TSTP Solution File: LCL638+1.001 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL638+1.001 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 04:56:52 EDT 2022
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL638+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n016.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Sep 1 23:04:49 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(r1_type, type, (
% 0.20/0.40 r1: ( $i * $i ) > $o)).
% 0.20/0.40 tff(tptp_fun_X_6_type, type, (
% 0.20/0.40 tptp_fun_X_6: $i > $i)).
% 0.20/0.40 tff(tptp_fun_Y_7_type, type, (
% 0.20/0.40 tptp_fun_Y_7: $i)).
% 0.20/0.40 tff(p1_type, type, (
% 0.20/0.40 p1: $i > $o)).
% 0.20/0.40 tff(tptp_fun_X_5_type, type, (
% 0.20/0.40 tptp_fun_X_5: $i > $i)).
% 0.20/0.40 tff(tptp_fun_X_0_type, type, (
% 0.20/0.40 tptp_fun_X_0: $i)).
% 0.20/0.40 tff(tptp_fun_X_4_type, type, (
% 0.20/0.40 tptp_fun_X_4: $i > $i)).
% 0.20/0.40 tff(tptp_fun_X_3_type, type, (
% 0.20/0.40 tptp_fun_X_3: $i > $i)).
% 0.20/0.40 tff(tptp_fun_Y_2_type, type, (
% 0.20/0.40 tptp_fun_Y_2: $i > $i)).
% 0.20/0.40 tff(tptp_fun_Y_1_type, type, (
% 0.20/0.40 tptp_fun_Y_1: $i > $i)).
% 0.20/0.40 tff(1,assumption,(~(p1(tptp_fun_X_5(Y!7)) | (~r1(Y!7, tptp_fun_X_5(Y!7))))), introduced(assumption)).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 ((p1(tptp_fun_X_5(Y!7)) | (~r1(Y!7, tptp_fun_X_5(Y!7)))) | r1(Y!7, tptp_fun_X_5(Y!7))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 (r1(Y!7, tptp_fun_X_5(Y!7))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.20/0.40 tff(4,plain,
% 0.20/0.40 ((p1(tptp_fun_X_5(Y!7)) | (~r1(Y!7, tptp_fun_X_5(Y!7)))) | (~p1(tptp_fun_X_5(Y!7)))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 (~p1(tptp_fun_X_5(Y!7))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.20/0.40 tff(6,plain,
% 0.20/0.40 (^[X: $i] : refl((p1(X) | (~r1(Y!7, X))) <=> (p1(X) | (~r1(Y!7, X))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(7,plain,
% 0.20/0.40 (![X: $i] : (p1(X) | (~r1(Y!7, X))) <=> ![X: $i] : (p1(X) | (~r1(Y!7, X)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 ((![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] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_2(X))) | (~r1(X, tptp_fun_Y_2(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_6(Y))) & ((~p1(Y!7)) & r1(X!0, Y!7) & ![X: $i] : (p1(X) | (~r1(Y!7, X))))) <=> (![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] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_2(X))) | (~r1(X, tptp_fun_Y_2(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_6(Y))) & (~p1(Y!7)) & r1(X!0, Y!7) & ![X: $i] : (p1(X) | (~r1(Y!7, X))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 (((~p1(Y!7)) & (~(~r1(X!0, Y!7))) & ![X: $i] : (p1(X) | (~r1(Y!7, X)))) <=> ((~p1(Y!7)) & r1(X!0, Y!7) & ![X: $i] : (p1(X) | (~r1(Y!7, X))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | (~(~r1(Y, tptp_fun_X_6(Y))))) <=> ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_6(Y))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(11,plain,
% 0.20/0.40 (![Y: $i] : ((~r1(X!0, Y)) | (~(~r1(Y, tptp_fun_X_6(Y))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_6(Y)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[10])).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 (^[Y: $i] : trans(monotonicity(rewrite((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))) <=> (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.40 tff(14,plain,
% 0.20/0.40 (^[Y: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~(~r1(Y, tptp_fun_X_4(Y)))) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))) <=> (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))), ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | ((~(~r1(Y, tptp_fun_X_4(Y)))) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))) <=> (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))))), rewrite((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))) <=> (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))), ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | ((~(~r1(Y, tptp_fun_X_4(Y)))) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))) <=> (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | ((~(~r1(Y, tptp_fun_X_4(Y)))) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | ((~(~r1(Y, tptp_fun_X_4(Y)))) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(15,plain,
% 0.20/0.40 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | ((~(~r1(Y, tptp_fun_X_4(Y)))) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[14])).
% 0.20/0.40 tff(16,plain,
% 0.20/0.40 (^[Y: $i] : trans(monotonicity(rewrite((![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_2(X))) | (~r1(X, tptp_fun_Y_2(X)))))) | (~p1(Y))) <=> ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_2(X))) | (~r1(X, tptp_fun_Y_2(X)))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_2(X))) | (~r1(X, tptp_fun_Y_2(X)))))) | (~p1(Y)))) <=> ((~r1(X!0, Y)) | ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_2(X))) | (~r1(X, tptp_fun_Y_2(X)))))))))), rewrite(((~r1(X!0, Y)) | ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_2(X))) | (~r1(X, tptp_fun_Y_2(X)))))))) <=> ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_2(X))) | (~r1(X, tptp_fun_Y_2(X)))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_2(X))) | (~r1(X, tptp_fun_Y_2(X)))))) | (~p1(Y)))) <=> ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_2(X))) | (~r1(X, tptp_fun_Y_2(X)))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_2(X))) | (~r1(X, tptp_fun_Y_2(X)))))) | (~p1(Y)))) <=> ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_2(X))) | (~r1(X, tptp_fun_Y_2(X)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[16])).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 (^[Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((~(~p1(Y))) <=> p1(Y)), ((![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(~p1(Y)))) <=> (![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | p1(Y)))), 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)))))))), ((![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)))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(19,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] : (p1(Y) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[18])).
% 0.20/0.40 tff(20,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)) | (~((~p1(tptp_fun_Y_2(X))) | (~r1(X, tptp_fun_Y_2(X)))))) | (~p1(Y)))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | ((~(~r1(Y, tptp_fun_X_4(Y)))) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | (~(~r1(Y, tptp_fun_X_6(Y))))) & ((~p1(Y!7)) & (~(~r1(X!0, Y!7))) & ![X: $i] : (p1(X) | (~r1(Y!7, X))))) <=> (![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] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_2(X))) | (~r1(X, tptp_fun_Y_2(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_6(Y))) & ((~p1(Y!7)) & r1(X!0, Y!7) & ![X: $i] : (p1(X) | (~r1(Y!7, X)))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[19, 17, 15, 13, 11, 9])).
% 0.20/0.40 tff(21,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)) | (~((~p1(tptp_fun_Y_2(X))) | (~r1(X, tptp_fun_Y_2(X)))))) | (~p1(Y)))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | ((~(~r1(Y, tptp_fun_X_4(Y)))) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | (~(~r1(Y, tptp_fun_X_6(Y))))) & ((~p1(Y!7)) & (~(~r1(X!0, Y!7))) & ![X: $i] : (p1(X) | (~r1(Y!7, X))))) <=> (![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] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_2(X))) | (~r1(X, tptp_fun_Y_2(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_6(Y))) & (~p1(Y!7)) & r1(X!0, Y!7) & ![X: $i] : (p1(X) | (~r1(Y!7, X))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[20, 8])).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 (?[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] : ((~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] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, 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] : ((~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] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(23,plain,
% 0.20/0.40 ((~(~?[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] : ((~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] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, 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] : ((~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] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(24,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)) | (~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))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))) | ![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] : ((~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] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(25,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)) | (~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))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))) | ![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] : ((~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] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[24])).
% 0.20/0.41 tff(26,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)) | (~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))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))) | ![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] : ((~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] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[25, 23])).
% 0.20/0.41 tff(27,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)) | (~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))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','main')).
% 0.20/0.41 tff(28,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] : ((~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] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[27, 26])).
% 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] : ((~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] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[28, 22])).
% 0.20/0.41 tff(30,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] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_2(X))) | (~r1(X, tptp_fun_Y_2(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_6(Y))) & (~p1(Y!7)) & r1(X!0, Y!7) & ![X: $i] : (p1(X) | (~r1(Y!7, X)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[29, 21])).
% 0.20/0.41 tff(31,plain,
% 0.20/0.41 (![X: $i] : (p1(X) | (~r1(Y!7, X)))),
% 0.20/0.41 inference(and_elim,[status(thm)],[30])).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 (![X: $i] : (p1(X) | (~r1(Y!7, X)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[31, 7])).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 (((~![X: $i] : (p1(X) | (~r1(Y!7, X)))) | (p1(tptp_fun_X_5(Y!7)) | (~r1(Y!7, tptp_fun_X_5(Y!7))))) <=> ((~![X: $i] : (p1(X) | (~r1(Y!7, X)))) | p1(tptp_fun_X_5(Y!7)) | (~r1(Y!7, tptp_fun_X_5(Y!7))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(34,plain,
% 0.20/0.41 ((~![X: $i] : (p1(X) | (~r1(Y!7, X)))) | (p1(tptp_fun_X_5(Y!7)) | (~r1(Y!7, tptp_fun_X_5(Y!7))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(35,plain,
% 0.20/0.41 ((~![X: $i] : (p1(X) | (~r1(Y!7, X)))) | p1(tptp_fun_X_5(Y!7)) | (~r1(Y!7, tptp_fun_X_5(Y!7)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.20/0.41 tff(36,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[35, 32, 5, 3])).
% 0.20/0.41 tff(37,plain,(p1(tptp_fun_X_5(Y!7)) | (~r1(Y!7, tptp_fun_X_5(Y!7)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 (r1(X!0, Y!7)),
% 0.20/0.41 inference(and_elim,[status(thm)],[30])).
% 0.20/0.41 tff(39,plain,
% 0.20/0.41 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))) <=> ((~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[39])).
% 0.20/0.41 tff(41,plain,
% 0.20/0.41 (^[Y: $i] : refl(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[41])).
% 0.20/0.41 tff(43,plain,
% 0.20/0.41 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[43])).
% 0.20/0.41 tff(45,plain,
% 0.20/0.41 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[44, 42])).
% 0.20/0.42 tff(46,plain,
% 0.20/0.42 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))),
% 0.20/0.42 inference(and_elim,[status(thm)],[30])).
% 0.20/0.42 tff(47,plain,
% 0.20/0.42 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.42 tff(48,plain,
% 0.20/0.42 (![Y: $i] : ((~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.20/0.42 tff(49,plain,
% 0.20/0.42 (((~![Y: $i] : ((~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | ((~r1(X!0, Y!7)) | (~(p1(tptp_fun_X_5(Y!7)) | (~r1(Y!7, tptp_fun_X_5(Y!7))))) | ![X: $i] : ((~r1(Y!7, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(X!0, Y!7)) | (~(p1(tptp_fun_X_5(Y!7)) | (~r1(Y!7, tptp_fun_X_5(Y!7))))) | ![X: $i] : ((~r1(Y!7, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(50,plain,
% 0.20/0.42 ((~![Y: $i] : ((~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | ((~r1(X!0, Y!7)) | (~(p1(tptp_fun_X_5(Y!7)) | (~r1(Y!7, tptp_fun_X_5(Y!7))))) | ![X: $i] : ((~r1(Y!7, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(51,plain,
% 0.20/0.42 ((~![Y: $i] : ((~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(X!0, Y!7)) | (~(p1(tptp_fun_X_5(Y!7)) | (~r1(Y!7, tptp_fun_X_5(Y!7))))) | ![X: $i] : ((~r1(Y!7, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.20/0.42 tff(52,plain,
% 0.20/0.42 ((~(p1(tptp_fun_X_5(Y!7)) | (~r1(Y!7, tptp_fun_X_5(Y!7))))) | ![X: $i] : ((~r1(Y!7, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[51, 48, 38])).
% 0.20/0.42 tff(53,plain,
% 0.20/0.42 (![X: $i] : ((~r1(Y!7, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[52, 37])).
% 0.20/0.42 tff(54,plain,
% 0.20/0.42 (^[Y: $i] : refl(((~r1(X!0, Y)) | r1(Y, tptp_fun_X_6(Y))) <=> ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_6(Y))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(55,plain,
% 0.20/0.42 (![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_6(Y))) <=> ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_6(Y)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[54])).
% 0.20/0.42 tff(56,plain,
% 0.20/0.42 (![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_6(Y)))),
% 0.20/0.42 inference(and_elim,[status(thm)],[30])).
% 0.20/0.42 tff(57,plain,
% 0.20/0.42 (![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_6(Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.20/0.42 tff(58,plain,
% 0.20/0.42 (((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_6(Y)))) | ((~r1(X!0, Y!7)) | r1(Y!7, tptp_fun_X_6(Y!7)))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_6(Y)))) | (~r1(X!0, Y!7)) | r1(Y!7, tptp_fun_X_6(Y!7)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(59,plain,
% 0.20/0.42 ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_6(Y)))) | ((~r1(X!0, Y!7)) | r1(Y!7, tptp_fun_X_6(Y!7)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(60,plain,
% 0.20/0.42 ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_6(Y)))) | (~r1(X!0, Y!7)) | r1(Y!7, tptp_fun_X_6(Y!7))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.20/0.42 tff(61,plain,
% 0.20/0.42 (r1(Y!7, tptp_fun_X_6(Y!7))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[60, 57, 38])).
% 0.20/0.42 tff(62,plain,
% 0.20/0.42 (((~![X: $i] : ((~r1(Y!7, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ((~r1(Y!7, tptp_fun_X_6(Y!7))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_6(Y!7), Y))))) <=> ((~![X: $i] : ((~r1(Y!7, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~r1(Y!7, tptp_fun_X_6(Y!7))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_6(Y!7), Y))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(63,plain,
% 0.20/0.42 ((~![X: $i] : ((~r1(Y!7, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ((~r1(Y!7, tptp_fun_X_6(Y!7))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_6(Y!7), Y))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(64,plain,
% 0.20/0.42 ((~![X: $i] : ((~r1(Y!7, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~r1(Y!7, tptp_fun_X_6(Y!7))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_6(Y!7), Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.20/0.42 tff(65,plain,
% 0.20/0.42 (![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_6(Y!7), Y)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[64, 61, 53])).
% 0.20/0.42 tff(66,plain,
% 0.20/0.42 (~p1(Y!7)),
% 0.20/0.42 inference(and_elim,[status(thm)],[30])).
% 0.20/0.42 tff(67,plain,
% 0.20/0.42 (^[Y: $i] : refl((p1(Y) | (~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)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(68,plain,
% 0.20/0.42 (![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] : (p1(Y) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[67])).
% 0.20/0.42 tff(69,plain,
% 0.20/0.42 (^[Y: $i] : rewrite((p1(Y) | (~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)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(70,plain,
% 0.20/0.42 (![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] : (p1(Y) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[69])).
% 0.20/0.42 tff(71,plain,
% 0.20/0.42 (![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] : (p1(Y) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[70, 68])).
% 0.20/0.42 tff(72,plain,
% 0.20/0.42 (![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)))))))),
% 0.20/0.42 inference(and_elim,[status(thm)],[30])).
% 0.20/0.42 tff(73,plain,
% 0.20/0.42 (![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)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.20/0.42 tff(74,plain,
% 0.20/0.42 (((~![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)))))))) | (p1(Y!7) | (~r1(X!0, Y!7)) | ![X: $i] : ((~r1(Y!7, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) <=> ((~![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)))))))) | p1(Y!7) | (~r1(X!0, Y!7)) | ![X: $i] : ((~r1(Y!7, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(75,plain,
% 0.20/0.42 ((~![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)))))))) | (p1(Y!7) | (~r1(X!0, Y!7)) | ![X: $i] : ((~r1(Y!7, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(76,plain,
% 0.20/0.42 ((~![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)))))))) | p1(Y!7) | (~r1(X!0, Y!7)) | ![X: $i] : ((~r1(Y!7, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.20/0.42 tff(77,plain,
% 0.20/0.42 (![X: $i] : ((~r1(Y!7, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[76, 73, 66, 38])).
% 0.20/0.42 tff(78,plain,
% 0.20/0.42 (((~![X: $i] : ((~r1(Y!7, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) | ((~r1(Y!7, tptp_fun_X_6(Y!7))) | (~(p1(tptp_fun_Y_1(tptp_fun_X_6(Y!7))) | (~r1(tptp_fun_X_6(Y!7), tptp_fun_Y_1(tptp_fun_X_6(Y!7)))))))) <=> ((~![X: $i] : ((~r1(Y!7, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) | (~r1(Y!7, tptp_fun_X_6(Y!7))) | (~(p1(tptp_fun_Y_1(tptp_fun_X_6(Y!7))) | (~r1(tptp_fun_X_6(Y!7), tptp_fun_Y_1(tptp_fun_X_6(Y!7)))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(79,plain,
% 0.20/0.42 ((~![X: $i] : ((~r1(Y!7, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) | ((~r1(Y!7, tptp_fun_X_6(Y!7))) | (~(p1(tptp_fun_Y_1(tptp_fun_X_6(Y!7))) | (~r1(tptp_fun_X_6(Y!7), tptp_fun_Y_1(tptp_fun_X_6(Y!7)))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(80,plain,
% 0.20/0.42 ((~![X: $i] : ((~r1(Y!7, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) | (~r1(Y!7, tptp_fun_X_6(Y!7))) | (~(p1(tptp_fun_Y_1(tptp_fun_X_6(Y!7))) | (~r1(tptp_fun_X_6(Y!7), tptp_fun_Y_1(tptp_fun_X_6(Y!7))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.20/0.42 tff(81,plain,
% 0.20/0.42 (~(p1(tptp_fun_Y_1(tptp_fun_X_6(Y!7))) | (~r1(tptp_fun_X_6(Y!7), tptp_fun_Y_1(tptp_fun_X_6(Y!7)))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[80, 77, 61])).
% 0.20/0.42 tff(82,plain,
% 0.20/0.42 ((p1(tptp_fun_Y_1(tptp_fun_X_6(Y!7))) | (~r1(tptp_fun_X_6(Y!7), tptp_fun_Y_1(tptp_fun_X_6(Y!7))))) | r1(tptp_fun_X_6(Y!7), tptp_fun_Y_1(tptp_fun_X_6(Y!7)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(83,plain,
% 0.20/0.42 (r1(tptp_fun_X_6(Y!7), tptp_fun_Y_1(tptp_fun_X_6(Y!7)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.20/0.42 tff(84,plain,
% 0.20/0.42 ((p1(tptp_fun_Y_1(tptp_fun_X_6(Y!7))) | (~r1(tptp_fun_X_6(Y!7), tptp_fun_Y_1(tptp_fun_X_6(Y!7))))) | (~p1(tptp_fun_Y_1(tptp_fun_X_6(Y!7))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(85,plain,
% 0.20/0.42 (~p1(tptp_fun_Y_1(tptp_fun_X_6(Y!7)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[84, 81])).
% 0.20/0.42 tff(86,plain,
% 0.20/0.42 (((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_6(Y!7), Y)))) | (p1(tptp_fun_Y_1(tptp_fun_X_6(Y!7))) | (~r1(tptp_fun_X_6(Y!7), tptp_fun_Y_1(tptp_fun_X_6(Y!7)))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_6(Y!7), Y)))) | p1(tptp_fun_Y_1(tptp_fun_X_6(Y!7))) | (~r1(tptp_fun_X_6(Y!7), tptp_fun_Y_1(tptp_fun_X_6(Y!7)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(87,plain,
% 0.20/0.42 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_6(Y!7), Y)))) | (p1(tptp_fun_Y_1(tptp_fun_X_6(Y!7))) | (~r1(tptp_fun_X_6(Y!7), tptp_fun_Y_1(tptp_fun_X_6(Y!7)))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(88,plain,
% 0.20/0.42 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_6(Y!7), Y)))) | p1(tptp_fun_Y_1(tptp_fun_X_6(Y!7))) | (~r1(tptp_fun_X_6(Y!7), tptp_fun_Y_1(tptp_fun_X_6(Y!7))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.20/0.42 tff(89,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[88, 85, 83, 65])).
% 0.20/0.42 % SZS output end Proof
%------------------------------------------------------------------------------