%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN080+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:38:11 AM UTC 2025
% Result : Theorem 0.18s 0.35s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN080+1 : TPTP v9.0.0. Released v2.0.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n010.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 12:29:12 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.18/0.35 % SZS status Theorem
% 0.18/0.35 % SZS output start Proof
% 0.18/0.35 tff(f_type, type, (
% 0.18/0.35 f: $i > $i)).
% 0.18/0.35 tff(g_type, type, (
% 0.18/0.35 g: $i > $i)).
% 0.18/0.35 tff(tptp_fun_Y_0_type, type, (
% 0.18/0.35 tptp_fun_Y_0: $i)).
% 0.18/0.35 tff(tptp_fun_X_1_type, type, (
% 0.18/0.35 tptp_fun_X_1: $i)).
% 0.18/0.35 tff(1,plain,
% 0.18/0.35 ((g(Y!0) = f(g(Y!0))) <=> (f(g(Y!0)) = g(Y!0))),
% 0.18/0.35 inference(commutativity,[status(thm)],[])).
% 0.18/0.35 tff(2,plain,
% 0.18/0.35 (^[X: $i, Y: $i] : refl((f(X) = g(Y)) <=> (f(X) = g(Y)))),
% 0.18/0.35 inference(bind,[status(th)],[])).
% 0.18/0.35 tff(3,plain,
% 0.18/0.35 (![X: $i, Y: $i] : (f(X) = g(Y)) <=> ![X: $i, Y: $i] : (f(X) = g(Y))),
% 0.18/0.35 inference(quant_intro,[status(thm)],[2])).
% 0.18/0.35 tff(4,plain,
% 0.18/0.35 (![X: $i, Y: $i] : (f(X) = g(Y)) <=> ![X: $i, Y: $i] : (f(X) = g(Y))),
% 0.18/0.35 inference(rewrite,[status(thm)],[])).
% 0.18/0.35 tff(5,axiom,(![X: $i, Y: $i] : (f(X) = g(Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel58_1')).
% 0.18/0.35 tff(6,plain,
% 0.18/0.35 (![X: $i, Y: $i] : (f(X) = g(Y))),
% 0.18/0.35 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.18/0.35 tff(7,plain,(
% 0.18/0.35 ![X: $i, Y: $i] : (f(X) = g(Y))),
% 0.18/0.35 inference(skolemize,[status(sab)],[6])).
% 0.18/0.35 tff(8,plain,
% 0.18/0.35 (![X: $i, Y: $i] : (f(X) = g(Y))),
% 0.18/0.35 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.18/0.35 tff(9,plain,
% 0.18/0.35 ((~![X: $i, Y: $i] : (f(X) = g(Y))) | (f(f(X!1)) = g(Y!0))),
% 0.18/0.35 inference(quant_inst,[status(thm)],[])).
% 0.18/0.35 tff(10,plain,
% 0.18/0.35 (f(f(X!1)) = g(Y!0)),
% 0.18/0.35 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.18/0.35 tff(11,plain,
% 0.18/0.35 ((f(f(X!1)) = f(g(Y!0))) <=> (g(Y!0) = f(g(Y!0)))),
% 0.18/0.35 inference(monotonicity,[status(thm)],[10])).
% 0.18/0.35 tff(12,plain,
% 0.18/0.35 ((f(f(X!1)) = f(g(Y!0))) <=> (f(g(Y!0)) = g(Y!0))),
% 0.18/0.35 inference(transitivity,[status(thm)],[11, 1])).
% 0.18/0.35 tff(13,plain,
% 0.18/0.35 ((f(g(Y!0)) = g(Y!0)) <=> (f(f(X!1)) = f(g(Y!0)))),
% 0.18/0.35 inference(symmetry,[status(thm)],[12])).
% 0.18/0.35 tff(14,plain,
% 0.18/0.35 ((~![X: $i, Y: $i] : (f(X) = g(Y))) | (f(g(Y!0)) = g(Y!0))),
% 0.18/0.35 inference(quant_inst,[status(thm)],[])).
% 0.18/0.35 tff(15,plain,
% 0.18/0.35 (f(g(Y!0)) = g(Y!0)),
% 0.18/0.35 inference(unit_resolution,[status(thm)],[14, 8])).
% 0.18/0.35 tff(16,plain,
% 0.18/0.35 (f(f(X!1)) = f(g(Y!0))),
% 0.18/0.35 inference(modus_ponens,[status(thm)],[15, 13])).
% 0.18/0.35 tff(17,plain,
% 0.18/0.35 ((~![X: $i, Y: $i] : (f(f(X)) = f(g(Y)))) <=> (~![X: $i, Y: $i] : (f(f(X)) = f(g(Y))))),
% 0.18/0.35 inference(rewrite,[status(thm)],[])).
% 0.18/0.35 tff(18,axiom,(~![X: $i, Y: $i] : (f(f(X)) = f(g(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel58')).
% 0.18/0.35 tff(19,plain,
% 0.18/0.35 (~![X: $i, Y: $i] : (f(f(X)) = f(g(Y)))),
% 0.18/0.35 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.18/0.35 tff(20,plain,
% 0.18/0.35 (~![X: $i, Y: $i] : (f(f(X)) = f(g(Y)))),
% 0.18/0.35 inference(modus_ponens,[status(thm)],[19, 17])).
% 0.18/0.35 tff(21,plain,
% 0.18/0.35 (~![X: $i, Y: $i] : (f(f(X)) = f(g(Y)))),
% 0.18/0.35 inference(modus_ponens,[status(thm)],[20, 17])).
% 0.18/0.35 tff(22,plain,
% 0.18/0.35 (~![X: $i, Y: $i] : (f(f(X)) = f(g(Y)))),
% 0.18/0.35 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.18/0.35 tff(23,plain,(
% 0.18/0.35 ~(f(f(X!1)) = f(g(Y!0)))),
% 0.18/0.35 inference(skolemize,[status(sab)],[22])).
% 0.18/0.35 tff(24,plain,
% 0.18/0.35 ($false),
% 0.18/0.35 inference(unit_resolution,[status(thm)],[23, 16])).
% 0.18/0.35 % SZS output end Proof
% 0.18/0.35 % E exiting
%------------------------------------------------------------------------------