%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU219+3 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:27:16 AM UTC 2025
% Result : Theorem 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SEU219+3 : TPTP v9.0.0. Released v3.2.0.
% 0.13/0.14 % Command : run_E %s %d THM
% 0.13/0.36 % Computer : n011.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Fri Jun 20 06:22:41 EDT 2025
% 0.21/0.36 % CPUTime :
% 0.21/0.40 % SZS status Theorem
% 0.21/0.40 % SZS output start Proof
% 0.21/0.40 tff(relation_dom_type, type, (
% 0.21/0.40 relation_dom: $i > $i)).
% 0.21/0.40 tff(function_inverse_type, type, (
% 0.21/0.40 function_inverse: $i > $i)).
% 0.21/0.40 tff(tptp_fun_A_11_type, type, (
% 0.21/0.40 tptp_fun_A_11: $i)).
% 0.21/0.40 tff(relation_rng_type, type, (
% 0.21/0.40 relation_rng: $i > $i)).
% 0.21/0.40 tff(relation_inverse_type, type, (
% 0.21/0.40 relation_inverse: $i > $i)).
% 0.21/0.40 tff(function_type, type, (
% 0.21/0.40 function: $i > $o)).
% 0.21/0.40 tff(relation_type, type, (
% 0.21/0.40 relation: $i > $o)).
% 0.21/0.40 tff(one_to_one_type, type, (
% 0.21/0.40 one_to_one: $i > $o)).
% 0.21/0.40 tff(1,plain,
% 0.21/0.40 ((~(((relation_rng(A!11) = relation_dom(function_inverse(A!11))) & (relation_dom(A!11) = relation_rng(function_inverse(A!11)))) | (~one_to_one(A!11)) | (~(relation(A!11) & function(A!11))))) <=> (~(((relation_rng(A!11) = relation_dom(function_inverse(A!11))) & (relation_dom(A!11) = relation_rng(function_inverse(A!11)))) | (~one_to_one(A!11)) | (~(relation(A!11) & function(A!11)))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(2,plain,
% 0.21/0.40 ((~![A: $i] : (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~one_to_one(A)) | (~(relation(A) & function(A))))) <=> (~![A: $i] : (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~one_to_one(A)) | (~(relation(A) & function(A)))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(3,plain,
% 0.21/0.40 ((~![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => ((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A))))))) <=> (~![A: $i] : (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~one_to_one(A)) | (~(relation(A) & function(A)))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(4,axiom,(~![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => ((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t55_funct_1')).
% 0.21/0.40 tff(5,plain,
% 0.21/0.40 (~![A: $i] : (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~one_to_one(A)) | (~(relation(A) & function(A))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.40 tff(6,plain,
% 0.21/0.40 (~![A: $i] : (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~one_to_one(A)) | (~(relation(A) & function(A))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.21/0.40 tff(7,plain,
% 0.21/0.40 (~![A: $i] : (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~one_to_one(A)) | (~(relation(A) & function(A))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.40 tff(8,plain,
% 0.21/0.40 (~![A: $i] : (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~one_to_one(A)) | (~(relation(A) & function(A))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.21/0.40 tff(9,plain,(
% 0.21/0.40 ~(((relation_rng(A!11) = relation_dom(function_inverse(A!11))) & (relation_dom(A!11) = relation_rng(function_inverse(A!11)))) | (~one_to_one(A!11)) | (~(relation(A!11) & function(A!11))))),
% 0.21/0.40 inference(skolemize,[status(sab)],[8])).
% 0.21/0.40 tff(10,plain,
% 0.21/0.40 (~(((relation_rng(A!11) = relation_dom(function_inverse(A!11))) & (relation_dom(A!11) = relation_rng(function_inverse(A!11)))) | (~one_to_one(A!11)) | (~(relation(A!11) & function(A!11))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.21/0.40 tff(11,plain,
% 0.21/0.40 (relation(A!11) & function(A!11)),
% 0.21/0.40 inference(or_elim,[status(thm)],[10])).
% 0.21/0.40 tff(12,plain,
% 0.21/0.40 (function(A!11)),
% 0.21/0.40 inference(and_elim,[status(thm)],[11])).
% 0.21/0.40 tff(13,plain,
% 0.21/0.40 (relation(A!11)),
% 0.21/0.40 inference(and_elim,[status(thm)],[11])).
% 0.21/0.40 tff(14,plain,
% 0.21/0.40 (one_to_one(A!11)),
% 0.21/0.40 inference(or_elim,[status(thm)],[10])).
% 0.21/0.40 tff(15,plain,
% 0.21/0.40 (^[A: $i] : refl(((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A))) <=> ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(16,plain,
% 0.21/0.41 (![A: $i] : ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A))) <=> ![A: $i] : ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[15])).
% 0.21/0.41 tff(17,plain,
% 0.21/0.41 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(A) & function(A)) <=> (~((~relation(A)) | (~function(A))))), ((~(relation(A) & function(A))) <=> (~(~((~relation(A)) | (~function(A))))))), rewrite((~(~((~relation(A)) | (~function(A))))) <=> ((~relation(A)) | (~function(A)))), ((~(relation(A) & function(A))) <=> ((~relation(A)) | (~function(A))))), (((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~(relation(A) & function(A)))) <=> ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | ((~relation(A)) | (~function(A)))))), rewrite(((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | ((~relation(A)) | (~function(A)))) <=> ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))), (((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~(relation(A) & function(A)))) <=> ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(18,plain,
% 0.21/0.41 (![A: $i] : ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~(relation(A) & function(A)))) <=> ![A: $i] : ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[17])).
% 0.21/0.41 tff(19,plain,
% 0.21/0.41 (![A: $i] : ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~(relation(A) & function(A)))) <=> ![A: $i] : ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~(relation(A) & function(A))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(20,plain,
% 0.21/0.41 (^[A: $i] : trans(monotonicity(rewrite((one_to_one(A) => (function_inverse(A) = relation_inverse(A))) <=> ((~one_to_one(A)) | (function_inverse(A) = relation_inverse(A)))), (((relation(A) & function(A)) => (one_to_one(A) => (function_inverse(A) = relation_inverse(A)))) <=> ((relation(A) & function(A)) => ((~one_to_one(A)) | (function_inverse(A) = relation_inverse(A)))))), rewrite(((relation(A) & function(A)) => ((~one_to_one(A)) | (function_inverse(A) = relation_inverse(A)))) <=> ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~(relation(A) & function(A))))), (((relation(A) & function(A)) => (one_to_one(A) => (function_inverse(A) = relation_inverse(A)))) <=> ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~(relation(A) & function(A))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(21,plain,
% 0.21/0.41 (![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => (function_inverse(A) = relation_inverse(A)))) <=> ![A: $i] : ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~(relation(A) & function(A))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[20])).
% 0.21/0.41 tff(22,axiom,(![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => (function_inverse(A) = relation_inverse(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d9_funct_1')).
% 0.21/0.41 tff(23,plain,
% 0.21/0.41 (![A: $i] : ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~(relation(A) & function(A))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.21/0.41 tff(24,plain,
% 0.21/0.41 (![A: $i] : ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~(relation(A) & function(A))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.21/0.41 tff(25,plain,(
% 0.21/0.41 ![A: $i] : ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~(relation(A) & function(A))))),
% 0.21/0.41 inference(skolemize,[status(sab)],[24])).
% 0.21/0.41 tff(26,plain,
% 0.21/0.41 (![A: $i] : ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.21/0.41 tff(27,plain,
% 0.21/0.41 (![A: $i] : ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[26, 16])).
% 0.21/0.41 tff(28,plain,
% 0.21/0.41 (((~![A: $i] : ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))) | ((~one_to_one(A!11)) | (function_inverse(A!11) = relation_inverse(A!11)) | (~relation(A!11)) | (~function(A!11)))) <=> ((~![A: $i] : ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))) | (~one_to_one(A!11)) | (function_inverse(A!11) = relation_inverse(A!11)) | (~relation(A!11)) | (~function(A!11)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(29,plain,
% 0.21/0.41 (((function_inverse(A!11) = relation_inverse(A!11)) | (~one_to_one(A!11)) | (~relation(A!11)) | (~function(A!11))) <=> ((~one_to_one(A!11)) | (function_inverse(A!11) = relation_inverse(A!11)) | (~relation(A!11)) | (~function(A!11)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(30,plain,
% 0.21/0.41 (((~![A: $i] : ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))) | ((function_inverse(A!11) = relation_inverse(A!11)) | (~one_to_one(A!11)) | (~relation(A!11)) | (~function(A!11)))) <=> ((~![A: $i] : ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))) | ((~one_to_one(A!11)) | (function_inverse(A!11) = relation_inverse(A!11)) | (~relation(A!11)) | (~function(A!11))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[29])).
% 0.21/0.41 tff(31,plain,
% 0.21/0.41 (((~![A: $i] : ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))) | ((function_inverse(A!11) = relation_inverse(A!11)) | (~one_to_one(A!11)) | (~relation(A!11)) | (~function(A!11)))) <=> ((~![A: $i] : ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))) | (~one_to_one(A!11)) | (function_inverse(A!11) = relation_inverse(A!11)) | (~relation(A!11)) | (~function(A!11)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[30, 28])).
% 0.21/0.41 tff(32,plain,
% 0.21/0.41 ((~![A: $i] : ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))) | ((function_inverse(A!11) = relation_inverse(A!11)) | (~one_to_one(A!11)) | (~relation(A!11)) | (~function(A!11)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(33,plain,
% 0.21/0.41 ((~![A: $i] : ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))) | (~one_to_one(A!11)) | (function_inverse(A!11) = relation_inverse(A!11)) | (~relation(A!11)) | (~function(A!11))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.21/0.41 tff(34,plain,
% 0.21/0.41 (function_inverse(A!11) = relation_inverse(A!11)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[33, 27, 14, 13, 12])).
% 0.21/0.41 tff(35,plain,
% 0.21/0.41 (relation_dom(function_inverse(A!11)) = relation_dom(relation_inverse(A!11))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[34])).
% 0.21/0.41 tff(36,plain,
% 0.21/0.41 (relation_dom(relation_inverse(A!11)) = relation_dom(function_inverse(A!11))),
% 0.21/0.41 inference(symmetry,[status(thm)],[35])).
% 0.21/0.41 tff(37,plain,
% 0.21/0.41 (^[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))))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(38,plain,
% 0.21/0.41 (![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)))))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[37])).
% 0.21/0.41 tff(39,plain,
% 0.21/0.41 (^[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))))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(40,plain,
% 0.21/0.41 (![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)))))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[39])).
% 0.21/0.41 tff(41,plain,
% 0.21/0.41 (![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)))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(42,plain,
% 0.21/0.41 (^[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))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(43,plain,
% 0.21/0.41 (![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)))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[42])).
% 0.21/0.41 tff(44,axiom,(![A: $i] : (relation(A) => ((relation_rng(A) = relation_dom(relation_inverse(A))) & (relation_dom(A) = relation_rng(relation_inverse(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t37_relat_1')).
% 0.21/0.41 tff(45,plain,
% 0.21/0.41 (![A: $i] : ((~relation(A)) | ((relation_rng(A) = relation_dom(relation_inverse(A))) & (relation_dom(A) = relation_rng(relation_inverse(A)))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.21/0.41 tff(46,plain,
% 0.21/0.41 (![A: $i] : ((~relation(A)) | ((relation_rng(A) = relation_dom(relation_inverse(A))) & (relation_dom(A) = relation_rng(relation_inverse(A)))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.21/0.41 tff(47,plain,(
% 0.21/0.41 ![A: $i] : ((~relation(A)) | ((relation_rng(A) = relation_dom(relation_inverse(A))) & (relation_dom(A) = relation_rng(relation_inverse(A)))))),
% 0.21/0.41 inference(skolemize,[status(sab)],[46])).
% 0.21/0.41 tff(48,plain,
% 0.21/0.41 (![A: $i] : ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A)))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.21/0.41 tff(49,plain,
% 0.21/0.41 (![A: $i] : ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A)))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[48, 38])).
% 0.21/0.41 tff(50,plain,
% 0.21/0.41 (((~![A: $i] : ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A)))))))) | ((~relation(A!11)) | (~((~(relation_rng(A!11) = relation_dom(relation_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(relation_inverse(A!11)))))))) <=> ((~![A: $i] : ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A)))))))) | (~relation(A!11)) | (~((~(relation_rng(A!11) = relation_dom(relation_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(relation_inverse(A!11)))))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(51,plain,
% 0.21/0.41 ((~![A: $i] : ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A)))))))) | ((~relation(A!11)) | (~((~(relation_rng(A!11) = relation_dom(relation_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(relation_inverse(A!11)))))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(52,plain,
% 0.21/0.41 ((~![A: $i] : ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A)))))))) | (~relation(A!11)) | (~((~(relation_rng(A!11) = relation_dom(relation_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(relation_inverse(A!11))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.21/0.41 tff(53,plain,
% 0.21/0.41 (~((~(relation_rng(A!11) = relation_dom(relation_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(relation_inverse(A!11)))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[52, 49, 13])).
% 0.21/0.41 tff(54,plain,
% 0.21/0.41 (((~(relation_rng(A!11) = relation_dom(relation_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(relation_inverse(A!11))))) | (relation_rng(A!11) = relation_dom(relation_inverse(A!11)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(55,plain,
% 0.21/0.41 (relation_rng(A!11) = relation_dom(relation_inverse(A!11))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.21/0.41 tff(56,plain,
% 0.21/0.41 (relation_rng(A!11) = relation_dom(function_inverse(A!11))),
% 0.21/0.41 inference(transitivity,[status(thm)],[55, 36])).
% 0.21/0.41 tff(57,plain,
% 0.21/0.41 (relation_rng(function_inverse(A!11)) = relation_rng(relation_inverse(A!11))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[34])).
% 0.21/0.41 tff(58,plain,
% 0.21/0.41 (relation_rng(relation_inverse(A!11)) = relation_rng(function_inverse(A!11))),
% 0.21/0.41 inference(symmetry,[status(thm)],[57])).
% 0.21/0.41 tff(59,plain,
% 0.21/0.41 (((~(relation_rng(A!11) = relation_dom(relation_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(relation_inverse(A!11))))) | (relation_dom(A!11) = relation_rng(relation_inverse(A!11)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(60,plain,
% 0.21/0.41 (relation_dom(A!11) = relation_rng(relation_inverse(A!11))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[59, 53])).
% 0.21/0.41 tff(61,plain,
% 0.21/0.41 (relation_dom(A!11) = relation_rng(function_inverse(A!11))),
% 0.21/0.41 inference(transitivity,[status(thm)],[60, 58])).
% 0.21/0.41 tff(62,plain,
% 0.21/0.41 ((~(~((~(relation_rng(A!11) = relation_dom(function_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(function_inverse(A!11))))))) <=> ((~(relation_rng(A!11) = relation_dom(function_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(function_inverse(A!11)))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(63,plain,
% 0.21/0.41 (((relation_rng(A!11) = relation_dom(function_inverse(A!11))) & (relation_dom(A!11) = relation_rng(function_inverse(A!11)))) <=> (~((~(relation_rng(A!11) = relation_dom(function_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(function_inverse(A!11))))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(64,plain,
% 0.21/0.41 ((~((relation_rng(A!11) = relation_dom(function_inverse(A!11))) & (relation_dom(A!11) = relation_rng(function_inverse(A!11))))) <=> (~(~((~(relation_rng(A!11) = relation_dom(function_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(function_inverse(A!11)))))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[63])).
% 0.21/0.41 tff(65,plain,
% 0.21/0.41 ((~((relation_rng(A!11) = relation_dom(function_inverse(A!11))) & (relation_dom(A!11) = relation_rng(function_inverse(A!11))))) <=> ((~(relation_rng(A!11) = relation_dom(function_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(function_inverse(A!11)))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[64, 62])).
% 0.21/0.41 tff(66,plain,
% 0.21/0.41 (~((relation_rng(A!11) = relation_dom(function_inverse(A!11))) & (relation_dom(A!11) = relation_rng(function_inverse(A!11))))),
% 0.21/0.41 inference(or_elim,[status(thm)],[10])).
% 0.21/0.41 tff(67,plain,
% 0.21/0.41 ((~(relation_rng(A!11) = relation_dom(function_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(function_inverse(A!11))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.21/0.41 tff(68,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[67, 61, 56])).
% 0.21/0.41 % SZS output end Proof
% 0.21/0.41 % E exiting
%------------------------------------------------------------------------------