%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN321-1 : TPTP v9.0.0. Released v1.2.0.
% 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 05:38:45 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN321-1 : TPTP v9.0.0. Released v1.2.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n001.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 12:34:50 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.36 % SZS status Unsatisfiable
% 0.11/0.36 % SZS output start Proof
% 0.11/0.36 tff(g_type, type, (
% 0.11/0.36 g: ( $i * $i ) > $o)).
% 0.11/0.36 tff(a_type, type, (
% 0.11/0.36 a: $i)).
% 0.11/0.36 tff(f_type, type, (
% 0.11/0.36 f: ( $i * $i ) > $o)).
% 0.11/0.36 tff(b_type, type, (
% 0.11/0.36 b: $i)).
% 0.11/0.36 tff(d_type, type, (
% 0.11/0.36 d: $i)).
% 0.11/0.36 tff(1,assumption,(~g(a, d)), introduced(assumption)).
% 0.11/0.36 tff(2,plain,
% 0.11/0.36 (^[U: $i] : refl((f(a, b) | g(a, U)) <=> (f(a, b) | g(a, U)))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(3,plain,
% 0.11/0.36 (![U: $i] : (f(a, b) | g(a, U)) <=> ![U: $i] : (f(a, b) | g(a, U))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[2])).
% 0.11/0.36 tff(4,plain,
% 0.11/0.36 (![U: $i] : (f(a, b) | g(a, U)) <=> ![U: $i] : (f(a, b) | g(a, U))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(5,axiom,(![U: $i] : (f(a, b) | g(a, U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause3')).
% 0.11/0.36 tff(6,plain,
% 0.11/0.36 (![U: $i] : (f(a, b) | g(a, U))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.11/0.36 tff(7,plain,(
% 0.11/0.36 ![U: $i] : (f(a, b) | g(a, U))),
% 0.11/0.36 inference(skolemize,[status(sab)],[6])).
% 0.11/0.36 tff(8,plain,
% 0.11/0.36 (![U: $i] : (f(a, b) | g(a, U))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.11/0.36 tff(9,plain,
% 0.11/0.36 (((~![U: $i] : (f(a, b) | g(a, U))) | (f(a, b) | g(a, d))) <=> ((~![U: $i] : (f(a, b) | g(a, U))) | f(a, b) | g(a, d))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(10,plain,
% 0.11/0.36 ((~![U: $i] : (f(a, b) | g(a, U))) | (f(a, b) | g(a, d))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(11,plain,
% 0.11/0.36 ((~![U: $i] : (f(a, b) | g(a, U))) | f(a, b) | g(a, d)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.11/0.36 tff(12,plain,
% 0.11/0.36 (f(a, b)),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[11, 8, 1])).
% 0.11/0.36 tff(13,plain,
% 0.11/0.36 (^[Z: $i, U: $i] : refl(((~f(a, Z)) | g(a, U)) <=> ((~f(a, Z)) | g(a, U)))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(14,plain,
% 0.11/0.36 (![Z: $i, U: $i] : ((~f(a, Z)) | g(a, U)) <=> ![Z: $i, U: $i] : ((~f(a, Z)) | g(a, U))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[13])).
% 0.11/0.36 tff(15,plain,
% 0.11/0.36 (![Z: $i, U: $i] : ((~f(a, Z)) | g(a, U)) <=> ![Z: $i, U: $i] : ((~f(a, Z)) | g(a, U))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(16,axiom,(![Z: $i, U: $i] : ((~f(a, Z)) | g(a, U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 0.11/0.36 tff(17,plain,
% 0.11/0.36 (![Z: $i, U: $i] : ((~f(a, Z)) | g(a, U))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.11/0.36 tff(18,plain,(
% 0.11/0.36 ![Z: $i, U: $i] : ((~f(a, Z)) | g(a, U))),
% 0.11/0.36 inference(skolemize,[status(sab)],[17])).
% 0.11/0.36 tff(19,plain,
% 0.11/0.36 (![Z: $i, U: $i] : ((~f(a, Z)) | g(a, U))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.11/0.36 tff(20,plain,
% 0.11/0.36 (((~![Z: $i, U: $i] : ((~f(a, Z)) | g(a, U))) | ((~f(a, b)) | g(a, d))) <=> ((~![Z: $i, U: $i] : ((~f(a, Z)) | g(a, U))) | (~f(a, b)) | g(a, d))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(21,plain,
% 0.11/0.36 ((~![Z: $i, U: $i] : ((~f(a, Z)) | g(a, U))) | ((~f(a, b)) | g(a, d))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(22,plain,
% 0.11/0.36 ((~![Z: $i, U: $i] : ((~f(a, Z)) | g(a, U))) | (~f(a, b)) | g(a, d)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.11/0.36 tff(23,plain,
% 0.11/0.36 ($false),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[22, 19, 12, 1])).
% 0.11/0.36 tff(24,plain,(g(a, d)), inference(lemma,lemma(discharge,[]))).
% 0.11/0.36 tff(25,plain,
% 0.11/0.36 (((~f(a, b)) | (~g(a, d))) <=> ((~f(a, b)) | (~g(a, d)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(26,axiom,((~f(a, b)) | (~g(a, d))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause4')).
% 0.11/0.36 tff(27,plain,
% 0.11/0.36 ((~f(a, b)) | (~g(a, d))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.11/0.36 tff(28,plain,
% 0.11/0.36 (~f(a, b)),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[27, 24])).
% 0.11/0.36 tff(29,plain,
% 0.11/0.36 (^[U: $i] : refl(((~g(U, U)) | f(U, b)) <=> ((~g(U, U)) | f(U, b)))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(30,plain,
% 0.11/0.36 (![U: $i] : ((~g(U, U)) | f(U, b)) <=> ![U: $i] : ((~g(U, U)) | f(U, b))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[29])).
% 0.11/0.36 tff(31,plain,
% 0.11/0.36 (![U: $i] : ((~g(U, U)) | f(U, b)) <=> ![U: $i] : ((~g(U, U)) | f(U, b))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(32,axiom,(![U: $i] : ((~g(U, U)) | f(U, b))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause2')).
% 0.11/0.36 tff(33,plain,
% 0.11/0.36 (![U: $i] : ((~g(U, U)) | f(U, b))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.11/0.37 tff(34,plain,(
% 0.11/0.37 ![U: $i] : ((~g(U, U)) | f(U, b))),
% 0.11/0.37 inference(skolemize,[status(sab)],[33])).
% 0.11/0.37 tff(35,plain,
% 0.11/0.37 (![U: $i] : ((~g(U, U)) | f(U, b))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.11/0.37 tff(36,plain,
% 0.11/0.37 (((~![U: $i] : ((~g(U, U)) | f(U, b))) | ((~g(a, a)) | f(a, b))) <=> ((~![U: $i] : ((~g(U, U)) | f(U, b))) | (~g(a, a)) | f(a, b))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(37,plain,
% 0.11/0.37 ((~![U: $i] : ((~g(U, U)) | f(U, b))) | ((~g(a, a)) | f(a, b))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(38,plain,
% 0.11/0.37 ((~![U: $i] : ((~g(U, U)) | f(U, b))) | (~g(a, a)) | f(a, b)),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.11/0.37 tff(39,plain,
% 0.11/0.37 (~g(a, a)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[38, 35, 28])).
% 0.11/0.37 tff(40,plain,
% 0.11/0.37 (((~![U: $i] : (f(a, b) | g(a, U))) | (f(a, b) | g(a, a))) <=> ((~![U: $i] : (f(a, b) | g(a, U))) | f(a, b) | g(a, a))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(41,plain,
% 0.11/0.37 ((~![U: $i] : (f(a, b) | g(a, U))) | (f(a, b) | g(a, a))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(42,plain,
% 0.11/0.37 ((~![U: $i] : (f(a, b) | g(a, U))) | f(a, b) | g(a, a)),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.11/0.37 tff(43,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[42, 8, 28, 39])).
% 0.11/0.37 % SZS output end Proof
% 0.11/0.37 % E exiting
%------------------------------------------------------------------------------