%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU041+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:26:49 AM UTC 2025
% Result : Theorem 0.79s 0.98s
% Output : Proof 0.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU041+1 : TPTP v9.0.0. Released v3.2.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n003.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 05:58:24 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.79/0.98 % SZS status Theorem
% 0.79/0.98 % SZS output start Proof
% 0.79/0.98 tff(relation_type, type, (
% 0.79/0.98 relation: $i > $o)).
% 0.79/0.98 tff(subset_type, type, (
% 0.79/0.98 subset: ( $i * $i ) > $o)).
% 0.79/0.98 tff(relation_dom_restriction_type, type, (
% 0.79/0.98 relation_dom_restriction: ( $i * $i ) > $i)).
% 0.79/0.98 tff(tptp_fun_C_11_type, type, (
% 0.79/0.98 tptp_fun_C_11: $i)).
% 0.79/0.98 tff(function_type, type, (
% 0.79/0.98 function: $i > $o)).
% 0.79/0.98 tff(tptp_fun_B_12_type, type, (
% 0.79/0.98 tptp_fun_B_12: $i)).
% 0.79/0.98 tff(tptp_fun_A_13_type, type, (
% 0.79/0.98 tptp_fun_A_13: $i)).
% 0.79/0.98 tff(1,plain,
% 0.79/0.98 (^[A: $i, B: $i, C: $i] : refl(((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C))) <=> ((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C))))),
% 0.79/0.98 inference(bind,[status(th)],[])).
% 0.79/0.98 tff(2,plain,
% 0.79/0.98 (![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C))) <=> ![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))),
% 0.79/0.98 inference(quant_intro,[status(thm)],[1])).
% 0.79/0.98 tff(3,plain,
% 0.79/0.98 (![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C))) <=> ![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(4,plain,
% 0.79/0.98 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((subset(A, B) => (relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A))) <=> ((~subset(A, B)) | (relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)))), ((relation(C) => (subset(A, B) => (relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)))) <=> (relation(C) => ((~subset(A, B)) | (relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)))))), rewrite((relation(C) => ((~subset(A, B)) | (relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)))) <=> ((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))), ((relation(C) => (subset(A, B) => (relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)))) <=> ((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))))),
% 0.79/0.98 inference(bind,[status(th)],[])).
% 0.79/0.98 tff(5,plain,
% 0.79/0.98 (![A: $i, B: $i, C: $i] : (relation(C) => (subset(A, B) => (relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)))) <=> ![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))),
% 0.79/0.98 inference(quant_intro,[status(thm)],[4])).
% 0.79/0.98 tff(6,axiom,(![A: $i, B: $i, C: $i] : (relation(C) => (subset(A, B) => (relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t102_relat_1')).
% 0.79/0.98 tff(7,plain,
% 0.79/0.98 (![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.79/0.98 tff(8,plain,
% 0.79/0.98 (![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.79/0.98 tff(9,plain,(
% 0.79/0.98 ![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))),
% 0.79/0.98 inference(skolemize,[status(sab)],[8])).
% 0.79/0.98 tff(10,plain,
% 0.79/0.98 (![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.79/0.99 tff(11,plain,
% 0.79/0.99 ((~(((relation_dom_restriction(relation_dom_restriction(C!11, A!13), B!12) = relation_dom_restriction(C!11, A!13)) & (relation_dom_restriction(relation_dom_restriction(C!11, B!12), A!13) = relation_dom_restriction(C!11, A!13))) | (~subset(A!13, B!12)) | (~(relation(C!11) & function(C!11))))) <=> (~(((relation_dom_restriction(relation_dom_restriction(C!11, A!13), B!12) = relation_dom_restriction(C!11, A!13)) & (relation_dom_restriction(relation_dom_restriction(C!11, B!12), A!13) = relation_dom_restriction(C!11, A!13))) | (~subset(A!13, B!12)) | (~(relation(C!11) & function(C!11)))))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(12,plain,
% 0.79/0.99 ((~![A: $i, B: $i, C: $i] : (((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) & (relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A))) | (~subset(A, B)) | (~(relation(C) & function(C))))) <=> (~![A: $i, B: $i, C: $i] : (((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) & (relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A))) | (~subset(A, B)) | (~(relation(C) & function(C)))))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(13,plain,
% 0.79/0.99 ((~![A: $i, B: $i, C: $i] : ((relation(C) & function(C)) => (subset(A, B) => ((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) & (relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)))))) <=> (~![A: $i, B: $i, C: $i] : (((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) & (relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A))) | (~subset(A, B)) | (~(relation(C) & function(C)))))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(14,axiom,(~![A: $i, B: $i, C: $i] : ((relation(C) & function(C)) => (subset(A, B) => ((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) & (relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t82_funct_1')).
% 0.79/0.99 tff(15,plain,
% 0.79/0.99 (~![A: $i, B: $i, C: $i] : (((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) & (relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A))) | (~subset(A, B)) | (~(relation(C) & function(C))))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.79/0.99 tff(16,plain,
% 0.79/0.99 (~![A: $i, B: $i, C: $i] : (((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) & (relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A))) | (~subset(A, B)) | (~(relation(C) & function(C))))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.79/0.99 tff(17,plain,
% 0.79/0.99 (~![A: $i, B: $i, C: $i] : (((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) & (relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A))) | (~subset(A, B)) | (~(relation(C) & function(C))))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.79/0.99 tff(18,plain,
% 0.79/0.99 (~![A: $i, B: $i, C: $i] : (((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) & (relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A))) | (~subset(A, B)) | (~(relation(C) & function(C))))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[17, 12])).
% 0.79/0.99 tff(19,plain,(
% 0.79/0.99 ~(((relation_dom_restriction(relation_dom_restriction(C!11, A!13), B!12) = relation_dom_restriction(C!11, A!13)) & (relation_dom_restriction(relation_dom_restriction(C!11, B!12), A!13) = relation_dom_restriction(C!11, A!13))) | (~subset(A!13, B!12)) | (~(relation(C!11) & function(C!11))))),
% 0.79/0.99 inference(skolemize,[status(sab)],[18])).
% 0.79/0.99 tff(20,plain,
% 0.79/0.99 (~(((relation_dom_restriction(relation_dom_restriction(C!11, A!13), B!12) = relation_dom_restriction(C!11, A!13)) & (relation_dom_restriction(relation_dom_restriction(C!11, B!12), A!13) = relation_dom_restriction(C!11, A!13))) | (~subset(A!13, B!12)) | (~(relation(C!11) & function(C!11))))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[19, 11])).
% 0.79/0.99 tff(21,plain,
% 0.79/0.99 (relation(C!11) & function(C!11)),
% 0.79/0.99 inference(or_elim,[status(thm)],[20])).
% 0.79/0.99 tff(22,plain,
% 0.79/0.99 (relation(C!11)),
% 0.79/0.99 inference(and_elim,[status(thm)],[21])).
% 0.79/0.99 tff(23,plain,
% 0.79/0.99 (subset(A!13, B!12)),
% 0.79/0.99 inference(or_elim,[status(thm)],[20])).
% 0.79/0.99 tff(24,plain,
% 0.79/0.99 (^[A: $i, B: $i, C: $i] : refl(((relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C))) <=> ((relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C))))),
% 0.79/0.99 inference(bind,[status(th)],[])).
% 0.79/0.99 tff(25,plain,
% 0.79/0.99 (![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C))) <=> ![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))),
% 0.79/0.99 inference(quant_intro,[status(thm)],[24])).
% 0.79/0.99 tff(26,plain,
% 0.79/0.99 (![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C))) <=> ![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(27,plain,
% 0.79/0.99 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((subset(A, B) => (relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A))) <=> ((~subset(A, B)) | (relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)))), ((relation(C) => (subset(A, B) => (relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)))) <=> (relation(C) => ((~subset(A, B)) | (relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)))))), rewrite((relation(C) => ((~subset(A, B)) | (relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)))) <=> ((relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))), ((relation(C) => (subset(A, B) => (relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)))) <=> ((relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))))),
% 0.79/0.99 inference(bind,[status(th)],[])).
% 0.79/0.99 tff(28,plain,
% 0.79/0.99 (![A: $i, B: $i, C: $i] : (relation(C) => (subset(A, B) => (relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)))) <=> ![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))),
% 0.79/0.99 inference(quant_intro,[status(thm)],[27])).
% 0.79/0.99 tff(29,axiom,(![A: $i, B: $i, C: $i] : (relation(C) => (subset(A, B) => (relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t103_relat_1')).
% 0.79/0.99 tff(30,plain,
% 0.79/0.99 (![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.79/0.99 tff(31,plain,
% 0.79/0.99 (![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.79/0.99 tff(32,plain,(
% 0.79/0.99 ![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))),
% 0.79/0.99 inference(skolemize,[status(sab)],[31])).
% 0.79/0.99 tff(33,plain,
% 0.79/0.99 (![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.79/0.99 tff(34,assumption,(~(relation_dom_restriction(relation_dom_restriction(C!11, B!12), A!13) = relation_dom_restriction(C!11, A!13))), introduced(assumption)).
% 0.79/0.99 tff(35,plain,
% 0.79/0.99 (((~![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))) | ((relation_dom_restriction(relation_dom_restriction(C!11, B!12), A!13) = relation_dom_restriction(C!11, A!13)) | (~subset(A!13, B!12)) | (~relation(C!11)))) <=> ((~![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))) | (relation_dom_restriction(relation_dom_restriction(C!11, B!12), A!13) = relation_dom_restriction(C!11, A!13)) | (~subset(A!13, B!12)) | (~relation(C!11)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(36,plain,
% 0.79/0.99 ((~![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))) | ((relation_dom_restriction(relation_dom_restriction(C!11, B!12), A!13) = relation_dom_restriction(C!11, A!13)) | (~subset(A!13, B!12)) | (~relation(C!11)))),
% 0.79/0.99 inference(quant_inst,[status(thm)],[])).
% 0.79/0.99 tff(37,plain,
% 0.79/0.99 ((~![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))) | (relation_dom_restriction(relation_dom_restriction(C!11, B!12), A!13) = relation_dom_restriction(C!11, A!13)) | (~subset(A!13, B!12)) | (~relation(C!11))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.79/0.99 tff(38,plain,
% 0.79/0.99 ($false),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[37, 34, 23, 22, 33])).
% 0.79/0.99 tff(39,plain,(relation_dom_restriction(relation_dom_restriction(C!11, B!12), A!13) = relation_dom_restriction(C!11, A!13)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.99 tff(40,plain,
% 0.79/0.99 ((~(~((~(relation_dom_restriction(relation_dom_restriction(C!11, A!13), B!12) = relation_dom_restriction(C!11, A!13))) | (~(relation_dom_restriction(relation_dom_restriction(C!11, B!12), A!13) = relation_dom_restriction(C!11, A!13)))))) <=> ((~(relation_dom_restriction(relation_dom_restriction(C!11, A!13), B!12) = relation_dom_restriction(C!11, A!13))) | (~(relation_dom_restriction(relation_dom_restriction(C!11, B!12), A!13) = relation_dom_restriction(C!11, A!13))))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(41,plain,
% 0.79/0.99 (((relation_dom_restriction(relation_dom_restriction(C!11, A!13), B!12) = relation_dom_restriction(C!11, A!13)) & (relation_dom_restriction(relation_dom_restriction(C!11, B!12), A!13) = relation_dom_restriction(C!11, A!13))) <=> (~((~(relation_dom_restriction(relation_dom_restriction(C!11, A!13), B!12) = relation_dom_restriction(C!11, A!13))) | (~(relation_dom_restriction(relation_dom_restriction(C!11, B!12), A!13) = relation_dom_restriction(C!11, A!13)))))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(42,plain,
% 0.79/0.99 ((~((relation_dom_restriction(relation_dom_restriction(C!11, A!13), B!12) = relation_dom_restriction(C!11, A!13)) & (relation_dom_restriction(relation_dom_restriction(C!11, B!12), A!13) = relation_dom_restriction(C!11, A!13)))) <=> (~(~((~(relation_dom_restriction(relation_dom_restriction(C!11, A!13), B!12) = relation_dom_restriction(C!11, A!13))) | (~(relation_dom_restriction(relation_dom_restriction(C!11, B!12), A!13) = relation_dom_restriction(C!11, A!13))))))),
% 0.79/0.99 inference(monotonicity,[status(thm)],[41])).
% 0.79/0.99 tff(43,plain,
% 0.79/0.99 ((~((relation_dom_restriction(relation_dom_restriction(C!11, A!13), B!12) = relation_dom_restriction(C!11, A!13)) & (relation_dom_restriction(relation_dom_restriction(C!11, B!12), A!13) = relation_dom_restriction(C!11, A!13)))) <=> ((~(relation_dom_restriction(relation_dom_restriction(C!11, A!13), B!12) = relation_dom_restriction(C!11, A!13))) | (~(relation_dom_restriction(relation_dom_restriction(C!11, B!12), A!13) = relation_dom_restriction(C!11, A!13))))),
% 0.79/0.99 inference(transitivity,[status(thm)],[42, 40])).
% 0.79/0.99 tff(44,plain,
% 0.79/0.99 (~((relation_dom_restriction(relation_dom_restriction(C!11, A!13), B!12) = relation_dom_restriction(C!11, A!13)) & (relation_dom_restriction(relation_dom_restriction(C!11, B!12), A!13) = relation_dom_restriction(C!11, A!13)))),
% 0.79/0.99 inference(or_elim,[status(thm)],[20])).
% 0.79/0.99 tff(45,plain,
% 0.79/0.99 ((~(relation_dom_restriction(relation_dom_restriction(C!11, A!13), B!12) = relation_dom_restriction(C!11, A!13))) | (~(relation_dom_restriction(relation_dom_restriction(C!11, B!12), A!13) = relation_dom_restriction(C!11, A!13)))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.79/0.99 tff(46,plain,
% 0.79/0.99 (~(relation_dom_restriction(relation_dom_restriction(C!11, A!13), B!12) = relation_dom_restriction(C!11, A!13))),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[45, 39])).
% 0.79/0.99 tff(47,plain,
% 0.79/0.99 (((~![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))) | ((relation_dom_restriction(relation_dom_restriction(C!11, A!13), B!12) = relation_dom_restriction(C!11, A!13)) | (~subset(A!13, B!12)) | (~relation(C!11)))) <=> ((~![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))) | (relation_dom_restriction(relation_dom_restriction(C!11, A!13), B!12) = relation_dom_restriction(C!11, A!13)) | (~subset(A!13, B!12)) | (~relation(C!11)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(48,plain,
% 0.79/0.99 ((~![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))) | ((relation_dom_restriction(relation_dom_restriction(C!11, A!13), B!12) = relation_dom_restriction(C!11, A!13)) | (~subset(A!13, B!12)) | (~relation(C!11)))),
% 0.79/0.99 inference(quant_inst,[status(thm)],[])).
% 0.79/0.99 tff(49,plain,
% 0.79/0.99 ((~![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))) | (relation_dom_restriction(relation_dom_restriction(C!11, A!13), B!12) = relation_dom_restriction(C!11, A!13)) | (~subset(A!13, B!12)) | (~relation(C!11))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.79/0.99 tff(50,plain,
% 0.79/0.99 ($false),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[49, 46, 23, 22, 10])).
% 0.79/0.99 % SZS output end Proof
% 0.79/0.99 % E exiting
%------------------------------------------------------------------------------