%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU188+2 : TPTP v9.0.0. Released v3.3.0.
% 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 05:27:11 AM UTC 2025
% Result : Theorem 1.77s 1.96s
% Output : Proof 1.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : SEU188+2 : TPTP v9.0.0. Released v3.3.0.
% 0.09/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n001.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 06:18:50 EDT 2025
% 0.12/0.34 % CPUTime :
% 1.77/1.96 % SZS status Theorem
% 1.77/1.96 % SZS output start Proof
% 1.77/1.96 tff(empty_set_type, type, (
% 1.77/1.96 empty_set: $i)).
% 1.77/1.96 tff(relation_dom_type, type, (
% 1.77/1.96 relation_dom: $i > $i)).
% 1.77/1.96 tff(tptp_fun_A_48_type, type, (
% 1.77/1.96 tptp_fun_A_48: $i)).
% 1.77/1.96 tff(relation_rng_type, type, (
% 1.77/1.96 relation_rng: $i > $i)).
% 1.77/1.96 tff(relation_inverse_type, type, (
% 1.77/1.96 relation_inverse: $i > $i)).
% 1.77/1.96 tff(relation_type, type, (
% 1.77/1.96 relation: $i > $o)).
% 1.77/1.96 tff(in_type, type, (
% 1.77/1.96 in: ( $i * $i ) > $o)).
% 1.77/1.96 tff(tptp_fun_B_47_type, type, (
% 1.77/1.96 tptp_fun_B_47: $i > $i)).
% 1.77/1.96 tff(tptp_fun_B_7_type, type, (
% 1.77/1.96 tptp_fun_B_7: $i > $i)).
% 1.77/1.96 tff(tptp_fun_C_46_type, type, (
% 1.77/1.96 tptp_fun_C_46: $i > $i)).
% 1.77/1.96 tff(ordered_pair_type, type, (
% 1.77/1.96 ordered_pair: ( $i * $i ) > $i)).
% 1.77/1.96 tff(1,plain,
% 1.77/1.96 ((~((A!48 = empty_set) | (~relation(A!48)) | (~((relation_dom(A!48) = empty_set) | (relation_rng(A!48) = empty_set))))) <=> (~((A!48 = empty_set) | (~relation(A!48)) | (~((relation_dom(A!48) = empty_set) | (relation_rng(A!48) = empty_set)))))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(2,plain,
% 1.77/1.96 ((~![A: $i] : ((A = empty_set) | (~relation(A)) | (~((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set))))) <=> (~![A: $i] : ((A = empty_set) | (~relation(A)) | (~((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set)))))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(3,plain,
% 1.77/1.96 ((~![A: $i] : (relation(A) => (((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set)) => (A = empty_set)))) <=> (~![A: $i] : ((A = empty_set) | (~relation(A)) | (~((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set)))))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(4,axiom,(~![A: $i] : (relation(A) => (((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set)) => (A = empty_set)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t64_relat_1')).
% 1.77/1.96 tff(5,plain,
% 1.77/1.96 (~![A: $i] : ((A = empty_set) | (~relation(A)) | (~((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set))))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[4, 3])).
% 1.77/1.96 tff(6,plain,
% 1.77/1.96 (~![A: $i] : ((A = empty_set) | (~relation(A)) | (~((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set))))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[5, 2])).
% 1.77/1.96 tff(7,plain,
% 1.77/1.96 (~![A: $i] : ((A = empty_set) | (~relation(A)) | (~((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set))))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[6, 2])).
% 1.77/1.96 tff(8,plain,
% 1.77/1.96 (~![A: $i] : ((A = empty_set) | (~relation(A)) | (~((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set))))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[7, 2])).
% 1.77/1.96 tff(9,plain,(
% 1.77/1.96 ~((A!48 = empty_set) | (~relation(A!48)) | (~((relation_dom(A!48) = empty_set) | (relation_rng(A!48) = empty_set))))),
% 1.77/1.96 inference(skolemize,[status(sab)],[8])).
% 1.77/1.96 tff(10,plain,
% 1.77/1.96 (~((A!48 = empty_set) | (~relation(A!48)) | (~((relation_dom(A!48) = empty_set) | (relation_rng(A!48) = empty_set))))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[9, 1])).
% 1.77/1.96 tff(11,plain,
% 1.77/1.96 (relation(A!48)),
% 1.77/1.96 inference(or_elim,[status(thm)],[10])).
% 1.77/1.96 tff(12,plain,
% 1.77/1.96 (^[A: $i] : refl(((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A))))))) <=> ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A))))))))),
% 1.77/1.96 inference(bind,[status(th)],[])).
% 1.77/1.96 tff(13,plain,
% 1.77/1.96 (![A: $i] : ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A))))))) <=> ![A: $i] : ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A)))))))),
% 1.77/1.96 inference(quant_intro,[status(thm)],[12])).
% 1.77/1.96 tff(14,plain,
% 1.77/1.96 (^[A: $i] : rewrite(((~relation(A)) | ((relation_rng(A) = relation_dom(relation_inverse(A))) & (relation_dom(A) = relation_rng(relation_inverse(A))))) <=> ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A))))))))),
% 1.77/1.96 inference(bind,[status(th)],[])).
% 1.77/1.96 tff(15,plain,
% 1.77/1.96 (![A: $i] : ((~relation(A)) | ((relation_rng(A) = relation_dom(relation_inverse(A))) & (relation_dom(A) = relation_rng(relation_inverse(A))))) <=> ![A: $i] : ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A)))))))),
% 1.77/1.96 inference(quant_intro,[status(thm)],[14])).
% 1.77/1.96 tff(16,plain,
% 1.77/1.96 (![A: $i] : ((~relation(A)) | ((relation_rng(A) = relation_dom(relation_inverse(A))) & (relation_dom(A) = relation_rng(relation_inverse(A))))) <=> ![A: $i] : ((~relation(A)) | ((relation_rng(A) = relation_dom(relation_inverse(A))) & (relation_dom(A) = relation_rng(relation_inverse(A)))))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(17,plain,
% 1.77/1.96 (^[A: $i] : rewrite((relation(A) => ((relation_rng(A) = relation_dom(relation_inverse(A))) & (relation_dom(A) = relation_rng(relation_inverse(A))))) <=> ((~relation(A)) | ((relation_rng(A) = relation_dom(relation_inverse(A))) & (relation_dom(A) = relation_rng(relation_inverse(A))))))),
% 1.77/1.96 inference(bind,[status(th)],[])).
% 1.77/1.96 tff(18,plain,
% 1.77/1.96 (![A: $i] : (relation(A) => ((relation_rng(A) = relation_dom(relation_inverse(A))) & (relation_dom(A) = relation_rng(relation_inverse(A))))) <=> ![A: $i] : ((~relation(A)) | ((relation_rng(A) = relation_dom(relation_inverse(A))) & (relation_dom(A) = relation_rng(relation_inverse(A)))))),
% 1.77/1.96 inference(quant_intro,[status(thm)],[17])).
% 1.77/1.96 tff(19,axiom,(![A: $i] : (relation(A) => ((relation_rng(A) = relation_dom(relation_inverse(A))) & (relation_dom(A) = relation_rng(relation_inverse(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t37_relat_1')).
% 1.77/1.96 tff(20,plain,
% 1.77/1.96 (![A: $i] : ((~relation(A)) | ((relation_rng(A) = relation_dom(relation_inverse(A))) & (relation_dom(A) = relation_rng(relation_inverse(A)))))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[19, 18])).
% 1.77/1.96 tff(21,plain,
% 1.77/1.96 (![A: $i] : ((~relation(A)) | ((relation_rng(A) = relation_dom(relation_inverse(A))) & (relation_dom(A) = relation_rng(relation_inverse(A)))))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[20, 16])).
% 1.77/1.96 tff(22,plain,(
% 1.77/1.96 ![A: $i] : ((~relation(A)) | ((relation_rng(A) = relation_dom(relation_inverse(A))) & (relation_dom(A) = relation_rng(relation_inverse(A)))))),
% 1.77/1.96 inference(skolemize,[status(sab)],[21])).
% 1.77/1.96 tff(23,plain,
% 1.77/1.96 (![A: $i] : ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A)))))))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[22, 15])).
% 1.77/1.96 tff(24,plain,
% 1.77/1.96 (![A: $i] : ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A)))))))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[23, 13])).
% 1.77/1.96 tff(25,plain,
% 1.77/1.96 (((~![A: $i] : ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A)))))))) | ((~relation(A!48)) | (~((~(relation_rng(A!48) = relation_dom(relation_inverse(A!48)))) | (~(relation_dom(A!48) = relation_rng(relation_inverse(A!48)))))))) <=> ((~![A: $i] : ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A)))))))) | (~relation(A!48)) | (~((~(relation_rng(A!48) = relation_dom(relation_inverse(A!48)))) | (~(relation_dom(A!48) = relation_rng(relation_inverse(A!48)))))))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(26,plain,
% 1.77/1.96 ((~![A: $i] : ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A)))))))) | ((~relation(A!48)) | (~((~(relation_rng(A!48) = relation_dom(relation_inverse(A!48)))) | (~(relation_dom(A!48) = relation_rng(relation_inverse(A!48)))))))),
% 1.77/1.96 inference(quant_inst,[status(thm)],[])).
% 1.77/1.96 tff(27,plain,
% 1.77/1.96 ((~![A: $i] : ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A)))))))) | (~relation(A!48)) | (~((~(relation_rng(A!48) = relation_dom(relation_inverse(A!48)))) | (~(relation_dom(A!48) = relation_rng(relation_inverse(A!48))))))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[26, 25])).
% 1.77/1.96 tff(28,plain,
% 1.77/1.96 (~((~(relation_rng(A!48) = relation_dom(relation_inverse(A!48)))) | (~(relation_dom(A!48) = relation_rng(relation_inverse(A!48)))))),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[27, 24, 11])).
% 1.77/1.96 tff(29,plain,
% 1.77/1.96 (((~(relation_rng(A!48) = relation_dom(relation_inverse(A!48)))) | (~(relation_dom(A!48) = relation_rng(relation_inverse(A!48))))) | (relation_dom(A!48) = relation_rng(relation_inverse(A!48)))),
% 1.77/1.96 inference(tautology,[status(thm)],[])).
% 1.77/1.96 tff(30,plain,
% 1.77/1.96 (relation_dom(A!48) = relation_rng(relation_inverse(A!48))),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[29, 28])).
% 1.77/1.96 tff(31,plain,
% 1.77/1.96 (relation_rng(relation_inverse(A!48)) = relation_dom(A!48)),
% 1.77/1.96 inference(symmetry,[status(thm)],[30])).
% 1.77/1.96 tff(32,plain,
% 1.77/1.96 ((relation_rng(relation_inverse(A!48)) = empty_set) <=> (relation_dom(A!48) = empty_set)),
% 1.77/1.96 inference(monotonicity,[status(thm)],[31])).
% 1.77/1.96 tff(33,plain,
% 1.77/1.96 ((~(relation_rng(relation_inverse(A!48)) = empty_set)) <=> (~(relation_dom(A!48) = empty_set))),
% 1.77/1.96 inference(monotonicity,[status(thm)],[32])).
% 1.77/1.96 tff(34,plain,
% 1.77/1.96 (^[A: $i, B: $i] : refl((~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_7(A), A))))) <=> (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_7(A), A))))))),
% 1.77/1.96 inference(bind,[status(th)],[])).
% 1.77/1.96 tff(35,plain,
% 1.77/1.96 (![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_7(A), A))))) <=> ![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_7(A), A)))))),
% 1.77/1.96 inference(quant_intro,[status(thm)],[34])).
% 1.77/1.96 tff(36,plain,
% 1.77/1.96 (![A: $i] : ![B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_7(A), A))))) <=> ![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_7(A), A)))))),
% 1.77/1.96 inference(pull_quant,[status(thm)],[])).
% 1.77/1.96 tff(37,plain,
% 1.77/1.96 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(A = empty_set)) | ![B: $i] : (~in(B, A))) <=> ![B: $i] : ((~(A = empty_set)) | (~in(B, A)))), ((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) <=> (~![B: $i] : ((~(A = empty_set)) | (~in(B, A)))))), pull_quant((~![B: $i] : ((~(A = empty_set)) | (~in(B, A)))) <=> ?[B: $i] : (~((~(A = empty_set)) | (~in(B, A))))), ((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) <=> ?[B: $i] : (~((~(A = empty_set)) | (~in(B, A)))))), (((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_7(A), A)))) <=> (?[B: $i] : (~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_7(A), A)))))), pull_quant((?[B: $i] : (~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_7(A), A)))) <=> ?[B: $i] : ((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_7(A), A))))), (((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_7(A), A)))) <=> ?[B: $i] : ((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_7(A), A)))))), ((~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_7(A), A))))) <=> (~?[B: $i] : ((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_7(A), A))))))), pull_quant((~?[B: $i] : ((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_7(A), A))))) <=> ![B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_7(A), A)))))), ((~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_7(A), A))))) <=> ![B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_7(A), A)))))))),
% 1.77/1.96 inference(bind,[status(th)],[])).
% 1.77/1.96 tff(38,plain,
% 1.77/1.96 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_7(A), A))))) <=> ![A: $i] : ![B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_7(A), A)))))),
% 1.77/1.96 inference(quant_intro,[status(thm)],[37])).
% 1.77/1.96 tff(39,plain,
% 1.77/1.96 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_7(A), A))))) <=> ![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_7(A), A)))))),
% 1.77/1.96 inference(transitivity,[status(thm)],[38, 36])).
% 1.77/1.96 tff(40,plain,
% 1.77/1.96 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_7(A), A))))) <=> ![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_7(A), A)))))),
% 1.77/1.96 inference(transitivity,[status(thm)],[39, 35])).
% 1.77/1.96 tff(41,plain,
% 1.77/1.96 (^[A: $i] : rewrite((~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_7(A), A))))) <=> (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_7(A), A))))))),
% 1.77/1.96 inference(bind,[status(th)],[])).
% 1.77/1.96 tff(42,plain,
% 1.77/1.96 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_7(A), A))))) <=> ![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_7(A), A)))))),
% 1.77/1.96 inference(quant_intro,[status(thm)],[41])).
% 1.77/1.96 tff(43,plain,
% 1.77/1.96 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_7(A), A))))) <=> ![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_7(A), A)))))),
% 1.77/1.96 inference(transitivity,[status(thm)],[42, 40])).
% 1.77/1.96 tff(44,plain,
% 1.77/1.96 (^[A: $i] : trans(monotonicity(rewrite(((~(A = empty_set)) | ![B: $i] : (~in(B, A))) <=> ((~(A = empty_set)) | ![B: $i] : (~in(B, A)))), ((((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_7(A), A))) <=> (((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_7(A), A))))), rewrite((((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_7(A), A))) <=> (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_7(A), A)))))), ((((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_7(A), A))) <=> (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_7(A), A)))))))),
% 1.77/1.96 inference(bind,[status(th)],[])).
% 1.77/1.96 tff(45,plain,
% 1.77/1.96 (![A: $i] : (((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_7(A), A))) <=> ![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_7(A), A)))))),
% 1.77/1.96 inference(quant_intro,[status(thm)],[44])).
% 1.77/1.96 tff(46,plain,
% 1.77/1.96 (![A: $i] : ((A = empty_set) <=> ![B: $i] : (~in(B, A))) <=> ![A: $i] : ((A = empty_set) <=> ![B: $i] : (~in(B, A)))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(47,axiom,(![A: $i] : ((A = empty_set) <=> ![B: $i] : (~in(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_xboole_0')).
% 1.77/1.96 tff(48,plain,
% 1.77/1.96 (![A: $i] : ((A = empty_set) <=> ![B: $i] : (~in(B, A)))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[47, 46])).
% 1.77/1.96 tff(49,plain,(
% 1.77/1.96 ![A: $i] : (((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_7(A), A)))),
% 1.77/1.96 inference(skolemize,[status(sab)],[48])).
% 1.77/1.96 tff(50,plain,
% 1.77/1.96 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_7(A), A)))))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[49, 45])).
% 1.77/1.96 tff(51,plain,
% 1.77/1.96 (![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_7(A), A)))))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[50, 43])).
% 1.77/1.96 tff(52,plain,
% 1.77/1.96 ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_7(A), A)))))) | (~((~((~(relation_rng(relation_inverse(A!48)) = empty_set)) | (~in(tptp_fun_B_47(A!48), relation_rng(relation_inverse(A!48)))))) | (~((relation_rng(relation_inverse(A!48)) = empty_set) | in(tptp_fun_B_7(relation_rng(relation_inverse(A!48))), relation_rng(relation_inverse(A!48)))))))),
% 1.77/1.96 inference(quant_inst,[status(thm)],[])).
% 1.77/1.96 tff(53,plain,
% 1.77/1.96 (~((~((~(relation_rng(relation_inverse(A!48)) = empty_set)) | (~in(tptp_fun_B_47(A!48), relation_rng(relation_inverse(A!48)))))) | (~((relation_rng(relation_inverse(A!48)) = empty_set) | in(tptp_fun_B_7(relation_rng(relation_inverse(A!48))), relation_rng(relation_inverse(A!48))))))),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[52, 51])).
% 1.77/1.96 tff(54,plain,
% 1.77/1.96 (((~((~(relation_rng(relation_inverse(A!48)) = empty_set)) | (~in(tptp_fun_B_47(A!48), relation_rng(relation_inverse(A!48)))))) | (~((relation_rng(relation_inverse(A!48)) = empty_set) | in(tptp_fun_B_7(relation_rng(relation_inverse(A!48))), relation_rng(relation_inverse(A!48)))))) | ((~(relation_rng(relation_inverse(A!48)) = empty_set)) | (~in(tptp_fun_B_47(A!48), relation_rng(relation_inverse(A!48)))))),
% 1.77/1.96 inference(tautology,[status(thm)],[])).
% 1.77/1.96 tff(55,plain,
% 1.77/1.96 ((~(relation_rng(relation_inverse(A!48)) = empty_set)) | (~in(tptp_fun_B_47(A!48), relation_rng(relation_inverse(A!48))))),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[54, 53])).
% 1.77/1.96 tff(56,plain,
% 1.77/1.96 (in(tptp_fun_B_47(A!48), relation_dom(A!48)) <=> in(tptp_fun_B_47(A!48), relation_rng(relation_inverse(A!48)))),
% 1.77/1.96 inference(monotonicity,[status(thm)],[30])).
% 1.77/1.96 tff(57,plain,
% 1.77/1.96 (~(A!48 = empty_set)),
% 1.77/1.96 inference(or_elim,[status(thm)],[10])).
% 1.77/1.96 tff(58,plain,
% 1.77/1.96 (^[A: $i] : refl(((A = empty_set) | (~relation(A)) | in(ordered_pair(tptp_fun_B_47(A), tptp_fun_C_46(A)), A)) <=> ((A = empty_set) | (~relation(A)) | in(ordered_pair(tptp_fun_B_47(A), tptp_fun_C_46(A)), A)))),
% 1.77/1.96 inference(bind,[status(th)],[])).
% 1.77/1.96 tff(59,plain,
% 1.77/1.96 (![A: $i] : ((A = empty_set) | (~relation(A)) | in(ordered_pair(tptp_fun_B_47(A), tptp_fun_C_46(A)), A)) <=> ![A: $i] : ((A = empty_set) | (~relation(A)) | in(ordered_pair(tptp_fun_B_47(A), tptp_fun_C_46(A)), A))),
% 1.77/1.96 inference(quant_intro,[status(thm)],[58])).
% 1.77/1.96 tff(60,plain,
% 1.77/1.96 (![A: $i] : ((A = empty_set) | (~relation(A)) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A)))) <=> ![A: $i] : ((A = empty_set) | (~relation(A)) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(61,plain,
% 1.77/1.96 (^[A: $i] : trans(monotonicity(rewrite((![B: $i, C: $i] : (~in(ordered_pair(B, C), A)) => (A = empty_set)) <=> ((~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))) | (A = empty_set))), ((relation(A) => (![B: $i, C: $i] : (~in(ordered_pair(B, C), A)) => (A = empty_set))) <=> (relation(A) => ((~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))) | (A = empty_set))))), rewrite((relation(A) => ((~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))) | (A = empty_set))) <=> ((A = empty_set) | (~relation(A)) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))))), ((relation(A) => (![B: $i, C: $i] : (~in(ordered_pair(B, C), A)) => (A = empty_set))) <=> ((A = empty_set) | (~relation(A)) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))))))),
% 1.77/1.96 inference(bind,[status(th)],[])).
% 1.77/1.96 tff(62,plain,
% 1.77/1.96 (![A: $i] : (relation(A) => (![B: $i, C: $i] : (~in(ordered_pair(B, C), A)) => (A = empty_set))) <=> ![A: $i] : ((A = empty_set) | (~relation(A)) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))))),
% 1.77/1.96 inference(quant_intro,[status(thm)],[61])).
% 1.77/1.96 tff(63,axiom,(![A: $i] : (relation(A) => (![B: $i, C: $i] : (~in(ordered_pair(B, C), A)) => (A = empty_set)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t56_relat_1')).
% 1.77/1.96 tff(64,plain,
% 1.77/1.96 (![A: $i] : ((A = empty_set) | (~relation(A)) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[63, 62])).
% 1.77/1.96 tff(65,plain,
% 1.77/1.96 (![A: $i] : ((A = empty_set) | (~relation(A)) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[64, 60])).
% 1.77/1.96 tff(66,plain,(
% 1.77/1.96 ![A: $i] : ((A = empty_set) | (~relation(A)) | in(ordered_pair(tptp_fun_B_47(A), tptp_fun_C_46(A)), A))),
% 1.77/1.96 inference(skolemize,[status(sab)],[65])).
% 1.77/1.96 tff(67,plain,
% 1.77/1.96 (![A: $i] : ((A = empty_set) | (~relation(A)) | in(ordered_pair(tptp_fun_B_47(A), tptp_fun_C_46(A)), A))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[66, 59])).
% 1.77/1.96 tff(68,plain,
% 1.77/1.96 (((~![A: $i] : ((A = empty_set) | (~relation(A)) | in(ordered_pair(tptp_fun_B_47(A), tptp_fun_C_46(A)), A))) | ((A!48 = empty_set) | (~relation(A!48)) | in(ordered_pair(tptp_fun_B_47(A!48), tptp_fun_C_46(A!48)), A!48))) <=> ((~![A: $i] : ((A = empty_set) | (~relation(A)) | in(ordered_pair(tptp_fun_B_47(A), tptp_fun_C_46(A)), A))) | (A!48 = empty_set) | (~relation(A!48)) | in(ordered_pair(tptp_fun_B_47(A!48), tptp_fun_C_46(A!48)), A!48))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(69,plain,
% 1.77/1.96 ((~![A: $i] : ((A = empty_set) | (~relation(A)) | in(ordered_pair(tptp_fun_B_47(A), tptp_fun_C_46(A)), A))) | ((A!48 = empty_set) | (~relation(A!48)) | in(ordered_pair(tptp_fun_B_47(A!48), tptp_fun_C_46(A!48)), A!48))),
% 1.77/1.96 inference(quant_inst,[status(thm)],[])).
% 1.77/1.96 tff(70,plain,
% 1.77/1.96 ((~![A: $i] : ((A = empty_set) | (~relation(A)) | in(ordered_pair(tptp_fun_B_47(A), tptp_fun_C_46(A)), A))) | (A!48 = empty_set) | (~relation(A!48)) | in(ordered_pair(tptp_fun_B_47(A!48), tptp_fun_C_46(A!48)), A!48)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[69, 68])).
% 1.77/1.96 tff(71,plain,
% 1.77/1.96 (in(ordered_pair(tptp_fun_B_47(A!48), tptp_fun_C_46(A!48)), A!48)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[70, 67, 57, 11])).
% 1.77/1.96 tff(72,plain,
% 1.77/1.96 (^[A: $i, B: $i, C: $i] : refl(((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C)))))) <=> ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C)))))))),
% 1.77/1.96 inference(bind,[status(th)],[])).
% 1.77/1.96 tff(73,plain,
% 1.77/1.96 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C)))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))),
% 1.77/1.96 inference(quant_intro,[status(thm)],[72])).
% 1.77/1.96 tff(74,plain,
% 1.77/1.96 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((in(A, relation_dom(C)) & in(B, relation_rng(C))) <=> (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C)))))), (((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C))) <=> ((~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))) | (~relation(C)) | (~in(ordered_pair(A, B), C))))), rewrite(((~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))) | (~relation(C)) | (~in(ordered_pair(A, B), C))) <=> ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))), (((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C))) <=> ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))))),
% 1.77/1.96 inference(bind,[status(th)],[])).
% 1.77/1.96 tff(75,plain,
% 1.77/1.96 (![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))),
% 1.77/1.96 inference(quant_intro,[status(thm)],[74])).
% 1.77/1.96 tff(76,plain,
% 1.77/1.96 (![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C))) <=> ![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(77,plain,
% 1.77/1.96 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((in(ordered_pair(A, B), C) => (in(A, relation_dom(C)) & in(B, relation_rng(C)))) <=> ((~in(ordered_pair(A, B), C)) | (in(A, relation_dom(C)) & in(B, relation_rng(C))))), ((relation(C) => (in(ordered_pair(A, B), C) => (in(A, relation_dom(C)) & in(B, relation_rng(C))))) <=> (relation(C) => ((~in(ordered_pair(A, B), C)) | (in(A, relation_dom(C)) & in(B, relation_rng(C))))))), rewrite((relation(C) => ((~in(ordered_pair(A, B), C)) | (in(A, relation_dom(C)) & in(B, relation_rng(C))))) <=> ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))), ((relation(C) => (in(ordered_pair(A, B), C) => (in(A, relation_dom(C)) & in(B, relation_rng(C))))) <=> ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))))),
% 1.77/1.96 inference(bind,[status(th)],[])).
% 1.77/1.96 tff(78,plain,
% 1.77/1.96 (![A: $i, B: $i, C: $i] : (relation(C) => (in(ordered_pair(A, B), C) => (in(A, relation_dom(C)) & in(B, relation_rng(C))))) <=> ![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 1.77/1.96 inference(quant_intro,[status(thm)],[77])).
% 1.77/1.96 tff(79,axiom,(![A: $i, B: $i, C: $i] : (relation(C) => (in(ordered_pair(A, B), C) => (in(A, relation_dom(C)) & in(B, relation_rng(C)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t20_relat_1')).
% 1.77/1.96 tff(80,plain,
% 1.77/1.96 (![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[79, 78])).
% 1.77/1.96 tff(81,plain,
% 1.77/1.96 (![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[80, 76])).
% 1.77/1.96 tff(82,plain,(
% 1.77/1.96 ![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 1.77/1.96 inference(skolemize,[status(sab)],[81])).
% 1.77/1.96 tff(83,plain,
% 1.77/1.96 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[82, 75])).
% 1.77/1.96 tff(84,plain,
% 1.77/1.96 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[83, 73])).
% 1.77/1.96 tff(85,plain,
% 1.77/1.96 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))) | ((~relation(A!48)) | (~in(ordered_pair(tptp_fun_B_47(A!48), tptp_fun_C_46(A!48)), A!48)) | (~((~in(tptp_fun_B_47(A!48), relation_dom(A!48))) | (~in(tptp_fun_C_46(A!48), relation_rng(A!48))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))) | (~relation(A!48)) | (~in(ordered_pair(tptp_fun_B_47(A!48), tptp_fun_C_46(A!48)), A!48)) | (~((~in(tptp_fun_B_47(A!48), relation_dom(A!48))) | (~in(tptp_fun_C_46(A!48), relation_rng(A!48))))))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(86,plain,
% 1.77/1.96 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))) | ((~relation(A!48)) | (~in(ordered_pair(tptp_fun_B_47(A!48), tptp_fun_C_46(A!48)), A!48)) | (~((~in(tptp_fun_B_47(A!48), relation_dom(A!48))) | (~in(tptp_fun_C_46(A!48), relation_rng(A!48))))))),
% 1.77/1.96 inference(quant_inst,[status(thm)],[])).
% 1.77/1.96 tff(87,plain,
% 1.77/1.96 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))) | (~relation(A!48)) | (~in(ordered_pair(tptp_fun_B_47(A!48), tptp_fun_C_46(A!48)), A!48)) | (~((~in(tptp_fun_B_47(A!48), relation_dom(A!48))) | (~in(tptp_fun_C_46(A!48), relation_rng(A!48)))))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[86, 85])).
% 1.77/1.96 tff(88,plain,
% 1.77/1.96 (~((~in(tptp_fun_B_47(A!48), relation_dom(A!48))) | (~in(tptp_fun_C_46(A!48), relation_rng(A!48))))),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[87, 84, 11, 71])).
% 1.77/1.96 tff(89,plain,
% 1.77/1.96 (((~in(tptp_fun_B_47(A!48), relation_dom(A!48))) | (~in(tptp_fun_C_46(A!48), relation_rng(A!48)))) | in(tptp_fun_B_47(A!48), relation_dom(A!48))),
% 1.77/1.96 inference(tautology,[status(thm)],[])).
% 1.77/1.96 tff(90,plain,
% 1.77/1.96 (in(tptp_fun_B_47(A!48), relation_dom(A!48))),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[89, 88])).
% 1.77/1.96 tff(91,plain,
% 1.77/1.96 (in(tptp_fun_B_47(A!48), relation_rng(relation_inverse(A!48)))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[90, 56])).
% 1.77/1.96 tff(92,plain,
% 1.77/1.96 ((~((~(relation_rng(relation_inverse(A!48)) = empty_set)) | (~in(tptp_fun_B_47(A!48), relation_rng(relation_inverse(A!48)))))) | (~(relation_rng(relation_inverse(A!48)) = empty_set)) | (~in(tptp_fun_B_47(A!48), relation_rng(relation_inverse(A!48))))),
% 1.77/1.96 inference(tautology,[status(thm)],[])).
% 1.77/1.96 tff(93,plain,
% 1.77/1.96 ((~((~(relation_rng(relation_inverse(A!48)) = empty_set)) | (~in(tptp_fun_B_47(A!48), relation_rng(relation_inverse(A!48)))))) | (~(relation_rng(relation_inverse(A!48)) = empty_set))),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[92, 91])).
% 1.77/1.96 tff(94,plain,
% 1.77/1.96 (~(relation_rng(relation_inverse(A!48)) = empty_set)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[93, 55])).
% 1.77/1.96 tff(95,plain,
% 1.77/1.96 (~(relation_dom(A!48) = empty_set)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[94, 33])).
% 1.77/1.96 tff(96,plain,
% 1.77/1.96 (((~(relation_rng(A!48) = relation_dom(relation_inverse(A!48)))) | (~(relation_dom(A!48) = relation_rng(relation_inverse(A!48))))) | (relation_rng(A!48) = relation_dom(relation_inverse(A!48)))),
% 1.77/1.96 inference(tautology,[status(thm)],[])).
% 1.77/1.96 tff(97,plain,
% 1.77/1.96 (relation_rng(A!48) = relation_dom(relation_inverse(A!48))),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[96, 28])).
% 1.77/1.96 tff(98,plain,
% 1.77/1.96 (relation_dom(relation_inverse(A!48)) = relation_rng(A!48)),
% 1.77/1.96 inference(symmetry,[status(thm)],[97])).
% 1.77/1.96 tff(99,plain,
% 1.77/1.96 ((relation_dom(relation_inverse(A!48)) = empty_set) <=> (relation_rng(A!48) = empty_set)),
% 1.77/1.96 inference(monotonicity,[status(thm)],[98])).
% 1.77/1.96 tff(100,plain,
% 1.77/1.96 ((~(relation_dom(relation_inverse(A!48)) = empty_set)) <=> (~(relation_rng(A!48) = empty_set))),
% 1.77/1.96 inference(monotonicity,[status(thm)],[99])).
% 1.77/1.96 tff(101,plain,
% 1.77/1.96 ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_7(A), A)))))) | (~((~((~(relation_dom(relation_inverse(A!48)) = empty_set)) | (~in(tptp_fun_C_46(A!48), relation_dom(relation_inverse(A!48)))))) | (~((relation_dom(relation_inverse(A!48)) = empty_set) | in(tptp_fun_B_7(relation_dom(relation_inverse(A!48))), relation_dom(relation_inverse(A!48)))))))),
% 1.77/1.96 inference(quant_inst,[status(thm)],[])).
% 1.77/1.96 tff(102,plain,
% 1.77/1.96 (~((~((~(relation_dom(relation_inverse(A!48)) = empty_set)) | (~in(tptp_fun_C_46(A!48), relation_dom(relation_inverse(A!48)))))) | (~((relation_dom(relation_inverse(A!48)) = empty_set) | in(tptp_fun_B_7(relation_dom(relation_inverse(A!48))), relation_dom(relation_inverse(A!48))))))),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[101, 51])).
% 1.77/1.96 tff(103,plain,
% 1.77/1.96 (((~((~(relation_dom(relation_inverse(A!48)) = empty_set)) | (~in(tptp_fun_C_46(A!48), relation_dom(relation_inverse(A!48)))))) | (~((relation_dom(relation_inverse(A!48)) = empty_set) | in(tptp_fun_B_7(relation_dom(relation_inverse(A!48))), relation_dom(relation_inverse(A!48)))))) | ((~(relation_dom(relation_inverse(A!48)) = empty_set)) | (~in(tptp_fun_C_46(A!48), relation_dom(relation_inverse(A!48)))))),
% 1.77/1.96 inference(tautology,[status(thm)],[])).
% 1.77/1.96 tff(104,plain,
% 1.77/1.96 ((~(relation_dom(relation_inverse(A!48)) = empty_set)) | (~in(tptp_fun_C_46(A!48), relation_dom(relation_inverse(A!48))))),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[103, 102])).
% 1.77/1.96 tff(105,plain,
% 1.77/1.96 (in(tptp_fun_C_46(A!48), relation_rng(A!48)) <=> in(tptp_fun_C_46(A!48), relation_dom(relation_inverse(A!48)))),
% 1.77/1.96 inference(monotonicity,[status(thm)],[97])).
% 1.77/1.96 tff(106,plain,
% 1.77/1.96 (((~in(tptp_fun_B_47(A!48), relation_dom(A!48))) | (~in(tptp_fun_C_46(A!48), relation_rng(A!48)))) | in(tptp_fun_C_46(A!48), relation_rng(A!48))),
% 1.77/1.96 inference(tautology,[status(thm)],[])).
% 1.77/1.96 tff(107,plain,
% 1.77/1.96 (in(tptp_fun_C_46(A!48), relation_rng(A!48))),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[106, 88])).
% 1.77/1.96 tff(108,plain,
% 1.77/1.96 (in(tptp_fun_C_46(A!48), relation_dom(relation_inverse(A!48)))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[107, 105])).
% 1.77/1.96 tff(109,plain,
% 1.77/1.96 ((~((~(relation_dom(relation_inverse(A!48)) = empty_set)) | (~in(tptp_fun_C_46(A!48), relation_dom(relation_inverse(A!48)))))) | (~(relation_dom(relation_inverse(A!48)) = empty_set)) | (~in(tptp_fun_C_46(A!48), relation_dom(relation_inverse(A!48))))),
% 1.77/1.96 inference(tautology,[status(thm)],[])).
% 1.77/1.96 tff(110,plain,
% 1.77/1.96 ((~((~(relation_dom(relation_inverse(A!48)) = empty_set)) | (~in(tptp_fun_C_46(A!48), relation_dom(relation_inverse(A!48)))))) | (~(relation_dom(relation_inverse(A!48)) = empty_set))),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[109, 108])).
% 1.77/1.97 tff(111,plain,
% 1.77/1.97 (~(relation_dom(relation_inverse(A!48)) = empty_set)),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[110, 104])).
% 1.77/1.97 tff(112,plain,
% 1.77/1.97 (~(relation_rng(A!48) = empty_set)),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[111, 100])).
% 1.77/1.97 tff(113,plain,
% 1.77/1.97 ((relation_dom(A!48) = empty_set) | (relation_rng(A!48) = empty_set)),
% 1.77/1.97 inference(or_elim,[status(thm)],[10])).
% 1.77/1.97 tff(114,plain,
% 1.77/1.97 ($false),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[113, 112, 95])).
% 1.77/1.97 % SZS output end Proof
% 1.77/1.98 % E exiting
%------------------------------------------------------------------------------