%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU247+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:27:23 AM UTC 2025
% Result : Theorem 0.20s 0.53s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU247+2 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n002.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 06:30:31 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.53 % SZS status Theorem
% 0.20/0.53 % SZS output start Proof
% 0.20/0.53 tff(relation_rng_restriction_type, type, (
% 0.20/0.53 relation_rng_restriction: ( $i * $i ) > $i)).
% 0.20/0.53 tff(relation_dom_restriction_type, type, (
% 0.20/0.53 relation_dom_restriction: ( $i * $i ) > $i)).
% 0.20/0.53 tff(tptp_fun_A_103_type, type, (
% 0.20/0.53 tptp_fun_A_103: $i)).
% 0.20/0.53 tff(tptp_fun_B_102_type, type, (
% 0.20/0.53 tptp_fun_B_102: $i)).
% 0.20/0.53 tff(relation_restriction_type, type, (
% 0.20/0.53 relation_restriction: ( $i * $i ) > $i)).
% 0.20/0.53 tff(relation_type, type, (
% 0.20/0.53 relation: $i > $o)).
% 0.20/0.53 tff(1,plain,
% 0.20/0.53 ((~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A))))) <=> (~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A)))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(2,plain,
% 0.20/0.53 ((~![A: $i, B: $i] : (relation(B) => (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A))))) <=> (~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A)))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(3,axiom,(~![A: $i, B: $i] : (relation(B) => (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t18_wellord1')).
% 0.20/0.53 tff(4,plain,
% 0.20/0.53 (~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.20/0.53 tff(5,plain,
% 0.20/0.53 (~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.20/0.53 tff(6,plain,
% 0.20/0.53 (~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.20/0.53 tff(7,plain,
% 0.20/0.53 (~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.20/0.53 tff(8,plain,(
% 0.20/0.53 ~((~relation(B!102)) | (relation_restriction(B!102, A!103) = relation_rng_restriction(A!103, relation_dom_restriction(B!102, A!103))))),
% 0.20/0.53 inference(skolemize,[status(sab)],[7])).
% 0.20/0.53 tff(9,plain,
% 0.20/0.53 (relation(B!102)),
% 0.20/0.53 inference(or_elim,[status(thm)],[8])).
% 0.20/0.53 tff(10,plain,
% 0.20/0.53 (^[A: $i, B: $i, C: $i] : refl(((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B)))) <=> ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B)))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(11,plain,
% 0.20/0.53 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B)))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[10])).
% 0.20/0.53 tff(12,plain,
% 0.20/0.53 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B)))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(13,plain,
% 0.20/0.53 (^[A: $i, B: $i, C: $i] : rewrite((relation(C) => (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B)))) <=> ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B)))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(14,plain,
% 0.20/0.53 (![A: $i, B: $i, C: $i] : (relation(C) => (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B)))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.53 tff(15,axiom,(![A: $i, B: $i, C: $i] : (relation(C) => (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t140_relat_1')).
% 0.20/0.53 tff(16,plain,
% 0.20/0.53 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.53 tff(17,plain,
% 0.20/0.53 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.20/0.53 tff(18,plain,(
% 0.20/0.53 ![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B))))),
% 0.20/0.53 inference(skolemize,[status(sab)],[17])).
% 0.20/0.53 tff(19,plain,
% 0.20/0.53 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.20/0.53 tff(20,plain,
% 0.20/0.53 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B))))) | ((~relation(B!102)) | (relation_dom_restriction(relation_rng_restriction(A!103, B!102), A!103) = relation_rng_restriction(A!103, relation_dom_restriction(B!102, A!103))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B))))) | (~relation(B!102)) | (relation_dom_restriction(relation_rng_restriction(A!103, B!102), A!103) = relation_rng_restriction(A!103, relation_dom_restriction(B!102, A!103))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(21,plain,
% 0.20/0.53 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B))))) | ((~relation(B!102)) | (relation_dom_restriction(relation_rng_restriction(A!103, B!102), A!103) = relation_rng_restriction(A!103, relation_dom_restriction(B!102, A!103))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(22,plain,
% 0.20/0.53 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B))))) | (~relation(B!102)) | (relation_dom_restriction(relation_rng_restriction(A!103, B!102), A!103) = relation_rng_restriction(A!103, relation_dom_restriction(B!102, A!103)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.20/0.53 tff(23,plain,
% 0.20/0.53 (relation_dom_restriction(relation_rng_restriction(A!103, B!102), A!103) = relation_rng_restriction(A!103, relation_dom_restriction(B!102, A!103))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[22, 19, 9])).
% 0.20/0.53 tff(24,plain,
% 0.20/0.53 (^[A: $i, B: $i] : refl(((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A))) <=> ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(25,plain,
% 0.20/0.53 (![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A))) <=> ![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.53 tff(26,plain,
% 0.20/0.53 (![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A))) <=> ![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(27,plain,
% 0.20/0.54 (^[A: $i, B: $i] : rewrite((relation(B) => (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A))) <=> ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(28,plain,
% 0.20/0.54 (![A: $i, B: $i] : (relation(B) => (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A))) <=> ![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[27])).
% 0.20/0.54 tff(29,axiom,(![A: $i, B: $i] : (relation(B) => (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t17_wellord1')).
% 0.20/0.54 tff(30,plain,
% 0.20/0.54 (![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.54 tff(31,plain,
% 0.20/0.54 (![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.20/0.54 tff(32,plain,(
% 0.20/0.54 ![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))),
% 0.20/0.54 inference(skolemize,[status(sab)],[31])).
% 0.20/0.54 tff(33,plain,
% 0.20/0.54 (![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.20/0.54 tff(34,plain,
% 0.20/0.54 (((~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))) | ((~relation(B!102)) | (relation_restriction(B!102, A!103) = relation_dom_restriction(relation_rng_restriction(A!103, B!102), A!103)))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))) | (~relation(B!102)) | (relation_restriction(B!102, A!103) = relation_dom_restriction(relation_rng_restriction(A!103, B!102), A!103)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(35,plain,
% 0.20/0.54 ((~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))) | ((~relation(B!102)) | (relation_restriction(B!102, A!103) = relation_dom_restriction(relation_rng_restriction(A!103, B!102), A!103)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(36,plain,
% 0.20/0.54 ((~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))) | (~relation(B!102)) | (relation_restriction(B!102, A!103) = relation_dom_restriction(relation_rng_restriction(A!103, B!102), A!103))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.20/0.54 tff(37,plain,
% 0.20/0.54 (relation_restriction(B!102, A!103) = relation_dom_restriction(relation_rng_restriction(A!103, B!102), A!103)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[36, 33, 9])).
% 0.20/0.54 tff(38,plain,
% 0.20/0.54 (relation_restriction(B!102, A!103) = relation_rng_restriction(A!103, relation_dom_restriction(B!102, A!103))),
% 0.20/0.54 inference(transitivity,[status(thm)],[37, 23])).
% 0.20/0.54 tff(39,plain,
% 0.20/0.54 (~(relation_restriction(B!102, A!103) = relation_rng_restriction(A!103, relation_dom_restriction(B!102, A!103)))),
% 0.20/0.54 inference(or_elim,[status(thm)],[8])).
% 0.20/0.54 tff(40,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.20/0.54 % SZS output end Proof
% 0.20/0.54 % E exiting
%------------------------------------------------------------------------------