%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN058-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:38:05 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
% 0.07/0.12 % Problem : SYN058-1 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n004.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 12:26:52 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(big_g_type, type, (
% 0.11/0.36 big_g: $i > $o)).
% 0.11/0.36 tff(d_type, type, (
% 0.11/0.36 d: $i)).
% 0.11/0.36 tff(big_f_type, type, (
% 0.11/0.36 big_f: $i > $o)).
% 0.11/0.36 tff(big_s_type, type, (
% 0.11/0.36 big_s: $i > $o)).
% 0.11/0.36 tff(c_type, type, (
% 0.11/0.36 c: $i)).
% 0.11/0.36 tff(big_q_type, type, (
% 0.11/0.36 big_q: $i > $o)).
% 0.11/0.36 tff(b_type, type, (
% 0.11/0.36 b: $i)).
% 0.11/0.36 tff(big_p_type, type, (
% 0.11/0.36 big_p: $i > $o)).
% 0.11/0.36 tff(1,plain,
% 0.11/0.36 ((~big_g(d)) <=> (~big_g(d))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(2,axiom,(~big_g(d)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_9')).
% 0.11/0.36 tff(3,plain,
% 0.11/0.36 (~big_g(d)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.11/0.36 tff(4,plain,
% 0.11/0.36 (big_f(d) <=> big_f(d)),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(5,axiom,(big_f(d)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_8')).
% 0.11/0.36 tff(6,plain,
% 0.11/0.36 (big_f(d)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.11/0.36 tff(7,plain,
% 0.11/0.36 (^[Y: $i, X: $i] : refl((big_g(X) | (~big_f(X)) | (~big_s(Y))) <=> (big_g(X) | (~big_f(X)) | (~big_s(Y))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(8,plain,
% 0.11/0.36 (![Y: $i, X: $i] : (big_g(X) | (~big_f(X)) | (~big_s(Y))) <=> ![Y: $i, X: $i] : (big_g(X) | (~big_f(X)) | (~big_s(Y)))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[7])).
% 0.11/0.36 tff(9,plain,
% 0.11/0.36 (![Y: $i, X: $i] : (big_g(X) | (~big_f(X)) | (~big_s(Y))) <=> ![Y: $i, X: $i] : (big_g(X) | (~big_f(X)) | (~big_s(Y)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(10,plain,
% 0.11/0.36 (^[Y: $i, X: $i] : trans(monotonicity(rewrite(((~big_s(Y)) | (~big_f(X))) <=> ((~big_f(X)) | (~big_s(Y)))), ((((~big_s(Y)) | (~big_f(X))) | big_g(X)) <=> (((~big_f(X)) | (~big_s(Y))) | big_g(X)))), rewrite((((~big_f(X)) | (~big_s(Y))) | big_g(X)) <=> (big_g(X) | (~big_f(X)) | (~big_s(Y)))), ((((~big_s(Y)) | (~big_f(X))) | big_g(X)) <=> (big_g(X) | (~big_f(X)) | (~big_s(Y)))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(11,plain,
% 0.11/0.36 (![Y: $i, X: $i] : (((~big_s(Y)) | (~big_f(X))) | big_g(X)) <=> ![Y: $i, X: $i] : (big_g(X) | (~big_f(X)) | (~big_s(Y)))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[10])).
% 0.11/0.36 tff(12,axiom,(![Y: $i, X: $i] : (((~big_s(Y)) | (~big_f(X))) | big_g(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_6')).
% 0.11/0.36 tff(13,plain,
% 0.11/0.36 (![Y: $i, X: $i] : (big_g(X) | (~big_f(X)) | (~big_s(Y)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.11/0.36 tff(14,plain,
% 0.11/0.36 (![Y: $i, X: $i] : (big_g(X) | (~big_f(X)) | (~big_s(Y)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.11/0.36 tff(15,plain,(
% 0.11/0.36 ![Y: $i, X: $i] : (big_g(X) | (~big_f(X)) | (~big_s(Y)))),
% 0.11/0.36 inference(skolemize,[status(sab)],[14])).
% 0.11/0.36 tff(16,plain,
% 0.11/0.36 (![Y: $i, X: $i] : (big_g(X) | (~big_f(X)) | (~big_s(Y)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.11/0.36 tff(17,plain,
% 0.11/0.36 (big_p(d) <=> big_p(d)),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(18,axiom,(big_p(d)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_7')).
% 0.11/0.36 tff(19,plain,
% 0.11/0.36 (big_p(d)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.11/0.36 tff(20,assumption,(~big_q(b)), introduced(assumption)).
% 0.11/0.36 tff(21,plain,
% 0.11/0.36 (^[Y: $i, X: $i] : refl((big_q(Y) | (~big_p(X))) <=> (big_q(Y) | (~big_p(X))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(22,plain,
% 0.11/0.36 (![Y: $i, X: $i] : (big_q(Y) | (~big_p(X))) <=> ![Y: $i, X: $i] : (big_q(Y) | (~big_p(X)))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[21])).
% 0.11/0.36 tff(23,plain,
% 0.11/0.36 (![Y: $i, X: $i] : (big_q(Y) | (~big_p(X))) <=> ![Y: $i, X: $i] : (big_q(Y) | (~big_p(X)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(24,plain,
% 0.11/0.36 (^[Y: $i, X: $i] : rewrite(((~big_p(X)) | big_q(Y)) <=> (big_q(Y) | (~big_p(X))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(25,plain,
% 0.11/0.36 (![Y: $i, X: $i] : ((~big_p(X)) | big_q(Y)) <=> ![Y: $i, X: $i] : (big_q(Y) | (~big_p(X)))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[24])).
% 0.11/0.36 tff(26,axiom,(![Y: $i, X: $i] : ((~big_p(X)) | big_q(Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_1')).
% 0.11/0.36 tff(27,plain,
% 0.11/0.36 (![Y: $i, X: $i] : (big_q(Y) | (~big_p(X)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.11/0.36 tff(28,plain,
% 0.11/0.36 (![Y: $i, X: $i] : (big_q(Y) | (~big_p(X)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.11/0.36 tff(29,plain,(
% 0.11/0.36 ![Y: $i, X: $i] : (big_q(Y) | (~big_p(X)))),
% 0.11/0.36 inference(skolemize,[status(sab)],[28])).
% 0.11/0.36 tff(30,plain,
% 0.11/0.36 (![Y: $i, X: $i] : (big_q(Y) | (~big_p(X)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.11/0.36 tff(31,plain,
% 0.11/0.36 (((~![Y: $i, X: $i] : (big_q(Y) | (~big_p(X)))) | (big_q(b) | (~big_p(d)))) <=> ((~![Y: $i, X: $i] : (big_q(Y) | (~big_p(X)))) | big_q(b) | (~big_p(d)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(32,plain,
% 0.11/0.36 ((~![Y: $i, X: $i] : (big_q(Y) | (~big_p(X)))) | (big_q(b) | (~big_p(d)))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(33,plain,
% 0.11/0.36 ((~![Y: $i, X: $i] : (big_q(Y) | (~big_p(X)))) | big_q(b) | (~big_p(d))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.11/0.36 tff(34,plain,
% 0.11/0.36 ($false),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[33, 30, 20, 19])).
% 0.11/0.36 tff(35,plain,(big_q(b)), inference(lemma,lemma(discharge,[]))).
% 0.11/0.36 tff(36,plain,
% 0.11/0.36 (((~big_q(b)) | big_s(c)) <=> ((~big_q(b)) | big_s(c))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(37,axiom,((~big_q(b)) | big_s(c)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_3')).
% 0.11/0.36 tff(38,plain,
% 0.11/0.36 ((~big_q(b)) | big_s(c)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.11/0.36 tff(39,plain,
% 0.11/0.36 ((~big_q(b)) | big_s(c)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[38, 36])).
% 0.11/0.36 tff(40,plain,
% 0.11/0.36 ((~big_q(b)) | big_s(c)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[39, 36])).
% 0.11/0.36 tff(41,plain,
% 0.11/0.36 ((~big_q(b)) | big_s(c)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.11/0.36 tff(42,plain,
% 0.11/0.36 ((~big_q(b)) | big_s(c)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[41, 36])).
% 0.11/0.36 tff(43,plain,
% 0.11/0.36 (big_s(c)),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[42, 35])).
% 0.11/0.36 tff(44,plain,
% 0.11/0.36 (((~![Y: $i, X: $i] : (big_g(X) | (~big_f(X)) | (~big_s(Y)))) | (big_g(d) | (~big_f(d)) | (~big_s(c)))) <=> ((~![Y: $i, X: $i] : (big_g(X) | (~big_f(X)) | (~big_s(Y)))) | big_g(d) | (~big_f(d)) | (~big_s(c)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(45,plain,
% 0.11/0.36 ((~![Y: $i, X: $i] : (big_g(X) | (~big_f(X)) | (~big_s(Y)))) | (big_g(d) | (~big_f(d)) | (~big_s(c)))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(46,plain,
% 0.11/0.36 ((~![Y: $i, X: $i] : (big_g(X) | (~big_f(X)) | (~big_s(Y)))) | big_g(d) | (~big_f(d)) | (~big_s(c))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.11/0.36 tff(47,plain,
% 0.11/0.36 ($false),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[46, 43, 16, 6, 3])).
% 0.11/0.36 % SZS output end Proof
% 0.11/0.37 % E exiting
%------------------------------------------------------------------------------