: $i] : ((~r1(Y!6, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X)))))))) | (~r1(Y!6, X!7)) | (~((~r1(X!7, tptp_fun_Y_2(X!7))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X!7), X))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.20/0.42 tff(82,plain,
% 0.20/0.42 (~((~r1(X!7, tptp_fun_Y_2(X!7))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X!7), X)))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[81, 78, 77])).
% 0.20/0.42 tff(83,plain,
% 0.20/0.42 (((~r1(X!7, tptp_fun_Y_2(X!7))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X!7), X))))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X!7), X)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(84,plain,
% 0.20/0.42 (![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X!7), X)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.20/0.42 tff(85,plain,
% 0.20/0.42 (((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X!7), X)))) | (p1(tptp_fun_X_4(tptp_fun_Y_2(X!7))) | (~r1(tptp_fun_Y_2(X!7), tptp_fun_X_4(tptp_fun_Y_2(X!7)))))) <=> ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X!7), X)))) | p1(tptp_fun_X_4(tptp_fun_Y_2(X!7))) | (~r1(tptp_fun_Y_2(X!7), tptp_fun_X_4(tptp_fun_Y_2(X!7)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(86,plain,
% 0.20/0.42 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X!7), X)))) | (p1(tptp_fun_X_4(tptp_fun_Y_2(X!7))) | (~r1(tptp_fun_Y_2(X!7), tptp_fun_X_4(tptp_fun_Y_2(X!7)))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(87,plain,
% 0.20/0.42 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X!7), X)))) | p1(tptp_fun_X_4(tptp_fun_Y_2(X!7))) | (~r1(tptp_fun_Y_2(X!7), tptp_fun_X_4(tptp_fun_Y_2(X!7))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.20/0.42 tff(88,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[87, 84, 5, 3])).
% 0.20/0.42 tff(89,plain,(p1(tptp_fun_X_4(tptp_fun_Y_2(X!7))) | (~r1(tptp_fun_Y_2(X!7), tptp_fun_X_4(tptp_fun_Y_2(X!7))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(90,plain,
% 0.20/0.42 (((~r1(X!7, tptp_fun_Y_2(X!7))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X!7), X))))) | r1(X!7, tptp_fun_Y_2(X!7))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(91,plain,
% 0.20/0.42 (r1(X!7, tptp_fun_Y_2(X!7))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[90, 82])).
% 0.20/0.42 tff(92,assumption,(![Y: $i] : ((~r1(X!7, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))))), introduced(assumption)).
% 0.20/0.42 tff(93,plain,
% 0.20/0.42 (((~![Y: $i] : ((~r1(X!7, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))))) | ((~r1(X!7, tptp_fun_Y_2(X!7))) | (~(p1(tptp_fun_X_4(tptp_fun_Y_2(X!7))) | (~r1(tptp_fun_Y_2(X!7), tptp_fun_X_4(tptp_fun_Y_2(X!7)))))))) <=> ((~![Y: $i] : ((~r1(X!7, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))))) | (~r1(X!7, tptp_fun_Y_2(X!7))) | (~(p1(tptp_fun_X_4(tptp_fun_Y_2(X!7))) | (~r1(tptp_fun_Y_2(X!7), tptp_fun_X_4(tptp_fun_Y_2(X!7)))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(94,plain,
% 0.20/0.42 ((~![Y: $i] : ((~r1(X!7, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))))) | ((~r1(X!7, tptp_fun_Y_2(X!7))) | (~(p1(tptp_fun_X_4(tptp_fun_Y_2(X!7))) | (~r1(tptp_fun_Y_2(X!7), tptp_fun_X_4(tptp_fun_Y_2(X!7)))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(95,plain,
% 0.20/0.42 ((~![Y: $i] : ((~r1(X!7, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))))) | (~r1(X!7, tptp_fun_Y_2(X!7))) | (~(p1(tptp_fun_X_4(tptp_fun_Y_2(X!7))) | (~r1(tptp_fun_Y_2(X!7), tptp_fun_X_4(tptp_fun_Y_2(X!7))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.20/0.42 tff(96,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[95, 92, 91, 89])).
% 0.20/0.42 tff(97,plain,(~![Y: $i] : ((~r1(X!7, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(98,plain,
% 0.20/0.42 (^[Y: $i] : refl(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(99,plain,
% 0.20/0.42 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[98])).
% 0.20/0.42 tff(100,plain,
% 0.20/0.42 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(101,plain,
% 0.20/0.42 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[100])).
% 0.20/0.42 tff(102,plain,
% 0.20/0.42 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[101, 99])).
% 0.20/0.42 tff(103,plain,
% 0.20/0.42 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))))))),
% 0.20/0.42 inference(and_elim,[status(thm)],[37])).
% 0.20/0.42 tff(104,plain,
% 0.20/0.42 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.20/0.42 tff(105,plain,
% 0.20/0.42 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))))))) | ((~r1(X!0, Y!6)) | ![X: $i] : ((~r1(Y!6, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))))))) | (~r1(X!0, Y!6)) | ![X: $i] : ((~r1(Y!6, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(106,plain,
% 0.20/0.42 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))))))) | ((~r1(X!0, Y!6)) | ![X: $i] : ((~r1(Y!6, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(107,plain,
% 0.20/0.42 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))))))) | (~r1(X!0, Y!6)) | ![X: $i] : ((~r1(Y!6, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.20/0.42 tff(108,plain,
% 0.20/0.42 (![X: $i] : ((~r1(Y!6, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[107, 104, 62])).
% 0.20/0.42 tff(109,plain,
% 0.20/0.42 (((~![X: $i] : ((~r1(Y!6, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) | ((~r1(Y!6, X!7)) | ![Y: $i] : (p1(Y) | (~r1(X!7, Y))) | ![Y: $i] : ((~r1(X!7, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) <=> ((~![X: $i] : ((~r1(Y!6, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) | (~r1(Y!6, X!7)) | ![Y: $i] : (p1(Y) | (~r1(X!7, Y))) | ![Y: $i] : ((~r1(X!7, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(110,plain,
% 0.20/0.42 ((~![X: $i] : ((~r1(Y!6, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) | ((~r1(Y!6, X!7)) | ![Y: $i] : (p1(Y) | (~r1(X!7, Y))) | ![Y: $i] : ((~r1(X!7, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(111,plain,
% 0.20/0.42 ((~![X: $i] : ((~r1(Y!6, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) | (~r1(Y!6, X!7)) | ![Y: $i] : (p1(Y) | (~r1(X!7, Y))) | ![Y: $i] : ((~r1(X!7, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.20/0.42 tff(112,plain,
% 0.20/0.42 (![Y: $i] : (p1(Y) | (~r1(X!7, Y))) | ![Y: $i] : ((~r1(X!7, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[111, 78, 108])).
% 0.20/0.42 tff(113,plain,
% 0.20/0.42 (![Y: $i] : (p1(Y) | (~r1(X!7, Y)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[112, 97])).
% 0.20/0.42 tff(114,plain,
% 0.20/0.42 (~(p1(Y!8) | (~r1(X!7, Y!8)))),
% 0.20/0.42 inference(and_elim,[status(thm)],[37])).
% 0.20/0.42 tff(115,plain,
% 0.20/0.42 (r1(X!7, Y!8)),
% 0.20/0.42 inference(or_elim,[status(thm)],[114])).
% 0.20/0.42 tff(116,plain,
% 0.20/0.42 (~p1(Y!8)),
% 0.20/0.42 inference(or_elim,[status(thm)],[114])).
% 0.20/0.42 tff(117,plain,
% 0.20/0.42 (((~![Y: $i] : (p1(Y) | (~r1(X!7, Y)))) | (p1(Y!8) | (~r1(X!7, Y!8)))) <=> ((~![Y: $i] : (p1(Y) | (~r1(X!7, Y)))) | p1(Y!8) | (~r1(X!7, Y!8)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(118,plain,
% 0.20/0.43 ((~![Y: $i] : (p1(Y) | (~r1(X!7, Y)))) | (p1(Y!8) | (~r1(X!7, Y!8)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(119,plain,
% 0.20/0.43 ((~![Y: $i] : (p1(Y) | (~r1(X!7, Y)))) | p1(Y!8) | (~r1(X!7, Y!8))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.20/0.43 tff(120,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[119, 116, 115, 113])).
% 0.20/0.43 % SZS output end Proof
%------------------------------------------------------------------------------