%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN919+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 : Sat Jun 21 05:41:00 AM UTC 2025
% Result : Theorem 0.13s 0.37s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.12 % Problem : SYN919+1 : TPTP v9.0.0. Released v3.1.0.
% 0.13/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n002.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 : Fri Jun 20 13:02:31 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.37 % SZS status Theorem
% 0.13/0.37 % SZS output start Proof
% 0.13/0.37 tff(r_type, type, (
% 0.13/0.37 r: ( $i * $i ) > $o)).
% 0.13/0.37 tff(tptp_fun_X_1_type, type, (
% 0.13/0.37 tptp_fun_X_1: $i)).
% 0.13/0.37 tff(tptp_fun_Y_0_type, type, (
% 0.13/0.37 tptp_fun_Y_0: $i)).
% 0.13/0.37 tff(1,plain,
% 0.13/0.37 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))) <=> (~![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X)))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(2,plain,
% 0.13/0.37 ((~((![X: $i, Y: $i] : (r(X, Y) => r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((r(X, Y) & r(Y, Z)) => r(X, Z))) => ![X: $i, Y: $i] : (r(X, Y) => r(X, X)))) <=> (~((~(![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)))) | ![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(3,axiom,(~((![X: $i, Y: $i] : (r(X, Y) => r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((r(X, Y) & r(Y, Z)) => r(X, Z))) => ![X: $i, Y: $i] : (r(X, Y) => r(X, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.13/0.37 tff(4,plain,
% 0.13/0.37 (~((~(![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)))) | ![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X)))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.13/0.37 tff(5,plain,
% 0.13/0.37 (~![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))),
% 0.13/0.37 inference(or_elim,[status(thm)],[4])).
% 0.13/0.37 tff(6,plain,
% 0.13/0.37 (~![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.13/0.37 tff(7,plain,
% 0.13/0.37 (~![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.13/0.37 tff(8,plain,
% 0.13/0.37 (~![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.13/0.37 tff(9,plain,(
% 0.13/0.37 ~((~r(X!1, Y!0)) | r(X!1, X!1))),
% 0.13/0.37 inference(skolemize,[status(sab)],[8])).
% 0.13/0.37 tff(10,plain,
% 0.13/0.37 (r(X!1, Y!0)),
% 0.13/0.37 inference(or_elim,[status(thm)],[9])).
% 0.13/0.37 tff(11,plain,
% 0.13/0.37 (^[X: $i, Y: $i] : refl(((~r(X, Y)) | r(Y, X)) <=> ((~r(X, Y)) | r(Y, X)))),
% 0.13/0.37 inference(bind,[status(th)],[])).
% 0.13/0.37 tff(12,plain,
% 0.13/0.37 (![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) <=> ![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))),
% 0.13/0.37 inference(quant_intro,[status(thm)],[11])).
% 0.13/0.37 tff(13,plain,
% 0.13/0.37 (![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) <=> ![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(14,plain,
% 0.13/0.37 (![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z))),
% 0.13/0.37 inference(or_elim,[status(thm)],[4])).
% 0.13/0.37 tff(15,plain,
% 0.13/0.37 (![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))),
% 0.13/0.37 inference(and_elim,[status(thm)],[14])).
% 0.13/0.37 tff(16,plain,
% 0.13/0.37 (![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[15, 13])).
% 0.13/0.37 tff(17,plain,(
% 0.13/0.37 ![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))),
% 0.13/0.37 inference(skolemize,[status(sab)],[16])).
% 0.13/0.37 tff(18,plain,
% 0.13/0.37 (![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[17, 12])).
% 0.13/0.37 tff(19,plain,
% 0.13/0.37 (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(X!1, Y!0)) | r(Y!0, X!1))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(X!1, Y!0)) | r(Y!0, X!1))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(20,plain,
% 0.13/0.37 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(X!1, Y!0)) | r(Y!0, X!1))),
% 0.13/0.37 inference(quant_inst,[status(thm)],[])).
% 0.13/0.37 tff(21,plain,
% 0.13/0.37 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(X!1, Y!0)) | r(Y!0, X!1)),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.13/0.37 tff(22,plain,
% 0.13/0.37 (r(Y!0, X!1)),
% 0.13/0.37 inference(unit_resolution,[status(thm)],[21, 18, 10])).
% 0.13/0.37 tff(23,plain,
% 0.13/0.37 (~r(X!1, X!1)),
% 0.13/0.37 inference(or_elim,[status(thm)],[9])).
% 0.13/0.37 tff(24,plain,
% 0.13/0.37 (![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y)))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(25,plain,
% 0.13/0.37 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((r(X, Y) & r(Y, Z)) <=> (~((~r(Y, Z)) | (~r(X, Y))))), ((~(r(X, Y) & r(Y, Z))) <=> (~(~((~r(Y, Z)) | (~r(X, Y))))))), rewrite((~(~((~r(Y, Z)) | (~r(X, Y))))) <=> ((~r(Y, Z)) | (~r(X, Y)))), ((~(r(X, Y) & r(Y, Z))) <=> ((~r(Y, Z)) | (~r(X, Y))))), (((~(r(X, Y) & r(Y, Z))) | r(X, Z)) <=> (((~r(Y, Z)) | (~r(X, Y))) | r(X, Z)))), rewrite((((~r(Y, Z)) | (~r(X, Y))) | r(X, Z)) <=> (r(X, Z) | (~r(Y, Z)) | (~r(X, Y)))), (((~(r(X, Y) & r(Y, Z))) | r(X, Z)) <=> (r(X, Z) | (~r(Y, Z)) | (~r(X, Y)))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(26,plain,
% 0.13/0.38 (![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y)))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[25])).
% 0.13/0.38 tff(27,plain,
% 0.13/0.38 (![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(28,plain,
% 0.13/0.38 (![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z))),
% 0.13/0.38 inference(and_elim,[status(thm)],[14])).
% 0.13/0.38 tff(29,plain,
% 0.13/0.38 (![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.13/0.38 tff(30,plain,(
% 0.13/0.38 ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z))),
% 0.13/0.38 inference(skolemize,[status(sab)],[29])).
% 0.13/0.38 tff(31,plain,
% 0.13/0.38 (![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.13/0.38 tff(32,plain,
% 0.13/0.38 (![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.13/0.38 tff(33,plain,
% 0.13/0.38 (((~![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y)))) | ((~r(X!1, Y!0)) | r(X!1, X!1) | (~r(Y!0, X!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y)))) | (~r(X!1, Y!0)) | r(X!1, X!1) | (~r(Y!0, X!1)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(34,plain,
% 0.13/0.38 ((r(X!1, X!1) | (~r(Y!0, X!1)) | (~r(X!1, Y!0))) <=> ((~r(X!1, Y!0)) | r(X!1, X!1) | (~r(Y!0, X!1)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(35,plain,
% 0.13/0.38 (((~![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y)))) | (r(X!1, X!1) | (~r(Y!0, X!1)) | (~r(X!1, Y!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y)))) | ((~r(X!1, Y!0)) | r(X!1, X!1) | (~r(Y!0, X!1))))),
% 0.13/0.38 inference(monotonicity,[status(thm)],[34])).
% 0.13/0.38 tff(36,plain,
% 0.13/0.38 (((~![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y)))) | (r(X!1, X!1) | (~r(Y!0, X!1)) | (~r(X!1, Y!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y)))) | (~r(X!1, Y!0)) | r(X!1, X!1) | (~r(Y!0, X!1)))),
% 0.13/0.38 inference(transitivity,[status(thm)],[35, 33])).
% 0.13/0.38 tff(37,plain,
% 0.13/0.38 ((~![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y)))) | (r(X!1, X!1) | (~r(Y!0, X!1)) | (~r(X!1, Y!0)))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(38,plain,
% 0.13/0.38 ((~![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y)))) | (~r(X!1, Y!0)) | r(X!1, X!1) | (~r(Y!0, X!1))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.13/0.38 tff(39,plain,
% 0.13/0.38 ($false),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[38, 32, 10, 23, 22])).
% 0.13/0.38 % SZS output end Proof
% 0.13/0.38 % E exiting
%------------------------------------------------------------------------------