TSTP Solution File: LCL686+1.001 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL686+1.001 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 04:57:54 EDT 2022
% Result : Theorem 0.20s 0.48s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : LCL686+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Sep 2 00:34:49 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.20/0.48 % SZS status Theorem
% 0.20/0.48 % SZS output start Proof
% 0.20/0.48 tff(p2_type, type, (
% 0.20/0.48 p2: $i > $o)).
% 0.20/0.48 tff(tptp_fun_Y_6_type, type, (
% 0.20/0.48 tptp_fun_Y_6: $i > $i)).
% 0.20/0.48 tff(tptp_fun_Y_4_type, type, (
% 0.20/0.48 tptp_fun_Y_4: $i > $i)).
% 0.20/0.48 tff(tptp_fun_Y_5_type, type, (
% 0.20/0.48 tptp_fun_Y_5: $i > $i)).
% 0.20/0.48 tff(tptp_fun_Y_3_type, type, (
% 0.20/0.48 tptp_fun_Y_3: $i)).
% 0.20/0.48 tff(p1_type, type, (
% 0.20/0.48 p1: $i > $o)).
% 0.20/0.48 tff(r1_type, type, (
% 0.20/0.48 r1: ( $i * $i ) > $o)).
% 0.20/0.48 tff(p3_type, type, (
% 0.20/0.48 p3: $i > $o)).
% 0.20/0.48 tff(tptp_fun_X_0_type, type, (
% 0.20/0.48 tptp_fun_X_0: $i)).
% 0.20/0.48 tff(tptp_fun_Y_1_type, type, (
% 0.20/0.48 tptp_fun_Y_1: $i)).
% 0.20/0.48 tff(tptp_fun_X_2_type, type, (
% 0.20/0.48 tptp_fun_X_2: $i)).
% 0.20/0.48 tff(1,assumption,(~p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))), introduced(assumption)).
% 0.20/0.48 tff(2,plain,
% 0.20/0.48 (^[X: $i] : refl(r1(X, X) <=> r1(X, X))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(3,plain,
% 0.20/0.48 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 0.20/0.48 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.48 tff(4,plain,
% 0.20/0.48 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(5,axiom,(![X: $i] : r1(X, X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','reflexivity')).
% 0.20/0.48 tff(6,plain,
% 0.20/0.48 (![X: $i] : r1(X, X)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.48 tff(7,plain,(
% 0.20/0.48 ![X: $i] : r1(X, X)),
% 0.20/0.48 inference(skolemize,[status(sab)],[6])).
% 0.20/0.48 tff(8,plain,
% 0.20/0.48 (![X: $i] : r1(X, X)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.48 tff(9,plain,
% 0.20/0.48 ((~![X: $i] : r1(X, X)) | r1(Y!3, Y!3)),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(10,plain,
% 0.20/0.48 (r1(Y!3, Y!3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.20/0.48 tff(11,plain,
% 0.20/0.48 (^[X: $i] : refl(((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_5(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y))))))))))) <=> ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_5(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y))))))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(12,plain,
% 0.20/0.48 (![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_5(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y))))))))))) <=> ![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_5(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[11])).
% 0.20/0.48 tff(13,plain,
% 0.20/0.48 (^[X: $i] : rewrite(((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_5(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y))))))))))) <=> ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_5(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y))))))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(14,plain,
% 0.20/0.48 (![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_5(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y))))))))))) <=> ![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_5(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.48 tff(15,plain,
% 0.20/0.48 (![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_5(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y))))))))))) <=> ![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_5(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[14, 12])).
% 0.20/0.48 tff(16,plain,
% 0.20/0.48 (^[X: $i] : rewrite(((~r1(Y!3, X)) | ((~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)))) & ![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y))))) & r1(X, tptp_fun_Y_5(X)) & (~((~r1(X, tptp_fun_Y_6(X))) | (p2(tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X))) | ((~p1(tptp_fun_Y_6(X))) & (~p2(tptp_fun_Y_6(X)))))))) <=> ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_5(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y))))))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(17,plain,
% 0.20/0.48 (![X: $i] : ((~r1(Y!3, X)) | ((~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)))) & ![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y))))) & r1(X, tptp_fun_Y_5(X)) & (~((~r1(X, tptp_fun_Y_6(X))) | (p2(tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X))) | ((~p1(tptp_fun_Y_6(X))) & (~p2(tptp_fun_Y_6(X)))))))) <=> ![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_5(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[16])).
% 0.20/0.48 tff(18,plain,
% 0.20/0.48 (((r1(X!0, Y!1) & (~((~r1(Y!1, X!2)) | (~p1(X!2)))) & p3(Y!1)) & (r1(X!0, Y!3) & ![X: $i] : ((~r1(Y!3, X)) | ((~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)))) & ![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y))))) & r1(X, tptp_fun_Y_5(X)) & (~((~r1(X, tptp_fun_Y_6(X))) | (p2(tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X))) | ((~p1(tptp_fun_Y_6(X))) & (~p2(tptp_fun_Y_6(X)))))))))) <=> (r1(X!0, Y!1) & (~((~r1(Y!1, X!2)) | (~p1(X!2)))) & p3(Y!1) & r1(X!0, Y!3) & ![X: $i] : ((~r1(Y!3, X)) | ((~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)))) & ![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y))))) & r1(X, tptp_fun_Y_5(X)) & (~((~r1(X, tptp_fun_Y_6(X))) | (p2(tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X))) | ((~p1(tptp_fun_Y_6(X))) & (~p2(tptp_fun_Y_6(X)))))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(19,plain,
% 0.20/0.48 (((~(~r1(X!0, Y!3))) & ![X: $i] : ((~r1(Y!3, X)) | ((~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)))) & ![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y))))) & (~(~r1(X, tptp_fun_Y_5(X)))) & (~((~r1(X, tptp_fun_Y_6(X))) | (p2(tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X))) | ((~p1(tptp_fun_Y_6(X))) & (~p2(tptp_fun_Y_6(X))))))))) <=> (r1(X!0, Y!3) & ![X: $i] : ((~r1(Y!3, X)) | ((~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)))) & ![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y))))) & r1(X, tptp_fun_Y_5(X)) & (~((~r1(X, tptp_fun_Y_6(X))) | (p2(tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X))) | ((~p1(tptp_fun_Y_6(X))) & (~p2(tptp_fun_Y_6(X)))))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(20,plain,
% 0.20/0.49 (((~(~r1(X!0, Y!1))) & (~((~r1(Y!1, X!2)) | (~p1(X!2)))) & (~(~p3(Y!1)))) <=> (r1(X!0, Y!1) & (~((~r1(Y!1, X!2)) | (~p1(X!2)))) & p3(Y!1))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(21,plain,
% 0.20/0.49 ((((~(~r1(X!0, Y!1))) & (~((~r1(Y!1, X!2)) | (~p1(X!2)))) & (~(~p3(Y!1)))) & ((~(~r1(X!0, Y!3))) & ![X: $i] : ((~r1(Y!3, X)) | ((~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)))) & ![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y))))) & (~(~r1(X, tptp_fun_Y_5(X)))) & (~((~r1(X, tptp_fun_Y_6(X))) | (p2(tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X))) | ((~p1(tptp_fun_Y_6(X))) & (~p2(tptp_fun_Y_6(X)))))))))) <=> ((r1(X!0, Y!1) & (~((~r1(Y!1, X!2)) | (~p1(X!2)))) & p3(Y!1)) & (r1(X!0, Y!3) & ![X: $i] : ((~r1(Y!3, X)) | ((~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)))) & ![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y))))) & r1(X, tptp_fun_Y_5(X)) & (~((~r1(X, tptp_fun_Y_6(X))) | (p2(tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X))) | ((~p1(tptp_fun_Y_6(X))) & (~p2(tptp_fun_Y_6(X))))))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[20, 19])).
% 0.20/0.49 tff(22,plain,
% 0.20/0.49 ((((~(~r1(X!0, Y!1))) & (~((~r1(Y!1, X!2)) | (~p1(X!2)))) & (~(~p3(Y!1)))) & ((~(~r1(X!0, Y!3))) & ![X: $i] : ((~r1(Y!3, X)) | ((~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)))) & ![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y))))) & (~(~r1(X, tptp_fun_Y_5(X)))) & (~((~r1(X, tptp_fun_Y_6(X))) | (p2(tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X))) | ((~p1(tptp_fun_Y_6(X))) & (~p2(tptp_fun_Y_6(X)))))))))) <=> (r1(X!0, Y!1) & (~((~r1(Y!1, X!2)) | (~p1(X!2)))) & p3(Y!1) & r1(X!0, Y!3) & ![X: $i] : ((~r1(Y!3, X)) | ((~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)))) & ![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y))))) & r1(X, tptp_fun_Y_5(X)) & (~((~r1(X, tptp_fun_Y_6(X))) | (p2(tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X))) | ((~p1(tptp_fun_Y_6(X))) & (~p2(tptp_fun_Y_6(X)))))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[21, 18])).
% 0.20/0.49 tff(23,plain,
% 0.20/0.49 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X))) | (~p3(Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y)))))) | ![Y: $i] : (~r1(X, Y)) | ![Y: $i] : ((~r1(X, Y)) | (p2(Y) & p1(Y)) | ((~p1(Y)) & (~p2(Y))))))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X))) | (~p3(Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y)))))) | ![Y: $i] : (~r1(X, Y)) | ![Y: $i] : ((~r1(X, Y)) | (p2(Y) & p1(Y)) | ((~p1(Y)) & (~p2(Y)))))))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(24,plain,
% 0.20/0.49 ((~(~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X))) | (~p3(Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y)))))) | ![Y: $i] : (~r1(X, Y)) | ![Y: $i] : ((~r1(X, Y)) | (p2(Y) & p1(Y)) | ((~p1(Y)) & (~p2(Y))))))))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X))) | (~p3(Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y)))))) | ![Y: $i] : (~r1(X, Y)) | ![Y: $i] : ((~r1(X, Y)) | (p2(Y) & p1(Y)) | ((~p1(Y)) & (~p2(Y)))))))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(25,plain,
% 0.20/0.49 ((~?[X: $i] : (~(![Y: $i] : (((~r1(X, Y)) | (~p3(Y))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~(((![Y: $i] : ((~r1(X, Y)) | $false) | (~![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | ![Y: $i] : (((~r1(X, Y)) | ((~p1(Y)) & (~p2(Y)))) | (p2(Y) & p1(Y))))))))))) <=> (~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X))) | (~p3(Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y)))))) | ![Y: $i] : (~r1(X, Y)) | ![Y: $i] : ((~r1(X, Y)) | (p2(Y) & p1(Y)) | ((~p1(Y)) & (~p2(Y))))))))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(26,plain,
% 0.20/0.49 ((~(~?[X: $i] : (~(![Y: $i] : (((~r1(X, Y)) | (~p3(Y))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~(((![Y: $i] : ((~r1(X, Y)) | $false) | (~![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | ![Y: $i] : (((~r1(X, Y)) | ((~p1(Y)) & (~p2(Y)))) | (p2(Y) & p1(Y)))))))))))) <=> (~(~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X))) | (~p3(Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y)))))) | ![Y: $i] : (~r1(X, Y)) | ![Y: $i] : ((~r1(X, Y)) | (p2(Y) & p1(Y)) | ((~p1(Y)) & (~p2(Y)))))))))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[25])).
% 0.20/0.49 tff(27,plain,
% 0.20/0.49 ((~(~?[X: $i] : (~(![Y: $i] : (((~r1(X, Y)) | (~p3(Y))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~(((![Y: $i] : ((~r1(X, Y)) | $false) | (~![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | ![Y: $i] : (((~r1(X, Y)) | ((~p1(Y)) & (~p2(Y)))) | (p2(Y) & p1(Y)))))))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X))) | (~p3(Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y)))))) | ![Y: $i] : (~r1(X, Y)) | ![Y: $i] : ((~r1(X, Y)) | (p2(Y) & p1(Y)) | ((~p1(Y)) & (~p2(Y)))))))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[26, 24])).
% 0.20/0.49 tff(28,axiom,(~(~?[X: $i] : (~(![Y: $i] : (((~r1(X, Y)) | (~p3(Y))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~(((![Y: $i] : ((~r1(X, Y)) | $false) | (~![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | ![Y: $i] : (((~r1(X, Y)) | ((~p1(Y)) & (~p2(Y)))) | (p2(Y) & p1(Y)))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','main')).
% 0.20/0.49 tff(29,plain,
% 0.20/0.49 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X))) | (~p3(Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y)))))) | ![Y: $i] : (~r1(X, Y)) | ![Y: $i] : ((~r1(X, Y)) | (p2(Y) & p1(Y)) | ((~p1(Y)) & (~p2(Y)))))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.49 tff(30,plain,
% 0.20/0.49 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X))) | (~p3(Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y)))))) | ![Y: $i] : (~r1(X, Y)) | ![Y: $i] : ((~r1(X, Y)) | (p2(Y) & p1(Y)) | ((~p1(Y)) & (~p2(Y)))))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[29, 23])).
% 0.20/0.49 tff(31,plain,
% 0.20/0.49 (r1(X!0, Y!1) & (~((~r1(Y!1, X!2)) | (~p1(X!2)))) & p3(Y!1) & r1(X!0, Y!3) & ![X: $i] : ((~r1(Y!3, X)) | ((~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)))) & ![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y))))) & r1(X, tptp_fun_Y_5(X)) & (~((~r1(X, tptp_fun_Y_6(X))) | (p2(tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X))) | ((~p1(tptp_fun_Y_6(X))) & (~p2(tptp_fun_Y_6(X))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[30, 22])).
% 0.20/0.49 tff(32,plain,
% 0.20/0.49 (![X: $i] : ((~r1(Y!3, X)) | ((~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)))) & ![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y))))) & r1(X, tptp_fun_Y_5(X)) & (~((~r1(X, tptp_fun_Y_6(X))) | (p2(tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X))) | ((~p1(tptp_fun_Y_6(X))) & (~p2(tptp_fun_Y_6(X))))))))),
% 0.20/0.49 inference(and_elim,[status(thm)],[31])).
% 0.20/0.49 tff(33,plain,
% 0.20/0.49 (![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_5(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[32, 17])).
% 0.20/0.49 tff(34,plain,
% 0.20/0.49 (![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_5(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[33, 15])).
% 0.20/0.49 tff(35,plain,
% 0.20/0.49 (((~![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_5(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))) | ((~r1(Y!3, Y!3)) | (~((~r1(Y!3, tptp_fun_Y_4(Y!3))) | p3(tptp_fun_Y_4(Y!3)) | (~![Y: $i] : ((~r1(Y!3, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~r1(Y!3, tptp_fun_Y_5(Y!3))) | (~(p1(tptp_fun_Y_6(Y!3)) | p2(tptp_fun_Y_6(Y!3)))) | (~((~p1(tptp_fun_Y_6(Y!3))) | (~p2(tptp_fun_Y_6(Y!3))))) | (~r1(Y!3, tptp_fun_Y_6(Y!3))))))) <=> ((~![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_5(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))) | (~r1(Y!3, Y!3)) | (~((~r1(Y!3, tptp_fun_Y_4(Y!3))) | p3(tptp_fun_Y_4(Y!3)) | (~![Y: $i] : ((~r1(Y!3, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~r1(Y!3, tptp_fun_Y_5(Y!3))) | (~(p1(tptp_fun_Y_6(Y!3)) | p2(tptp_fun_Y_6(Y!3)))) | (~((~p1(tptp_fun_Y_6(Y!3))) | (~p2(tptp_fun_Y_6(Y!3))))) | (~r1(Y!3, tptp_fun_Y_6(Y!3))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(36,plain,
% 0.20/0.49 (((~r1(Y!3, Y!3)) | (~((~r1(Y!3, tptp_fun_Y_4(Y!3))) | p3(tptp_fun_Y_4(Y!3)) | (~r1(Y!3, tptp_fun_Y_5(Y!3))) | (~r1(Y!3, tptp_fun_Y_6(Y!3))) | (~((~p1(tptp_fun_Y_6(Y!3))) | (~p2(tptp_fun_Y_6(Y!3))))) | (~(p1(tptp_fun_Y_6(Y!3)) | p2(tptp_fun_Y_6(Y!3)))) | (~![Y: $i] : ((~r1(Y!3, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y))))))))))) <=> ((~r1(Y!3, Y!3)) | (~((~r1(Y!3, tptp_fun_Y_4(Y!3))) | p3(tptp_fun_Y_4(Y!3)) | (~![Y: $i] : ((~r1(Y!3, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~r1(Y!3, tptp_fun_Y_5(Y!3))) | (~(p1(tptp_fun_Y_6(Y!3)) | p2(tptp_fun_Y_6(Y!3)))) | (~((~p1(tptp_fun_Y_6(Y!3))) | (~p2(tptp_fun_Y_6(Y!3))))) | (~r1(Y!3, tptp_fun_Y_6(Y!3))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(37,plain,
% 0.20/0.49 (((~![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_5(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))) | ((~r1(Y!3, Y!3)) | (~((~r1(Y!3, tptp_fun_Y_4(Y!3))) | p3(tptp_fun_Y_4(Y!3)) | (~r1(Y!3, tptp_fun_Y_5(Y!3))) | (~r1(Y!3, tptp_fun_Y_6(Y!3))) | (~((~p1(tptp_fun_Y_6(Y!3))) | (~p2(tptp_fun_Y_6(Y!3))))) | (~(p1(tptp_fun_Y_6(Y!3)) | p2(tptp_fun_Y_6(Y!3)))) | (~![Y: $i] : ((~r1(Y!3, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))) <=> ((~![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_5(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))) | ((~r1(Y!3, Y!3)) | (~((~r1(Y!3, tptp_fun_Y_4(Y!3))) | p3(tptp_fun_Y_4(Y!3)) | (~![Y: $i] : ((~r1(Y!3, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~r1(Y!3, tptp_fun_Y_5(Y!3))) | (~(p1(tptp_fun_Y_6(Y!3)) | p2(tptp_fun_Y_6(Y!3)))) | (~((~p1(tptp_fun_Y_6(Y!3))) | (~p2(tptp_fun_Y_6(Y!3))))) | (~r1(Y!3, tptp_fun_Y_6(Y!3)))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[36])).
% 0.20/0.49 tff(38,plain,
% 0.20/0.49 (((~![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_5(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))) | ((~r1(Y!3, Y!3)) | (~((~r1(Y!3, tptp_fun_Y_4(Y!3))) | p3(tptp_fun_Y_4(Y!3)) | (~r1(Y!3, tptp_fun_Y_5(Y!3))) | (~r1(Y!3, tptp_fun_Y_6(Y!3))) | (~((~p1(tptp_fun_Y_6(Y!3))) | (~p2(tptp_fun_Y_6(Y!3))))) | (~(p1(tptp_fun_Y_6(Y!3)) | p2(tptp_fun_Y_6(Y!3)))) | (~![Y: $i] : ((~r1(Y!3, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))) <=> ((~![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_5(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))) | (~r1(Y!3, Y!3)) | (~((~r1(Y!3, tptp_fun_Y_4(Y!3))) | p3(tptp_fun_Y_4(Y!3)) | (~![Y: $i] : ((~r1(Y!3, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~r1(Y!3, tptp_fun_Y_5(Y!3))) | (~(p1(tptp_fun_Y_6(Y!3)) | p2(tptp_fun_Y_6(Y!3)))) | (~((~p1(tptp_fun_Y_6(Y!3))) | (~p2(tptp_fun_Y_6(Y!3))))) | (~r1(Y!3, tptp_fun_Y_6(Y!3))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[37, 35])).
% 0.20/0.49 tff(39,plain,
% 0.20/0.49 ((~![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_5(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))) | ((~r1(Y!3, Y!3)) | (~((~r1(Y!3, tptp_fun_Y_4(Y!3))) | p3(tptp_fun_Y_4(Y!3)) | (~r1(Y!3, tptp_fun_Y_5(Y!3))) | (~r1(Y!3, tptp_fun_Y_6(Y!3))) | (~((~p1(tptp_fun_Y_6(Y!3))) | (~p2(tptp_fun_Y_6(Y!3))))) | (~(p1(tptp_fun_Y_6(Y!3)) | p2(tptp_fun_Y_6(Y!3)))) | (~![Y: $i] : ((~r1(Y!3, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(40,plain,
% 0.20/0.49 ((~![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_5(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))) | (~r1(Y!3, Y!3)) | (~((~r1(Y!3, tptp_fun_Y_4(Y!3))) | p3(tptp_fun_Y_4(Y!3)) | (~![Y: $i] : ((~r1(Y!3, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~r1(Y!3, tptp_fun_Y_5(Y!3))) | (~(p1(tptp_fun_Y_6(Y!3)) | p2(tptp_fun_Y_6(Y!3)))) | (~((~p1(tptp_fun_Y_6(Y!3))) | (~p2(tptp_fun_Y_6(Y!3))))) | (~r1(Y!3, tptp_fun_Y_6(Y!3)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.20/0.49 tff(41,plain,
% 0.20/0.49 (~((~r1(Y!3, tptp_fun_Y_4(Y!3))) | p3(tptp_fun_Y_4(Y!3)) | (~![Y: $i] : ((~r1(Y!3, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~r1(Y!3, tptp_fun_Y_5(Y!3))) | (~(p1(tptp_fun_Y_6(Y!3)) | p2(tptp_fun_Y_6(Y!3)))) | (~((~p1(tptp_fun_Y_6(Y!3))) | (~p2(tptp_fun_Y_6(Y!3))))) | (~r1(Y!3, tptp_fun_Y_6(Y!3))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[40, 34, 10])).
% 0.20/0.49 tff(42,plain,
% 0.20/0.49 (((~r1(Y!3, tptp_fun_Y_4(Y!3))) | p3(tptp_fun_Y_4(Y!3)) | (~![Y: $i] : ((~r1(Y!3, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~r1(Y!3, tptp_fun_Y_5(Y!3))) | (~(p1(tptp_fun_Y_6(Y!3)) | p2(tptp_fun_Y_6(Y!3)))) | (~((~p1(tptp_fun_Y_6(Y!3))) | (~p2(tptp_fun_Y_6(Y!3))))) | (~r1(Y!3, tptp_fun_Y_6(Y!3)))) | r1(Y!3, tptp_fun_Y_6(Y!3))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(43,plain,
% 0.20/0.49 (r1(Y!3, tptp_fun_Y_6(Y!3))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.20/0.49 tff(44,plain,
% 0.20/0.49 (((~![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_5(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))) | ((~r1(Y!3, tptp_fun_Y_6(Y!3))) | (~(p3(tptp_fun_Y_4(tptp_fun_Y_6(Y!3))) | (~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | (~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_4(tptp_fun_Y_6(Y!3)))) | (~![Y: $i] : ((~r1(tptp_fun_Y_6(Y!3), Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~(p1(tptp_fun_Y_6(tptp_fun_Y_6(Y!3))) | p2(tptp_fun_Y_6(tptp_fun_Y_6(Y!3))))) | (~((~p1(tptp_fun_Y_6(tptp_fun_Y_6(Y!3)))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_6(Y!3)))))) | (~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_6(tptp_fun_Y_6(Y!3)))))))) <=> ((~![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_5(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))) | (~r1(Y!3, tptp_fun_Y_6(Y!3))) | (~(p3(tptp_fun_Y_4(tptp_fun_Y_6(Y!3))) | (~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | (~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_4(tptp_fun_Y_6(Y!3)))) | (~![Y: $i] : ((~r1(tptp_fun_Y_6(Y!3), Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~(p1(tptp_fun_Y_6(tptp_fun_Y_6(Y!3))) | p2(tptp_fun_Y_6(tptp_fun_Y_6(Y!3))))) | (~((~p1(tptp_fun_Y_6(tptp_fun_Y_6(Y!3)))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_6(Y!3)))))) | (~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_6(tptp_fun_Y_6(Y!3)))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(45,plain,
% 0.20/0.49 (((~r1(Y!3, tptp_fun_Y_6(Y!3))) | (~((~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_4(tptp_fun_Y_6(Y!3)))) | p3(tptp_fun_Y_4(tptp_fun_Y_6(Y!3))) | (~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | (~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_6(tptp_fun_Y_6(Y!3)))) | (~((~p1(tptp_fun_Y_6(tptp_fun_Y_6(Y!3)))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_6(Y!3)))))) | (~(p1(tptp_fun_Y_6(tptp_fun_Y_6(Y!3))) | p2(tptp_fun_Y_6(tptp_fun_Y_6(Y!3))))) | (~![Y: $i] : ((~r1(tptp_fun_Y_6(Y!3), Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y))))))))))) <=> ((~r1(Y!3, tptp_fun_Y_6(Y!3))) | (~(p3(tptp_fun_Y_4(tptp_fun_Y_6(Y!3))) | (~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | (~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_4(tptp_fun_Y_6(Y!3)))) | (~![Y: $i] : ((~r1(tptp_fun_Y_6(Y!3), Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~(p1(tptp_fun_Y_6(tptp_fun_Y_6(Y!3))) | p2(tptp_fun_Y_6(tptp_fun_Y_6(Y!3))))) | (~((~p1(tptp_fun_Y_6(tptp_fun_Y_6(Y!3)))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_6(Y!3)))))) | (~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_6(tptp_fun_Y_6(Y!3)))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(46,plain,
% 0.20/0.49 (((~![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_5(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))) | ((~r1(Y!3, tptp_fun_Y_6(Y!3))) | (~((~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_4(tptp_fun_Y_6(Y!3)))) | p3(tptp_fun_Y_4(tptp_fun_Y_6(Y!3))) | (~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | (~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_6(tptp_fun_Y_6(Y!3)))) | (~((~p1(tptp_fun_Y_6(tptp_fun_Y_6(Y!3)))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_6(Y!3)))))) | (~(p1(tptp_fun_Y_6(tptp_fun_Y_6(Y!3))) | p2(tptp_fun_Y_6(tptp_fun_Y_6(Y!3))))) | (~![Y: $i] : ((~r1(tptp_fun_Y_6(Y!3), Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))) <=> ((~![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_5(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))) | ((~r1(Y!3, tptp_fun_Y_6(Y!3))) | (~(p3(tptp_fun_Y_4(tptp_fun_Y_6(Y!3))) | (~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | (~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_4(tptp_fun_Y_6(Y!3)))) | (~![Y: $i] : ((~r1(tptp_fun_Y_6(Y!3), Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~(p1(tptp_fun_Y_6(tptp_fun_Y_6(Y!3))) | p2(tptp_fun_Y_6(tptp_fun_Y_6(Y!3))))) | (~((~p1(tptp_fun_Y_6(tptp_fun_Y_6(Y!3)))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_6(Y!3)))))) | (~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_6(tptp_fun_Y_6(Y!3))))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[45])).
% 0.20/0.49 tff(47,plain,
% 0.20/0.49 (((~![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_5(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))) | ((~r1(Y!3, tptp_fun_Y_6(Y!3))) | (~((~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_4(tptp_fun_Y_6(Y!3)))) | p3(tptp_fun_Y_4(tptp_fun_Y_6(Y!3))) | (~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | (~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_6(tptp_fun_Y_6(Y!3)))) | (~((~p1(tptp_fun_Y_6(tptp_fun_Y_6(Y!3)))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_6(Y!3)))))) | (~(p1(tptp_fun_Y_6(tptp_fun_Y_6(Y!3))) | p2(tptp_fun_Y_6(tptp_fun_Y_6(Y!3))))) | (~![Y: $i] : ((~r1(tptp_fun_Y_6(Y!3), Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))) <=> ((~![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_5(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))) | (~r1(Y!3, tptp_fun_Y_6(Y!3))) | (~(p3(tptp_fun_Y_4(tptp_fun_Y_6(Y!3))) | (~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | (~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_4(tptp_fun_Y_6(Y!3)))) | (~![Y: $i] : ((~r1(tptp_fun_Y_6(Y!3), Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~(p1(tptp_fun_Y_6(tptp_fun_Y_6(Y!3))) | p2(tptp_fun_Y_6(tptp_fun_Y_6(Y!3))))) | (~((~p1(tptp_fun_Y_6(tptp_fun_Y_6(Y!3)))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_6(Y!3)))))) | (~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_6(tptp_fun_Y_6(Y!3)))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[46, 44])).
% 0.20/0.49 tff(48,plain,
% 0.20/0.49 ((~![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_5(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))) | ((~r1(Y!3, tptp_fun_Y_6(Y!3))) | (~((~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_4(tptp_fun_Y_6(Y!3)))) | p3(tptp_fun_Y_4(tptp_fun_Y_6(Y!3))) | (~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | (~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_6(tptp_fun_Y_6(Y!3)))) | (~((~p1(tptp_fun_Y_6(tptp_fun_Y_6(Y!3)))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_6(Y!3)))))) | (~(p1(tptp_fun_Y_6(tptp_fun_Y_6(Y!3))) | p2(tptp_fun_Y_6(tptp_fun_Y_6(Y!3))))) | (~![Y: $i] : ((~r1(tptp_fun_Y_6(Y!3), Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(49,plain,
% 0.20/0.49 ((~![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_5(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))) | (~r1(Y!3, tptp_fun_Y_6(Y!3))) | (~(p3(tptp_fun_Y_4(tptp_fun_Y_6(Y!3))) | (~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | (~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_4(tptp_fun_Y_6(Y!3)))) | (~![Y: $i] : ((~r1(tptp_fun_Y_6(Y!3), Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~(p1(tptp_fun_Y_6(tptp_fun_Y_6(Y!3))) | p2(tptp_fun_Y_6(tptp_fun_Y_6(Y!3))))) | (~((~p1(tptp_fun_Y_6(tptp_fun_Y_6(Y!3)))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_6(Y!3)))))) | (~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_6(tptp_fun_Y_6(Y!3))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.20/0.50 tff(50,plain,
% 0.20/0.50 (~(p3(tptp_fun_Y_4(tptp_fun_Y_6(Y!3))) | (~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | (~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_4(tptp_fun_Y_6(Y!3)))) | (~![Y: $i] : ((~r1(tptp_fun_Y_6(Y!3), Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~(p1(tptp_fun_Y_6(tptp_fun_Y_6(Y!3))) | p2(tptp_fun_Y_6(tptp_fun_Y_6(Y!3))))) | (~((~p1(tptp_fun_Y_6(tptp_fun_Y_6(Y!3)))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_6(Y!3)))))) | (~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_6(tptp_fun_Y_6(Y!3)))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[49, 34, 43])).
% 0.20/0.50 tff(51,plain,
% 0.20/0.50 ((p3(tptp_fun_Y_4(tptp_fun_Y_6(Y!3))) | (~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | (~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_4(tptp_fun_Y_6(Y!3)))) | (~![Y: $i] : ((~r1(tptp_fun_Y_6(Y!3), Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~(p1(tptp_fun_Y_6(tptp_fun_Y_6(Y!3))) | p2(tptp_fun_Y_6(tptp_fun_Y_6(Y!3))))) | (~((~p1(tptp_fun_Y_6(tptp_fun_Y_6(Y!3)))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_6(Y!3)))))) | (~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_6(tptp_fun_Y_6(Y!3))))) | r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(52,plain,
% 0.20/0.50 (r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.20/0.50 tff(53,plain,
% 0.20/0.50 (![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(54,plain,
% 0.20/0.50 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((r1(X, Y) & r1(Y, Z)) <=> (~((~r1(Y, Z)) | (~r1(X, Y))))), ((~(r1(X, Y) & r1(Y, Z))) <=> (~(~((~r1(Y, Z)) | (~r1(X, Y))))))), rewrite((~(~((~r1(Y, Z)) | (~r1(X, Y))))) <=> ((~r1(Y, Z)) | (~r1(X, Y)))), ((~(r1(X, Y) & r1(Y, Z))) <=> ((~r1(Y, Z)) | (~r1(X, Y))))), (((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z)) <=> (((~r1(Y, Z)) | (~r1(X, Y))) | r1(X, Z)))), rewrite((((~r1(Y, Z)) | (~r1(X, Y))) | r1(X, Z)) <=> (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))), (((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z)) <=> (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(55,plain,
% 0.20/0.50 (![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[54])).
% 0.20/0.50 tff(56,plain,
% 0.20/0.50 (![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(57,plain,
% 0.20/0.50 (^[X: $i, Y: $i, Z: $i] : rewrite(((r1(X, Y) & r1(Y, Z)) => r1(X, Z)) <=> ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z)))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(58,plain,
% 0.20/0.50 (![X: $i, Y: $i, Z: $i] : ((r1(X, Y) & r1(Y, Z)) => r1(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[57])).
% 0.20/0.50 tff(59,axiom,(![X: $i, Y: $i, Z: $i] : ((r1(X, Y) & r1(Y, Z)) => r1(X, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','transitivity')).
% 0.20/0.50 tff(60,plain,
% 0.20/0.50 (![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.20/0.50 tff(61,plain,
% 0.20/0.50 (![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.20/0.50 tff(62,plain,(
% 0.20/0.50 ![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 0.20/0.50 inference(skolemize,[status(sab)],[61])).
% 0.20/0.50 tff(63,plain,
% 0.20/0.50 (![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.20/0.50 tff(64,plain,
% 0.20/0.50 (![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[63, 53])).
% 0.20/0.50 tff(65,plain,
% 0.20/0.50 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | (~r1(Y!3, tptp_fun_Y_6(Y!3))) | r1(Y!3, tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | (~r1(Y!3, tptp_fun_Y_6(Y!3))) | r1(Y!3, tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(66,plain,
% 0.20/0.50 ((r1(Y!3, tptp_fun_Y_5(tptp_fun_Y_6(Y!3))) | (~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | (~r1(Y!3, tptp_fun_Y_6(Y!3)))) <=> ((~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | (~r1(Y!3, tptp_fun_Y_6(Y!3))) | r1(Y!3, tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(67,plain,
% 0.20/0.50 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!3, tptp_fun_Y_5(tptp_fun_Y_6(Y!3))) | (~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | (~r1(Y!3, tptp_fun_Y_6(Y!3))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | (~r1(Y!3, tptp_fun_Y_6(Y!3))) | r1(Y!3, tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[66])).
% 0.20/0.50 tff(68,plain,
% 0.20/0.50 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!3, tptp_fun_Y_5(tptp_fun_Y_6(Y!3))) | (~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | (~r1(Y!3, tptp_fun_Y_6(Y!3))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | (~r1(Y!3, tptp_fun_Y_6(Y!3))) | r1(Y!3, tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[67, 65])).
% 0.20/0.50 tff(69,plain,
% 0.20/0.50 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!3, tptp_fun_Y_5(tptp_fun_Y_6(Y!3))) | (~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | (~r1(Y!3, tptp_fun_Y_6(Y!3))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(70,plain,
% 0.20/0.50 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(tptp_fun_Y_6(Y!3), tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | (~r1(Y!3, tptp_fun_Y_6(Y!3))) | r1(Y!3, tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.20/0.50 tff(71,plain,
% 0.20/0.50 (r1(Y!3, tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[70, 64, 43, 52])).
% 0.20/0.50 tff(72,plain,
% 0.20/0.50 (((~![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_5(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))) | ((~r1(Y!3, tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | (~((~r1(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | p3(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | (~r1(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)), tptp_fun_Y_5(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~r1(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)), tptp_fun_Y_6(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~((~p1(tptp_fun_Y_6(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))))) | (~(p1(tptp_fun_Y_6(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | p2(tptp_fun_Y_6(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | (~![Y: $i] : ((~r1(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)), Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))) <=> ((~![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_5(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))) | (~r1(Y!3, tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | (~((~r1(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | p3(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | (~r1(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)), tptp_fun_Y_5(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~r1(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)), tptp_fun_Y_6(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~((~p1(tptp_fun_Y_6(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))))) | (~(p1(tptp_fun_Y_6(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | p2(tptp_fun_Y_6(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | (~![Y: $i] : ((~r1(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)), Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(73,plain,
% 0.20/0.50 ((~![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_5(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))) | ((~r1(Y!3, tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | (~((~r1(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | p3(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | (~r1(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)), tptp_fun_Y_5(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~r1(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)), tptp_fun_Y_6(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~((~p1(tptp_fun_Y_6(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))))) | (~(p1(tptp_fun_Y_6(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | p2(tptp_fun_Y_6(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | (~![Y: $i] : ((~r1(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)), Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(74,plain,
% 0.20/0.50 ((~![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_5(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))) | (~r1(Y!3, tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | (~((~r1(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | p3(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | (~r1(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)), tptp_fun_Y_5(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~r1(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)), tptp_fun_Y_6(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~((~p1(tptp_fun_Y_6(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))))) | (~(p1(tptp_fun_Y_6(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | p2(tptp_fun_Y_6(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | (~![Y: $i] : ((~r1(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)), Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y))))))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.20/0.50 tff(75,plain,
% 0.20/0.50 (~((~r1(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | p3(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | (~r1(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)), tptp_fun_Y_5(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~r1(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)), tptp_fun_Y_6(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~((~p1(tptp_fun_Y_6(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))))) | (~(p1(tptp_fun_Y_6(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | p2(tptp_fun_Y_6(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | (~![Y: $i] : ((~r1(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)), Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[74, 34, 71])).
% 0.20/0.50 tff(76,plain,
% 0.20/0.50 (((~r1(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | p3(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | (~r1(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)), tptp_fun_Y_5(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~r1(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)), tptp_fun_Y_6(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~((~p1(tptp_fun_Y_6(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))))) | (~(p1(tptp_fun_Y_6(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | p2(tptp_fun_Y_6(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | (~![Y: $i] : ((~r1(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)), Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y))))))))) | r1(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(77,plain,
% 0.20/0.50 (r1(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.20/0.50 tff(78,plain,
% 0.20/0.50 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!3, tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | (~r1(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | r1(Y!3, tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!3, tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | (~r1(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | r1(Y!3, tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(79,plain,
% 0.20/0.50 ((r1(Y!3, tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | (~r1(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~r1(Y!3, tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) <=> ((~r1(Y!3, tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | (~r1(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | r1(Y!3, tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(80,plain,
% 0.20/0.50 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!3, tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | (~r1(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~r1(Y!3, tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!3, tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | (~r1(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | r1(Y!3, tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[79])).
% 0.20/0.50 tff(81,plain,
% 0.20/0.50 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!3, tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | (~r1(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~r1(Y!3, tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!3, tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | (~r1(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | r1(Y!3, tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[80, 78])).
% 0.20/0.50 tff(82,plain,
% 0.20/0.50 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!3, tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | (~r1(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~r1(Y!3, tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(83,plain,
% 0.20/0.50 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!3, tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))) | (~r1(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | r1(Y!3, tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.50 tff(84,plain,
% 0.20/0.50 (r1(Y!3, tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[83, 64, 71, 77])).
% 0.20/0.50 tff(85,plain,
% 0.20/0.50 (((~![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_5(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))) | ((~r1(Y!3, tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~((~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), tptp_fun_Y_4(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | p3(tptp_fun_Y_4(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), tptp_fun_Y_5(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | (~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | (~((~p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))))) | (~(p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))))) | (~![Y: $i] : ((~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))) <=> ((~![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_5(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))) | (~r1(Y!3, tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~((~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), tptp_fun_Y_4(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | p3(tptp_fun_Y_4(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), tptp_fun_Y_5(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | (~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | (~((~p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))))) | (~(p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))))) | (~![Y: $i] : ((~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(86,plain,
% 0.20/0.50 ((~![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_5(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))) | ((~r1(Y!3, tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~((~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), tptp_fun_Y_4(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | p3(tptp_fun_Y_4(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), tptp_fun_Y_5(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | (~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | (~((~p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))))) | (~(p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))))) | (~![Y: $i] : ((~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(87,plain,
% 0.20/0.50 ((~![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_5(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))) | (~r1(Y!3, tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~((~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), tptp_fun_Y_4(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | p3(tptp_fun_Y_4(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), tptp_fun_Y_5(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | (~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | (~((~p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))))) | (~(p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))))) | (~![Y: $i] : ((~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y))))))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.20/0.50 tff(88,plain,
% 0.20/0.50 (~((~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), tptp_fun_Y_4(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | p3(tptp_fun_Y_4(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), tptp_fun_Y_5(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | (~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | (~((~p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))))) | (~(p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))))) | (~![Y: $i] : ((~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[87, 34, 84])).
% 0.20/0.50 tff(89,plain,
% 0.20/0.50 (((~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), tptp_fun_Y_4(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | p3(tptp_fun_Y_4(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), tptp_fun_Y_5(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | (~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | (~((~p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))))) | (~(p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))))) | (~![Y: $i] : ((~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y))))))))) | (p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(90,plain,
% 0.20/0.50 (p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.20/0.50 tff(91,plain,
% 0.20/0.50 ((~(p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))))) | p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(92,plain,
% 0.20/0.50 (p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.20/0.50 tff(93,plain,
% 0.20/0.50 (p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[92, 1])).
% 0.20/0.50 tff(94,plain,
% 0.20/0.50 (((~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), tptp_fun_Y_4(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | p3(tptp_fun_Y_4(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), tptp_fun_Y_5(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | (~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | (~((~p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))))) | (~(p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))))) | (~![Y: $i] : ((~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y))))))))) | ![Y: $i] : ((~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(95,plain,
% 0.20/0.50 (![Y: $i] : ((~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[94, 88])).
% 0.20/0.50 tff(96,plain,
% 0.20/0.50 (((~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), tptp_fun_Y_4(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | p3(tptp_fun_Y_4(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), tptp_fun_Y_5(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | (~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | (~((~p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))))) | (~(p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))))) | (~![Y: $i] : ((~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y))))))))) | r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(97,plain,
% 0.20/0.50 (r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[96, 88])).
% 0.20/0.50 tff(98,plain,
% 0.20/0.50 (((~![Y: $i] : ((~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | ((~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | (~((~(p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))))) | (~(p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))))))))) <=> ((~![Y: $i] : ((~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | (~((~(p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))))) | (~(p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(99,plain,
% 0.20/0.50 ((~![Y: $i] : ((~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | ((~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | (~((~(p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))))) | (~(p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))))))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(100,plain,
% 0.20/0.50 ((~![Y: $i] : ((~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | (~((~(p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))))) | (~(p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.20/0.50 tff(101,plain,
% 0.20/0.50 (~((~(p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))))) | (~(p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[100, 97, 95])).
% 0.20/0.50 tff(102,plain,
% 0.20/0.50 (((~(p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))))) | (~(p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))))))) | (p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(103,plain,
% 0.20/0.50 (p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.20/0.50 tff(104,plain,
% 0.20/0.50 ((~(p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))))) | p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(105,plain,
% 0.20/0.50 (p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.20/0.50 tff(106,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[105, 93, 1])).
% 0.20/0.50 tff(107,plain,(p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(108,plain,
% 0.20/0.50 (((~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), tptp_fun_Y_4(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | p3(tptp_fun_Y_4(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), tptp_fun_Y_5(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | (~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | (~((~p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))))) | (~(p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))))) | (~![Y: $i] : ((~r1(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))), Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y))))))))) | ((~p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(109,plain,
% 0.20/0.50 ((~p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[108, 88])).
% 0.20/0.50 tff(110,plain,
% 0.20/0.50 ((~((~p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))))) | (~p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(111,plain,
% 0.20/0.50 ((~p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.20/0.50 tff(112,plain,
% 0.20/0.50 (~p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[111, 107])).
% 0.20/0.50 tff(113,plain,
% 0.20/0.50 (((~(p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))))) | (~(p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))))))) | (p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(114,plain,
% 0.20/0.50 (p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[113, 101])).
% 0.20/0.50 tff(115,plain,
% 0.20/0.50 ((~(p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3)))))))) | p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(116,plain,
% 0.20/0.51 (p1(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))) | (~p2(tptp_fun_Y_6(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_6(Y!3))))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[115, 114])).
% 0.20/0.51 tff(117,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[116, 112, 107])).
% 0.20/0.51 % SZS output end Proof
%------------------------------------------------------------------------------