%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU032+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 0.13s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU032+1 : TPTP v9.0.0. Released v3.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.13/0.32 % Computer : n010.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Fri Jun 20 05:58:41 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.13/0.38 % SZS status Theorem
% 0.13/0.38 % SZS output start Proof
% 0.13/0.38 tff(tptp_fun_A_11_type, type, (
% 0.13/0.38 tptp_fun_A_11: $i)).
% 0.13/0.38 tff(function_inverse_type, type, (
% 0.13/0.38 function_inverse: $i > $i)).
% 0.13/0.38 tff(identity_relation_type, type, (
% 0.13/0.38 identity_relation: $i > $i)).
% 0.13/0.38 tff(relation_dom_type, type, (
% 0.13/0.38 relation_dom: $i > $i)).
% 0.13/0.38 tff(relation_composition_type, type, (
% 0.13/0.38 relation_composition: ( $i * $i ) > $i)).
% 0.13/0.38 tff(relation_rng_type, type, (
% 0.13/0.38 relation_rng: $i > $i)).
% 0.13/0.38 tff(one_to_one_type, type, (
% 0.13/0.38 one_to_one: $i > $o)).
% 0.13/0.38 tff(function_type, type, (
% 0.13/0.38 function: $i > $o)).
% 0.13/0.38 tff(relation_type, type, (
% 0.13/0.38 relation: $i > $o)).
% 0.13/0.38 tff(1,plain,
% 0.13/0.38 ((~((function_inverse(function_inverse(A!11)) = A!11) | (~(relation(A!11) & function(A!11))) | (~one_to_one(A!11)))) <=> (~((function_inverse(function_inverse(A!11)) = A!11) | (~(relation(A!11) & function(A!11))) | (~one_to_one(A!11))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(2,plain,
% 0.13/0.38 ((~![A: $i] : ((function_inverse(function_inverse(A)) = A) | (~(relation(A) & function(A))) | (~one_to_one(A)))) <=> (~![A: $i] : ((function_inverse(function_inverse(A)) = A) | (~(relation(A) & function(A))) | (~one_to_one(A))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(3,plain,
% 0.13/0.38 ((~![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => (function_inverse(function_inverse(A)) = A)))) <=> (~![A: $i] : ((function_inverse(function_inverse(A)) = A) | (~(relation(A) & function(A))) | (~one_to_one(A))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(4,axiom,(~![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => (function_inverse(function_inverse(A)) = A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t65_funct_1')).
% 0.13/0.38 tff(5,plain,
% 0.13/0.38 (~![A: $i] : ((function_inverse(function_inverse(A)) = A) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.13/0.38 tff(6,plain,
% 0.13/0.38 (~![A: $i] : ((function_inverse(function_inverse(A)) = A) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.13/0.38 tff(7,plain,
% 0.13/0.38 (~![A: $i] : ((function_inverse(function_inverse(A)) = A) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.13/0.38 tff(8,plain,
% 0.13/0.38 (~![A: $i] : ((function_inverse(function_inverse(A)) = A) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.13/0.38 tff(9,plain,(
% 0.13/0.38 ~((function_inverse(function_inverse(A!11)) = A!11) | (~(relation(A!11) & function(A!11))) | (~one_to_one(A!11)))),
% 0.13/0.38 inference(skolemize,[status(sab)],[8])).
% 0.13/0.38 tff(10,plain,
% 0.13/0.38 (~((function_inverse(function_inverse(A!11)) = A!11) | (~(relation(A!11) & function(A!11))) | (~one_to_one(A!11)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.13/0.38 tff(11,plain,
% 0.13/0.38 (one_to_one(A!11)),
% 0.13/0.38 inference(or_elim,[status(thm)],[10])).
% 0.13/0.38 tff(12,plain,
% 0.13/0.38 (relation(A!11) & function(A!11)),
% 0.13/0.38 inference(or_elim,[status(thm)],[10])).
% 0.13/0.38 tff(13,plain,
% 0.13/0.38 (function(A!11)),
% 0.13/0.38 inference(and_elim,[status(thm)],[12])).
% 0.13/0.38 tff(14,plain,
% 0.13/0.38 (relation(A!11)),
% 0.13/0.38 inference(and_elim,[status(thm)],[12])).
% 0.13/0.38 tff(15,plain,
% 0.13/0.38 (^[A: $i] : refl(((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A))))))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A))))))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(16,plain,
% 0.13/0.38 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A))))))) <=> ![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[15])).
% 0.13/0.38 tff(17,plain,
% 0.13/0.38 (^[A: $i] : trans(monotonicity(rewrite(((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) <=> (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A))))))), 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))))), ((((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ((~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))) | ((~relation(A)) | (~function(A))) | (~one_to_one(A))))), rewrite(((~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))) | ((~relation(A)) | (~function(A))) | (~one_to_one(A))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))), ((((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(18,plain,
% 0.13/0.38 (![A: $i] : (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[17])).
% 0.13/0.38 tff(19,plain,
% 0.13/0.38 (![A: $i] : (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ![A: $i] : (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(20,plain,
% 0.13/0.38 (^[A: $i] : trans(monotonicity(rewrite((one_to_one(A) => ((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A))))) <=> ((~one_to_one(A)) | ((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))))), (((relation(A) & function(A)) => (one_to_one(A) => ((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))))) <=> ((relation(A) & function(A)) => ((~one_to_one(A)) | ((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))))))), rewrite(((relation(A) & function(A)) => ((~one_to_one(A)) | ((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))))) <=> (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))), (((relation(A) & function(A)) => (one_to_one(A) => ((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))))) <=> (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(21,plain,
% 0.13/0.38 (![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)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[20])).
% 0.13/0.38 tff(22,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/sandbox/benchmark/theBenchmark.p','t55_funct_1')).
% 0.13/0.38 tff(23,plain,
% 0.13/0.38 (![A: $i] : (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.13/0.38 tff(24,plain,
% 0.13/0.38 (![A: $i] : (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.13/0.38 tff(25,plain,(
% 0.13/0.38 ![A: $i] : (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.13/0.38 inference(skolemize,[status(sab)],[24])).
% 0.13/0.38 tff(26,plain,
% 0.13/0.38 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.13/0.38 tff(27,plain,
% 0.13/0.38 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[26, 16])).
% 0.13/0.38 tff(28,plain,
% 0.13/0.38 (((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))) | ((~one_to_one(A!11)) | (~function(A!11)) | (~relation(A!11)) | (~((~(relation_rng(A!11) = relation_dom(function_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(function_inverse(A!11)))))))) <=> ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))) | (~one_to_one(A!11)) | (~function(A!11)) | (~relation(A!11)) | (~((~(relation_rng(A!11) = relation_dom(function_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(function_inverse(A!11)))))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(29,plain,
% 0.13/0.38 (((~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)) | (~function(A!11)) | (~relation(A!11)) | (~((~(relation_rng(A!11) = relation_dom(function_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(function_inverse(A!11)))))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(30,plain,
% 0.13/0.38 ((~((~(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))))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(31,plain,
% 0.13/0.38 (((~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)) | (~((~(relation_rng(A!11) = relation_dom(function_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(function_inverse(A!11)))))))),
% 0.13/0.38 inference(monotonicity,[status(thm)],[30])).
% 0.13/0.38 tff(32,plain,
% 0.13/0.38 (((~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)) | (~function(A!11)) | (~relation(A!11)) | (~((~(relation_rng(A!11) = relation_dom(function_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(function_inverse(A!11)))))))),
% 0.13/0.39 inference(transitivity,[status(thm)],[31, 29])).
% 0.13/0.39 tff(33,plain,
% 0.13/0.39 (((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))) | ((~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)))))))) <=> ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))) | ((~one_to_one(A!11)) | (~function(A!11)) | (~relation(A!11)) | (~((~(relation_rng(A!11) = relation_dom(function_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(function_inverse(A!11))))))))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[32])).
% 0.13/0.39 tff(34,plain,
% 0.13/0.39 (((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))) | ((~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)))))))) <=> ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))) | (~one_to_one(A!11)) | (~function(A!11)) | (~relation(A!11)) | (~((~(relation_rng(A!11) = relation_dom(function_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(function_inverse(A!11)))))))),
% 0.13/0.39 inference(transitivity,[status(thm)],[33, 28])).
% 0.13/0.39 tff(35,plain,
% 0.13/0.39 ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))) | ((~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)))))))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(36,plain,
% 0.13/0.39 ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))) | (~one_to_one(A!11)) | (~function(A!11)) | (~relation(A!11)) | (~((~(relation_rng(A!11) = relation_dom(function_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(function_inverse(A!11))))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.13/0.39 tff(37,plain,
% 0.13/0.39 (~((~(relation_rng(A!11) = relation_dom(function_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(function_inverse(A!11)))))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[36, 27, 14, 13, 11])).
% 0.13/0.39 tff(38,plain,
% 0.13/0.39 (((~(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)))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(39,plain,
% 0.13/0.39 (relation_rng(A!11) = relation_dom(function_inverse(A!11))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.13/0.39 tff(40,plain,
% 0.13/0.39 (identity_relation(relation_rng(A!11)) = identity_relation(relation_dom(function_inverse(A!11)))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[39])).
% 0.13/0.39 tff(41,plain,
% 0.13/0.39 (^[A: $i] : refl(((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A))))))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(42,plain,
% 0.13/0.39 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A))))))) <=> ![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[41])).
% 0.13/0.39 tff(43,plain,
% 0.13/0.39 (^[A: $i] : trans(monotonicity(rewrite(((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))) <=> (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A))))))), 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))))), ((((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ((~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))) | ((~relation(A)) | (~function(A))) | (~one_to_one(A))))), rewrite(((~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))) | ((~relation(A)) | (~function(A))) | (~one_to_one(A))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))))), ((((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(44,plain,
% 0.13/0.39 (![A: $i] : (((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[43])).
% 0.13/0.39 tff(45,plain,
% 0.13/0.39 (![A: $i] : (((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ![A: $i] : (((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(46,plain,
% 0.13/0.39 (^[A: $i] : trans(monotonicity(rewrite((one_to_one(A) => ((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A))))) <=> ((~one_to_one(A)) | ((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))), (((relation(A) & function(A)) => (one_to_one(A) => ((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))) <=> ((relation(A) & function(A)) => ((~one_to_one(A)) | ((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))))), rewrite(((relation(A) & function(A)) => ((~one_to_one(A)) | ((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))) <=> (((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))), (((relation(A) & function(A)) => (one_to_one(A) => ((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))) <=> (((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(47,plain,
% 0.13/0.39 (![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => ((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))) <=> ![A: $i] : (((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[46])).
% 0.13/0.39 tff(48,axiom,(![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => ((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t61_funct_1')).
% 0.13/0.39 tff(49,plain,
% 0.13/0.39 (![A: $i] : (((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.13/0.39 tff(50,plain,
% 0.13/0.39 (![A: $i] : (((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.13/0.39 tff(51,plain,(
% 0.13/0.39 ![A: $i] : (((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[50])).
% 0.13/0.39 tff(52,plain,
% 0.13/0.39 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.13/0.39 tff(53,plain,
% 0.13/0.39 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[52, 42])).
% 0.13/0.39 tff(54,plain,
% 0.13/0.39 (((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))))) | ((~one_to_one(A!11)) | (~function(A!11)) | (~relation(A!11)) | (~((~(relation_composition(A!11, function_inverse(A!11)) = identity_relation(relation_dom(A!11)))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_rng(A!11)))))))) <=> ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))))) | (~one_to_one(A!11)) | (~function(A!11)) | (~relation(A!11)) | (~((~(relation_composition(A!11, function_inverse(A!11)) = identity_relation(relation_dom(A!11)))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_rng(A!11)))))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(55,plain,
% 0.13/0.39 (((~one_to_one(A!11)) | (~relation(A!11)) | (~function(A!11)) | (~((~(relation_composition(A!11, function_inverse(A!11)) = identity_relation(relation_dom(A!11)))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_rng(A!11))))))) <=> ((~one_to_one(A!11)) | (~function(A!11)) | (~relation(A!11)) | (~((~(relation_composition(A!11, function_inverse(A!11)) = identity_relation(relation_dom(A!11)))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_rng(A!11)))))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(56,plain,
% 0.13/0.39 (((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))))) | ((~one_to_one(A!11)) | (~relation(A!11)) | (~function(A!11)) | (~((~(relation_composition(A!11, function_inverse(A!11)) = identity_relation(relation_dom(A!11)))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_rng(A!11)))))))) <=> ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))))) | ((~one_to_one(A!11)) | (~function(A!11)) | (~relation(A!11)) | (~((~(relation_composition(A!11, function_inverse(A!11)) = identity_relation(relation_dom(A!11)))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_rng(A!11))))))))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[55])).
% 0.13/0.39 tff(57,plain,
% 0.13/0.39 (((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))))) | ((~one_to_one(A!11)) | (~relation(A!11)) | (~function(A!11)) | (~((~(relation_composition(A!11, function_inverse(A!11)) = identity_relation(relation_dom(A!11)))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_rng(A!11)))))))) <=> ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))))) | (~one_to_one(A!11)) | (~function(A!11)) | (~relation(A!11)) | (~((~(relation_composition(A!11, function_inverse(A!11)) = identity_relation(relation_dom(A!11)))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_rng(A!11)))))))),
% 0.13/0.39 inference(transitivity,[status(thm)],[56, 54])).
% 0.13/0.39 tff(58,plain,
% 0.13/0.39 ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))))) | ((~one_to_one(A!11)) | (~relation(A!11)) | (~function(A!11)) | (~((~(relation_composition(A!11, function_inverse(A!11)) = identity_relation(relation_dom(A!11)))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_rng(A!11)))))))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(59,plain,
% 0.13/0.39 ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))))) | (~one_to_one(A!11)) | (~function(A!11)) | (~relation(A!11)) | (~((~(relation_composition(A!11, function_inverse(A!11)) = identity_relation(relation_dom(A!11)))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_rng(A!11))))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.13/0.39 tff(60,plain,
% 0.13/0.39 (~((~(relation_composition(A!11, function_inverse(A!11)) = identity_relation(relation_dom(A!11)))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_rng(A!11)))))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[59, 53, 14, 13, 11])).
% 0.13/0.39 tff(61,plain,
% 0.13/0.39 (((~(relation_composition(A!11, function_inverse(A!11)) = identity_relation(relation_dom(A!11)))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_rng(A!11))))) | (relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_rng(A!11)))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(62,plain,
% 0.13/0.39 (relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_rng(A!11))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.13/0.39 tff(63,plain,
% 0.13/0.39 (relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(function_inverse(A!11)))),
% 0.13/0.39 inference(transitivity,[status(thm)],[62, 40])).
% 0.13/0.39 tff(64,plain,
% 0.13/0.39 (((~(relation_rng(A!11) = relation_dom(function_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(function_inverse(A!11))))) | (relation_dom(A!11) = relation_rng(function_inverse(A!11)))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(65,plain,
% 0.13/0.39 (relation_dom(A!11) = relation_rng(function_inverse(A!11))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[64, 37])).
% 0.13/0.39 tff(66,plain,
% 0.13/0.39 (relation_rng(function_inverse(A!11)) = relation_dom(A!11)),
% 0.13/0.39 inference(symmetry,[status(thm)],[65])).
% 0.13/0.39 tff(67,plain,
% 0.13/0.39 (^[A: $i] : refl(((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A)))))) <=> ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A)))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(68,plain,
% 0.13/0.39 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A)))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[67])).
% 0.13/0.39 tff(69,plain,
% 0.13/0.39 (^[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))))), rewrite((relation(function_inverse(A)) & function(function_inverse(A))) <=> (~((~relation(function_inverse(A))) | (~function(function_inverse(A)))))), (((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A)))) <=> (((~relation(A)) | (~function(A))) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A)))))))), rewrite((((~relation(A)) | (~function(A))) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A)))))) <=> ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))), (((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A)))) <=> ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(70,plain,
% 0.13/0.39 (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A)))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[69])).
% 0.13/0.39 tff(71,plain,
% 0.13/0.39 (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A)))) <=> ![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(72,plain,
% 0.13/0.39 (^[A: $i] : rewrite(((relation(A) & function(A)) => (relation(function_inverse(A)) & function(function_inverse(A)))) <=> ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(73,plain,
% 0.13/0.39 (![A: $i] : ((relation(A) & function(A)) => (relation(function_inverse(A)) & function(function_inverse(A)))) <=> ![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[72])).
% 0.13/0.39 tff(74,axiom,(![A: $i] : ((relation(A) & function(A)) => (relation(function_inverse(A)) & function(function_inverse(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k2_funct_1')).
% 0.13/0.39 tff(75,plain,
% 0.13/0.39 (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.13/0.39 tff(76,plain,
% 0.13/0.39 (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.13/0.39 tff(77,plain,(
% 0.13/0.39 ![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 0.13/0.39 inference(skolemize,[status(sab)],[76])).
% 0.13/0.39 tff(78,plain,
% 0.13/0.39 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[77, 70])).
% 0.13/0.39 tff(79,plain,
% 0.13/0.39 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[78, 68])).
% 0.13/0.39 tff(80,plain,
% 0.13/0.39 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | ((~function(A!11)) | (~relation(A!11)) | (~((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | (~function(A!11)) | (~relation(A!11)) | (~((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(81,plain,
% 0.13/0.39 (((~relation(A!11)) | (~function(A!11)) | (~((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11)))))) <=> ((~function(A!11)) | (~relation(A!11)) | (~((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(82,plain,
% 0.13/0.39 ((~((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))))) <=> (~((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11)))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(83,plain,
% 0.13/0.39 (((~relation(A!11)) | (~function(A!11)) | (~((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11)))))) <=> ((~relation(A!11)) | (~function(A!11)) | (~((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))))))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[82])).
% 0.13/0.39 tff(84,plain,
% 0.13/0.39 (((~relation(A!11)) | (~function(A!11)) | (~((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11)))))) <=> ((~function(A!11)) | (~relation(A!11)) | (~((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))))))),
% 0.13/0.40 inference(transitivity,[status(thm)],[83, 81])).
% 0.13/0.40 tff(85,plain,
% 0.13/0.40 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | ((~relation(A!11)) | (~function(A!11)) | (~((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | ((~function(A!11)) | (~relation(A!11)) | (~((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11)))))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[84])).
% 0.13/0.40 tff(86,plain,
% 0.13/0.40 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | ((~relation(A!11)) | (~function(A!11)) | (~((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | (~function(A!11)) | (~relation(A!11)) | (~((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))))))),
% 0.13/0.40 inference(transitivity,[status(thm)],[85, 80])).
% 0.13/0.40 tff(87,plain,
% 0.13/0.40 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | ((~relation(A!11)) | (~function(A!11)) | (~((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(88,plain,
% 0.13/0.40 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | (~function(A!11)) | (~relation(A!11)) | (~((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.13/0.40 tff(89,plain,
% 0.13/0.40 (~((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[88, 79, 14, 13])).
% 0.13/0.40 tff(90,plain,
% 0.13/0.40 (((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11)))) | relation(function_inverse(A!11))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(91,plain,
% 0.13/0.40 (relation(function_inverse(A!11))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.13/0.40 tff(92,plain,
% 0.13/0.40 (((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11)))) | function(function_inverse(A!11))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(93,plain,
% 0.13/0.40 (function(function_inverse(A!11))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[92, 89])).
% 0.13/0.40 tff(94,plain,
% 0.13/0.40 (^[A: $i] : refl(((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A)))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A)))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(95,plain,
% 0.13/0.40 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A)))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[94])).
% 0.13/0.40 tff(96,plain,
% 0.13/0.40 (^[A: $i] : rewrite(((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A)))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A)))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(97,plain,
% 0.20/0.40 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A)))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[96])).
% 0.20/0.40 tff(98,plain,
% 0.20/0.40 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A)))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[97, 95])).
% 0.20/0.40 tff(99,plain,
% 0.20/0.40 (^[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))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(B) & function(B)) <=> (~((~relation(B)) | (~function(B))))), ((~(relation(B) & function(B))) <=> (~(~((~relation(B)) | (~function(B))))))), rewrite((~(~((~relation(B)) | (~function(B))))) <=> ((~relation(B)) | (~function(B)))), ((~(relation(B) & function(B))) <=> ((~relation(B)) | (~function(B))))), trans(monotonicity(rewrite((one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A)))) <=> (~((~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A))))))), ((~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A))))) <=> (~(~((~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A))))))))), rewrite((~(~((~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A))))))) <=> ((~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A)))))), ((~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A))))) <=> ((~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A))))))), (((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A)))))) <=> ((B = function_inverse(A)) | ((~relation(B)) | (~function(B))) | ((~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A)))))))), rewrite(((B = function_inverse(A)) | ((~relation(B)) | (~function(B))) | ((~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A)))))) <=> ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A)))))), (((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A)))))) <=> ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A)))))))), (![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A)))))) <=> ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A))))))), (((~(relation(A) & function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A))))))) <=> (((~relation(A)) | (~function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A)))))))), rewrite((((~relation(A)) | (~function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A)))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A))))))), (((~(relation(A) & function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(100,plain,
% 0.20/0.40 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[99])).
% 0.20/0.40 tff(101,plain,
% 0.20/0.40 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A))))))) <=> ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A)))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(102,plain,
% 0.20/0.40 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((one_to_one(A) & (relation_rng(A) = relation_dom(B))) & (relation_composition(A, B) = identity_relation(relation_dom(A)))) <=> (one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A))))), ((((one_to_one(A) & (relation_rng(A) = relation_dom(B))) & (relation_composition(A, B) = identity_relation(relation_dom(A)))) => (B = function_inverse(A))) <=> ((one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A)))) => (B = function_inverse(A))))), rewrite(((one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A)))) => (B = function_inverse(A))) <=> ((~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A))))) | (B = function_inverse(A)))), ((((one_to_one(A) & (relation_rng(A) = relation_dom(B))) & (relation_composition(A, B) = identity_relation(relation_dom(A)))) => (B = function_inverse(A))) <=> ((~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A))))) | (B = function_inverse(A))))), (((relation(B) & function(B)) => (((one_to_one(A) & (relation_rng(A) = relation_dom(B))) & (relation_composition(A, B) = identity_relation(relation_dom(A)))) => (B = function_inverse(A)))) <=> ((relation(B) & function(B)) => ((~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A))))) | (B = function_inverse(A)))))), rewrite(((relation(B) & function(B)) => ((~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A))))) | (B = function_inverse(A)))) <=> ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A))))))), (((relation(B) & function(B)) => (((one_to_one(A) & (relation_rng(A) = relation_dom(B))) & (relation_composition(A, B) = identity_relation(relation_dom(A)))) => (B = function_inverse(A)))) <=> ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A))))))))), (![B: $i] : ((relation(B) & function(B)) => (((one_to_one(A) & (relation_rng(A) = relation_dom(B))) & (relation_composition(A, B) = identity_relation(relation_dom(A)))) => (B = function_inverse(A)))) <=> ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A)))))))), (((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => (((one_to_one(A) & (relation_rng(A) = relation_dom(B))) & (relation_composition(A, B) = identity_relation(relation_dom(A)))) => (B = function_inverse(A))))) <=> ((relation(A) & function(A)) => ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A))))))))), rewrite(((relation(A) & function(A)) => ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A))))))) <=> ((~(relation(A) & function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A)))))))), (((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => (((one_to_one(A) & (relation_rng(A) = relation_dom(B))) & (relation_composition(A, B) = identity_relation(relation_dom(A)))) => (B = function_inverse(A))))) <=> ((~(relation(A) & function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A)))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(103,plain,
% 0.20/0.40 (![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => (((one_to_one(A) & (relation_rng(A) = relation_dom(B))) & (relation_composition(A, B) = identity_relation(relation_dom(A)))) => (B = function_inverse(A))))) <=> ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[102])).
% 0.20/0.40 tff(104,axiom,(![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => (((one_to_one(A) & (relation_rng(A) = relation_dom(B))) & (relation_composition(A, B) = identity_relation(relation_dom(A)))) => (B = function_inverse(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t63_funct_1')).
% 0.20/0.40 tff(105,plain,
% 0.20/0.40 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A)))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.20/0.40 tff(106,plain,
% 0.20/0.40 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A)))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.20/0.40 tff(107,plain,(
% 0.20/0.40 ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A)))))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[106])).
% 0.20/0.40 tff(108,plain,
% 0.20/0.40 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[107, 100])).
% 0.20/0.40 tff(109,plain,
% 0.20/0.40 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[108, 98])).
% 0.20/0.40 tff(110,plain,
% 0.20/0.40 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A))))))) | ((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![B: $i] : ((~relation(B)) | (~function(B)) | (B = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11)))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A))))))) | (~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![B: $i] : ((~relation(B)) | (~function(B)) | (B = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11)))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(111,plain,
% 0.20/0.40 (((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![B: $i] : ((~relation(B)) | (~function(B)) | (B = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11))))))) <=> ((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![B: $i] : ((~relation(B)) | (~function(B)) | (B = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11)))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(112,plain,
% 0.20/0.40 (^[B: $i] : rewrite(((B = function_inverse(function_inverse(A!11))) | (~relation(B)) | (~function(B)) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11)))))) <=> ((~relation(B)) | (~function(B)) | (B = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11)))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(113,plain,
% 0.20/0.40 (![B: $i] : ((B = function_inverse(function_inverse(A!11))) | (~relation(B)) | (~function(B)) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11)))))) <=> ![B: $i] : ((~relation(B)) | (~function(B)) | (B = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[112])).
% 0.20/0.40 tff(114,plain,
% 0.20/0.40 (((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![B: $i] : ((B = function_inverse(function_inverse(A!11))) | (~relation(B)) | (~function(B)) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11))))))) <=> ((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![B: $i] : ((~relation(B)) | (~function(B)) | (B = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11)))))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[113])).
% 0.20/0.40 tff(115,plain,
% 0.20/0.40 (((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![B: $i] : ((B = function_inverse(function_inverse(A!11))) | (~relation(B)) | (~function(B)) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11))))))) <=> ((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![B: $i] : ((~relation(B)) | (~function(B)) | (B = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11)))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[114, 111])).
% 0.20/0.40 tff(116,plain,
% 0.20/0.40 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A))))))) | ((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![B: $i] : ((B = function_inverse(function_inverse(A!11))) | (~relation(B)) | (~function(B)) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11)))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A))))))) | ((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![B: $i] : ((~relation(B)) | (~function(B)) | (B = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11))))))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[115])).
% 0.20/0.40 tff(117,plain,
% 0.20/0.40 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A))))))) | ((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![B: $i] : ((B = function_inverse(function_inverse(A!11))) | (~relation(B)) | (~function(B)) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11)))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A))))))) | (~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![B: $i] : ((~relation(B)) | (~function(B)) | (B = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11)))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[116, 110])).
% 0.20/0.40 tff(118,plain,
% 0.20/0.40 ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A))))))) | ((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![B: $i] : ((B = function_inverse(function_inverse(A!11))) | (~relation(B)) | (~function(B)) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11)))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(119,plain,
% 0.20/0.40 ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A))))))) | (~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![B: $i] : ((~relation(B)) | (~function(B)) | (B = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.20/0.40 tff(120,plain,
% 0.20/0.40 ((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![B: $i] : ((~relation(B)) | (~function(B)) | (B = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11))))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[119, 109])).
% 0.20/0.40 tff(121,plain,
% 0.20/0.40 (![B: $i] : ((~relation(B)) | (~function(B)) | (B = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[120, 93, 91])).
% 0.20/0.41 tff(122,plain,
% 0.20/0.41 (^[A: $i] : refl((one_to_one(function_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A))) <=> (one_to_one(function_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(123,plain,
% 0.20/0.41 (![A: $i] : (one_to_one(function_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A))) <=> ![A: $i] : (one_to_one(function_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[122])).
% 0.20/0.41 tff(124,plain,
% 0.20/0.41 (^[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))))), ((one_to_one(function_inverse(A)) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> (one_to_one(function_inverse(A)) | ((~relation(A)) | (~function(A))) | (~one_to_one(A))))), rewrite((one_to_one(function_inverse(A)) | ((~relation(A)) | (~function(A))) | (~one_to_one(A))) <=> (one_to_one(function_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))), ((one_to_one(function_inverse(A)) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> (one_to_one(function_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(125,plain,
% 0.20/0.41 (![A: $i] : (one_to_one(function_inverse(A)) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ![A: $i] : (one_to_one(function_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[124])).
% 0.20/0.41 tff(126,plain,
% 0.20/0.41 (![A: $i] : (one_to_one(function_inverse(A)) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ![A: $i] : (one_to_one(function_inverse(A)) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(127,plain,
% 0.20/0.41 (^[A: $i] : trans(monotonicity(rewrite((one_to_one(A) => one_to_one(function_inverse(A))) <=> ((~one_to_one(A)) | one_to_one(function_inverse(A)))), (((relation(A) & function(A)) => (one_to_one(A) => one_to_one(function_inverse(A)))) <=> ((relation(A) & function(A)) => ((~one_to_one(A)) | one_to_one(function_inverse(A)))))), rewrite(((relation(A) & function(A)) => ((~one_to_one(A)) | one_to_one(function_inverse(A)))) <=> (one_to_one(function_inverse(A)) | (~(relation(A) & function(A))) | (~one_to_one(A)))), (((relation(A) & function(A)) => (one_to_one(A) => one_to_one(function_inverse(A)))) <=> (one_to_one(function_inverse(A)) | (~(relation(A) & function(A))) | (~one_to_one(A)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(128,plain,
% 0.20/0.41 (![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => one_to_one(function_inverse(A)))) <=> ![A: $i] : (one_to_one(function_inverse(A)) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[127])).
% 0.20/0.41 tff(129,axiom,(![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => one_to_one(function_inverse(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t62_funct_1')).
% 0.20/0.41 tff(130,plain,
% 0.20/0.41 (![A: $i] : (one_to_one(function_inverse(A)) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.20/0.41 tff(131,plain,
% 0.20/0.41 (![A: $i] : (one_to_one(function_inverse(A)) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[130, 126])).
% 0.20/0.41 tff(132,plain,(
% 0.20/0.41 ![A: $i] : (one_to_one(function_inverse(A)) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[131])).
% 0.20/0.41 tff(133,plain,
% 0.20/0.41 (![A: $i] : (one_to_one(function_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[132, 125])).
% 0.20/0.41 tff(134,plain,
% 0.20/0.41 (![A: $i] : (one_to_one(function_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[133, 123])).
% 0.20/0.41 tff(135,plain,
% 0.20/0.41 (((~![A: $i] : (one_to_one(function_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))) | ((~one_to_one(A!11)) | (~function(A!11)) | (~relation(A!11)) | one_to_one(function_inverse(A!11)))) <=> ((~![A: $i] : (one_to_one(function_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))) | (~one_to_one(A!11)) | (~function(A!11)) | (~relation(A!11)) | one_to_one(function_inverse(A!11)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(136,plain,
% 0.20/0.41 ((one_to_one(function_inverse(A!11)) | (~one_to_one(A!11)) | (~relation(A!11)) | (~function(A!11))) <=> ((~one_to_one(A!11)) | (~function(A!11)) | (~relation(A!11)) | one_to_one(function_inverse(A!11)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(137,plain,
% 0.20/0.41 (((~![A: $i] : (one_to_one(function_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))) | (one_to_one(function_inverse(A!11)) | (~one_to_one(A!11)) | (~relation(A!11)) | (~function(A!11)))) <=> ((~![A: $i] : (one_to_one(function_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))) | ((~one_to_one(A!11)) | (~function(A!11)) | (~relation(A!11)) | one_to_one(function_inverse(A!11))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[136])).
% 0.20/0.41 tff(138,plain,
% 0.20/0.41 (((~![A: $i] : (one_to_one(function_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))) | (one_to_one(function_inverse(A!11)) | (~one_to_one(A!11)) | (~relation(A!11)) | (~function(A!11)))) <=> ((~![A: $i] : (one_to_one(function_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))) | (~one_to_one(A!11)) | (~function(A!11)) | (~relation(A!11)) | one_to_one(function_inverse(A!11)))),
% 0.20/0.41 inference(transitivity,[status(thm)],[137, 135])).
% 0.20/0.41 tff(139,plain,
% 0.20/0.41 ((~![A: $i] : (one_to_one(function_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))) | (one_to_one(function_inverse(A!11)) | (~one_to_one(A!11)) | (~relation(A!11)) | (~function(A!11)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(140,plain,
% 0.20/0.41 ((~![A: $i] : (one_to_one(function_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))) | (~one_to_one(A!11)) | (~function(A!11)) | (~relation(A!11)) | one_to_one(function_inverse(A!11))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.20/0.41 tff(141,plain,
% 0.20/0.41 (one_to_one(function_inverse(A!11))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[140, 134, 14, 13, 11])).
% 0.20/0.41 tff(142,plain,
% 0.20/0.41 (((~![B: $i] : ((~relation(B)) | (~function(B)) | (B = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11))))))) | ((~function(A!11)) | (~relation(A!11)) | (~one_to_one(function_inverse(A!11))) | (A!11 = function_inverse(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(A!11))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(function_inverse(A!11))))))) <=> ((~![B: $i] : ((~relation(B)) | (~function(B)) | (B = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11))))))) | (~function(A!11)) | (~relation(A!11)) | (~one_to_one(function_inverse(A!11))) | (A!11 = function_inverse(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(A!11))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(function_inverse(A!11))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(143,plain,
% 0.20/0.41 (((~relation(A!11)) | (~function(A!11)) | (A!11 = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(A!11))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(function_inverse(A!11)))))) <=> ((~function(A!11)) | (~relation(A!11)) | (~one_to_one(function_inverse(A!11))) | (A!11 = function_inverse(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(A!11))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(function_inverse(A!11))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(144,plain,
% 0.20/0.41 (((~![B: $i] : ((~relation(B)) | (~function(B)) | (B = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11))))))) | ((~relation(A!11)) | (~function(A!11)) | (A!11 = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(A!11))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(function_inverse(A!11))))))) <=> ((~![B: $i] : ((~relation(B)) | (~function(B)) | (B = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11))))))) | ((~function(A!11)) | (~relation(A!11)) | (~one_to_one(function_inverse(A!11))) | (A!11 = function_inverse(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(A!11))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(function_inverse(A!11)))))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[143])).
% 0.20/0.41 tff(145,plain,
% 0.20/0.41 (((~![B: $i] : ((~relation(B)) | (~function(B)) | (B = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11))))))) | ((~relation(A!11)) | (~function(A!11)) | (A!11 = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(A!11))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(function_inverse(A!11))))))) <=> ((~![B: $i] : ((~relation(B)) | (~function(B)) | (B = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11))))))) | (~function(A!11)) | (~relation(A!11)) | (~one_to_one(function_inverse(A!11))) | (A!11 = function_inverse(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(A!11))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(function_inverse(A!11))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[144, 142])).
% 0.20/0.41 tff(146,plain,
% 0.20/0.41 ((~![B: $i] : ((~relation(B)) | (~function(B)) | (B = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11))))))) | ((~relation(A!11)) | (~function(A!11)) | (A!11 = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(A!11))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(function_inverse(A!11))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(147,plain,
% 0.20/0.41 ((~![B: $i] : ((~relation(B)) | (~function(B)) | (B = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11))))))) | (~function(A!11)) | (~relation(A!11)) | (~one_to_one(function_inverse(A!11))) | (A!11 = function_inverse(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(A!11))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(function_inverse(A!11)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.20/0.41 tff(148,plain,
% 0.20/0.41 (A!11 = function_inverse(function_inverse(A!11))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[147, 14, 13, 141, 121, 66, 63])).
% 0.20/0.41 tff(149,plain,
% 0.20/0.41 (function_inverse(function_inverse(A!11)) = A!11),
% 0.20/0.41 inference(symmetry,[status(thm)],[148])).
% 0.20/0.41 tff(150,plain,
% 0.20/0.41 (~(function_inverse(function_inverse(A!11)) = A!11)),
% 0.20/0.41 inference(or_elim,[status(thm)],[10])).
% 0.20/0.41 tff(151,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[150, 149])).
% 0.20/0.41 % SZS output end Proof
% 0.20/0.42 % E exiting
%------------------------------------------------------------------------------