%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN354-1 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN354-1 : TPTP v9.0.0. Released v1.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 12:31:40 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.19/0.37 % SZS status Unsatisfiable
% 0.19/0.37 % SZS output start Proof
% 0.19/0.37 tff(f_type, type, (
% 0.19/0.37 f: ( $i * $i ) > $o)).
% 0.19/0.37 tff(b_type, type, (
% 0.19/0.37 b: $i)).
% 0.19/0.37 tff(g_type, type, (
% 0.19/0.37 g: ( $i * $i ) > $o)).
% 0.19/0.37 tff(z_type, type, (
% 0.19/0.37 z: ( $i * $i ) > $i)).
% 0.19/0.37 tff(a_type, type, (
% 0.19/0.37 a: $i)).
% 0.19/0.37 tff(1,assumption,(~f(b, b)), introduced(assumption)).
% 0.19/0.37 tff(2,plain,
% 0.19/0.37 (^[Y2: $i, Y1: $i] : refl((f(b, Y2) | (~f(Y1, Y2)) | g(Y2, z(Y1, Y2)) | g(b, z(Y1, Y2))) <=> (f(b, Y2) | (~f(Y1, Y2)) | g(Y2, z(Y1, Y2)) | g(b, z(Y1, Y2))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(3,plain,
% 0.19/0.37 (![Y2: $i, Y1: $i] : (f(b, Y2) | (~f(Y1, Y2)) | g(Y2, z(Y1, Y2)) | g(b, z(Y1, Y2))) <=> ![Y2: $i, Y1: $i] : (f(b, Y2) | (~f(Y1, Y2)) | g(Y2, z(Y1, Y2)) | g(b, z(Y1, Y2)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.37 tff(4,plain,
% 0.19/0.37 (![Y2: $i, Y1: $i] : (f(b, Y2) | (~f(Y1, Y2)) | g(Y2, z(Y1, Y2)) | g(b, z(Y1, Y2))) <=> ![Y2: $i, Y1: $i] : (f(b, Y2) | (~f(Y1, Y2)) | g(Y2, z(Y1, Y2)) | g(b, z(Y1, Y2)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(5,plain,
% 0.19/0.37 (^[Y2: $i, Y1: $i] : trans(monotonicity(rewrite(((g(b, z(Y1, Y2)) | g(Y2, z(Y1, Y2))) | (~f(Y1, Y2))) <=> ((~f(Y1, Y2)) | g(Y2, z(Y1, Y2)) | g(b, z(Y1, Y2)))), ((((g(b, z(Y1, Y2)) | g(Y2, z(Y1, Y2))) | (~f(Y1, Y2))) | f(b, Y2)) <=> (((~f(Y1, Y2)) | g(Y2, z(Y1, Y2)) | g(b, z(Y1, Y2))) | f(b, Y2)))), rewrite((((~f(Y1, Y2)) | g(Y2, z(Y1, Y2)) | g(b, z(Y1, Y2))) | f(b, Y2)) <=> (f(b, Y2) | (~f(Y1, Y2)) | g(Y2, z(Y1, Y2)) | g(b, z(Y1, Y2)))), ((((g(b, z(Y1, Y2)) | g(Y2, z(Y1, Y2))) | (~f(Y1, Y2))) | f(b, Y2)) <=> (f(b, Y2) | (~f(Y1, Y2)) | g(Y2, z(Y1, Y2)) | g(b, z(Y1, Y2)))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(6,plain,
% 0.19/0.37 (![Y2: $i, Y1: $i] : (((g(b, z(Y1, Y2)) | g(Y2, z(Y1, Y2))) | (~f(Y1, Y2))) | f(b, Y2)) <=> ![Y2: $i, Y1: $i] : (f(b, Y2) | (~f(Y1, Y2)) | g(Y2, z(Y1, Y2)) | g(b, z(Y1, Y2)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[5])).
% 0.19/0.37 tff(7,axiom,(![Y2: $i, Y1: $i] : (((g(b, z(Y1, Y2)) | g(Y2, z(Y1, Y2))) | (~f(Y1, Y2))) | f(b, Y2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause3')).
% 0.19/0.37 tff(8,plain,
% 0.19/0.37 (![Y2: $i, Y1: $i] : (f(b, Y2) | (~f(Y1, Y2)) | g(Y2, z(Y1, Y2)) | g(b, z(Y1, Y2)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.19/0.37 tff(9,plain,
% 0.19/0.37 (![Y2: $i, Y1: $i] : (f(b, Y2) | (~f(Y1, Y2)) | g(Y2, z(Y1, Y2)) | g(b, z(Y1, Y2)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.19/0.37 tff(10,plain,(
% 0.19/0.37 ![Y2: $i, Y1: $i] : (f(b, Y2) | (~f(Y1, Y2)) | g(Y2, z(Y1, Y2)) | g(b, z(Y1, Y2)))),
% 0.19/0.37 inference(skolemize,[status(sab)],[9])).
% 0.19/0.37 tff(11,plain,
% 0.19/0.37 (![Y2: $i, Y1: $i] : (f(b, Y2) | (~f(Y1, Y2)) | g(Y2, z(Y1, Y2)) | g(b, z(Y1, Y2)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.19/0.37 tff(12,plain,
% 0.19/0.37 (f(a, b) <=> f(a, b)),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(13,axiom,(f(a, b)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause1')).
% 0.19/0.37 tff(14,plain,
% 0.19/0.37 (f(a, b)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.19/0.37 tff(15,plain,
% 0.19/0.37 (((~![Y2: $i, Y1: $i] : (f(b, Y2) | (~f(Y1, Y2)) | g(Y2, z(Y1, Y2)) | g(b, z(Y1, Y2)))) | ((~f(a, b)) | f(b, b) | g(b, z(a, b)))) <=> ((~![Y2: $i, Y1: $i] : (f(b, Y2) | (~f(Y1, Y2)) | g(Y2, z(Y1, Y2)) | g(b, z(Y1, Y2)))) | (~f(a, b)) | f(b, b) | g(b, z(a, b)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(16,plain,
% 0.19/0.37 ((f(b, b) | (~f(a, b)) | g(b, z(a, b)) | g(b, z(a, b))) <=> ((~f(a, b)) | f(b, b) | g(b, z(a, b)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(17,plain,
% 0.19/0.37 (((~![Y2: $i, Y1: $i] : (f(b, Y2) | (~f(Y1, Y2)) | g(Y2, z(Y1, Y2)) | g(b, z(Y1, Y2)))) | (f(b, b) | (~f(a, b)) | g(b, z(a, b)) | g(b, z(a, b)))) <=> ((~![Y2: $i, Y1: $i] : (f(b, Y2) | (~f(Y1, Y2)) | g(Y2, z(Y1, Y2)) | g(b, z(Y1, Y2)))) | ((~f(a, b)) | f(b, b) | g(b, z(a, b))))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[16])).
% 0.19/0.37 tff(18,plain,
% 0.19/0.37 (((~![Y2: $i, Y1: $i] : (f(b, Y2) | (~f(Y1, Y2)) | g(Y2, z(Y1, Y2)) | g(b, z(Y1, Y2)))) | (f(b, b) | (~f(a, b)) | g(b, z(a, b)) | g(b, z(a, b)))) <=> ((~![Y2: $i, Y1: $i] : (f(b, Y2) | (~f(Y1, Y2)) | g(Y2, z(Y1, Y2)) | g(b, z(Y1, Y2)))) | (~f(a, b)) | f(b, b) | g(b, z(a, b)))),
% 0.19/0.37 inference(transitivity,[status(thm)],[17, 15])).
% 0.19/0.38 tff(19,plain,
% 0.19/0.38 ((~![Y2: $i, Y1: $i] : (f(b, Y2) | (~f(Y1, Y2)) | g(Y2, z(Y1, Y2)) | g(b, z(Y1, Y2)))) | (f(b, b) | (~f(a, b)) | g(b, z(a, b)) | g(b, z(a, b)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(20,plain,
% 0.19/0.38 ((~![Y2: $i, Y1: $i] : (f(b, Y2) | (~f(Y1, Y2)) | g(Y2, z(Y1, Y2)) | g(b, z(Y1, Y2)))) | (~f(a, b)) | f(b, b) | g(b, z(a, b))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.19/0.38 tff(21,plain,
% 0.19/0.38 (f(b, b) | g(b, z(a, b))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[20, 14, 11])).
% 0.19/0.38 tff(22,plain,
% 0.19/0.38 (g(b, z(a, b))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[21, 1])).
% 0.19/0.38 tff(23,plain,
% 0.19/0.38 (^[Y2: $i, Y1: $i] : refl((f(b, Y2) | (~f(Y1, Y2)) | (~g(Y2, z(Y1, Y2))) | (~g(b, z(Y1, Y2)))) <=> (f(b, Y2) | (~f(Y1, Y2)) | (~g(Y2, z(Y1, Y2))) | (~g(b, z(Y1, Y2)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(24,plain,
% 0.19/0.38 (![Y2: $i, Y1: $i] : (f(b, Y2) | (~f(Y1, Y2)) | (~g(Y2, z(Y1, Y2))) | (~g(b, z(Y1, Y2)))) <=> ![Y2: $i, Y1: $i] : (f(b, Y2) | (~f(Y1, Y2)) | (~g(Y2, z(Y1, Y2))) | (~g(b, z(Y1, Y2))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[23])).
% 0.19/0.38 tff(25,plain,
% 0.19/0.38 (![Y2: $i, Y1: $i] : (f(b, Y2) | (~f(Y1, Y2)) | (~g(Y2, z(Y1, Y2))) | (~g(b, z(Y1, Y2)))) <=> ![Y2: $i, Y1: $i] : (f(b, Y2) | (~f(Y1, Y2)) | (~g(Y2, z(Y1, Y2))) | (~g(b, z(Y1, Y2))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(26,plain,
% 0.19/0.38 (^[Y2: $i, Y1: $i] : trans(monotonicity(rewrite((((~g(b, z(Y1, Y2))) | (~g(Y2, z(Y1, Y2)))) | (~f(Y1, Y2))) <=> ((~f(Y1, Y2)) | (~g(Y2, z(Y1, Y2))) | (~g(b, z(Y1, Y2))))), (((((~g(b, z(Y1, Y2))) | (~g(Y2, z(Y1, Y2)))) | (~f(Y1, Y2))) | f(b, Y2)) <=> (((~f(Y1, Y2)) | (~g(Y2, z(Y1, Y2))) | (~g(b, z(Y1, Y2)))) | f(b, Y2)))), rewrite((((~f(Y1, Y2)) | (~g(Y2, z(Y1, Y2))) | (~g(b, z(Y1, Y2)))) | f(b, Y2)) <=> (f(b, Y2) | (~f(Y1, Y2)) | (~g(Y2, z(Y1, Y2))) | (~g(b, z(Y1, Y2))))), (((((~g(b, z(Y1, Y2))) | (~g(Y2, z(Y1, Y2)))) | (~f(Y1, Y2))) | f(b, Y2)) <=> (f(b, Y2) | (~f(Y1, Y2)) | (~g(Y2, z(Y1, Y2))) | (~g(b, z(Y1, Y2))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(27,plain,
% 0.19/0.38 (![Y2: $i, Y1: $i] : ((((~g(b, z(Y1, Y2))) | (~g(Y2, z(Y1, Y2)))) | (~f(Y1, Y2))) | f(b, Y2)) <=> ![Y2: $i, Y1: $i] : (f(b, Y2) | (~f(Y1, Y2)) | (~g(Y2, z(Y1, Y2))) | (~g(b, z(Y1, Y2))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[26])).
% 0.19/0.38 tff(28,axiom,(![Y2: $i, Y1: $i] : ((((~g(b, z(Y1, Y2))) | (~g(Y2, z(Y1, Y2)))) | (~f(Y1, Y2))) | f(b, Y2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause4')).
% 0.19/0.38 tff(29,plain,
% 0.19/0.38 (![Y2: $i, Y1: $i] : (f(b, Y2) | (~f(Y1, Y2)) | (~g(Y2, z(Y1, Y2))) | (~g(b, z(Y1, Y2))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.19/0.38 tff(30,plain,
% 0.19/0.38 (![Y2: $i, Y1: $i] : (f(b, Y2) | (~f(Y1, Y2)) | (~g(Y2, z(Y1, Y2))) | (~g(b, z(Y1, Y2))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.19/0.38 tff(31,plain,(
% 0.19/0.38 ![Y2: $i, Y1: $i] : (f(b, Y2) | (~f(Y1, Y2)) | (~g(Y2, z(Y1, Y2))) | (~g(b, z(Y1, Y2))))),
% 0.19/0.38 inference(skolemize,[status(sab)],[30])).
% 0.19/0.38 tff(32,plain,
% 0.19/0.38 (![Y2: $i, Y1: $i] : (f(b, Y2) | (~f(Y1, Y2)) | (~g(Y2, z(Y1, Y2))) | (~g(b, z(Y1, Y2))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.19/0.38 tff(33,plain,
% 0.19/0.38 (((~![Y2: $i, Y1: $i] : (f(b, Y2) | (~f(Y1, Y2)) | (~g(Y2, z(Y1, Y2))) | (~g(b, z(Y1, Y2))))) | ((~f(a, b)) | f(b, b) | (~g(b, z(a, b))))) <=> ((~![Y2: $i, Y1: $i] : (f(b, Y2) | (~f(Y1, Y2)) | (~g(Y2, z(Y1, Y2))) | (~g(b, z(Y1, Y2))))) | (~f(a, b)) | f(b, b) | (~g(b, z(a, b))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(34,plain,
% 0.19/0.38 ((f(b, b) | (~f(a, b)) | (~g(b, z(a, b))) | (~g(b, z(a, b)))) <=> ((~f(a, b)) | f(b, b) | (~g(b, z(a, b))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(35,plain,
% 0.19/0.38 (((~![Y2: $i, Y1: $i] : (f(b, Y2) | (~f(Y1, Y2)) | (~g(Y2, z(Y1, Y2))) | (~g(b, z(Y1, Y2))))) | (f(b, b) | (~f(a, b)) | (~g(b, z(a, b))) | (~g(b, z(a, b))))) <=> ((~![Y2: $i, Y1: $i] : (f(b, Y2) | (~f(Y1, Y2)) | (~g(Y2, z(Y1, Y2))) | (~g(b, z(Y1, Y2))))) | ((~f(a, b)) | f(b, b) | (~g(b, z(a, b)))))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[34])).
% 0.19/0.38 tff(36,plain,
% 0.19/0.38 (((~![Y2: $i, Y1: $i] : (f(b, Y2) | (~f(Y1, Y2)) | (~g(Y2, z(Y1, Y2))) | (~g(b, z(Y1, Y2))))) | (f(b, b) | (~f(a, b)) | (~g(b, z(a, b))) | (~g(b, z(a, b))))) <=> ((~![Y2: $i, Y1: $i] : (f(b, Y2) | (~f(Y1, Y2)) | (~g(Y2, z(Y1, Y2))) | (~g(b, z(Y1, Y2))))) | (~f(a, b)) | f(b, b) | (~g(b, z(a, b))))),
% 0.19/0.38 inference(transitivity,[status(thm)],[35, 33])).
% 0.19/0.38 tff(37,plain,
% 0.19/0.38 ((~![Y2: $i, Y1: $i] : (f(b, Y2) | (~f(Y1, Y2)) | (~g(Y2, z(Y1, Y2))) | (~g(b, z(Y1, Y2))))) | (f(b, b) | (~f(a, b)) | (~g(b, z(a, b))) | (~g(b, z(a, b))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(38,plain,
% 0.19/0.38 ((~![Y2: $i, Y1: $i] : (f(b, Y2) | (~f(Y1, Y2)) | (~g(Y2, z(Y1, Y2))) | (~g(b, z(Y1, Y2))))) | (~f(a, b)) | f(b, b) | (~g(b, z(a, b)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.38 tff(39,plain,
% 0.19/0.38 (f(b, b) | (~g(b, z(a, b)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[38, 14, 32])).
% 0.19/0.38 tff(40,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[39, 22, 1])).
% 0.19/0.38 tff(41,plain,(f(b, b)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.38 tff(42,plain,
% 0.19/0.38 (^[Y2: $i, Y1: $i] : refl(((~f(Y1, Y2)) | (~f(b, Y1)) | (~f(a, Y1))) <=> ((~f(Y1, Y2)) | (~f(b, Y1)) | (~f(a, Y1))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(43,plain,
% 0.19/0.38 (![Y2: $i, Y1: $i] : ((~f(Y1, Y2)) | (~f(b, Y1)) | (~f(a, Y1))) <=> ![Y2: $i, Y1: $i] : ((~f(Y1, Y2)) | (~f(b, Y1)) | (~f(a, Y1)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[42])).
% 0.19/0.38 tff(44,plain,
% 0.19/0.38 (![Y2: $i, Y1: $i] : ((~f(Y1, Y2)) | (~f(b, Y1)) | (~f(a, Y1))) <=> ![Y2: $i, Y1: $i] : ((~f(Y1, Y2)) | (~f(b, Y1)) | (~f(a, Y1)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(45,plain,
% 0.19/0.38 (^[Y2: $i, Y1: $i] : rewrite((((~f(a, Y1)) | (~f(b, Y1))) | (~f(Y1, Y2))) <=> ((~f(Y1, Y2)) | (~f(b, Y1)) | (~f(a, Y1))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(46,plain,
% 0.19/0.38 (![Y2: $i, Y1: $i] : (((~f(a, Y1)) | (~f(b, Y1))) | (~f(Y1, Y2))) <=> ![Y2: $i, Y1: $i] : ((~f(Y1, Y2)) | (~f(b, Y1)) | (~f(a, Y1)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[45])).
% 0.19/0.38 tff(47,axiom,(![Y2: $i, Y1: $i] : (((~f(a, Y1)) | (~f(b, Y1))) | (~f(Y1, Y2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause7')).
% 0.19/0.38 tff(48,plain,
% 0.19/0.38 (![Y2: $i, Y1: $i] : ((~f(Y1, Y2)) | (~f(b, Y1)) | (~f(a, Y1)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.19/0.38 tff(49,plain,
% 0.19/0.38 (![Y2: $i, Y1: $i] : ((~f(Y1, Y2)) | (~f(b, Y1)) | (~f(a, Y1)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.19/0.38 tff(50,plain,(
% 0.19/0.38 ![Y2: $i, Y1: $i] : ((~f(Y1, Y2)) | (~f(b, Y1)) | (~f(a, Y1)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[49])).
% 0.19/0.38 tff(51,plain,
% 0.19/0.38 (![Y2: $i, Y1: $i] : ((~f(Y1, Y2)) | (~f(b, Y1)) | (~f(a, Y1)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.19/0.38 tff(52,plain,
% 0.19/0.38 (((~![Y2: $i, Y1: $i] : ((~f(Y1, Y2)) | (~f(b, Y1)) | (~f(a, Y1)))) | ((~f(a, b)) | (~f(b, b)))) <=> ((~![Y2: $i, Y1: $i] : ((~f(Y1, Y2)) | (~f(b, Y1)) | (~f(a, Y1)))) | (~f(a, b)) | (~f(b, b)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(53,plain,
% 0.19/0.38 (((~f(b, b)) | (~f(b, b)) | (~f(a, b))) <=> ((~f(a, b)) | (~f(b, b)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(54,plain,
% 0.19/0.38 (((~![Y2: $i, Y1: $i] : ((~f(Y1, Y2)) | (~f(b, Y1)) | (~f(a, Y1)))) | ((~f(b, b)) | (~f(b, b)) | (~f(a, b)))) <=> ((~![Y2: $i, Y1: $i] : ((~f(Y1, Y2)) | (~f(b, Y1)) | (~f(a, Y1)))) | ((~f(a, b)) | (~f(b, b))))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[53])).
% 0.19/0.38 tff(55,plain,
% 0.19/0.38 (((~![Y2: $i, Y1: $i] : ((~f(Y1, Y2)) | (~f(b, Y1)) | (~f(a, Y1)))) | ((~f(b, b)) | (~f(b, b)) | (~f(a, b)))) <=> ((~![Y2: $i, Y1: $i] : ((~f(Y1, Y2)) | (~f(b, Y1)) | (~f(a, Y1)))) | (~f(a, b)) | (~f(b, b)))),
% 0.19/0.38 inference(transitivity,[status(thm)],[54, 52])).
% 0.19/0.38 tff(56,plain,
% 0.19/0.38 ((~![Y2: $i, Y1: $i] : ((~f(Y1, Y2)) | (~f(b, Y1)) | (~f(a, Y1)))) | ((~f(b, b)) | (~f(b, b)) | (~f(a, b)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(57,plain,
% 0.19/0.38 ((~![Y2: $i, Y1: $i] : ((~f(Y1, Y2)) | (~f(b, Y1)) | (~f(a, Y1)))) | (~f(a, b)) | (~f(b, b))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.19/0.38 tff(58,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[57, 14, 51, 41])).
% 0.19/0.38 % SZS output end Proof
% 0.19/0.38 % E exiting
%------------------------------------------------------------------------------