TSTP Solution File: SET047+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET047+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 05:05:09 EDT 2022
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET047+1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 01:46:39 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(element_type, type, (
% 0.13/0.39 element: ( $i * $i ) > $o)).
% 0.13/0.39 tff(tptp_fun_X_2_type, type, (
% 0.13/0.39 tptp_fun_X_2: $i)).
% 0.13/0.39 tff(tptp_fun_Z_0_type, type, (
% 0.13/0.39 tptp_fun_Z_0: ( $i * $i ) > $i)).
% 0.13/0.39 tff(tptp_fun_Y_1_type, type, (
% 0.13/0.39 tptp_fun_Y_1: $i)).
% 0.13/0.39 tff(set_equal_type, type, (
% 0.13/0.39 set_equal: ( $i * $i ) > $o)).
% 0.13/0.39 tff(1,assumption,(~set_equal(Y!1, X!2)), introduced(assumption)).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 ((~(set_equal(X!2, Y!1) <=> set_equal(Y!1, X!2))) <=> ((~set_equal(X!2, Y!1)) <=> set_equal(Y!1, X!2))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 ((~![X: $i, Y: $i] : (set_equal(X, Y) <=> set_equal(Y, X))) <=> (~![X: $i, Y: $i] : (set_equal(X, Y) <=> set_equal(Y, X)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(4,axiom,(~![X: $i, Y: $i] : (set_equal(X, Y) <=> set_equal(Y, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel43')).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (~![X: $i, Y: $i] : (set_equal(X, Y) <=> set_equal(Y, X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 (~![X: $i, Y: $i] : (set_equal(X, Y) <=> set_equal(Y, X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[5, 3])).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (~![X: $i, Y: $i] : (set_equal(X, Y) <=> set_equal(Y, X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[6, 3])).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 (~![X: $i, Y: $i] : (set_equal(X, Y) <=> set_equal(Y, X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 (~![X: $i, Y: $i] : (set_equal(X, Y) <=> set_equal(Y, X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 (~![X: $i, Y: $i] : (set_equal(X, Y) <=> set_equal(Y, X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[9, 3])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 (~![X: $i, Y: $i] : (set_equal(X, Y) <=> set_equal(Y, X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.13/0.39 tff(12,plain,(
% 0.13/0.39 ~(set_equal(X!2, Y!1) <=> set_equal(Y!1, X!2))),
% 0.13/0.39 inference(skolemize,[status(sab)],[11])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 ((~set_equal(X!2, Y!1)) <=> set_equal(Y!1, X!2)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 (set_equal(X!2, Y!1) | set_equal(Y!1, X!2) | (~((~set_equal(X!2, Y!1)) <=> set_equal(Y!1, X!2)))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (set_equal(X!2, Y!1) | set_equal(Y!1, X!2)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 (set_equal(X!2, Y!1)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[15, 1])).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 (^[X: $i, Y: $i] : refl((~((~((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y)))) | (~(set_equal(X, Y) | ((~element(tptp_fun_Z_0(Y, X), X)) <=> element(tptp_fun_Z_0(Y, X), Y)))))) <=> (~((~((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y)))) | (~(set_equal(X, Y) | ((~element(tptp_fun_Z_0(Y, X), X)) <=> element(tptp_fun_Z_0(Y, X), Y)))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 (![X: $i, Y: $i] : (~((~((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y)))) | (~(set_equal(X, Y) | ((~element(tptp_fun_Z_0(Y, X), X)) <=> element(tptp_fun_Z_0(Y, X), Y)))))) <=> ![X: $i, Y: $i] : (~((~((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y)))) | (~(set_equal(X, Y) | ((~element(tptp_fun_Z_0(Y, X), X)) <=> element(tptp_fun_Z_0(Y, X), Y))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[17])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 (^[X: $i, Y: $i] : rewrite((~((~((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y)))) | (~(set_equal(X, Y) | ((~element(tptp_fun_Z_0(Y, X), X)) <=> element(tptp_fun_Z_0(Y, X), Y)))))) <=> (~((~((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y)))) | (~(set_equal(X, Y) | ((~element(tptp_fun_Z_0(Y, X), X)) <=> element(tptp_fun_Z_0(Y, X), Y)))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 (![X: $i, Y: $i] : (~((~((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y)))) | (~(set_equal(X, Y) | ((~element(tptp_fun_Z_0(Y, X), X)) <=> element(tptp_fun_Z_0(Y, X), Y)))))) <=> ![X: $i, Y: $i] : (~((~((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y)))) | (~(set_equal(X, Y) | ((~element(tptp_fun_Z_0(Y, X), X)) <=> element(tptp_fun_Z_0(Y, X), Y))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[19])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 (![X: $i, Y: $i] : (~((~((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y)))) | (~(set_equal(X, Y) | ((~element(tptp_fun_Z_0(Y, X), X)) <=> element(tptp_fun_Z_0(Y, X), Y)))))) <=> ![X: $i, Y: $i] : (~((~((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y)))) | (~(set_equal(X, Y) | ((~element(tptp_fun_Z_0(Y, X), X)) <=> element(tptp_fun_Z_0(Y, X), Y))))))),
% 0.13/0.39 inference(transitivity,[status(thm)],[20, 18])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 (^[X: $i, Y: $i] : trans(monotonicity(rewrite(((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y))) <=> ((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y)))), ((((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y))) & (set_equal(X, Y) | ((~element(tptp_fun_Z_0(Y, X), X)) <=> element(tptp_fun_Z_0(Y, X), Y)))) <=> (((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y))) & (set_equal(X, Y) | ((~element(tptp_fun_Z_0(Y, X), X)) <=> element(tptp_fun_Z_0(Y, X), Y)))))), rewrite((((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y))) & (set_equal(X, Y) | ((~element(tptp_fun_Z_0(Y, X), X)) <=> element(tptp_fun_Z_0(Y, X), Y)))) <=> (~((~((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y)))) | (~(set_equal(X, Y) | ((~element(tptp_fun_Z_0(Y, X), X)) <=> element(tptp_fun_Z_0(Y, X), Y))))))), ((((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y))) & (set_equal(X, Y) | ((~element(tptp_fun_Z_0(Y, X), X)) <=> element(tptp_fun_Z_0(Y, X), Y)))) <=> (~((~((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y)))) | (~(set_equal(X, Y) | ((~element(tptp_fun_Z_0(Y, X), X)) <=> element(tptp_fun_Z_0(Y, X), Y))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(23,plain,
% 0.13/0.39 (![X: $i, Y: $i] : (((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y))) & (set_equal(X, Y) | ((~element(tptp_fun_Z_0(Y, X), X)) <=> element(tptp_fun_Z_0(Y, X), Y)))) <=> ![X: $i, Y: $i] : (~((~((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y)))) | (~(set_equal(X, Y) | ((~element(tptp_fun_Z_0(Y, X), X)) <=> element(tptp_fun_Z_0(Y, X), Y))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[22])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 (^[X: $i, Y: $i] : rewrite((((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y))) & (set_equal(X, Y) | (~(element(tptp_fun_Z_0(Y, X), X) <=> element(tptp_fun_Z_0(Y, X), Y))))) <=> (((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y))) & (set_equal(X, Y) | ((~element(tptp_fun_Z_0(Y, X), X)) <=> element(tptp_fun_Z_0(Y, X), Y)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 (![X: $i, Y: $i] : (((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y))) & (set_equal(X, Y) | (~(element(tptp_fun_Z_0(Y, X), X) <=> element(tptp_fun_Z_0(Y, X), Y))))) <=> ![X: $i, Y: $i] : (((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y))) & (set_equal(X, Y) | ((~element(tptp_fun_Z_0(Y, X), X)) <=> element(tptp_fun_Z_0(Y, X), Y))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[24])).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 (![X: $i, Y: $i] : (set_equal(X, Y) <=> ![Z: $i] : (element(Z, X) <=> element(Z, Y))) <=> ![X: $i, Y: $i] : (set_equal(X, Y) <=> ![Z: $i] : (element(Z, X) <=> element(Z, Y)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(27,axiom,(![X: $i, Y: $i] : (set_equal(X, Y) <=> ![Z: $i] : (element(Z, X) <=> element(Z, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel43_1')).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 (![X: $i, Y: $i] : (set_equal(X, Y) <=> ![Z: $i] : (element(Z, X) <=> element(Z, Y)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.13/0.39 tff(29,plain,(
% 0.13/0.39 ![X: $i, Y: $i] : (((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y))) & (set_equal(X, Y) | (~(element(tptp_fun_Z_0(Y, X), X) <=> element(tptp_fun_Z_0(Y, X), Y)))))),
% 0.13/0.39 inference(skolemize,[status(sab)],[28])).
% 0.13/0.39 tff(30,plain,
% 0.13/0.39 (![X: $i, Y: $i] : (((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y))) & (set_equal(X, Y) | ((~element(tptp_fun_Z_0(Y, X), X)) <=> element(tptp_fun_Z_0(Y, X), Y))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.13/0.39 tff(31,plain,
% 0.13/0.39 (![X: $i, Y: $i] : (~((~((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y)))) | (~(set_equal(X, Y) | ((~element(tptp_fun_Z_0(Y, X), X)) <=> element(tptp_fun_Z_0(Y, X), Y))))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.13/0.39 tff(32,plain,
% 0.13/0.39 (![X: $i, Y: $i] : (~((~((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y)))) | (~(set_equal(X, Y) | ((~element(tptp_fun_Z_0(Y, X), X)) <=> element(tptp_fun_Z_0(Y, X), Y))))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[31, 21])).
% 0.13/0.39 tff(33,plain,
% 0.13/0.39 ((~![X: $i, Y: $i] : (~((~((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y)))) | (~(set_equal(X, Y) | ((~element(tptp_fun_Z_0(Y, X), X)) <=> element(tptp_fun_Z_0(Y, X), Y))))))) | (~((~((~set_equal(X!2, Y!1)) | ![Z: $i] : (element(Z, X!2) <=> element(Z, Y!1)))) | (~(set_equal(X!2, Y!1) | ((~element(tptp_fun_Z_0(Y!1, X!2), X!2)) <=> element(tptp_fun_Z_0(Y!1, X!2), Y!1))))))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(34,plain,
% 0.13/0.39 (~((~((~set_equal(X!2, Y!1)) | ![Z: $i] : (element(Z, X!2) <=> element(Z, Y!1)))) | (~(set_equal(X!2, Y!1) | ((~element(tptp_fun_Z_0(Y!1, X!2), X!2)) <=> element(tptp_fun_Z_0(Y!1, X!2), Y!1)))))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.13/0.39 tff(35,plain,
% 0.13/0.39 (((~((~set_equal(X!2, Y!1)) | ![Z: $i] : (element(Z, X!2) <=> element(Z, Y!1)))) | (~(set_equal(X!2, Y!1) | ((~element(tptp_fun_Z_0(Y!1, X!2), X!2)) <=> element(tptp_fun_Z_0(Y!1, X!2), Y!1))))) | ((~set_equal(X!2, Y!1)) | ![Z: $i] : (element(Z, X!2) <=> element(Z, Y!1)))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(36,plain,
% 0.13/0.39 ((~set_equal(X!2, Y!1)) | ![Z: $i] : (element(Z, X!2) <=> element(Z, Y!1))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.13/0.39 tff(37,plain,
% 0.13/0.39 ((~((~set_equal(X!2, Y!1)) | ![Z: $i] : (element(Z, X!2) <=> element(Z, Y!1)))) | (~set_equal(X!2, Y!1)) | ![Z: $i] : (element(Z, X!2) <=> element(Z, Y!1))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(38,plain,
% 0.13/0.39 ((~set_equal(X!2, Y!1)) | ![Z: $i] : (element(Z, X!2) <=> element(Z, Y!1))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.13/0.39 tff(39,plain,
% 0.13/0.39 (![Z: $i] : (element(Z, X!2) <=> element(Z, Y!1))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[38, 16])).
% 0.13/0.39 tff(40,plain,
% 0.13/0.39 ((~![Z: $i] : (element(Z, X!2) <=> element(Z, Y!1))) | (element(tptp_fun_Z_0(X!2, Y!1), X!2) <=> element(tptp_fun_Z_0(X!2, Y!1), Y!1))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(41,plain,
% 0.13/0.39 (element(tptp_fun_Z_0(X!2, Y!1), X!2) <=> element(tptp_fun_Z_0(X!2, Y!1), Y!1)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.13/0.39 tff(42,plain,
% 0.13/0.39 ((~![X: $i, Y: $i] : (~((~((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y)))) | (~(set_equal(X, Y) | ((~element(tptp_fun_Z_0(Y, X), X)) <=> element(tptp_fun_Z_0(Y, X), Y))))))) | (~((~((~set_equal(Y!1, X!2)) | ![Z: $i] : (element(Z, Y!1) <=> element(Z, X!2)))) | (~(set_equal(Y!1, X!2) | ((~element(tptp_fun_Z_0(X!2, Y!1), Y!1)) <=> element(tptp_fun_Z_0(X!2, Y!1), X!2))))))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(43,plain,
% 0.13/0.39 (~((~((~set_equal(Y!1, X!2)) | ![Z: $i] : (element(Z, Y!1) <=> element(Z, X!2)))) | (~(set_equal(Y!1, X!2) | ((~element(tptp_fun_Z_0(X!2, Y!1), Y!1)) <=> element(tptp_fun_Z_0(X!2, Y!1), X!2)))))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[42, 32])).
% 0.13/0.39 tff(44,plain,
% 0.13/0.39 (((~((~set_equal(Y!1, X!2)) | ![Z: $i] : (element(Z, Y!1) <=> element(Z, X!2)))) | (~(set_equal(Y!1, X!2) | ((~element(tptp_fun_Z_0(X!2, Y!1), Y!1)) <=> element(tptp_fun_Z_0(X!2, Y!1), X!2))))) | (set_equal(Y!1, X!2) | ((~element(tptp_fun_Z_0(X!2, Y!1), Y!1)) <=> element(tptp_fun_Z_0(X!2, Y!1), X!2)))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(45,plain,
% 0.13/0.39 (set_equal(Y!1, X!2) | ((~element(tptp_fun_Z_0(X!2, Y!1), Y!1)) <=> element(tptp_fun_Z_0(X!2, Y!1), X!2))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.13/0.39 tff(46,plain,
% 0.13/0.39 ((~(set_equal(Y!1, X!2) | ((~element(tptp_fun_Z_0(X!2, Y!1), Y!1)) <=> element(tptp_fun_Z_0(X!2, Y!1), X!2)))) | set_equal(Y!1, X!2) | ((~element(tptp_fun_Z_0(X!2, Y!1), Y!1)) <=> element(tptp_fun_Z_0(X!2, Y!1), X!2))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(47,plain,
% 0.13/0.40 (set_equal(Y!1, X!2) | ((~element(tptp_fun_Z_0(X!2, Y!1), Y!1)) <=> element(tptp_fun_Z_0(X!2, Y!1), X!2))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.13/0.40 tff(48,plain,
% 0.13/0.40 ((~element(tptp_fun_Z_0(X!2, Y!1), Y!1)) <=> element(tptp_fun_Z_0(X!2, Y!1), X!2)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[47, 1])).
% 0.13/0.40 tff(49,assumption,(element(tptp_fun_Z_0(X!2, Y!1), X!2) <=> element(tptp_fun_Z_0(X!2, Y!1), Y!1)), introduced(assumption)).
% 0.13/0.40 tff(50,assumption,(~element(tptp_fun_Z_0(X!2, Y!1), Y!1)), introduced(assumption)).
% 0.13/0.40 tff(51,assumption,((~element(tptp_fun_Z_0(X!2, Y!1), Y!1)) <=> element(tptp_fun_Z_0(X!2, Y!1), X!2)), introduced(assumption)).
% 0.13/0.40 tff(52,plain,
% 0.13/0.40 ((~((~element(tptp_fun_Z_0(X!2, Y!1), Y!1)) <=> element(tptp_fun_Z_0(X!2, Y!1), X!2))) | element(tptp_fun_Z_0(X!2, Y!1), Y!1) | element(tptp_fun_Z_0(X!2, Y!1), X!2)),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(53,plain,
% 0.13/0.40 (element(tptp_fun_Z_0(X!2, Y!1), X!2)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[52, 50, 51])).
% 0.13/0.40 tff(54,plain,
% 0.13/0.40 ((~(element(tptp_fun_Z_0(X!2, Y!1), X!2) <=> element(tptp_fun_Z_0(X!2, Y!1), Y!1))) | (~element(tptp_fun_Z_0(X!2, Y!1), X!2)) | element(tptp_fun_Z_0(X!2, Y!1), Y!1)),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(55,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[54, 53, 50, 49])).
% 0.13/0.40 tff(56,plain,(element(tptp_fun_Z_0(X!2, Y!1), Y!1) | (~(element(tptp_fun_Z_0(X!2, Y!1), X!2) <=> element(tptp_fun_Z_0(X!2, Y!1), Y!1))) | (~((~element(tptp_fun_Z_0(X!2, Y!1), Y!1)) <=> element(tptp_fun_Z_0(X!2, Y!1), X!2)))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(57,plain,
% 0.13/0.40 (element(tptp_fun_Z_0(X!2, Y!1), Y!1)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[56, 41, 48])).
% 0.13/0.40 tff(58,plain,
% 0.13/0.40 ((~((~element(tptp_fun_Z_0(X!2, Y!1), Y!1)) <=> element(tptp_fun_Z_0(X!2, Y!1), X!2))) | (~element(tptp_fun_Z_0(X!2, Y!1), Y!1)) | (~element(tptp_fun_Z_0(X!2, Y!1), X!2))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(59,plain,
% 0.13/0.40 (~element(tptp_fun_Z_0(X!2, Y!1), X!2)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[58, 57, 48])).
% 0.13/0.40 tff(60,plain,
% 0.13/0.40 ((~(element(tptp_fun_Z_0(X!2, Y!1), X!2) <=> element(tptp_fun_Z_0(X!2, Y!1), Y!1))) | element(tptp_fun_Z_0(X!2, Y!1), X!2) | (~element(tptp_fun_Z_0(X!2, Y!1), Y!1))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(61,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[60, 59, 57, 41])).
% 0.13/0.40 tff(62,plain,(set_equal(Y!1, X!2)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(63,plain,
% 0.13/0.40 (((~((~set_equal(Y!1, X!2)) | ![Z: $i] : (element(Z, Y!1) <=> element(Z, X!2)))) | (~(set_equal(Y!1, X!2) | ((~element(tptp_fun_Z_0(X!2, Y!1), Y!1)) <=> element(tptp_fun_Z_0(X!2, Y!1), X!2))))) | ((~set_equal(Y!1, X!2)) | ![Z: $i] : (element(Z, Y!1) <=> element(Z, X!2)))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(64,plain,
% 0.13/0.40 ((~set_equal(Y!1, X!2)) | ![Z: $i] : (element(Z, Y!1) <=> element(Z, X!2))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[63, 43])).
% 0.13/0.40 tff(65,plain,
% 0.13/0.40 ((~((~set_equal(Y!1, X!2)) | ![Z: $i] : (element(Z, Y!1) <=> element(Z, X!2)))) | (~set_equal(Y!1, X!2)) | ![Z: $i] : (element(Z, Y!1) <=> element(Z, X!2))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(66,plain,
% 0.13/0.40 ((~set_equal(Y!1, X!2)) | ![Z: $i] : (element(Z, Y!1) <=> element(Z, X!2))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.13/0.40 tff(67,plain,
% 0.13/0.40 (![Z: $i] : (element(Z, Y!1) <=> element(Z, X!2))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[66, 62])).
% 0.13/0.40 tff(68,plain,
% 0.13/0.40 ((~![Z: $i] : (element(Z, Y!1) <=> element(Z, X!2))) | (element(tptp_fun_Z_0(Y!1, X!2), Y!1) <=> element(tptp_fun_Z_0(Y!1, X!2), X!2))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(69,plain,
% 0.13/0.40 (element(tptp_fun_Z_0(Y!1, X!2), Y!1) <=> element(tptp_fun_Z_0(Y!1, X!2), X!2)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.13/0.40 tff(70,assumption,(~element(tptp_fun_Z_0(Y!1, X!2), X!2)), introduced(assumption)).
% 0.13/0.40 tff(71,plain,
% 0.13/0.40 ((~set_equal(X!2, Y!1)) | (~set_equal(Y!1, X!2)) | (~((~set_equal(X!2, Y!1)) <=> set_equal(Y!1, X!2)))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(72,plain,
% 0.13/0.40 ((~set_equal(X!2, Y!1)) | (~set_equal(Y!1, X!2))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[71, 13])).
% 0.13/0.40 tff(73,plain,
% 0.13/0.40 (~set_equal(X!2, Y!1)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[72, 62])).
% 0.13/0.40 tff(74,plain,
% 0.13/0.40 (((~((~set_equal(X!2, Y!1)) | ![Z: $i] : (element(Z, X!2) <=> element(Z, Y!1)))) | (~(set_equal(X!2, Y!1) | ((~element(tptp_fun_Z_0(Y!1, X!2), X!2)) <=> element(tptp_fun_Z_0(Y!1, X!2), Y!1))))) | (set_equal(X!2, Y!1) | ((~element(tptp_fun_Z_0(Y!1, X!2), X!2)) <=> element(tptp_fun_Z_0(Y!1, X!2), Y!1)))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(75,plain,
% 0.13/0.40 (set_equal(X!2, Y!1) | ((~element(tptp_fun_Z_0(Y!1, X!2), X!2)) <=> element(tptp_fun_Z_0(Y!1, X!2), Y!1))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[74, 34])).
% 0.13/0.40 tff(76,plain,
% 0.13/0.40 ((~(set_equal(X!2, Y!1) | ((~element(tptp_fun_Z_0(Y!1, X!2), X!2)) <=> element(tptp_fun_Z_0(Y!1, X!2), Y!1)))) | set_equal(X!2, Y!1) | ((~element(tptp_fun_Z_0(Y!1, X!2), X!2)) <=> element(tptp_fun_Z_0(Y!1, X!2), Y!1))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(77,plain,
% 0.13/0.40 (set_equal(X!2, Y!1) | ((~element(tptp_fun_Z_0(Y!1, X!2), X!2)) <=> element(tptp_fun_Z_0(Y!1, X!2), Y!1))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.13/0.40 tff(78,plain,
% 0.13/0.40 ((~element(tptp_fun_Z_0(Y!1, X!2), X!2)) <=> element(tptp_fun_Z_0(Y!1, X!2), Y!1)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[77, 73])).
% 0.13/0.40 tff(79,plain,
% 0.13/0.40 ((~((~element(tptp_fun_Z_0(Y!1, X!2), X!2)) <=> element(tptp_fun_Z_0(Y!1, X!2), Y!1))) | element(tptp_fun_Z_0(Y!1, X!2), X!2) | element(tptp_fun_Z_0(Y!1, X!2), Y!1)),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(80,plain,
% 0.13/0.40 (element(tptp_fun_Z_0(Y!1, X!2), Y!1)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[79, 70, 78])).
% 0.13/0.40 tff(81,plain,
% 0.13/0.40 ((~(element(tptp_fun_Z_0(Y!1, X!2), Y!1) <=> element(tptp_fun_Z_0(Y!1, X!2), X!2))) | (~element(tptp_fun_Z_0(Y!1, X!2), Y!1)) | element(tptp_fun_Z_0(Y!1, X!2), X!2)),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(82,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[81, 80, 70, 69])).
% 0.13/0.40 tff(83,plain,(element(tptp_fun_Z_0(Y!1, X!2), X!2)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(84,plain,
% 0.13/0.40 ((~((~element(tptp_fun_Z_0(Y!1, X!2), X!2)) <=> element(tptp_fun_Z_0(Y!1, X!2), Y!1))) | (~element(tptp_fun_Z_0(Y!1, X!2), X!2)) | (~element(tptp_fun_Z_0(Y!1, X!2), Y!1))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(85,plain,
% 0.13/0.40 (~element(tptp_fun_Z_0(Y!1, X!2), Y!1)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[84, 83, 78])).
% 0.13/0.40 tff(86,plain,
% 0.13/0.40 ((~(element(tptp_fun_Z_0(Y!1, X!2), Y!1) <=> element(tptp_fun_Z_0(Y!1, X!2), X!2))) | element(tptp_fun_Z_0(Y!1, X!2), Y!1) | (~element(tptp_fun_Z_0(Y!1, X!2), X!2))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(87,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[86, 85, 83, 69])).
% 0.13/0.40 % SZS output end Proof
%------------------------------------------------------------------------------