%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU034+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 0.11s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU034+1 : TPTP v9.0.0. Released v3.2.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n007.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 05:59:20 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.39 % SZS status Theorem
% 0.11/0.39 % SZS output start Proof
% 0.11/0.39 tff(identity_relation_type, type, (
% 0.11/0.39 identity_relation: $i > $i)).
% 0.11/0.39 tff(relation_dom_type, type, (
% 0.11/0.39 relation_dom: $i > $i)).
% 0.11/0.39 tff(tptp_fun_A_11_type, type, (
% 0.11/0.39 tptp_fun_A_11: $i)).
% 0.11/0.39 tff(relation_composition_type, type, (
% 0.11/0.39 relation_composition: ( $i * $i ) > $i)).
% 0.11/0.39 tff(function_inverse_type, type, (
% 0.11/0.39 function_inverse: $i > $i)).
% 0.11/0.39 tff(relation_rng_type, type, (
% 0.11/0.39 relation_rng: $i > $i)).
% 0.11/0.39 tff(relation_type, type, (
% 0.11/0.39 relation: $i > $o)).
% 0.11/0.39 tff(one_to_one_type, type, (
% 0.11/0.39 one_to_one: $i > $o)).
% 0.11/0.39 tff(function_type, type, (
% 0.11/0.39 function: $i > $o)).
% 0.11/0.39 tff(1,plain,
% 0.11/0.39 (^[A: $i] : refl(relation(identity_relation(A)) <=> relation(identity_relation(A)))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(2,plain,
% 0.11/0.39 (![A: $i] : relation(identity_relation(A)) <=> ![A: $i] : relation(identity_relation(A))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.39 tff(3,plain,
% 0.11/0.39 (![A: $i] : relation(identity_relation(A)) <=> ![A: $i] : relation(identity_relation(A))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(4,axiom,(![A: $i] : relation(identity_relation(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k6_relat_1')).
% 0.11/0.39 tff(5,plain,
% 0.11/0.39 (![A: $i] : relation(identity_relation(A))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.11/0.39 tff(6,plain,(
% 0.11/0.39 ![A: $i] : relation(identity_relation(A))),
% 0.11/0.39 inference(skolemize,[status(sab)],[5])).
% 0.11/0.39 tff(7,plain,
% 0.11/0.39 (![A: $i] : relation(identity_relation(A))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.11/0.39 tff(8,plain,
% 0.11/0.39 ((~![A: $i] : relation(identity_relation(A))) | relation(identity_relation(A!11))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(9,plain,
% 0.11/0.39 (relation(identity_relation(A!11))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.11/0.39 tff(10,plain,
% 0.11/0.39 (^[A: $i] : refl(one_to_one(identity_relation(A)) <=> one_to_one(identity_relation(A)))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(11,plain,
% 0.11/0.39 (![A: $i] : one_to_one(identity_relation(A)) <=> ![A: $i] : one_to_one(identity_relation(A))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[10])).
% 0.11/0.39 tff(12,plain,
% 0.11/0.39 (![A: $i] : one_to_one(identity_relation(A)) <=> ![A: $i] : one_to_one(identity_relation(A))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(13,axiom,(![A: $i] : one_to_one(identity_relation(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t52_funct_1')).
% 0.11/0.39 tff(14,plain,
% 0.11/0.39 (![A: $i] : one_to_one(identity_relation(A))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.11/0.39 tff(15,plain,(
% 0.11/0.39 ![A: $i] : one_to_one(identity_relation(A))),
% 0.11/0.39 inference(skolemize,[status(sab)],[14])).
% 0.11/0.39 tff(16,plain,
% 0.11/0.39 (![A: $i] : one_to_one(identity_relation(A))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.11/0.39 tff(17,plain,
% 0.11/0.39 ((~![A: $i] : one_to_one(identity_relation(A))) | one_to_one(identity_relation(A!11))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(18,plain,
% 0.11/0.39 (one_to_one(identity_relation(A!11))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.11/0.39 tff(19,plain,
% 0.11/0.39 (^[A: $i] : refl((~((~relation(identity_relation(A))) | (~function(identity_relation(A))))) <=> (~((~relation(identity_relation(A))) | (~function(identity_relation(A))))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(20,plain,
% 0.11/0.39 (![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A))))) <=> ![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[19])).
% 0.11/0.39 tff(21,plain,
% 0.11/0.39 (^[A: $i] : rewrite((relation(identity_relation(A)) & function(identity_relation(A))) <=> (~((~relation(identity_relation(A))) | (~function(identity_relation(A))))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(22,plain,
% 0.11/0.39 (![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A))) <=> ![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[21])).
% 0.11/0.39 tff(23,plain,
% 0.11/0.39 (![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A))) <=> ![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(24,axiom,(![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc2_funct_1')).
% 0.11/0.39 tff(25,plain,
% 0.11/0.39 (![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.11/0.39 tff(26,plain,(
% 0.11/0.39 ![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))),
% 0.11/0.39 inference(skolemize,[status(sab)],[25])).
% 0.11/0.39 tff(27,plain,
% 0.11/0.39 (![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.11/0.39 tff(28,plain,
% 0.11/0.39 (![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.11/0.39 tff(29,plain,
% 0.11/0.39 ((~![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))) | (~((~relation(identity_relation(A!11))) | (~function(identity_relation(A!11)))))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(30,plain,
% 0.11/0.39 (~((~relation(identity_relation(A!11))) | (~function(identity_relation(A!11))))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.11/0.39 tff(31,plain,
% 0.11/0.39 (((~relation(identity_relation(A!11))) | (~function(identity_relation(A!11)))) | function(identity_relation(A!11))),
% 0.11/0.39 inference(tautology,[status(thm)],[])).
% 0.11/0.39 tff(32,plain,
% 0.11/0.39 (function(identity_relation(A!11))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.11/0.39 tff(33,plain,
% 0.11/0.39 (^[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))))))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(34,plain,
% 0.11/0.39 (![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)))))))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[33])).
% 0.11/0.39 tff(35,plain,
% 0.11/0.39 (^[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)))))))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(36,plain,
% 0.11/0.39 (![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)))))))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[35])).
% 0.11/0.39 tff(37,plain,
% 0.11/0.39 (![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)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(38,plain,
% 0.11/0.39 (^[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)))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(39,plain,
% 0.11/0.39 (![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)))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[38])).
% 0.11/0.40 tff(40,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/sandbox2/benchmark/theBenchmark.p','t61_funct_1')).
% 0.11/0.40 tff(41,plain,
% 0.11/0.40 (![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)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.11/0.40 tff(42,plain,
% 0.11/0.40 (![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)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.11/0.40 tff(43,plain,(
% 0.11/0.40 ![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)))),
% 0.11/0.40 inference(skolemize,[status(sab)],[42])).
% 0.11/0.40 tff(44,plain,
% 0.11/0.40 (![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)))))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.11/0.40 tff(45,plain,
% 0.11/0.40 (![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)))))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[44, 34])).
% 0.11/0.40 tff(46,plain,
% 0.11/0.40 (((~![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(identity_relation(A!11))) | (~relation(identity_relation(A!11))) | (~function(identity_relation(A!11))) | (~((~(relation_composition(identity_relation(A!11), function_inverse(identity_relation(A!11))) = identity_relation(relation_dom(identity_relation(A!11))))) | (~(relation_composition(function_inverse(identity_relation(A!11)), identity_relation(A!11)) = identity_relation(relation_rng(identity_relation(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(identity_relation(A!11))) | (~relation(identity_relation(A!11))) | (~function(identity_relation(A!11))) | (~((~(relation_composition(identity_relation(A!11), function_inverse(identity_relation(A!11))) = identity_relation(relation_dom(identity_relation(A!11))))) | (~(relation_composition(function_inverse(identity_relation(A!11)), identity_relation(A!11)) = identity_relation(relation_rng(identity_relation(A!11))))))))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(47,plain,
% 0.11/0.40 ((~![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(identity_relation(A!11))) | (~relation(identity_relation(A!11))) | (~function(identity_relation(A!11))) | (~((~(relation_composition(identity_relation(A!11), function_inverse(identity_relation(A!11))) = identity_relation(relation_dom(identity_relation(A!11))))) | (~(relation_composition(function_inverse(identity_relation(A!11)), identity_relation(A!11)) = identity_relation(relation_rng(identity_relation(A!11))))))))),
% 0.11/0.40 inference(quant_inst,[status(thm)],[])).
% 0.11/0.40 tff(48,plain,
% 0.11/0.40 ((~![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(identity_relation(A!11))) | (~relation(identity_relation(A!11))) | (~function(identity_relation(A!11))) | (~((~(relation_composition(identity_relation(A!11), function_inverse(identity_relation(A!11))) = identity_relation(relation_dom(identity_relation(A!11))))) | (~(relation_composition(function_inverse(identity_relation(A!11)), identity_relation(A!11)) = identity_relation(relation_rng(identity_relation(A!11)))))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.11/0.40 tff(49,plain,
% 0.11/0.40 ((~one_to_one(identity_relation(A!11))) | (~relation(identity_relation(A!11))) | (~function(identity_relation(A!11))) | (~((~(relation_composition(identity_relation(A!11), function_inverse(identity_relation(A!11))) = identity_relation(relation_dom(identity_relation(A!11))))) | (~(relation_composition(function_inverse(identity_relation(A!11)), identity_relation(A!11)) = identity_relation(relation_rng(identity_relation(A!11)))))))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[48, 45])).
% 0.11/0.40 tff(50,plain,
% 0.11/0.40 (~((~(relation_composition(identity_relation(A!11), function_inverse(identity_relation(A!11))) = identity_relation(relation_dom(identity_relation(A!11))))) | (~(relation_composition(function_inverse(identity_relation(A!11)), identity_relation(A!11)) = identity_relation(relation_rng(identity_relation(A!11))))))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[49, 32, 18, 9])).
% 0.11/0.40 tff(51,plain,
% 0.11/0.40 (((~(relation_composition(identity_relation(A!11), function_inverse(identity_relation(A!11))) = identity_relation(relation_dom(identity_relation(A!11))))) | (~(relation_composition(function_inverse(identity_relation(A!11)), identity_relation(A!11)) = identity_relation(relation_rng(identity_relation(A!11)))))) | (relation_composition(identity_relation(A!11), function_inverse(identity_relation(A!11))) = identity_relation(relation_dom(identity_relation(A!11))))),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(52,plain,
% 0.11/0.40 (relation_composition(identity_relation(A!11), function_inverse(identity_relation(A!11))) = identity_relation(relation_dom(identity_relation(A!11)))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.11/0.40 tff(53,plain,
% 0.11/0.40 (^[A: $i] : refl((~((~(relation_dom(identity_relation(A)) = A)) | (~(relation_rng(identity_relation(A)) = A)))) <=> (~((~(relation_dom(identity_relation(A)) = A)) | (~(relation_rng(identity_relation(A)) = A)))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(54,plain,
% 0.11/0.40 (![A: $i] : (~((~(relation_dom(identity_relation(A)) = A)) | (~(relation_rng(identity_relation(A)) = A)))) <=> ![A: $i] : (~((~(relation_dom(identity_relation(A)) = A)) | (~(relation_rng(identity_relation(A)) = A))))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[53])).
% 0.11/0.40 tff(55,plain,
% 0.11/0.40 (^[A: $i] : rewrite(((relation_dom(identity_relation(A)) = A) & (relation_rng(identity_relation(A)) = A)) <=> (~((~(relation_dom(identity_relation(A)) = A)) | (~(relation_rng(identity_relation(A)) = A)))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(56,plain,
% 0.11/0.40 (![A: $i] : ((relation_dom(identity_relation(A)) = A) & (relation_rng(identity_relation(A)) = A)) <=> ![A: $i] : (~((~(relation_dom(identity_relation(A)) = A)) | (~(relation_rng(identity_relation(A)) = A))))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[55])).
% 0.11/0.40 tff(57,plain,
% 0.11/0.40 (![A: $i] : ((relation_dom(identity_relation(A)) = A) & (relation_rng(identity_relation(A)) = A)) <=> ![A: $i] : ((relation_dom(identity_relation(A)) = A) & (relation_rng(identity_relation(A)) = A))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(58,axiom,(![A: $i] : ((relation_dom(identity_relation(A)) = A) & (relation_rng(identity_relation(A)) = A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t71_relat_1')).
% 0.11/0.40 tff(59,plain,
% 0.11/0.40 (![A: $i] : ((relation_dom(identity_relation(A)) = A) & (relation_rng(identity_relation(A)) = A))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.11/0.40 tff(60,plain,(
% 0.11/0.40 ![A: $i] : ((relation_dom(identity_relation(A)) = A) & (relation_rng(identity_relation(A)) = A))),
% 0.11/0.40 inference(skolemize,[status(sab)],[59])).
% 0.11/0.40 tff(61,plain,
% 0.11/0.40 (![A: $i] : (~((~(relation_dom(identity_relation(A)) = A)) | (~(relation_rng(identity_relation(A)) = A))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.11/0.40 tff(62,plain,
% 0.11/0.40 (![A: $i] : (~((~(relation_dom(identity_relation(A)) = A)) | (~(relation_rng(identity_relation(A)) = A))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.11/0.40 tff(63,plain,
% 0.11/0.40 ((~![A: $i] : (~((~(relation_dom(identity_relation(A)) = A)) | (~(relation_rng(identity_relation(A)) = A))))) | (~((~(relation_dom(identity_relation(A!11)) = A!11)) | (~(relation_rng(identity_relation(A!11)) = A!11))))),
% 0.11/0.40 inference(quant_inst,[status(thm)],[])).
% 0.11/0.40 tff(64,plain,
% 0.11/0.40 (~((~(relation_dom(identity_relation(A!11)) = A!11)) | (~(relation_rng(identity_relation(A!11)) = A!11)))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.11/0.40 tff(65,plain,
% 0.11/0.40 (((~(relation_dom(identity_relation(A!11)) = A!11)) | (~(relation_rng(identity_relation(A!11)) = A!11))) | (relation_dom(identity_relation(A!11)) = A!11)),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(66,plain,
% 0.11/0.40 (relation_dom(identity_relation(A!11)) = A!11),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.11/0.40 tff(67,plain,
% 0.11/0.40 (A!11 = relation_dom(identity_relation(A!11))),
% 0.11/0.40 inference(symmetry,[status(thm)],[66])).
% 0.11/0.40 tff(68,plain,
% 0.11/0.40 (identity_relation(A!11) = identity_relation(relation_dom(identity_relation(A!11)))),
% 0.11/0.40 inference(monotonicity,[status(thm)],[67])).
% 0.11/0.40 tff(69,plain,
% 0.11/0.40 (identity_relation(relation_dom(identity_relation(A!11))) = identity_relation(A!11)),
% 0.11/0.40 inference(symmetry,[status(thm)],[68])).
% 0.11/0.40 tff(70,plain,
% 0.11/0.40 (relation_composition(identity_relation(relation_dom(identity_relation(A!11))), function_inverse(identity_relation(A!11))) = relation_composition(identity_relation(A!11), function_inverse(identity_relation(A!11)))),
% 0.11/0.40 inference(monotonicity,[status(thm)],[69])).
% 0.11/0.40 tff(71,plain,
% 0.11/0.40 (relation_composition(identity_relation(relation_dom(identity_relation(A!11))), function_inverse(identity_relation(A!11))) = identity_relation(relation_dom(identity_relation(A!11)))),
% 0.11/0.40 inference(transitivity,[status(thm)],[70, 52])).
% 0.11/0.40 tff(72,plain,
% 0.11/0.40 (^[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))))))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(73,plain,
% 0.11/0.40 (![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)))))))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[72])).
% 0.11/0.40 tff(74,plain,
% 0.11/0.40 (^[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)))))))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(75,plain,
% 0.11/0.40 (![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)))))))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[74])).
% 0.11/0.40 tff(76,plain,
% 0.11/0.40 (![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)))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(77,plain,
% 0.11/0.40 (^[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)))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(78,plain,
% 0.11/0.40 (![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)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[77])).
% 0.11/0.40 tff(79,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')).
% 0.11/0.40 tff(80,plain,
% 0.11/0.40 (![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)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.19/0.40 tff(81,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.19/0.40 tff(82,plain,(
% 0.19/0.40 ![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)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[81])).
% 0.19/0.40 tff(83,plain,
% 0.19/0.40 (![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)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.19/0.40 tff(84,plain,
% 0.19/0.40 (![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)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[83, 73])).
% 0.19/0.40 tff(85,plain,
% 0.19/0.40 (((~![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(identity_relation(A!11))) | (~relation(identity_relation(A!11))) | (~function(identity_relation(A!11))) | (~((~(relation_rng(identity_relation(A!11)) = relation_dom(function_inverse(identity_relation(A!11))))) | (~(relation_dom(identity_relation(A!11)) = relation_rng(function_inverse(identity_relation(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(identity_relation(A!11))) | (~relation(identity_relation(A!11))) | (~function(identity_relation(A!11))) | (~((~(relation_rng(identity_relation(A!11)) = relation_dom(function_inverse(identity_relation(A!11))))) | (~(relation_dom(identity_relation(A!11)) = relation_rng(function_inverse(identity_relation(A!11))))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(86,plain,
% 0.19/0.40 ((~![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(identity_relation(A!11))) | (~relation(identity_relation(A!11))) | (~function(identity_relation(A!11))) | (~((~(relation_rng(identity_relation(A!11)) = relation_dom(function_inverse(identity_relation(A!11))))) | (~(relation_dom(identity_relation(A!11)) = relation_rng(function_inverse(identity_relation(A!11))))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(87,plain,
% 0.19/0.40 ((~![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(identity_relation(A!11))) | (~relation(identity_relation(A!11))) | (~function(identity_relation(A!11))) | (~((~(relation_rng(identity_relation(A!11)) = relation_dom(function_inverse(identity_relation(A!11))))) | (~(relation_dom(identity_relation(A!11)) = relation_rng(function_inverse(identity_relation(A!11)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.19/0.40 tff(88,plain,
% 0.19/0.40 ((~one_to_one(identity_relation(A!11))) | (~relation(identity_relation(A!11))) | (~function(identity_relation(A!11))) | (~((~(relation_rng(identity_relation(A!11)) = relation_dom(function_inverse(identity_relation(A!11))))) | (~(relation_dom(identity_relation(A!11)) = relation_rng(function_inverse(identity_relation(A!11)))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[87, 84])).
% 0.19/0.40 tff(89,plain,
% 0.19/0.40 (~((~(relation_rng(identity_relation(A!11)) = relation_dom(function_inverse(identity_relation(A!11))))) | (~(relation_dom(identity_relation(A!11)) = relation_rng(function_inverse(identity_relation(A!11))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[88, 32, 18, 9])).
% 0.19/0.40 tff(90,plain,
% 0.19/0.40 (((~(relation_rng(identity_relation(A!11)) = relation_dom(function_inverse(identity_relation(A!11))))) | (~(relation_dom(identity_relation(A!11)) = relation_rng(function_inverse(identity_relation(A!11)))))) | (relation_rng(identity_relation(A!11)) = relation_dom(function_inverse(identity_relation(A!11))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(91,plain,
% 0.19/0.40 (relation_rng(identity_relation(A!11)) = relation_dom(function_inverse(identity_relation(A!11)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.19/0.40 tff(92,plain,
% 0.19/0.40 (relation_rng(identity_relation(relation_dom(identity_relation(A!11)))) = relation_rng(identity_relation(A!11))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[69])).
% 0.19/0.40 tff(93,plain,
% 0.19/0.40 (relation_rng(identity_relation(relation_dom(identity_relation(A!11)))) = relation_dom(function_inverse(identity_relation(A!11)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[92, 91])).
% 0.19/0.40 tff(94,plain,
% 0.19/0.40 (((~(relation_dom(identity_relation(A!11)) = A!11)) | (~(relation_rng(identity_relation(A!11)) = A!11))) | (relation_rng(identity_relation(A!11)) = A!11)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(95,plain,
% 0.19/0.40 (relation_rng(identity_relation(A!11)) = A!11),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[94, 64])).
% 0.19/0.40 tff(96,plain,
% 0.19/0.40 (relation_dom(function_inverse(identity_relation(A!11))) = relation_rng(identity_relation(A!11))),
% 0.19/0.40 inference(symmetry,[status(thm)],[91])).
% 0.19/0.40 tff(97,plain,
% 0.19/0.40 (relation_dom(function_inverse(identity_relation(A!11))) = A!11),
% 0.19/0.40 inference(transitivity,[status(thm)],[96, 95])).
% 0.19/0.40 tff(98,plain,
% 0.19/0.40 (identity_relation(relation_dom(function_inverse(identity_relation(A!11)))) = identity_relation(A!11)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[97])).
% 0.19/0.40 tff(99,plain,
% 0.19/0.40 ((function_inverse(identity_relation(A!11)) = identity_relation(relation_dom(function_inverse(identity_relation(A!11))))) <=> (function_inverse(identity_relation(A!11)) = identity_relation(A!11))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[98])).
% 0.19/0.40 tff(100,plain,
% 0.19/0.40 ((function_inverse(identity_relation(A!11)) = identity_relation(A!11)) <=> (function_inverse(identity_relation(A!11)) = identity_relation(relation_dom(function_inverse(identity_relation(A!11)))))),
% 0.19/0.40 inference(symmetry,[status(thm)],[99])).
% 0.19/0.40 tff(101,plain,
% 0.19/0.40 ((~(function_inverse(identity_relation(A!11)) = identity_relation(A!11))) <=> (~(function_inverse(identity_relation(A!11)) = identity_relation(relation_dom(function_inverse(identity_relation(A!11))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[100])).
% 0.19/0.40 tff(102,plain,
% 0.19/0.40 ((~![A: $i] : (function_inverse(identity_relation(A)) = identity_relation(A))) <=> (~![A: $i] : (function_inverse(identity_relation(A)) = identity_relation(A)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(103,axiom,(~![A: $i] : (function_inverse(identity_relation(A)) = identity_relation(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t67_funct_1')).
% 0.19/0.40 tff(104,plain,
% 0.19/0.40 (~![A: $i] : (function_inverse(identity_relation(A)) = identity_relation(A))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.19/0.40 tff(105,plain,
% 0.19/0.40 (~![A: $i] : (function_inverse(identity_relation(A)) = identity_relation(A))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[104, 102])).
% 0.19/0.40 tff(106,plain,
% 0.19/0.40 (~![A: $i] : (function_inverse(identity_relation(A)) = identity_relation(A))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[105, 102])).
% 0.19/0.40 tff(107,plain,
% 0.19/0.40 (~![A: $i] : (function_inverse(identity_relation(A)) = identity_relation(A))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[106, 102])).
% 0.19/0.40 tff(108,plain,(
% 0.19/0.40 ~(function_inverse(identity_relation(A!11)) = identity_relation(A!11))),
% 0.19/0.40 inference(skolemize,[status(sab)],[107])).
% 0.19/0.40 tff(109,plain,
% 0.19/0.40 (~(function_inverse(identity_relation(A!11)) = identity_relation(relation_dom(function_inverse(identity_relation(A!11)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[108, 101])).
% 0.19/0.40 tff(110,plain,
% 0.19/0.40 (function(identity_relation(relation_dom(identity_relation(A!11)))) <=> function(identity_relation(A!11))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[69])).
% 0.19/0.40 tff(111,plain,
% 0.19/0.40 (function(identity_relation(A!11)) <=> function(identity_relation(relation_dom(identity_relation(A!11))))),
% 0.19/0.40 inference(symmetry,[status(thm)],[110])).
% 0.19/0.40 tff(112,plain,
% 0.19/0.40 (function(identity_relation(relation_dom(identity_relation(A!11))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[32, 111])).
% 0.19/0.40 tff(113,plain,
% 0.19/0.40 (relation(identity_relation(relation_dom(identity_relation(A!11)))) <=> relation(identity_relation(A!11))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[69])).
% 0.19/0.40 tff(114,plain,
% 0.19/0.40 (relation(identity_relation(A!11)) <=> relation(identity_relation(relation_dom(identity_relation(A!11))))),
% 0.19/0.40 inference(symmetry,[status(thm)],[113])).
% 0.19/0.40 tff(115,plain,
% 0.19/0.40 (relation(identity_relation(relation_dom(identity_relation(A!11))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[9, 114])).
% 0.19/0.40 tff(116,plain,
% 0.19/0.40 (^[A: $i] : refl(((~relation(A)) | (~function(A)) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = A)))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = A)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(117,plain,
% 0.19/0.40 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = A)))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = A))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[116])).
% 0.19/0.40 tff(118,plain,
% 0.19/0.40 (^[A: $i] : rewrite(((~relation(A)) | (~function(A)) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = A)))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = A)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(119,plain,
% 0.19/0.40 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = A)))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = A))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[118])).
% 0.19/0.40 tff(120,plain,
% 0.19/0.40 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = A)))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = A))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[119, 117])).
% 0.19/0.40 tff(121,plain,
% 0.19/0.40 (^[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(((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A)) <=> (~((~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = A))))), ((~((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A))) <=> (~(~((~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = A))))))), rewrite((~(~((~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = A))))) <=> ((~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = A)))), ((~((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A))) <=> ((~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = A))))), (((B = identity_relation(relation_dom(B))) | (~(relation(B) & function(B))) | (~((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A)))) <=> ((B = identity_relation(relation_dom(B))) | ((~relation(B)) | (~function(B))) | ((~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = A)))))), rewrite(((B = identity_relation(relation_dom(B))) | ((~relation(B)) | (~function(B))) | ((~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = A)))) <=> ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = A)))), (((B = identity_relation(relation_dom(B))) | (~(relation(B) & function(B))) | (~((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A)))) <=> ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = A)))))), (![B: $i] : ((B = identity_relation(relation_dom(B))) | (~(relation(B) & function(B))) | (~((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A)))) <=> ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = A))))), (((~(relation(A) & function(A))) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~(relation(B) & function(B))) | (~((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A))))) <=> (((~relation(A)) | (~function(A))) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = A)))))), rewrite((((~relation(A)) | (~function(A))) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = A)))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = A))))), (((~(relation(A) & function(A))) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~(relation(B) & function(B))) | (~((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = A))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(122,plain,
% 0.19/0.41 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~(relation(B) & function(B))) | (~((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = A))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[121])).
% 0.19/0.41 tff(123,plain,
% 0.19/0.41 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~(relation(B) & function(B))) | (~((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A))))) <=> ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~(relation(B) & function(B))) | (~((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(124,plain,
% 0.19/0.41 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A)) => (B = identity_relation(relation_dom(B)))) <=> ((~((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A))) | (B = identity_relation(relation_dom(B))))), (((relation(B) & function(B)) => (((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A)) => (B = identity_relation(relation_dom(B))))) <=> ((relation(B) & function(B)) => ((~((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A))) | (B = identity_relation(relation_dom(B))))))), rewrite(((relation(B) & function(B)) => ((~((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A))) | (B = identity_relation(relation_dom(B))))) <=> ((B = identity_relation(relation_dom(B))) | (~(relation(B) & function(B))) | (~((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A))))), (((relation(B) & function(B)) => (((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A)) => (B = identity_relation(relation_dom(B))))) <=> ((B = identity_relation(relation_dom(B))) | (~(relation(B) & function(B))) | (~((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A))))))), (![B: $i] : ((relation(B) & function(B)) => (((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A)) => (B = identity_relation(relation_dom(B))))) <=> ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~(relation(B) & function(B))) | (~((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A)))))), (((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => (((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A)) => (B = identity_relation(relation_dom(B)))))) <=> ((relation(A) & function(A)) => ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~(relation(B) & function(B))) | (~((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A))))))), rewrite(((relation(A) & function(A)) => ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~(relation(B) & function(B))) | (~((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A))))) <=> ((~(relation(A) & function(A))) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~(relation(B) & function(B))) | (~((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A)))))), (((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => (((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A)) => (B = identity_relation(relation_dom(B)))))) <=> ((~(relation(A) & function(A))) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~(relation(B) & function(B))) | (~((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A)))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(125,plain,
% 0.19/0.41 (![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => (((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A)) => (B = identity_relation(relation_dom(B)))))) <=> ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~(relation(B) & function(B))) | (~((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A)))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[124])).
% 0.19/0.41 tff(126,axiom,(![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => (((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A)) => (B = identity_relation(relation_dom(B))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t44_funct_1')).
% 0.19/0.41 tff(127,plain,
% 0.19/0.41 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~(relation(B) & function(B))) | (~((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.19/0.41 tff(128,plain,
% 0.19/0.41 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~(relation(B) & function(B))) | (~((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[127, 123])).
% 0.19/0.41 tff(129,plain,(
% 0.19/0.41 ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~(relation(B) & function(B))) | (~((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A)))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[128])).
% 0.19/0.41 tff(130,plain,
% 0.19/0.41 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = A))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[129, 122])).
% 0.19/0.41 tff(131,plain,
% 0.19/0.41 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = A))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[130, 120])).
% 0.19/0.41 tff(132,plain,
% 0.19/0.41 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = A))))) | ((~relation(identity_relation(relation_dom(identity_relation(A!11))))) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(identity_relation(relation_dom(identity_relation(A!11)))) = relation_dom(B))) | (~(relation_composition(identity_relation(relation_dom(identity_relation(A!11))), B) = identity_relation(relation_dom(identity_relation(A!11)))))) | (~function(identity_relation(relation_dom(identity_relation(A!11))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = A))))) | (~relation(identity_relation(relation_dom(identity_relation(A!11))))) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(identity_relation(relation_dom(identity_relation(A!11)))) = relation_dom(B))) | (~(relation_composition(identity_relation(relation_dom(identity_relation(A!11))), B) = identity_relation(relation_dom(identity_relation(A!11)))))) | (~function(identity_relation(relation_dom(identity_relation(A!11))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(133,plain,
% 0.19/0.41 (((~relation(identity_relation(relation_dom(identity_relation(A!11))))) | (~function(identity_relation(relation_dom(identity_relation(A!11))))) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(identity_relation(relation_dom(identity_relation(A!11)))) = relation_dom(B))) | (~(relation_composition(identity_relation(relation_dom(identity_relation(A!11))), B) = identity_relation(relation_dom(identity_relation(A!11))))))) <=> ((~relation(identity_relation(relation_dom(identity_relation(A!11))))) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(identity_relation(relation_dom(identity_relation(A!11)))) = relation_dom(B))) | (~(relation_composition(identity_relation(relation_dom(identity_relation(A!11))), B) = identity_relation(relation_dom(identity_relation(A!11)))))) | (~function(identity_relation(relation_dom(identity_relation(A!11))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(134,plain,
% 0.19/0.41 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = A))))) | ((~relation(identity_relation(relation_dom(identity_relation(A!11))))) | (~function(identity_relation(relation_dom(identity_relation(A!11))))) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(identity_relation(relation_dom(identity_relation(A!11)))) = relation_dom(B))) | (~(relation_composition(identity_relation(relation_dom(identity_relation(A!11))), B) = identity_relation(relation_dom(identity_relation(A!11)))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = A))))) | ((~relation(identity_relation(relation_dom(identity_relation(A!11))))) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(identity_relation(relation_dom(identity_relation(A!11)))) = relation_dom(B))) | (~(relation_composition(identity_relation(relation_dom(identity_relation(A!11))), B) = identity_relation(relation_dom(identity_relation(A!11)))))) | (~function(identity_relation(relation_dom(identity_relation(A!11)))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[133])).
% 0.19/0.41 tff(135,plain,
% 0.19/0.41 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = A))))) | ((~relation(identity_relation(relation_dom(identity_relation(A!11))))) | (~function(identity_relation(relation_dom(identity_relation(A!11))))) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(identity_relation(relation_dom(identity_relation(A!11)))) = relation_dom(B))) | (~(relation_composition(identity_relation(relation_dom(identity_relation(A!11))), B) = identity_relation(relation_dom(identity_relation(A!11)))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = A))))) | (~relation(identity_relation(relation_dom(identity_relation(A!11))))) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(identity_relation(relation_dom(identity_relation(A!11)))) = relation_dom(B))) | (~(relation_composition(identity_relation(relation_dom(identity_relation(A!11))), B) = identity_relation(relation_dom(identity_relation(A!11)))))) | (~function(identity_relation(relation_dom(identity_relation(A!11))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[134, 132])).
% 0.19/0.41 tff(136,plain,
% 0.19/0.41 ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = A))))) | ((~relation(identity_relation(relation_dom(identity_relation(A!11))))) | (~function(identity_relation(relation_dom(identity_relation(A!11))))) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(identity_relation(relation_dom(identity_relation(A!11)))) = relation_dom(B))) | (~(relation_composition(identity_relation(relation_dom(identity_relation(A!11))), B) = identity_relation(relation_dom(identity_relation(A!11)))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(137,plain,
% 0.19/0.41 ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = A))))) | (~relation(identity_relation(relation_dom(identity_relation(A!11))))) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(identity_relation(relation_dom(identity_relation(A!11)))) = relation_dom(B))) | (~(relation_composition(identity_relation(relation_dom(identity_relation(A!11))), B) = identity_relation(relation_dom(identity_relation(A!11)))))) | (~function(identity_relation(relation_dom(identity_relation(A!11)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.19/0.41 tff(138,plain,
% 0.19/0.41 ((~relation(identity_relation(relation_dom(identity_relation(A!11))))) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(identity_relation(relation_dom(identity_relation(A!11)))) = relation_dom(B))) | (~(relation_composition(identity_relation(relation_dom(identity_relation(A!11))), B) = identity_relation(relation_dom(identity_relation(A!11)))))) | (~function(identity_relation(relation_dom(identity_relation(A!11)))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[137, 131])).
% 0.19/0.41 tff(139,plain,
% 0.19/0.41 (![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(identity_relation(relation_dom(identity_relation(A!11)))) = relation_dom(B))) | (~(relation_composition(identity_relation(relation_dom(identity_relation(A!11))), B) = identity_relation(relation_dom(identity_relation(A!11))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[138, 115, 112])).
% 0.19/0.41 tff(140,plain,
% 0.19/0.41 (^[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)))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(141,plain,
% 0.19/0.41 (![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))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[140])).
% 0.19/0.41 tff(142,plain,
% 0.19/0.41 (^[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))))), 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))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(143,plain,
% 0.19/0.41 (![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))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[142])).
% 0.19/0.41 tff(144,plain,
% 0.19/0.41 (![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))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(145,plain,
% 0.19/0.41 (^[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)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(146,plain,
% 0.19/0.41 (![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))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[145])).
% 0.19/0.41 tff(147,axiom,(![A: $i] : ((relation(A) & function(A)) => (relation(function_inverse(A)) & function(function_inverse(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k2_funct_1')).
% 0.19/0.41 tff(148,plain,
% 0.19/0.41 (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.19/0.41 tff(149,plain,
% 0.19/0.41 (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[148, 144])).
% 0.19/0.41 tff(150,plain,(
% 0.19/0.41 ![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[149])).
% 0.19/0.41 tff(151,plain,
% 0.19/0.41 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[150, 143])).
% 0.19/0.41 tff(152,plain,
% 0.19/0.41 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[151, 141])).
% 0.19/0.41 tff(153,plain,
% 0.19/0.41 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | ((~relation(identity_relation(A!11))) | (~function(identity_relation(A!11))) | (~((~relation(function_inverse(identity_relation(A!11)))) | (~function(function_inverse(identity_relation(A!11)))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | (~relation(identity_relation(A!11))) | (~function(identity_relation(A!11))) | (~((~relation(function_inverse(identity_relation(A!11)))) | (~function(function_inverse(identity_relation(A!11)))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(154,plain,
% 0.19/0.41 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | ((~relation(identity_relation(A!11))) | (~function(identity_relation(A!11))) | (~((~relation(function_inverse(identity_relation(A!11)))) | (~function(function_inverse(identity_relation(A!11)))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(155,plain,
% 0.19/0.41 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | (~relation(identity_relation(A!11))) | (~function(identity_relation(A!11))) | (~((~relation(function_inverse(identity_relation(A!11)))) | (~function(function_inverse(identity_relation(A!11))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.19/0.41 tff(156,plain,
% 0.19/0.41 ((~relation(identity_relation(A!11))) | (~function(identity_relation(A!11))) | (~((~relation(function_inverse(identity_relation(A!11)))) | (~function(function_inverse(identity_relation(A!11))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[155, 152])).
% 0.19/0.41 tff(157,plain,
% 0.19/0.41 (~((~relation(function_inverse(identity_relation(A!11)))) | (~function(function_inverse(identity_relation(A!11)))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[156, 32, 9])).
% 0.19/0.41 tff(158,plain,
% 0.19/0.41 (((~relation(function_inverse(identity_relation(A!11)))) | (~function(function_inverse(identity_relation(A!11))))) | function(function_inverse(identity_relation(A!11)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(159,plain,
% 0.19/0.41 (function(function_inverse(identity_relation(A!11)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[158, 157])).
% 0.19/0.41 tff(160,plain,
% 0.19/0.41 (((~relation(function_inverse(identity_relation(A!11)))) | (~function(function_inverse(identity_relation(A!11))))) | relation(function_inverse(identity_relation(A!11)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(161,plain,
% 0.19/0.41 (relation(function_inverse(identity_relation(A!11)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[160, 157])).
% 0.19/0.41 tff(162,plain,
% 0.19/0.41 (((~![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(identity_relation(relation_dom(identity_relation(A!11)))) = relation_dom(B))) | (~(relation_composition(identity_relation(relation_dom(identity_relation(A!11))), B) = identity_relation(relation_dom(identity_relation(A!11))))))) | ((~relation(function_inverse(identity_relation(A!11)))) | (~function(function_inverse(identity_relation(A!11)))) | (function_inverse(identity_relation(A!11)) = identity_relation(relation_dom(function_inverse(identity_relation(A!11))))) | (~(relation_rng(identity_relation(relation_dom(identity_relation(A!11)))) = relation_dom(function_inverse(identity_relation(A!11))))) | (~(relation_composition(identity_relation(relation_dom(identity_relation(A!11))), function_inverse(identity_relation(A!11))) = identity_relation(relation_dom(identity_relation(A!11))))))) <=> ((~![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(identity_relation(relation_dom(identity_relation(A!11)))) = relation_dom(B))) | (~(relation_composition(identity_relation(relation_dom(identity_relation(A!11))), B) = identity_relation(relation_dom(identity_relation(A!11))))))) | (~relation(function_inverse(identity_relation(A!11)))) | (~function(function_inverse(identity_relation(A!11)))) | (function_inverse(identity_relation(A!11)) = identity_relation(relation_dom(function_inverse(identity_relation(A!11))))) | (~(relation_rng(identity_relation(relation_dom(identity_relation(A!11)))) = relation_dom(function_inverse(identity_relation(A!11))))) | (~(relation_composition(identity_relation(relation_dom(identity_relation(A!11))), function_inverse(identity_relation(A!11))) = identity_relation(relation_dom(identity_relation(A!11))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(163,plain,
% 0.19/0.42 (((function_inverse(identity_relation(A!11)) = identity_relation(relation_dom(function_inverse(identity_relation(A!11))))) | (~relation(function_inverse(identity_relation(A!11)))) | (~function(function_inverse(identity_relation(A!11)))) | (~(relation_rng(identity_relation(relation_dom(identity_relation(A!11)))) = relation_dom(function_inverse(identity_relation(A!11))))) | (~(relation_composition(identity_relation(relation_dom(identity_relation(A!11))), function_inverse(identity_relation(A!11))) = identity_relation(relation_dom(identity_relation(A!11)))))) <=> ((~relation(function_inverse(identity_relation(A!11)))) | (~function(function_inverse(identity_relation(A!11)))) | (function_inverse(identity_relation(A!11)) = identity_relation(relation_dom(function_inverse(identity_relation(A!11))))) | (~(relation_rng(identity_relation(relation_dom(identity_relation(A!11)))) = relation_dom(function_inverse(identity_relation(A!11))))) | (~(relation_composition(identity_relation(relation_dom(identity_relation(A!11))), function_inverse(identity_relation(A!11))) = identity_relation(relation_dom(identity_relation(A!11))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(164,plain,
% 0.19/0.42 (((~![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(identity_relation(relation_dom(identity_relation(A!11)))) = relation_dom(B))) | (~(relation_composition(identity_relation(relation_dom(identity_relation(A!11))), B) = identity_relation(relation_dom(identity_relation(A!11))))))) | ((function_inverse(identity_relation(A!11)) = identity_relation(relation_dom(function_inverse(identity_relation(A!11))))) | (~relation(function_inverse(identity_relation(A!11)))) | (~function(function_inverse(identity_relation(A!11)))) | (~(relation_rng(identity_relation(relation_dom(identity_relation(A!11)))) = relation_dom(function_inverse(identity_relation(A!11))))) | (~(relation_composition(identity_relation(relation_dom(identity_relation(A!11))), function_inverse(identity_relation(A!11))) = identity_relation(relation_dom(identity_relation(A!11))))))) <=> ((~![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(identity_relation(relation_dom(identity_relation(A!11)))) = relation_dom(B))) | (~(relation_composition(identity_relation(relation_dom(identity_relation(A!11))), B) = identity_relation(relation_dom(identity_relation(A!11))))))) | ((~relation(function_inverse(identity_relation(A!11)))) | (~function(function_inverse(identity_relation(A!11)))) | (function_inverse(identity_relation(A!11)) = identity_relation(relation_dom(function_inverse(identity_relation(A!11))))) | (~(relation_rng(identity_relation(relation_dom(identity_relation(A!11)))) = relation_dom(function_inverse(identity_relation(A!11))))) | (~(relation_composition(identity_relation(relation_dom(identity_relation(A!11))), function_inverse(identity_relation(A!11))) = identity_relation(relation_dom(identity_relation(A!11)))))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[163])).
% 0.19/0.42 tff(165,plain,
% 0.19/0.42 (((~![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(identity_relation(relation_dom(identity_relation(A!11)))) = relation_dom(B))) | (~(relation_composition(identity_relation(relation_dom(identity_relation(A!11))), B) = identity_relation(relation_dom(identity_relation(A!11))))))) | ((function_inverse(identity_relation(A!11)) = identity_relation(relation_dom(function_inverse(identity_relation(A!11))))) | (~relation(function_inverse(identity_relation(A!11)))) | (~function(function_inverse(identity_relation(A!11)))) | (~(relation_rng(identity_relation(relation_dom(identity_relation(A!11)))) = relation_dom(function_inverse(identity_relation(A!11))))) | (~(relation_composition(identity_relation(relation_dom(identity_relation(A!11))), function_inverse(identity_relation(A!11))) = identity_relation(relation_dom(identity_relation(A!11))))))) <=> ((~![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(identity_relation(relation_dom(identity_relation(A!11)))) = relation_dom(B))) | (~(relation_composition(identity_relation(relation_dom(identity_relation(A!11))), B) = identity_relation(relation_dom(identity_relation(A!11))))))) | (~relation(function_inverse(identity_relation(A!11)))) | (~function(function_inverse(identity_relation(A!11)))) | (function_inverse(identity_relation(A!11)) = identity_relation(relation_dom(function_inverse(identity_relation(A!11))))) | (~(relation_rng(identity_relation(relation_dom(identity_relation(A!11)))) = relation_dom(function_inverse(identity_relation(A!11))))) | (~(relation_composition(identity_relation(relation_dom(identity_relation(A!11))), function_inverse(identity_relation(A!11))) = identity_relation(relation_dom(identity_relation(A!11))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[164, 162])).
% 0.19/0.42 tff(166,plain,
% 0.19/0.42 ((~![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(identity_relation(relation_dom(identity_relation(A!11)))) = relation_dom(B))) | (~(relation_composition(identity_relation(relation_dom(identity_relation(A!11))), B) = identity_relation(relation_dom(identity_relation(A!11))))))) | ((function_inverse(identity_relation(A!11)) = identity_relation(relation_dom(function_inverse(identity_relation(A!11))))) | (~relation(function_inverse(identity_relation(A!11)))) | (~function(function_inverse(identity_relation(A!11)))) | (~(relation_rng(identity_relation(relation_dom(identity_relation(A!11)))) = relation_dom(function_inverse(identity_relation(A!11))))) | (~(relation_composition(identity_relation(relation_dom(identity_relation(A!11))), function_inverse(identity_relation(A!11))) = identity_relation(relation_dom(identity_relation(A!11))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(167,plain,
% 0.19/0.42 ((~![B: $i] : ((B = identity_relation(relation_dom(B))) | (~relation(B)) | (~function(B)) | (~(relation_rng(identity_relation(relation_dom(identity_relation(A!11)))) = relation_dom(B))) | (~(relation_composition(identity_relation(relation_dom(identity_relation(A!11))), B) = identity_relation(relation_dom(identity_relation(A!11))))))) | (~relation(function_inverse(identity_relation(A!11)))) | (~function(function_inverse(identity_relation(A!11)))) | (function_inverse(identity_relation(A!11)) = identity_relation(relation_dom(function_inverse(identity_relation(A!11))))) | (~(relation_rng(identity_relation(relation_dom(identity_relation(A!11)))) = relation_dom(function_inverse(identity_relation(A!11))))) | (~(relation_composition(identity_relation(relation_dom(identity_relation(A!11))), function_inverse(identity_relation(A!11))) = identity_relation(relation_dom(identity_relation(A!11)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.19/0.42 tff(168,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[167, 161, 159, 139, 109, 93, 71])).
% 0.19/0.42 % SZS output end Proof
% 0.19/0.42 % E exiting
%------------------------------------------------------------------------------