%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN352-1 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:38:52 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.40s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN352-1 : TPTP v9.0.0. Released v1.2.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n009.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:31:18 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.40 % SZS status Unsatisfiable
% 0.11/0.40 % SZS output start Proof
% 0.11/0.40 tff(f_type, type, (
% 0.11/0.40 f: ( $i * $i ) > $o)).
% 0.11/0.40 tff(z_type, type, (
% 0.11/0.40 z: ( $i * $i ) > $i)).
% 0.11/0.40 tff(a_type, type, (
% 0.11/0.40 a: $i)).
% 0.11/0.40 tff(b_type, type, (
% 0.11/0.40 b: $i)).
% 0.11/0.40 tff(1,assumption,(~f(z(b, a), z(b, a))), introduced(assumption)).
% 0.11/0.40 tff(2,plain,
% 0.11/0.40 (^[Y: $i, X: $i] : refl((f(z(X, Y), z(X, Y)) | (~f(X, z(X, Y))) | (~f(b, z(X, Y)))) <=> (f(z(X, Y), z(X, Y)) | (~f(X, z(X, Y))) | (~f(b, z(X, Y)))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(3,plain,
% 0.11/0.40 (![Y: $i, X: $i] : (f(z(X, Y), z(X, Y)) | (~f(X, z(X, Y))) | (~f(b, z(X, Y)))) <=> ![Y: $i, X: $i] : (f(z(X, Y), z(X, Y)) | (~f(X, z(X, Y))) | (~f(b, z(X, Y))))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[2])).
% 0.11/0.40 tff(4,plain,
% 0.11/0.40 (![Y: $i, X: $i] : (f(z(X, Y), z(X, Y)) | (~f(X, z(X, Y))) | (~f(b, z(X, Y)))) <=> ![Y: $i, X: $i] : (f(z(X, Y), z(X, Y)) | (~f(X, z(X, Y))) | (~f(b, z(X, Y))))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(5,plain,
% 0.11/0.40 (^[Y: $i, X: $i] : rewrite((((~f(b, z(X, Y))) | (~f(X, z(X, Y)))) | f(z(X, Y), z(X, Y))) <=> (f(z(X, Y), z(X, Y)) | (~f(X, z(X, Y))) | (~f(b, z(X, Y)))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(6,plain,
% 0.11/0.40 (![Y: $i, X: $i] : (((~f(b, z(X, Y))) | (~f(X, z(X, Y)))) | f(z(X, Y), z(X, Y))) <=> ![Y: $i, X: $i] : (f(z(X, Y), z(X, Y)) | (~f(X, z(X, Y))) | (~f(b, z(X, Y))))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[5])).
% 0.11/0.40 tff(7,axiom,(![Y: $i, X: $i] : (((~f(b, z(X, Y))) | (~f(X, z(X, Y)))) | f(z(X, Y), z(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause5')).
% 0.11/0.40 tff(8,plain,
% 0.11/0.40 (![Y: $i, X: $i] : (f(z(X, Y), z(X, Y)) | (~f(X, z(X, Y))) | (~f(b, z(X, Y))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.11/0.40 tff(9,plain,
% 0.11/0.40 (![Y: $i, X: $i] : (f(z(X, Y), z(X, Y)) | (~f(X, z(X, Y))) | (~f(b, z(X, Y))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.11/0.40 tff(10,plain,(
% 0.11/0.40 ![Y: $i, X: $i] : (f(z(X, Y), z(X, Y)) | (~f(X, z(X, Y))) | (~f(b, z(X, Y))))),
% 0.11/0.40 inference(skolemize,[status(sab)],[9])).
% 0.11/0.40 tff(11,plain,
% 0.11/0.40 (![Y: $i, X: $i] : (f(z(X, Y), z(X, Y)) | (~f(X, z(X, Y))) | (~f(b, z(X, Y))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.11/0.40 tff(12,plain,
% 0.11/0.40 (((~![Y: $i, X: $i] : (f(z(X, Y), z(X, Y)) | (~f(X, z(X, Y))) | (~f(b, z(X, Y))))) | (f(z(b, a), z(b, a)) | (~f(b, z(b, a))))) <=> ((~![Y: $i, X: $i] : (f(z(X, Y), z(X, Y)) | (~f(X, z(X, Y))) | (~f(b, z(X, Y))))) | f(z(b, a), z(b, a)) | (~f(b, z(b, a))))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(13,plain,
% 0.11/0.40 ((f(z(b, a), z(b, a)) | (~f(b, z(b, a))) | (~f(b, z(b, a)))) <=> (f(z(b, a), z(b, a)) | (~f(b, z(b, a))))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(14,plain,
% 0.11/0.40 (((~![Y: $i, X: $i] : (f(z(X, Y), z(X, Y)) | (~f(X, z(X, Y))) | (~f(b, z(X, Y))))) | (f(z(b, a), z(b, a)) | (~f(b, z(b, a))) | (~f(b, z(b, a))))) <=> ((~![Y: $i, X: $i] : (f(z(X, Y), z(X, Y)) | (~f(X, z(X, Y))) | (~f(b, z(X, Y))))) | (f(z(b, a), z(b, a)) | (~f(b, z(b, a)))))),
% 0.11/0.40 inference(monotonicity,[status(thm)],[13])).
% 0.11/0.40 tff(15,plain,
% 0.11/0.40 (((~![Y: $i, X: $i] : (f(z(X, Y), z(X, Y)) | (~f(X, z(X, Y))) | (~f(b, z(X, Y))))) | (f(z(b, a), z(b, a)) | (~f(b, z(b, a))) | (~f(b, z(b, a))))) <=> ((~![Y: $i, X: $i] : (f(z(X, Y), z(X, Y)) | (~f(X, z(X, Y))) | (~f(b, z(X, Y))))) | f(z(b, a), z(b, a)) | (~f(b, z(b, a))))),
% 0.11/0.40 inference(transitivity,[status(thm)],[14, 12])).
% 0.11/0.40 tff(16,plain,
% 0.11/0.40 ((~![Y: $i, X: $i] : (f(z(X, Y), z(X, Y)) | (~f(X, z(X, Y))) | (~f(b, z(X, Y))))) | (f(z(b, a), z(b, a)) | (~f(b, z(b, a))) | (~f(b, z(b, a))))),
% 0.11/0.40 inference(quant_inst,[status(thm)],[])).
% 0.11/0.40 tff(17,plain,
% 0.11/0.40 ((~![Y: $i, X: $i] : (f(z(X, Y), z(X, Y)) | (~f(X, z(X, Y))) | (~f(b, z(X, Y))))) | f(z(b, a), z(b, a)) | (~f(b, z(b, a)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.11/0.40 tff(18,plain,
% 0.11/0.40 (f(z(b, a), z(b, a)) | (~f(b, z(b, a)))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[17, 11])).
% 0.11/0.40 tff(19,plain,
% 0.11/0.40 (~f(b, z(b, a))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[18, 1])).
% 0.11/0.40 tff(20,plain,
% 0.11/0.40 (^[Y: $i, X: $i] : refl((f(z(X, Y), z(X, Y)) | f(b, z(X, Y)) | f(X, z(X, Y))) <=> (f(z(X, Y), z(X, Y)) | f(b, z(X, Y)) | f(X, z(X, Y))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(21,plain,
% 0.11/0.40 (![Y: $i, X: $i] : (f(z(X, Y), z(X, Y)) | f(b, z(X, Y)) | f(X, z(X, Y))) <=> ![Y: $i, X: $i] : (f(z(X, Y), z(X, Y)) | f(b, z(X, Y)) | f(X, z(X, Y)))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[20])).
% 0.11/0.40 tff(22,plain,
% 0.11/0.40 (![Y: $i, X: $i] : (f(z(X, Y), z(X, Y)) | f(b, z(X, Y)) | f(X, z(X, Y))) <=> ![Y: $i, X: $i] : (f(z(X, Y), z(X, Y)) | f(b, z(X, Y)) | f(X, z(X, Y)))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(23,plain,
% 0.11/0.40 (^[Y: $i, X: $i] : rewrite(((f(b, z(X, Y)) | f(X, z(X, Y))) | f(z(X, Y), z(X, Y))) <=> (f(z(X, Y), z(X, Y)) | f(b, z(X, Y)) | f(X, z(X, Y))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(24,plain,
% 0.11/0.40 (![Y: $i, X: $i] : ((f(b, z(X, Y)) | f(X, z(X, Y))) | f(z(X, Y), z(X, Y))) <=> ![Y: $i, X: $i] : (f(z(X, Y), z(X, Y)) | f(b, z(X, Y)) | f(X, z(X, Y)))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[23])).
% 0.11/0.40 tff(25,axiom,(![Y: $i, X: $i] : ((f(b, z(X, Y)) | f(X, z(X, Y))) | f(z(X, Y), z(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause4')).
% 0.11/0.40 tff(26,plain,
% 0.11/0.40 (![Y: $i, X: $i] : (f(z(X, Y), z(X, Y)) | f(b, z(X, Y)) | f(X, z(X, Y)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.11/0.40 tff(27,plain,
% 0.11/0.40 (![Y: $i, X: $i] : (f(z(X, Y), z(X, Y)) | f(b, z(X, Y)) | f(X, z(X, Y)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.11/0.40 tff(28,plain,(
% 0.11/0.40 ![Y: $i, X: $i] : (f(z(X, Y), z(X, Y)) | f(b, z(X, Y)) | f(X, z(X, Y)))),
% 0.11/0.40 inference(skolemize,[status(sab)],[27])).
% 0.11/0.40 tff(29,plain,
% 0.11/0.40 (![Y: $i, X: $i] : (f(z(X, Y), z(X, Y)) | f(b, z(X, Y)) | f(X, z(X, Y)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.11/0.40 tff(30,plain,
% 0.11/0.40 (((~![Y: $i, X: $i] : (f(z(X, Y), z(X, Y)) | f(b, z(X, Y)) | f(X, z(X, Y)))) | (f(z(b, a), z(b, a)) | f(b, z(b, a)))) <=> ((~![Y: $i, X: $i] : (f(z(X, Y), z(X, Y)) | f(b, z(X, Y)) | f(X, z(X, Y)))) | f(z(b, a), z(b, a)) | f(b, z(b, a)))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(31,plain,
% 0.11/0.40 ((f(z(b, a), z(b, a)) | f(b, z(b, a)) | f(b, z(b, a))) <=> (f(z(b, a), z(b, a)) | f(b, z(b, a)))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(32,plain,
% 0.11/0.40 (((~![Y: $i, X: $i] : (f(z(X, Y), z(X, Y)) | f(b, z(X, Y)) | f(X, z(X, Y)))) | (f(z(b, a), z(b, a)) | f(b, z(b, a)) | f(b, z(b, a)))) <=> ((~![Y: $i, X: $i] : (f(z(X, Y), z(X, Y)) | f(b, z(X, Y)) | f(X, z(X, Y)))) | (f(z(b, a), z(b, a)) | f(b, z(b, a))))),
% 0.11/0.40 inference(monotonicity,[status(thm)],[31])).
% 0.11/0.40 tff(33,plain,
% 0.11/0.40 (((~![Y: $i, X: $i] : (f(z(X, Y), z(X, Y)) | f(b, z(X, Y)) | f(X, z(X, Y)))) | (f(z(b, a), z(b, a)) | f(b, z(b, a)) | f(b, z(b, a)))) <=> ((~![Y: $i, X: $i] : (f(z(X, Y), z(X, Y)) | f(b, z(X, Y)) | f(X, z(X, Y)))) | f(z(b, a), z(b, a)) | f(b, z(b, a)))),
% 0.11/0.40 inference(transitivity,[status(thm)],[32, 30])).
% 0.11/0.40 tff(34,plain,
% 0.11/0.40 ((~![Y: $i, X: $i] : (f(z(X, Y), z(X, Y)) | f(b, z(X, Y)) | f(X, z(X, Y)))) | (f(z(b, a), z(b, a)) | f(b, z(b, a)) | f(b, z(b, a)))),
% 0.11/0.40 inference(quant_inst,[status(thm)],[])).
% 0.11/0.40 tff(35,plain,
% 0.11/0.40 ((~![Y: $i, X: $i] : (f(z(X, Y), z(X, Y)) | f(b, z(X, Y)) | f(X, z(X, Y)))) | f(z(b, a), z(b, a)) | f(b, z(b, a))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.11/0.40 tff(36,plain,
% 0.11/0.40 ($false),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[35, 29, 1, 19])).
% 0.11/0.40 tff(37,plain,(f(z(b, a), z(b, a))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.40 tff(38,plain,
% 0.11/0.40 (^[Y: $i, X: $i] : refl((f(Y, z(X, Y)) | (~f(X, Y)) | f(X, z(X, Y))) <=> (f(Y, z(X, Y)) | (~f(X, Y)) | f(X, z(X, Y))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(39,plain,
% 0.11/0.40 (![Y: $i, X: $i] : (f(Y, z(X, Y)) | (~f(X, Y)) | f(X, z(X, Y))) <=> ![Y: $i, X: $i] : (f(Y, z(X, Y)) | (~f(X, Y)) | f(X, z(X, Y)))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[38])).
% 0.11/0.40 tff(40,plain,
% 0.11/0.40 (![Y: $i, X: $i] : (f(Y, z(X, Y)) | (~f(X, Y)) | f(X, z(X, Y))) <=> ![Y: $i, X: $i] : (f(Y, z(X, Y)) | (~f(X, Y)) | f(X, z(X, Y)))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(41,plain,
% 0.11/0.40 (^[Y: $i, X: $i] : rewrite((((~f(X, Y)) | f(X, z(X, Y))) | f(Y, z(X, Y))) <=> (f(Y, z(X, Y)) | (~f(X, Y)) | f(X, z(X, Y))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(42,plain,
% 0.11/0.40 (![Y: $i, X: $i] : (((~f(X, Y)) | f(X, z(X, Y))) | f(Y, z(X, Y))) <=> ![Y: $i, X: $i] : (f(Y, z(X, Y)) | (~f(X, Y)) | f(X, z(X, Y)))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[41])).
% 0.11/0.40 tff(43,axiom,(![Y: $i, X: $i] : (((~f(X, Y)) | f(X, z(X, Y))) | f(Y, z(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause7')).
% 0.11/0.40 tff(44,plain,
% 0.11/0.40 (![Y: $i, X: $i] : (f(Y, z(X, Y)) | (~f(X, Y)) | f(X, z(X, Y)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.11/0.40 tff(45,plain,
% 0.11/0.40 (![Y: $i, X: $i] : (f(Y, z(X, Y)) | (~f(X, Y)) | f(X, z(X, Y)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.11/0.40 tff(46,plain,(
% 0.11/0.40 ![Y: $i, X: $i] : (f(Y, z(X, Y)) | (~f(X, Y)) | f(X, z(X, Y)))),
% 0.11/0.40 inference(skolemize,[status(sab)],[45])).
% 0.11/0.40 tff(47,plain,
% 0.11/0.40 (![Y: $i, X: $i] : (f(Y, z(X, Y)) | (~f(X, Y)) | f(X, z(X, Y)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[46, 39])).
% 0.11/0.40 tff(48,plain,
% 0.11/0.40 (((~![Y: $i, X: $i] : (f(Y, z(X, Y)) | (~f(X, Y)) | f(X, z(X, Y)))) | (f(z(b, a), z(z(b, a), z(b, a))) | (~f(z(b, a), z(b, a))))) <=> ((~![Y: $i, X: $i] : (f(Y, z(X, Y)) | (~f(X, Y)) | f(X, z(X, Y)))) | f(z(b, a), z(z(b, a), z(b, a))) | (~f(z(b, a), z(b, a))))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(49,plain,
% 0.11/0.40 ((f(z(b, a), z(z(b, a), z(b, a))) | (~f(z(b, a), z(b, a))) | f(z(b, a), z(z(b, a), z(b, a)))) <=> (f(z(b, a), z(z(b, a), z(b, a))) | (~f(z(b, a), z(b, a))))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(50,plain,
% 0.11/0.40 (((~![Y: $i, X: $i] : (f(Y, z(X, Y)) | (~f(X, Y)) | f(X, z(X, Y)))) | (f(z(b, a), z(z(b, a), z(b, a))) | (~f(z(b, a), z(b, a))) | f(z(b, a), z(z(b, a), z(b, a))))) <=> ((~![Y: $i, X: $i] : (f(Y, z(X, Y)) | (~f(X, Y)) | f(X, z(X, Y)))) | (f(z(b, a), z(z(b, a), z(b, a))) | (~f(z(b, a), z(b, a)))))),
% 0.11/0.40 inference(monotonicity,[status(thm)],[49])).
% 0.11/0.40 tff(51,plain,
% 0.11/0.40 (((~![Y: $i, X: $i] : (f(Y, z(X, Y)) | (~f(X, Y)) | f(X, z(X, Y)))) | (f(z(b, a), z(z(b, a), z(b, a))) | (~f(z(b, a), z(b, a))) | f(z(b, a), z(z(b, a), z(b, a))))) <=> ((~![Y: $i, X: $i] : (f(Y, z(X, Y)) | (~f(X, Y)) | f(X, z(X, Y)))) | f(z(b, a), z(z(b, a), z(b, a))) | (~f(z(b, a), z(b, a))))),
% 0.11/0.40 inference(transitivity,[status(thm)],[50, 48])).
% 0.11/0.40 tff(52,plain,
% 0.11/0.40 ((~![Y: $i, X: $i] : (f(Y, z(X, Y)) | (~f(X, Y)) | f(X, z(X, Y)))) | (f(z(b, a), z(z(b, a), z(b, a))) | (~f(z(b, a), z(b, a))) | f(z(b, a), z(z(b, a), z(b, a))))),
% 0.11/0.40 inference(quant_inst,[status(thm)],[])).
% 0.11/0.40 tff(53,plain,
% 0.11/0.40 ((~![Y: $i, X: $i] : (f(Y, z(X, Y)) | (~f(X, Y)) | f(X, z(X, Y)))) | f(z(b, a), z(z(b, a), z(b, a))) | (~f(z(b, a), z(b, a)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.11/0.40 tff(54,plain,
% 0.11/0.40 (f(z(b, a), z(z(b, a), z(b, a)))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[53, 47, 37])).
% 0.11/0.40 tff(55,plain,
% 0.11/0.40 (^[Y: $i, X: $i] : refl(((~f(X, Y)) | (~f(X, z(X, Y))) | (~f(Y, z(X, Y)))) <=> ((~f(X, Y)) | (~f(X, z(X, Y))) | (~f(Y, z(X, Y)))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(56,plain,
% 0.11/0.40 (![Y: $i, X: $i] : ((~f(X, Y)) | (~f(X, z(X, Y))) | (~f(Y, z(X, Y)))) <=> ![Y: $i, X: $i] : ((~f(X, Y)) | (~f(X, z(X, Y))) | (~f(Y, z(X, Y))))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[55])).
% 0.11/0.40 tff(57,plain,
% 0.11/0.40 (![Y: $i, X: $i] : ((~f(X, Y)) | (~f(X, z(X, Y))) | (~f(Y, z(X, Y)))) <=> ![Y: $i, X: $i] : ((~f(X, Y)) | (~f(X, z(X, Y))) | (~f(Y, z(X, Y))))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(58,plain,
% 0.11/0.40 (^[Y: $i, X: $i] : rewrite((((~f(X, Y)) | (~f(X, z(X, Y)))) | (~f(Y, z(X, Y)))) <=> ((~f(X, Y)) | (~f(X, z(X, Y))) | (~f(Y, z(X, Y)))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(59,plain,
% 0.11/0.40 (![Y: $i, X: $i] : (((~f(X, Y)) | (~f(X, z(X, Y)))) | (~f(Y, z(X, Y)))) <=> ![Y: $i, X: $i] : ((~f(X, Y)) | (~f(X, z(X, Y))) | (~f(Y, z(X, Y))))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[58])).
% 0.11/0.40 tff(60,axiom,(![Y: $i, X: $i] : (((~f(X, Y)) | (~f(X, z(X, Y)))) | (~f(Y, z(X, Y))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause6')).
% 0.11/0.40 tff(61,plain,
% 0.11/0.40 (![Y: $i, X: $i] : ((~f(X, Y)) | (~f(X, z(X, Y))) | (~f(Y, z(X, Y))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.11/0.40 tff(62,plain,
% 0.11/0.40 (![Y: $i, X: $i] : ((~f(X, Y)) | (~f(X, z(X, Y))) | (~f(Y, z(X, Y))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.11/0.40 tff(63,plain,(
% 0.11/0.40 ![Y: $i, X: $i] : ((~f(X, Y)) | (~f(X, z(X, Y))) | (~f(Y, z(X, Y))))),
% 0.11/0.41 inference(skolemize,[status(sab)],[62])).
% 0.11/0.41 tff(64,plain,
% 0.11/0.41 (![Y: $i, X: $i] : ((~f(X, Y)) | (~f(X, z(X, Y))) | (~f(Y, z(X, Y))))),
% 0.11/0.41 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.11/0.41 tff(65,plain,
% 0.11/0.41 (((~![Y: $i, X: $i] : ((~f(X, Y)) | (~f(X, z(X, Y))) | (~f(Y, z(X, Y))))) | ((~f(z(b, a), z(b, a))) | (~f(z(b, a), z(z(b, a), z(b, a)))))) <=> ((~![Y: $i, X: $i] : ((~f(X, Y)) | (~f(X, z(X, Y))) | (~f(Y, z(X, Y))))) | (~f(z(b, a), z(b, a))) | (~f(z(b, a), z(z(b, a), z(b, a)))))),
% 0.11/0.41 inference(rewrite,[status(thm)],[])).
% 0.11/0.41 tff(66,plain,
% 0.11/0.41 (((~f(z(b, a), z(b, a))) | (~f(z(b, a), z(z(b, a), z(b, a)))) | (~f(z(b, a), z(z(b, a), z(b, a))))) <=> ((~f(z(b, a), z(b, a))) | (~f(z(b, a), z(z(b, a), z(b, a)))))),
% 0.11/0.41 inference(rewrite,[status(thm)],[])).
% 0.11/0.41 tff(67,plain,
% 0.11/0.41 (((~![Y: $i, X: $i] : ((~f(X, Y)) | (~f(X, z(X, Y))) | (~f(Y, z(X, Y))))) | ((~f(z(b, a), z(b, a))) | (~f(z(b, a), z(z(b, a), z(b, a)))) | (~f(z(b, a), z(z(b, a), z(b, a)))))) <=> ((~![Y: $i, X: $i] : ((~f(X, Y)) | (~f(X, z(X, Y))) | (~f(Y, z(X, Y))))) | ((~f(z(b, a), z(b, a))) | (~f(z(b, a), z(z(b, a), z(b, a))))))),
% 0.11/0.41 inference(monotonicity,[status(thm)],[66])).
% 0.11/0.41 tff(68,plain,
% 0.11/0.41 (((~![Y: $i, X: $i] : ((~f(X, Y)) | (~f(X, z(X, Y))) | (~f(Y, z(X, Y))))) | ((~f(z(b, a), z(b, a))) | (~f(z(b, a), z(z(b, a), z(b, a)))) | (~f(z(b, a), z(z(b, a), z(b, a)))))) <=> ((~![Y: $i, X: $i] : ((~f(X, Y)) | (~f(X, z(X, Y))) | (~f(Y, z(X, Y))))) | (~f(z(b, a), z(b, a))) | (~f(z(b, a), z(z(b, a), z(b, a)))))),
% 0.11/0.41 inference(transitivity,[status(thm)],[67, 65])).
% 0.11/0.41 tff(69,plain,
% 0.11/0.41 ((~![Y: $i, X: $i] : ((~f(X, Y)) | (~f(X, z(X, Y))) | (~f(Y, z(X, Y))))) | ((~f(z(b, a), z(b, a))) | (~f(z(b, a), z(z(b, a), z(b, a)))) | (~f(z(b, a), z(z(b, a), z(b, a)))))),
% 0.11/0.41 inference(quant_inst,[status(thm)],[])).
% 0.11/0.41 tff(70,plain,
% 0.11/0.41 ((~![Y: $i, X: $i] : ((~f(X, Y)) | (~f(X, z(X, Y))) | (~f(Y, z(X, Y))))) | (~f(z(b, a), z(b, a))) | (~f(z(b, a), z(z(b, a), z(b, a))))),
% 0.11/0.41 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.11/0.41 tff(71,plain,
% 0.11/0.41 ($false),
% 0.11/0.41 inference(unit_resolution,[status(thm)],[70, 64, 37, 54])).
% 0.11/0.41 % SZS output end Proof
% 0.11/0.41 % E exiting
%------------------------------------------------------------------------------