%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN083+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 : Sat Jun 21 05:38:12 AM UTC 2025
% Result : Theorem 0.18s 0.36s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN083+1 : TPTP v9.0.0. Released v2.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n006.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 12:27:20 EDT 2025
% 0.12/0.32 % CPUTime :
% 0.18/0.36 % SZS status Theorem
% 0.18/0.36 % SZS output start Proof
% 0.18/0.36 tff(f_type, type, (
% 0.18/0.36 f: ( $i * $i ) > $i)).
% 0.18/0.36 tff(tptp_fun_W_0_type, type, (
% 0.18/0.36 tptp_fun_W_0: $i)).
% 0.18/0.36 tff(tptp_fun_Z_1_type, type, (
% 0.18/0.36 tptp_fun_Z_1: $i)).
% 0.18/0.36 tff(tptp_fun_Y_2_type, type, (
% 0.18/0.36 tptp_fun_Y_2: $i)).
% 0.18/0.36 tff(tptp_fun_X_3_type, type, (
% 0.18/0.36 tptp_fun_X_3: $i)).
% 0.18/0.36 tff(1,plain,
% 0.18/0.36 (^[X: $i, Y: $i, Z: $i] : refl((f(X, f(Y, Z)) = f(f(X, Y), Z)) <=> (f(X, f(Y, Z)) = f(f(X, Y), Z)))),
% 0.18/0.36 inference(bind,[status(th)],[])).
% 0.18/0.36 tff(2,plain,
% 0.18/0.36 (![X: $i, Y: $i, Z: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z)) <=> ![X: $i, Y: $i, Z: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))),
% 0.18/0.36 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.36 tff(3,plain,
% 0.18/0.36 (![X: $i, Y: $i, Z: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z)) <=> ![X: $i, Y: $i, Z: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(4,axiom,(![X: $i, Y: $i, Z: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p61_1')).
% 0.18/0.36 tff(5,plain,
% 0.18/0.36 (![X: $i, Y: $i, Z: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.18/0.36 tff(6,plain,(
% 0.18/0.36 ![X: $i, Y: $i, Z: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))),
% 0.18/0.36 inference(skolemize,[status(sab)],[5])).
% 0.18/0.36 tff(7,plain,
% 0.18/0.36 (![X: $i, Y: $i, Z: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.18/0.36 tff(8,plain,
% 0.18/0.36 ((~![X: $i, Y: $i, Z: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))) | (f(X!3, f(Y!2, f(Z!1, W!0))) = f(f(X!3, Y!2), f(Z!1, W!0)))),
% 0.18/0.36 inference(quant_inst,[status(thm)],[])).
% 0.18/0.36 tff(9,plain,
% 0.18/0.36 (f(X!3, f(Y!2, f(Z!1, W!0))) = f(f(X!3, Y!2), f(Z!1, W!0))),
% 0.18/0.36 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.18/0.36 tff(10,plain,
% 0.18/0.36 ((f(X!3, f(Y!2, f(Z!1, W!0))) = f(f(f(X!3, Y!2), Z!1), W!0)) <=> (f(f(X!3, Y!2), f(Z!1, W!0)) = f(f(f(X!3, Y!2), Z!1), W!0))),
% 0.18/0.36 inference(monotonicity,[status(thm)],[9])).
% 0.18/0.36 tff(11,plain,
% 0.18/0.36 ((f(f(X!3, Y!2), f(Z!1, W!0)) = f(f(f(X!3, Y!2), Z!1), W!0)) <=> (f(X!3, f(Y!2, f(Z!1, W!0))) = f(f(f(X!3, Y!2), Z!1), W!0))),
% 0.18/0.36 inference(symmetry,[status(thm)],[10])).
% 0.18/0.36 tff(12,plain,
% 0.18/0.36 ((~![X: $i, Y: $i, Z: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))) | (f(f(X!3, Y!2), f(Z!1, W!0)) = f(f(f(X!3, Y!2), Z!1), W!0))),
% 0.18/0.36 inference(quant_inst,[status(thm)],[])).
% 0.18/0.36 tff(13,plain,
% 0.18/0.36 (f(f(X!3, Y!2), f(Z!1, W!0)) = f(f(f(X!3, Y!2), Z!1), W!0)),
% 0.18/0.36 inference(unit_resolution,[status(thm)],[12, 7])).
% 0.18/0.36 tff(14,plain,
% 0.18/0.36 (f(X!3, f(Y!2, f(Z!1, W!0))) = f(f(f(X!3, Y!2), Z!1), W!0)),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[13, 11])).
% 0.18/0.36 tff(15,plain,
% 0.18/0.36 ((~![X: $i, Y: $i, Z: $i, W: $i] : (f(X, f(Y, f(Z, W))) = f(f(f(X, Y), Z), W))) <=> (~![X: $i, Y: $i, Z: $i, W: $i] : (f(X, f(Y, f(Z, W))) = f(f(f(X, Y), Z), W)))),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(16,axiom,(~![X: $i, Y: $i, Z: $i, W: $i] : (f(X, f(Y, f(Z, W))) = f(f(f(X, Y), Z), W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel61')).
% 0.18/0.36 tff(17,plain,
% 0.18/0.36 (~![X: $i, Y: $i, Z: $i, W: $i] : (f(X, f(Y, f(Z, W))) = f(f(f(X, Y), Z), W))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.18/0.36 tff(18,plain,
% 0.18/0.36 (~![X: $i, Y: $i, Z: $i, W: $i] : (f(X, f(Y, f(Z, W))) = f(f(f(X, Y), Z), W))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[17, 15])).
% 0.18/0.36 tff(19,plain,
% 0.18/0.36 (~![X: $i, Y: $i, Z: $i, W: $i] : (f(X, f(Y, f(Z, W))) = f(f(f(X, Y), Z), W))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[18, 15])).
% 0.18/0.36 tff(20,plain,
% 0.18/0.36 (~![X: $i, Y: $i, Z: $i, W: $i] : (f(X, f(Y, f(Z, W))) = f(f(f(X, Y), Z), W))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.18/0.36 tff(21,plain,(
% 0.18/0.36 ~(f(X!3, f(Y!2, f(Z!1, W!0))) = f(f(f(X!3, Y!2), Z!1), W!0))),
% 0.18/0.36 inference(skolemize,[status(sab)],[20])).
% 0.18/0.36 tff(22,plain,
% 0.18/0.36 ($false),
% 0.18/0.36 inference(unit_resolution,[status(thm)],[21, 14])).
% 0.18/0.36 % SZS output end Proof
% 0.18/0.36 % E exiting
%------------------------------------------------------------------------------