%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN411+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:39:00 AM UTC 2025
% Result : Theorem 0.20s 0.36s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYN411+1 : TPTP v9.0.0. Released v2.0.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n001.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 12:37:50 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.20/0.36 % SZS status Theorem
% 0.20/0.36 % SZS output start Proof
% 0.20/0.36 tff(f_type, type, (
% 0.20/0.36 f: ( $i * $i * $i ) > $o)).
% 0.20/0.36 tff(tptp_fun_W_0_type, type, (
% 0.20/0.36 tptp_fun_W_0: $i)).
% 0.20/0.36 tff(tptp_fun_V_1_type, type, (
% 0.20/0.36 tptp_fun_V_1: $i)).
% 0.20/0.36 tff(tptp_fun_U_2_type, type, (
% 0.20/0.36 tptp_fun_U_2: $i)).
% 0.20/0.36 tff(tptp_fun_Z_3_type, type, (
% 0.20/0.36 tptp_fun_Z_3: $i)).
% 0.20/0.36 tff(tptp_fun_Y_4_type, type, (
% 0.20/0.36 tptp_fun_Y_4: $i)).
% 0.20/0.36 tff(tptp_fun_X_5_type, type, (
% 0.20/0.36 tptp_fun_X_5: $i)).
% 0.20/0.36 tff(1,assumption,(~f(X!5, Y!4, Z!3)), introduced(assumption)).
% 0.20/0.36 tff(2,assumption,(![U: $i, V: $i, W: $i] : f(U, V, W)), introduced(assumption)).
% 0.20/0.36 tff(3,plain,
% 0.20/0.36 ((~![U: $i, V: $i, W: $i] : f(U, V, W)) | f(X!5, Y!4, Z!3)),
% 0.20/0.36 inference(quant_inst,[status(thm)],[])).
% 0.20/0.36 tff(4,plain,
% 0.20/0.36 ($false),
% 0.20/0.36 inference(unit_resolution,[status(thm)],[3, 2, 1])).
% 0.20/0.36 tff(5,plain,((~![U: $i, V: $i, W: $i] : f(U, V, W)) | f(X!5, Y!4, Z!3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.36 tff(6,plain,
% 0.20/0.36 (~![U: $i, V: $i, W: $i] : f(U, V, W)),
% 0.20/0.36 inference(unit_resolution,[status(thm)],[5, 1])).
% 0.20/0.36 tff(7,plain,
% 0.20/0.36 ((![U: $i, V: $i, W: $i] : f(U, V, W) | ![X: $i, Y: $i, Z: $i] : f(X, Y, Z)) <=> (![U: $i, V: $i, W: $i] : f(U, V, W) | ![X: $i, Y: $i, Z: $i] : f(X, Y, Z))),
% 0.20/0.36 inference(rewrite,[status(thm)],[])).
% 0.20/0.36 tff(8,plain,
% 0.20/0.36 ((![U: $i, V: $i, W: $i] : f(U, V, W) | ![X: $i, Y: $i, Z: $i] : f(X, Y, Z)) <=> (![U: $i, V: $i, W: $i] : f(U, V, W) | ![X: $i, Y: $i, Z: $i] : f(X, Y, Z))),
% 0.20/0.36 inference(rewrite,[status(thm)],[])).
% 0.20/0.36 tff(9,plain,
% 0.20/0.36 (((![U: $i, V: $i, W: $i] : f(U, V, W) | ![X: $i, Y: $i, Z: $i] : f(X, Y, Z)) & ((~f(U!2, V!1, W!0)) | (~f(X!5, Y!4, Z!3)))) <=> ((![U: $i, V: $i, W: $i] : f(U, V, W) | ![X: $i, Y: $i, Z: $i] : f(X, Y, Z)) & ((~f(U!2, V!1, W!0)) | (~f(X!5, Y!4, Z!3))))),
% 0.20/0.36 inference(monotonicity,[status(thm)],[8])).
% 0.20/0.36 tff(10,plain,
% 0.20/0.36 ((?[U: $i, V: $i, W: $i] : (~f(U, V, W)) <=> ![X: $i, Y: $i, Z: $i] : f(X, Y, Z)) <=> (?[U: $i, V: $i, W: $i] : (~f(U, V, W)) <=> ![X: $i, Y: $i, Z: $i] : f(X, Y, Z))),
% 0.20/0.36 inference(rewrite,[status(thm)],[])).
% 0.20/0.36 tff(11,plain,
% 0.20/0.36 ((~(~(?[U: $i, V: $i, W: $i] : (~f(U, V, W)) <=> ![X: $i, Y: $i, Z: $i] : f(X, Y, Z)))) <=> (?[U: $i, V: $i, W: $i] : (~f(U, V, W)) <=> ![X: $i, Y: $i, Z: $i] : f(X, Y, Z))),
% 0.20/0.36 inference(rewrite,[status(thm)],[])).
% 0.20/0.36 tff(12,plain,
% 0.20/0.36 ((~(?[U: $i, V: $i, W: $i] : (~f(U, V, W)) <=> ![X: $i, Y: $i, Z: $i] : f(X, Y, Z))) <=> (~(?[U: $i, V: $i, W: $i] : (~f(U, V, W)) <=> ![X: $i, Y: $i, Z: $i] : f(X, Y, Z)))),
% 0.20/0.36 inference(rewrite,[status(thm)],[])).
% 0.20/0.36 tff(13,plain,
% 0.20/0.36 ((![X: $i, Y: $i, Z: $i] : f(X, Y, Z) <=> (~?[U: $i, V: $i, W: $i] : (~f(U, V, W)))) <=> (~(?[U: $i, V: $i, W: $i] : (~f(U, V, W)) <=> ![X: $i, Y: $i, Z: $i] : f(X, Y, Z)))),
% 0.20/0.36 inference(rewrite,[status(thm)],[])).
% 0.20/0.36 tff(14,plain,
% 0.20/0.36 ((~?[U: $i, V: $i, W: $i] : (~f(U, V, W))) <=> (~?[U: $i, V: $i, W: $i] : (~f(U, V, W)))),
% 0.20/0.36 inference(rewrite,[status(thm)],[])).
% 0.20/0.36 tff(15,plain,
% 0.20/0.36 ((![X: $i, Y: $i, Z: $i] : f(X, Y, Z) <=> (~?[U: $i, V: $i, W: $i] : (~f(U, V, W)))) <=> (![X: $i, Y: $i, Z: $i] : f(X, Y, Z) <=> (~?[U: $i, V: $i, W: $i] : (~f(U, V, W))))),
% 0.20/0.36 inference(monotonicity,[status(thm)],[14])).
% 0.20/0.36 tff(16,plain,
% 0.20/0.36 ((![X: $i, Y: $i, Z: $i] : f(X, Y, Z) <=> (~?[U: $i, V: $i, W: $i] : (~f(U, V, W)))) <=> (~(?[U: $i, V: $i, W: $i] : (~f(U, V, W)) <=> ![X: $i, Y: $i, Z: $i] : f(X, Y, Z)))),
% 0.20/0.36 inference(transitivity,[status(thm)],[15, 13])).
% 0.20/0.36 tff(17,plain,
% 0.20/0.36 ((![X: $i, Y: $i, Z: $i] : f(X, Y, Z) <=> (~?[U: $i, V: $i, W: $i] : (~f(U, V, W)))) <=> (~(?[U: $i, V: $i, W: $i] : (~f(U, V, W)) <=> ![X: $i, Y: $i, Z: $i] : f(X, Y, Z)))),
% 0.20/0.36 inference(transitivity,[status(thm)],[16, 12])).
% 0.20/0.36 tff(18,plain,
% 0.20/0.36 ((~(![X: $i, Y: $i, Z: $i] : f(X, Y, Z) <=> (~?[U: $i, V: $i, W: $i] : (~f(U, V, W))))) <=> (~(~(?[U: $i, V: $i, W: $i] : (~f(U, V, W)) <=> ![X: $i, Y: $i, Z: $i] : f(X, Y, Z))))),
% 0.20/0.36 inference(monotonicity,[status(thm)],[17])).
% 0.20/0.36 tff(19,plain,
% 0.20/0.36 ((~(![X: $i, Y: $i, Z: $i] : f(X, Y, Z) <=> (~?[U: $i, V: $i, W: $i] : (~f(U, V, W))))) <=> (?[U: $i, V: $i, W: $i] : (~f(U, V, W)) <=> ![X: $i, Y: $i, Z: $i] : f(X, Y, Z))),
% 0.20/0.36 inference(transitivity,[status(thm)],[18, 11])).
% 0.20/0.36 tff(20,axiom,(~(![X: $i, Y: $i, Z: $i] : f(X, Y, Z) <=> (~?[U: $i, V: $i, W: $i] : (~f(U, V, W))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','kalish250')).
% 0.20/0.36 tff(21,plain,
% 0.20/0.36 (?[U: $i, V: $i, W: $i] : (~f(U, V, W)) <=> ![X: $i, Y: $i, Z: $i] : f(X, Y, Z)),
% 0.20/0.36 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.20/0.36 tff(22,plain,
% 0.20/0.36 (?[U: $i, V: $i, W: $i] : (~f(U, V, W)) <=> ![X: $i, Y: $i, Z: $i] : f(X, Y, Z)),
% 0.20/0.36 inference(modus_ponens,[status(thm)],[21, 10])).
% 0.20/0.36 tff(23,plain,
% 0.20/0.36 (?[U: $i, V: $i, W: $i] : (~f(U, V, W)) <=> ![X: $i, Y: $i, Z: $i] : f(X, Y, Z)),
% 0.20/0.36 inference(modus_ponens,[status(thm)],[22, 10])).
% 0.20/0.36 tff(24,plain,
% 0.20/0.36 (?[U: $i, V: $i, W: $i] : (~f(U, V, W)) <=> ![X: $i, Y: $i, Z: $i] : f(X, Y, Z)),
% 0.20/0.36 inference(modus_ponens,[status(thm)],[23, 10])).
% 0.20/0.36 tff(25,plain,(
% 0.20/0.36 (![U: $i, V: $i, W: $i] : f(U, V, W) | ![X: $i, Y: $i, Z: $i] : f(X, Y, Z)) & ((~f(U!2, V!1, W!0)) | (~f(X!5, Y!4, Z!3)))),
% 0.20/0.36 inference(skolemize,[status(sab)],[24])).
% 0.20/0.36 tff(26,plain,
% 0.20/0.36 ((![U: $i, V: $i, W: $i] : f(U, V, W) | ![X: $i, Y: $i, Z: $i] : f(X, Y, Z)) & ((~f(U!2, V!1, W!0)) | (~f(X!5, Y!4, Z!3)))),
% 0.20/0.36 inference(modus_ponens,[status(thm)],[25, 9])).
% 0.20/0.36 tff(27,plain,
% 0.20/0.36 (![U: $i, V: $i, W: $i] : f(U, V, W) | ![X: $i, Y: $i, Z: $i] : f(X, Y, Z)),
% 0.20/0.36 inference(and_elim,[status(thm)],[26])).
% 0.20/0.36 tff(28,plain,
% 0.20/0.36 (![U: $i, V: $i, W: $i] : f(U, V, W) | ![X: $i, Y: $i, Z: $i] : f(X, Y, Z)),
% 0.20/0.36 inference(modus_ponens,[status(thm)],[27, 7])).
% 0.20/0.36 tff(29,plain,
% 0.20/0.36 (![X: $i, Y: $i, Z: $i] : f(X, Y, Z)),
% 0.20/0.36 inference(unit_resolution,[status(thm)],[28, 6])).
% 0.20/0.36 tff(30,plain,
% 0.20/0.36 ((~![X: $i, Y: $i, Z: $i] : f(X, Y, Z)) | f(X!5, Y!4, Z!3)),
% 0.20/0.36 inference(quant_inst,[status(thm)],[])).
% 0.20/0.36 tff(31,plain,
% 0.20/0.36 ($false),
% 0.20/0.36 inference(unit_resolution,[status(thm)],[30, 29, 1])).
% 0.20/0.36 tff(32,plain,(f(X!5, Y!4, Z!3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.36 tff(33,plain,
% 0.20/0.36 ((~f(U!2, V!1, W!0)) | (~f(X!5, Y!4, Z!3))),
% 0.20/0.36 inference(and_elim,[status(thm)],[26])).
% 0.20/0.36 tff(34,plain,
% 0.20/0.36 (~f(U!2, V!1, W!0)),
% 0.20/0.36 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.20/0.36 tff(35,assumption,(![X: $i, Y: $i, Z: $i] : f(X, Y, Z)), introduced(assumption)).
% 0.20/0.36 tff(36,plain,
% 0.20/0.36 ((~![X: $i, Y: $i, Z: $i] : f(X, Y, Z)) | f(U!2, V!1, W!0)),
% 0.20/0.36 inference(quant_inst,[status(thm)],[])).
% 0.20/0.36 tff(37,plain,
% 0.20/0.36 ($false),
% 0.20/0.36 inference(unit_resolution,[status(thm)],[36, 35, 34])).
% 0.20/0.36 tff(38,plain,(~![X: $i, Y: $i, Z: $i] : f(X, Y, Z)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.36 tff(39,plain,
% 0.20/0.36 (![U: $i, V: $i, W: $i] : f(U, V, W)),
% 0.20/0.36 inference(unit_resolution,[status(thm)],[28, 38])).
% 0.20/0.36 tff(40,plain,
% 0.20/0.36 ((~![U: $i, V: $i, W: $i] : f(U, V, W)) | f(U!2, V!1, W!0)),
% 0.20/0.36 inference(quant_inst,[status(thm)],[])).
% 0.20/0.36 tff(41,plain,
% 0.20/0.36 ($false),
% 0.20/0.36 inference(unit_resolution,[status(thm)],[40, 39, 34])).
% 0.20/0.36 % SZS output end Proof
% 0.20/0.36 % E exiting
%------------------------------------------------------------------------------