%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU028+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:26:48 AM UTC 2025
% Result : Theorem 1.31s 1.48s
% Output : Proof 1.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU028+1 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n012.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 05:56:25 EDT 2025
% 0.13/0.35 % CPUTime :
% 1.31/1.48 % SZS status Theorem
% 1.31/1.48 % SZS output start Proof
% 1.31/1.48 tff(tptp_fun_C_11_type, type, (
% 1.31/1.48 tptp_fun_C_11: ( $i * $i ) > $i)).
% 1.31/1.48 tff(relation_dom_type, type, (
% 1.31/1.48 relation_dom: $i > $i)).
% 1.31/1.48 tff(tptp_fun_A_12_type, type, (
% 1.31/1.48 tptp_fun_A_12: $i)).
% 1.31/1.48 tff(relation_composition_type, type, (
% 1.31/1.48 relation_composition: ( $i * $i ) > $i)).
% 1.31/1.48 tff(function_inverse_type, type, (
% 1.31/1.48 function_inverse: $i > $i)).
% 1.31/1.48 tff(apply_type, type, (
% 1.31/1.48 apply: ( $i * $i ) > $i)).
% 1.31/1.48 tff(in_type, type, (
% 1.31/1.48 in: ( $i * $i ) > $o)).
% 1.31/1.48 tff(identity_relation_type, type, (
% 1.31/1.48 identity_relation: $i > $i)).
% 1.31/1.48 tff(function_type, type, (
% 1.31/1.48 function: $i > $o)).
% 1.31/1.48 tff(relation_type, type, (
% 1.31/1.48 relation: $i > $o)).
% 1.31/1.48 tff(one_to_one_type, type, (
% 1.31/1.48 one_to_one: $i > $o)).
% 1.31/1.48 tff(relation_rng_type, type, (
% 1.31/1.48 relation_rng: $i > $i)).
% 1.31/1.48 tff(1,plain,
% 1.31/1.48 ((~(((relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12))) & (relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12)))) | (~(relation(A!12) & function(A!12))) | (~one_to_one(A!12)))) <=> (~(((relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12))) & (relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12)))) | (~(relation(A!12) & function(A!12))) | (~one_to_one(A!12))))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(2,plain,
% 1.31/1.48 ((~![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))))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(3,plain,
% 1.31/1.48 ((~![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))))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(4,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')).
% 1.31/1.48 tff(5,plain,
% 1.31/1.48 (~![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)))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[4, 3])).
% 1.31/1.48 tff(6,plain,
% 1.31/1.48 (~![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)))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[5, 2])).
% 1.31/1.48 tff(7,plain,
% 1.31/1.48 (~![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)))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[6, 2])).
% 1.31/1.48 tff(8,plain,
% 1.31/1.48 (~![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)))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[7, 2])).
% 1.31/1.48 tff(9,plain,(
% 1.31/1.48 ~(((relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12))) & (relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12)))) | (~(relation(A!12) & function(A!12))) | (~one_to_one(A!12)))),
% 1.31/1.48 inference(skolemize,[status(sab)],[8])).
% 1.31/1.48 tff(10,plain,
% 1.31/1.48 (~(((relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12))) & (relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12)))) | (~(relation(A!12) & function(A!12))) | (~one_to_one(A!12)))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[9, 1])).
% 1.31/1.48 tff(11,plain,
% 1.31/1.48 (relation(A!12) & function(A!12)),
% 1.31/1.48 inference(or_elim,[status(thm)],[10])).
% 1.31/1.48 tff(12,plain,
% 1.31/1.48 (function(A!12)),
% 1.31/1.48 inference(and_elim,[status(thm)],[11])).
% 1.31/1.48 tff(13,plain,
% 1.31/1.48 (relation(A!12)),
% 1.31/1.48 inference(and_elim,[status(thm)],[11])).
% 1.31/1.48 tff(14,plain,
% 1.31/1.48 (^[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)))))))),
% 1.31/1.48 inference(bind,[status(th)],[])).
% 1.31/1.48 tff(15,plain,
% 1.31/1.48 (![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))))))),
% 1.31/1.48 inference(quant_intro,[status(thm)],[14])).
% 1.31/1.48 tff(16,plain,
% 1.31/1.48 (^[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))))))))),
% 1.31/1.48 inference(bind,[status(th)],[])).
% 1.31/1.48 tff(17,plain,
% 1.31/1.48 (![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))))))),
% 1.31/1.48 inference(quant_intro,[status(thm)],[16])).
% 1.31/1.48 tff(18,plain,
% 1.31/1.48 (![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))))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(19,plain,
% 1.31/1.48 (^[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)))))),
% 1.31/1.48 inference(bind,[status(th)],[])).
% 1.31/1.48 tff(20,plain,
% 1.31/1.48 (![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))))),
% 1.31/1.48 inference(quant_intro,[status(thm)],[19])).
% 1.31/1.48 tff(21,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')).
% 1.31/1.48 tff(22,plain,
% 1.31/1.48 (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[21, 20])).
% 1.31/1.48 tff(23,plain,
% 1.31/1.48 (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[22, 18])).
% 1.31/1.48 tff(24,plain,(
% 1.31/1.48 ![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 1.31/1.48 inference(skolemize,[status(sab)],[23])).
% 1.31/1.48 tff(25,plain,
% 1.31/1.48 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[24, 17])).
% 1.31/1.48 tff(26,plain,
% 1.31/1.48 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[25, 15])).
% 1.31/1.48 tff(27,plain,
% 1.31/1.48 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | ((~relation(A!12)) | (~function(A!12)) | (~((~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | (~relation(A!12)) | (~function(A!12)) | (~((~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))))))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(28,plain,
% 1.31/1.48 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | ((~relation(A!12)) | (~function(A!12)) | (~((~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))))))),
% 1.31/1.48 inference(quant_inst,[status(thm)],[])).
% 1.31/1.48 tff(29,plain,
% 1.31/1.48 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | (~relation(A!12)) | (~function(A!12)) | (~((~relation(function_inverse(A!12))) | (~function(function_inverse(A!12)))))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[28, 27])).
% 1.31/1.48 tff(30,plain,
% 1.31/1.48 (~((~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))))),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[29, 26, 13, 12])).
% 1.31/1.48 tff(31,plain,
% 1.31/1.48 (((~relation(function_inverse(A!12))) | (~function(function_inverse(A!12)))) | relation(function_inverse(A!12))),
% 1.31/1.48 inference(tautology,[status(thm)],[])).
% 1.31/1.48 tff(32,plain,
% 1.31/1.48 (relation(function_inverse(A!12))),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[31, 30])).
% 1.31/1.48 tff(33,plain,
% 1.31/1.48 (((~relation(function_inverse(A!12))) | (~function(function_inverse(A!12)))) | function(function_inverse(A!12))),
% 1.31/1.48 inference(tautology,[status(thm)],[])).
% 1.31/1.48 tff(34,plain,
% 1.31/1.48 (function(function_inverse(A!12))),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[33, 30])).
% 1.31/1.48 tff(35,plain,
% 1.31/1.48 (^[A: $i, B: $i] : refl(((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B)))))) <=> ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B)))))))),
% 1.31/1.48 inference(bind,[status(th)],[])).
% 1.31/1.48 tff(36,plain,
% 1.31/1.48 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B)))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))),
% 1.31/1.48 inference(quant_intro,[status(thm)],[35])).
% 1.31/1.48 tff(37,plain,
% 1.31/1.48 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(A) & function(A) & relation(B) & function(B)) <=> (~((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A))))), ((~(relation(A) & function(A) & relation(B) & function(B))) <=> (~(~((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A))))))), rewrite((~(~((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A))))) <=> ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)))), ((~(relation(A) & function(A) & relation(B) & function(B))) <=> ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A))))), rewrite((relation(relation_composition(A, B)) & function(relation_composition(A, B))) <=> (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B)))))), (((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> (((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A))) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B)))))))), rewrite((((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A))) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B)))))) <=> ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))), (((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))))),
% 1.31/1.48 inference(bind,[status(th)],[])).
% 1.31/1.48 tff(38,plain,
% 1.31/1.48 (![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))),
% 1.31/1.48 inference(quant_intro,[status(thm)],[37])).
% 1.31/1.48 tff(39,plain,
% 1.31/1.48 (![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> ![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(40,plain,
% 1.31/1.48 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((relation(A) & function(A)) & relation(B)) <=> (relation(A) & function(A) & relation(B))), ((((relation(A) & function(A)) & relation(B)) & function(B)) <=> ((relation(A) & function(A) & relation(B)) & function(B)))), rewrite(((relation(A) & function(A) & relation(B)) & function(B)) <=> (relation(A) & function(A) & relation(B) & function(B))), ((((relation(A) & function(A)) & relation(B)) & function(B)) <=> (relation(A) & function(A) & relation(B) & function(B)))), (((((relation(A) & function(A)) & relation(B)) & function(B)) => (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> ((relation(A) & function(A) & relation(B) & function(B)) => (relation(relation_composition(A, B)) & function(relation_composition(A, B)))))), rewrite(((relation(A) & function(A) & relation(B) & function(B)) => (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))), (((((relation(A) & function(A)) & relation(B)) & function(B)) => (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))))),
% 1.31/1.48 inference(bind,[status(th)],[])).
% 1.31/1.48 tff(41,plain,
% 1.31/1.48 (![A: $i, B: $i] : ((((relation(A) & function(A)) & relation(B)) & function(B)) => (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> ![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))),
% 1.31/1.48 inference(quant_intro,[status(thm)],[40])).
% 1.31/1.48 tff(42,axiom,(![A: $i, B: $i] : ((((relation(A) & function(A)) & relation(B)) & function(B)) => (relation(relation_composition(A, B)) & function(relation_composition(A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_funct_1')).
% 1.31/1.48 tff(43,plain,
% 1.31/1.48 (![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[42, 41])).
% 1.31/1.48 tff(44,plain,
% 1.31/1.48 (![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[43, 39])).
% 1.31/1.48 tff(45,plain,(
% 1.31/1.48 ![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))),
% 1.31/1.48 inference(skolemize,[status(sab)],[44])).
% 1.31/1.48 tff(46,plain,
% 1.31/1.48 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[45, 38])).
% 1.31/1.48 tff(47,plain,
% 1.31/1.48 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[46, 36])).
% 1.31/1.48 tff(48,plain,
% 1.31/1.48 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | ((~relation(A!12)) | (~function(A!12)) | (~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))) | (~((~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!12)))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | (~relation(A!12)) | (~function(A!12)) | (~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))) | (~((~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!12)))))))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(49,plain,
% 1.31/1.48 (((~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))) | (~relation(A!12)) | (~function(A!12)) | (~((~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!12))))))) <=> ((~relation(A!12)) | (~function(A!12)) | (~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))) | (~((~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!12)))))))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(50,plain,
% 1.31/1.48 ((~((~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!12)))))) <=> (~((~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!12))))))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(51,plain,
% 1.31/1.48 (((~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))) | (~relation(A!12)) | (~function(A!12)) | (~((~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!12))))))) <=> ((~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))) | (~relation(A!12)) | (~function(A!12)) | (~((~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!12)))))))),
% 1.31/1.48 inference(monotonicity,[status(thm)],[50])).
% 1.31/1.48 tff(52,plain,
% 1.31/1.48 (((~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))) | (~relation(A!12)) | (~function(A!12)) | (~((~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!12))))))) <=> ((~relation(A!12)) | (~function(A!12)) | (~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))) | (~((~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!12)))))))),
% 1.31/1.48 inference(transitivity,[status(thm)],[51, 49])).
% 1.31/1.48 tff(53,plain,
% 1.31/1.48 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | ((~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))) | (~relation(A!12)) | (~function(A!12)) | (~((~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!12)))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | ((~relation(A!12)) | (~function(A!12)) | (~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))) | (~((~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!12))))))))),
% 1.31/1.48 inference(monotonicity,[status(thm)],[52])).
% 1.31/1.48 tff(54,plain,
% 1.31/1.48 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | ((~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))) | (~relation(A!12)) | (~function(A!12)) | (~((~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!12)))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | (~relation(A!12)) | (~function(A!12)) | (~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))) | (~((~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!12)))))))),
% 1.31/1.48 inference(transitivity,[status(thm)],[53, 48])).
% 1.31/1.48 tff(55,plain,
% 1.31/1.48 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | ((~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))) | (~relation(A!12)) | (~function(A!12)) | (~((~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!12)))))))),
% 1.31/1.48 inference(quant_inst,[status(thm)],[])).
% 1.31/1.48 tff(56,plain,
% 1.31/1.48 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | (~relation(A!12)) | (~function(A!12)) | (~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))) | (~((~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!12))))))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[55, 54])).
% 1.31/1.48 tff(57,plain,
% 1.31/1.48 ((~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))) | (~((~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!12))))))),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[56, 47, 13, 12])).
% 1.31/1.48 tff(58,plain,
% 1.31/1.48 (~((~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!12)))))),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[57, 34, 32])).
% 1.31/1.48 tff(59,plain,
% 1.31/1.48 (((~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!12))))) | function(relation_composition(A!12, function_inverse(A!12)))),
% 1.31/1.48 inference(tautology,[status(thm)],[])).
% 1.31/1.48 tff(60,plain,
% 1.31/1.48 (function(relation_composition(A!12, function_inverse(A!12)))),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[59, 58])).
% 1.31/1.48 tff(61,plain,
% 1.31/1.48 (^[A: $i, B: $i] : refl((relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A))) <=> (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A))))),
% 1.31/1.48 inference(bind,[status(th)],[])).
% 1.31/1.48 tff(62,plain,
% 1.31/1.48 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A))) <=> ![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))),
% 1.31/1.48 inference(quant_intro,[status(thm)],[61])).
% 1.31/1.48 tff(63,plain,
% 1.31/1.48 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(A) & relation(B)) <=> (~((~relation(B)) | (~relation(A))))), ((~(relation(A) & relation(B))) <=> (~(~((~relation(B)) | (~relation(A))))))), rewrite((~(~((~relation(B)) | (~relation(A))))) <=> ((~relation(B)) | (~relation(A)))), ((~(relation(A) & relation(B))) <=> ((~relation(B)) | (~relation(A))))), ((relation(relation_composition(A, B)) | (~(relation(A) & relation(B)))) <=> (relation(relation_composition(A, B)) | ((~relation(B)) | (~relation(A)))))), rewrite((relation(relation_composition(A, B)) | ((~relation(B)) | (~relation(A)))) <=> (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))), ((relation(relation_composition(A, B)) | (~(relation(A) & relation(B)))) <=> (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))))),
% 1.31/1.48 inference(bind,[status(th)],[])).
% 1.31/1.48 tff(64,plain,
% 1.31/1.48 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B)))) <=> ![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))),
% 1.31/1.48 inference(quant_intro,[status(thm)],[63])).
% 1.31/1.48 tff(65,plain,
% 1.31/1.48 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B)))) <=> ![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(66,plain,
% 1.31/1.48 (^[A: $i, B: $i] : rewrite(((relation(A) & relation(B)) => relation(relation_composition(A, B))) <=> (relation(relation_composition(A, B)) | (~(relation(A) & relation(B)))))),
% 1.31/1.48 inference(bind,[status(th)],[])).
% 1.31/1.48 tff(67,plain,
% 1.31/1.48 (![A: $i, B: $i] : ((relation(A) & relation(B)) => relation(relation_composition(A, B))) <=> ![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 1.31/1.48 inference(quant_intro,[status(thm)],[66])).
% 1.31/1.48 tff(68,axiom,(![A: $i, B: $i] : ((relation(A) & relation(B)) => relation(relation_composition(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k5_relat_1')).
% 1.31/1.48 tff(69,plain,
% 1.31/1.48 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[68, 67])).
% 1.31/1.48 tff(70,plain,
% 1.31/1.48 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[69, 65])).
% 1.31/1.48 tff(71,plain,(
% 1.31/1.48 ![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 1.31/1.48 inference(skolemize,[status(sab)],[70])).
% 1.31/1.48 tff(72,plain,
% 1.31/1.48 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[71, 64])).
% 1.31/1.48 tff(73,plain,
% 1.31/1.48 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[72, 62])).
% 1.31/1.48 tff(74,plain,
% 1.31/1.48 (((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | ((~relation(A!12)) | relation(relation_composition(A!12, function_inverse(A!12))) | (~relation(function_inverse(A!12))))) <=> ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (~relation(A!12)) | relation(relation_composition(A!12, function_inverse(A!12))) | (~relation(function_inverse(A!12))))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(75,plain,
% 1.31/1.48 ((relation(relation_composition(A!12, function_inverse(A!12))) | (~relation(function_inverse(A!12))) | (~relation(A!12))) <=> ((~relation(A!12)) | relation(relation_composition(A!12, function_inverse(A!12))) | (~relation(function_inverse(A!12))))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(76,plain,
% 1.31/1.48 (((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (relation(relation_composition(A!12, function_inverse(A!12))) | (~relation(function_inverse(A!12))) | (~relation(A!12)))) <=> ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | ((~relation(A!12)) | relation(relation_composition(A!12, function_inverse(A!12))) | (~relation(function_inverse(A!12)))))),
% 1.31/1.48 inference(monotonicity,[status(thm)],[75])).
% 1.31/1.48 tff(77,plain,
% 1.31/1.48 (((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (relation(relation_composition(A!12, function_inverse(A!12))) | (~relation(function_inverse(A!12))) | (~relation(A!12)))) <=> ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (~relation(A!12)) | relation(relation_composition(A!12, function_inverse(A!12))) | (~relation(function_inverse(A!12))))),
% 1.31/1.48 inference(transitivity,[status(thm)],[76, 74])).
% 1.31/1.48 tff(78,plain,
% 1.31/1.48 ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (relation(relation_composition(A!12, function_inverse(A!12))) | (~relation(function_inverse(A!12))) | (~relation(A!12)))),
% 1.31/1.48 inference(quant_inst,[status(thm)],[])).
% 1.31/1.48 tff(79,plain,
% 1.31/1.48 ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (~relation(A!12)) | relation(relation_composition(A!12, function_inverse(A!12))) | (~relation(function_inverse(A!12)))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[78, 77])).
% 1.31/1.48 tff(80,plain,
% 1.31/1.48 (relation(relation_composition(A!12, function_inverse(A!12))) | (~relation(function_inverse(A!12)))),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[79, 73, 13])).
% 1.31/1.48 tff(81,plain,
% 1.31/1.48 (relation(relation_composition(A!12, function_inverse(A!12)))),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[80, 32])).
% 1.31/1.48 tff(82,plain,
% 1.31/1.48 (^[A: $i, B: $i] : trans(monotonicity(rewrite((~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))))) <=> (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))))))), (((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))))))))), rewrite(((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))), (((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))))),
% 1.31/1.49 inference(bind,[status(th)],[])).
% 1.31/1.49 tff(83,plain,
% 1.31/1.49 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))),
% 1.31/1.49 inference(quant_intro,[status(thm)],[82])).
% 1.31/1.49 tff(84,plain,
% 1.31/1.49 (^[A: $i, B: $i] : refl(((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))))))))),
% 1.31/1.49 inference(bind,[status(th)],[])).
% 1.31/1.49 tff(85,plain,
% 1.31/1.49 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))))))),
% 1.31/1.49 inference(quant_intro,[status(thm)],[84])).
% 1.31/1.49 tff(86,plain,
% 1.31/1.49 (^[A: $i, B: $i] : rewrite(((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))))))))),
% 1.31/1.49 inference(bind,[status(th)],[])).
% 1.31/1.49 tff(87,plain,
% 1.31/1.49 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))))))),
% 1.31/1.49 inference(quant_intro,[status(thm)],[86])).
% 1.31/1.49 tff(88,plain,
% 1.31/1.49 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))))))),
% 1.31/1.49 inference(transitivity,[status(thm)],[87, 85])).
% 1.31/1.49 tff(89,plain,
% 1.31/1.49 (^[A: $i, 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(((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) <=> ((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))), rewrite(((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))) <=> ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))), ((((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) <=> (((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))))), rewrite((((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) <=> (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))))))), ((((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) <=> (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))))))), (((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))))) <=> (((~relation(B)) | (~function(B))) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))))))))), rewrite((((~relation(B)) | (~function(B))) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))))))), (((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))))))))),
% 1.31/1.49 inference(bind,[status(th)],[])).
% 1.31/1.49 tff(90,plain,
% 1.31/1.49 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))))))),
% 1.31/1.49 inference(quant_intro,[status(thm)],[89])).
% 1.31/1.49 tff(91,plain,
% 1.31/1.49 (^[A: $i, B: $i] : rewrite(((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | ((~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))))) <=> ((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))))))),
% 1.31/1.49 inference(bind,[status(th)],[])).
% 1.31/1.49 tff(92,plain,
% 1.31/1.49 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | ((~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))))),
% 1.31/1.49 inference(quant_intro,[status(thm)],[91])).
% 1.31/1.49 tff(93,plain,
% 1.31/1.49 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(94,plain,
% 1.31/1.49 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : (in(C, A) => (apply(B, C) = C)))) <=> ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))), (((relation(B) & function(B)) => ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : (in(C, A) => (apply(B, C) = C))))) <=> ((relation(B) & function(B)) => ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))), rewrite(((relation(B) & function(B)) => ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))) <=> ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))), (((relation(B) & function(B)) => ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : (in(C, A) => (apply(B, C) = C))))) <=> ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))))),
% 1.31/1.49 inference(bind,[status(th)],[])).
% 1.31/1.49 tff(95,plain,
% 1.31/1.49 (![A: $i, B: $i] : ((relation(B) & function(B)) => ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : (in(C, A) => (apply(B, C) = C))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))),
% 1.31/1.49 inference(quant_intro,[status(thm)],[94])).
% 1.31/1.49 tff(96,axiom,(![A: $i, B: $i] : ((relation(B) & function(B)) => ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : (in(C, A) => (apply(B, C) = C)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t34_funct_1')).
% 1.31/1.49 tff(97,plain,
% 1.31/1.49 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[96, 95])).
% 1.31/1.49 tff(98,plain,
% 1.31/1.49 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[97, 93])).
% 1.31/1.49 tff(99,plain,(
% 1.31/1.49 ![A: $i, B: $i] : ((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | ((~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))))))),
% 1.31/1.49 inference(skolemize,[status(sab)],[98])).
% 1.31/1.49 tff(100,plain,
% 1.31/1.49 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[99, 92])).
% 1.31/1.49 tff(101,plain,
% 1.31/1.49 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))))))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[100, 90])).
% 1.31/1.49 tff(102,plain,
% 1.31/1.49 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))))))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[101, 88])).
% 1.31/1.49 tff(103,plain,
% 1.31/1.49 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[102, 83])).
% 1.31/1.49 tff(104,plain,
% 1.31/1.49 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!12)))) | (~((~((relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12))) | (~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))) = tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))) | (~((~(relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12)))) | (~((~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~![C: $i] : ((~in(C, relation_dom(A!12))) | (apply(relation_composition(A!12, function_inverse(A!12)), C) = C))))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | (~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!12)))) | (~((~((relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12))) | (~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))) = tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))) | (~((~(relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12)))) | (~((~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~![C: $i] : ((~in(C, relation_dom(A!12))) | (apply(relation_composition(A!12, function_inverse(A!12)), C) = C))))))))))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(105,plain,
% 1.31/1.49 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!12)))) | (~((~((relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12))) | (~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))) = tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))) | (~((~(relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12)))) | (~((~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~![C: $i] : ((~in(C, relation_dom(A!12))) | (apply(relation_composition(A!12, function_inverse(A!12)), C) = C))))))))))),
% 1.31/1.49 inference(quant_inst,[status(thm)],[])).
% 1.31/1.49 tff(106,plain,
% 1.31/1.49 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | (~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!12)))) | (~((~((relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12))) | (~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))) = tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))) | (~((~(relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12)))) | (~((~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~![C: $i] : ((~in(C, relation_dom(A!12))) | (apply(relation_composition(A!12, function_inverse(A!12)), C) = C)))))))))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[105, 104])).
% 1.31/1.49 tff(107,plain,
% 1.31/1.49 (~((~((relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12))) | (~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))) = tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))) | (~((~(relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12)))) | (~((~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~![C: $i] : ((~in(C, relation_dom(A!12))) | (apply(relation_composition(A!12, function_inverse(A!12)), C) = C))))))))),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[106, 103, 81, 60])).
% 1.31/1.49 tff(108,plain,
% 1.31/1.49 (((~((relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12))) | (~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))) = tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))) | (~((~(relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12)))) | (~((~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~![C: $i] : ((~in(C, relation_dom(A!12))) | (apply(relation_composition(A!12, function_inverse(A!12)), C) = C)))))))) | ((relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12))) | (~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))) = tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))),
% 1.31/1.49 inference(tautology,[status(thm)],[])).
% 1.31/1.49 tff(109,plain,
% 1.31/1.49 ((relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12))) | (~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))) = tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[108, 107])).
% 1.31/1.49 tff(110,plain,
% 1.31/1.49 (one_to_one(A!12)),
% 1.31/1.49 inference(or_elim,[status(thm)],[10])).
% 1.31/1.49 tff(111,plain,
% 1.31/1.49 (^[A: $i] : refl(((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A)))))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A)))))))),
% 1.31/1.49 inference(bind,[status(th)],[])).
% 1.31/1.49 tff(112,plain,
% 1.31/1.49 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A)))))) <=> ![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))))))),
% 1.31/1.49 inference(quant_intro,[status(thm)],[111])).
% 1.31/1.49 tff(113,plain,
% 1.31/1.49 (^[A: $i] : trans(monotonicity(rewrite(((relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A)) & (relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))) <=> (~((~(relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(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_dom(relation_composition(A, function_inverse(A))) = relation_dom(A)) & (relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ((~((~(relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))))) | ((~relation(A)) | (~function(A))) | (~one_to_one(A))))), rewrite(((~((~(relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))))) | ((~relation(A)) | (~function(A))) | (~one_to_one(A))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))))))), ((((relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A)) & (relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))))))))),
% 1.31/1.49 inference(bind,[status(th)],[])).
% 1.31/1.49 tff(114,plain,
% 1.31/1.49 (![A: $i] : (((relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A)) & (relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))))))),
% 1.31/1.49 inference(quant_intro,[status(thm)],[113])).
% 1.31/1.49 tff(115,plain,
% 1.31/1.49 (![A: $i] : (((relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A)) & (relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ![A: $i] : (((relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A)) & (relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(116,plain,
% 1.31/1.49 (^[A: $i] : trans(monotonicity(rewrite((one_to_one(A) => ((relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A)) & (relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A)))) <=> ((~one_to_one(A)) | ((relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A)) & (relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))))), (((relation(A) & function(A)) => (one_to_one(A) => ((relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A)) & (relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))))) <=> ((relation(A) & function(A)) => ((~one_to_one(A)) | ((relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A)) & (relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))))))), rewrite(((relation(A) & function(A)) => ((~one_to_one(A)) | ((relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A)) & (relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))))) <=> (((relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A)) & (relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation(A) & function(A))) | (~one_to_one(A)))), (((relation(A) & function(A)) => (one_to_one(A) => ((relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A)) & (relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))))) <=> (((relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A)) & (relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation(A) & function(A))) | (~one_to_one(A)))))),
% 1.31/1.49 inference(bind,[status(th)],[])).
% 1.31/1.49 tff(117,plain,
% 1.31/1.49 (![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => ((relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A)) & (relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))))) <=> ![A: $i] : (((relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A)) & (relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 1.31/1.49 inference(quant_intro,[status(thm)],[116])).
% 1.31/1.49 tff(118,axiom,(![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => ((relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A)) & (relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t58_funct_1')).
% 1.31/1.49 tff(119,plain,
% 1.31/1.49 (![A: $i] : (((relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A)) & (relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[118, 117])).
% 1.31/1.49 tff(120,plain,
% 1.31/1.49 (![A: $i] : (((relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A)) & (relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[119, 115])).
% 1.31/1.49 tff(121,plain,(
% 1.31/1.49 ![A: $i] : (((relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A)) & (relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 1.31/1.49 inference(skolemize,[status(sab)],[120])).
% 1.31/1.49 tff(122,plain,
% 1.31/1.49 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))))))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[121, 114])).
% 1.31/1.49 tff(123,plain,
% 1.31/1.49 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))))))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[122, 112])).
% 1.31/1.49 tff(124,plain,
% 1.31/1.49 (((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))))))) | ((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~(relation_rng(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))))))) <=> ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))))))) | (~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~(relation_rng(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))))))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(125,plain,
% 1.31/1.49 ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))))))) | ((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~(relation_rng(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))))))),
% 1.31/1.49 inference(quant_inst,[status(thm)],[])).
% 1.31/1.49 tff(126,plain,
% 1.31/1.49 ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))))))) | (~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~(relation_rng(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12)))))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[125, 124])).
% 1.31/1.49 tff(127,plain,
% 1.31/1.49 (~((~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~(relation_rng(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))))),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[126, 123, 13, 12, 110])).
% 1.31/1.49 tff(128,plain,
% 1.31/1.49 (((~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~(relation_rng(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12)))) | (relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))),
% 1.31/1.49 inference(tautology,[status(thm)],[])).
% 1.31/1.49 tff(129,plain,
% 1.31/1.49 (relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[128, 127])).
% 1.31/1.49 tff(130,assumption,((~((relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12))) | (~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))) = tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))) | (~((~(relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12)))) | (~((~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~![C: $i] : ((~in(C, relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), C) = C)))))))), introduced(assumption)).
% 1.31/1.49 tff(131,plain,
% 1.31/1.49 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | ((~relation(A!12)) | (~function(A!12)) | (~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))) | (~((~relation(relation_composition(function_inverse(A!12), A!12))) | (~function(relation_composition(function_inverse(A!12), A!12))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | (~relation(A!12)) | (~function(A!12)) | (~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))) | (~((~relation(relation_composition(function_inverse(A!12), A!12))) | (~function(relation_composition(function_inverse(A!12), A!12))))))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(132,plain,
% 1.31/1.49 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | ((~relation(A!12)) | (~function(A!12)) | (~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))) | (~((~relation(relation_composition(function_inverse(A!12), A!12))) | (~function(relation_composition(function_inverse(A!12), A!12))))))),
% 1.31/1.49 inference(quant_inst,[status(thm)],[])).
% 1.31/1.49 tff(133,plain,
% 1.31/1.49 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | (~relation(A!12)) | (~function(A!12)) | (~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))) | (~((~relation(relation_composition(function_inverse(A!12), A!12))) | (~function(relation_composition(function_inverse(A!12), A!12)))))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[132, 131])).
% 1.31/1.49 tff(134,plain,
% 1.31/1.49 ((~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))) | (~((~relation(relation_composition(function_inverse(A!12), A!12))) | (~function(relation_composition(function_inverse(A!12), A!12)))))),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[133, 47, 13, 12])).
% 1.31/1.49 tff(135,plain,
% 1.31/1.49 (~((~relation(relation_composition(function_inverse(A!12), A!12))) | (~function(relation_composition(function_inverse(A!12), A!12))))),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[134, 34, 32])).
% 1.31/1.49 tff(136,plain,
% 1.31/1.49 (((~relation(relation_composition(function_inverse(A!12), A!12))) | (~function(relation_composition(function_inverse(A!12), A!12)))) | function(relation_composition(function_inverse(A!12), A!12))),
% 1.31/1.49 inference(tautology,[status(thm)],[])).
% 1.31/1.49 tff(137,plain,
% 1.31/1.49 (function(relation_composition(function_inverse(A!12), A!12))),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[136, 135])).
% 1.31/1.49 tff(138,plain,
% 1.31/1.49 (((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | ((~relation(A!12)) | relation(relation_composition(function_inverse(A!12), A!12)) | (~relation(function_inverse(A!12))))) <=> ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (~relation(A!12)) | relation(relation_composition(function_inverse(A!12), A!12)) | (~relation(function_inverse(A!12))))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(139,plain,
% 1.31/1.49 ((relation(relation_composition(function_inverse(A!12), A!12)) | (~relation(A!12)) | (~relation(function_inverse(A!12)))) <=> ((~relation(A!12)) | relation(relation_composition(function_inverse(A!12), A!12)) | (~relation(function_inverse(A!12))))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(140,plain,
% 1.31/1.49 (((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (relation(relation_composition(function_inverse(A!12), A!12)) | (~relation(A!12)) | (~relation(function_inverse(A!12))))) <=> ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | ((~relation(A!12)) | relation(relation_composition(function_inverse(A!12), A!12)) | (~relation(function_inverse(A!12)))))),
% 1.31/1.49 inference(monotonicity,[status(thm)],[139])).
% 1.31/1.49 tff(141,plain,
% 1.31/1.49 (((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (relation(relation_composition(function_inverse(A!12), A!12)) | (~relation(A!12)) | (~relation(function_inverse(A!12))))) <=> ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (~relation(A!12)) | relation(relation_composition(function_inverse(A!12), A!12)) | (~relation(function_inverse(A!12))))),
% 1.31/1.49 inference(transitivity,[status(thm)],[140, 138])).
% 1.31/1.49 tff(142,plain,
% 1.31/1.49 ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (relation(relation_composition(function_inverse(A!12), A!12)) | (~relation(A!12)) | (~relation(function_inverse(A!12))))),
% 1.31/1.49 inference(quant_inst,[status(thm)],[])).
% 1.31/1.49 tff(143,plain,
% 1.31/1.49 ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (~relation(A!12)) | relation(relation_composition(function_inverse(A!12), A!12)) | (~relation(function_inverse(A!12)))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[142, 141])).
% 1.31/1.49 tff(144,plain,
% 1.31/1.49 (relation(relation_composition(function_inverse(A!12), A!12)) | (~relation(function_inverse(A!12)))),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[143, 73, 13])).
% 1.31/1.49 tff(145,plain,
% 1.31/1.49 (relation(relation_composition(function_inverse(A!12), A!12))),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[144, 32])).
% 1.31/1.49 tff(146,plain,
% 1.31/1.49 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(relation_composition(function_inverse(A!12), A!12))) | (~function(relation_composition(function_inverse(A!12), A!12))) | (~((~((relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12))) | (~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))) = tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))) | (~((~(relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12)))) | (~((~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~![C: $i] : ((~in(C, relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), C) = C))))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | (~relation(relation_composition(function_inverse(A!12), A!12))) | (~function(relation_composition(function_inverse(A!12), A!12))) | (~((~((relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12))) | (~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))) = tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))) | (~((~(relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12)))) | (~((~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~![C: $i] : ((~in(C, relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), C) = C))))))))))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(147,plain,
% 1.31/1.49 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(relation_composition(function_inverse(A!12), A!12))) | (~function(relation_composition(function_inverse(A!12), A!12))) | (~((~((relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12))) | (~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))) = tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))) | (~((~(relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12)))) | (~((~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~![C: $i] : ((~in(C, relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), C) = C))))))))))),
% 1.31/1.49 inference(quant_inst,[status(thm)],[])).
% 1.31/1.49 tff(148,plain,
% 1.31/1.49 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | (~relation(relation_composition(function_inverse(A!12), A!12))) | (~function(relation_composition(function_inverse(A!12), A!12))) | (~((~((relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12))) | (~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))) = tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))) | (~((~(relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12)))) | (~((~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~![C: $i] : ((~in(C, relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), C) = C)))))))))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[147, 146])).
% 1.31/1.49 tff(149,plain,
% 1.31/1.49 ($false),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[148, 103, 145, 137, 130])).
% 1.31/1.49 tff(150,plain,(~((~((relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12))) | (~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))) = tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))) | (~((~(relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12)))) | (~((~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~![C: $i] : ((~in(C, relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), C) = C))))))))), inference(lemma,lemma(discharge,[]))).
% 1.31/1.50 tff(151,plain,
% 1.31/1.50 (((~((relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12))) | (~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))) = tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))) | (~((~(relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12)))) | (~((~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~![C: $i] : ((~in(C, relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), C) = C)))))))) | ((relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12))) | (~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))) = tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))),
% 1.31/1.50 inference(tautology,[status(thm)],[])).
% 1.31/1.50 tff(152,plain,
% 1.31/1.50 ((relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12))) | (~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))) = tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[151, 150])).
% 1.31/1.50 tff(153,assumption,(~((~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))) = tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))), introduced(assumption)).
% 1.31/1.50 tff(154,plain,
% 1.31/1.50 (((~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))) = tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))) | in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))),
% 1.31/1.50 inference(tautology,[status(thm)],[])).
% 1.31/1.50 tff(155,plain,
% 1.31/1.50 (in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[154, 153])).
% 1.31/1.50 tff(156,plain,
% 1.31/1.50 (^[A: $i, B: $i] : refl(((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B)))) <=> ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B)))))),
% 1.31/1.50 inference(bind,[status(th)],[])).
% 1.31/1.50 tff(157,plain,
% 1.31/1.50 (![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B)))) <=> ![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))),
% 1.31/1.50 inference(quant_intro,[status(thm)],[156])).
% 1.31/1.50 tff(158,plain,
% 1.31/1.50 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) <=> (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A)))))), 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(B) & in(A, relation_rng(B))) <=> (~((~one_to_one(B)) | (~in(A, relation_rng(B)))))), ((~(one_to_one(B) & in(A, relation_rng(B)))) <=> (~(~((~one_to_one(B)) | (~in(A, relation_rng(B)))))))), rewrite((~(~((~one_to_one(B)) | (~in(A, relation_rng(B)))))) <=> ((~one_to_one(B)) | (~in(A, relation_rng(B))))), ((~(one_to_one(B) & in(A, relation_rng(B)))) <=> ((~one_to_one(B)) | (~in(A, relation_rng(B)))))), ((((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B))))) <=> ((~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | ((~relation(B)) | (~function(B))) | ((~one_to_one(B)) | (~in(A, relation_rng(B))))))), rewrite(((~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | ((~relation(B)) | (~function(B))) | ((~one_to_one(B)) | (~in(A, relation_rng(B))))) <=> ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))), ((((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B))))) <=> ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))))),
% 1.31/1.50 inference(bind,[status(th)],[])).
% 1.31/1.50 tff(159,plain,
% 1.31/1.50 (![A: $i, B: $i] : (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B))))) <=> ![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))),
% 1.31/1.50 inference(quant_intro,[status(thm)],[158])).
% 1.31/1.50 tff(160,plain,
% 1.31/1.50 (![A: $i, B: $i] : (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B))))) <=> ![A: $i, B: $i] : (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B)))))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(161,plain,
% 1.31/1.50 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((one_to_one(B) & in(A, relation_rng(B))) => ((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A)))) <=> ((~(one_to_one(B) & in(A, relation_rng(B)))) | ((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))))), (((relation(B) & function(B)) => ((one_to_one(B) & in(A, relation_rng(B))) => ((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))))) <=> ((relation(B) & function(B)) => ((~(one_to_one(B) & in(A, relation_rng(B)))) | ((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))))))), rewrite(((relation(B) & function(B)) => ((~(one_to_one(B) & in(A, relation_rng(B)))) | ((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))))) <=> (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B)))))), (((relation(B) & function(B)) => ((one_to_one(B) & in(A, relation_rng(B))) => ((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))))) <=> (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B)))))))),
% 1.31/1.50 inference(bind,[status(th)],[])).
% 1.31/1.50 tff(162,plain,
% 1.31/1.50 (![A: $i, B: $i] : ((relation(B) & function(B)) => ((one_to_one(B) & in(A, relation_rng(B))) => ((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))))) <=> ![A: $i, B: $i] : (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B)))))),
% 1.31/1.50 inference(quant_intro,[status(thm)],[161])).
% 1.31/1.50 tff(163,axiom,(![A: $i, B: $i] : ((relation(B) & function(B)) => ((one_to_one(B) & in(A, relation_rng(B))) => ((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t57_funct_1')).
% 1.31/1.50 tff(164,plain,
% 1.31/1.50 (![A: $i, B: $i] : (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B)))))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[163, 162])).
% 1.31/1.50 tff(165,plain,
% 1.31/1.50 (![A: $i, B: $i] : (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B)))))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[164, 160])).
% 1.31/1.50 tff(166,plain,(
% 1.31/1.50 ![A: $i, B: $i] : (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B)))))),
% 1.31/1.50 inference(skolemize,[status(sab)],[165])).
% 1.31/1.50 tff(167,plain,
% 1.31/1.50 (![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[166, 159])).
% 1.31/1.50 tff(168,plain,
% 1.31/1.50 (![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[167, 157])).
% 1.31/1.50 tff(169,plain,
% 1.31/1.50 (((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))) | ((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (~((~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(A!12, apply(function_inverse(A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))) | (~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))))) <=> ((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))) | (~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (~((~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(A!12, apply(function_inverse(A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))) | (~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(170,plain,
% 1.31/1.50 (((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(A!12, apply(function_inverse(A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))) | (~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))) | (~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12)))) <=> ((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (~((~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(A!12, apply(function_inverse(A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))) | (~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(171,plain,
% 1.31/1.50 ((~((~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(A!12, apply(function_inverse(A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))) | (~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))) <=> (~((~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(A!12, apply(function_inverse(A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))) | (~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(172,plain,
% 1.31/1.50 (((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(A!12, apply(function_inverse(A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))) | (~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))) | (~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12)))) <=> ((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(A!12, apply(function_inverse(A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))) | (~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))) | (~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))))),
% 1.31/1.50 inference(monotonicity,[status(thm)],[171])).
% 1.31/1.50 tff(173,plain,
% 1.31/1.50 (((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(A!12, apply(function_inverse(A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))) | (~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))) | (~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12)))) <=> ((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (~((~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(A!12, apply(function_inverse(A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))) | (~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))))),
% 1.31/1.50 inference(transitivity,[status(thm)],[172, 170])).
% 1.31/1.50 tff(174,plain,
% 1.31/1.50 (((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))) | ((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(A!12, apply(function_inverse(A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))) | (~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))) | (~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))))) <=> ((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))) | ((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (~((~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(A!12, apply(function_inverse(A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))) | (~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))))))),
% 1.31/1.50 inference(monotonicity,[status(thm)],[173])).
% 1.31/1.50 tff(175,plain,
% 1.31/1.50 (((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))) | ((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(A!12, apply(function_inverse(A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))) | (~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))) | (~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))))) <=> ((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))) | (~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (~((~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(A!12, apply(function_inverse(A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))) | (~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))))),
% 1.31/1.50 inference(transitivity,[status(thm)],[174, 169])).
% 1.31/1.50 tff(176,plain,
% 1.31/1.50 ((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))) | ((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(A!12, apply(function_inverse(A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))) | (~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))) | (~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))))),
% 1.31/1.50 inference(quant_inst,[status(thm)],[])).
% 1.31/1.50 tff(177,plain,
% 1.31/1.50 ((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))) | (~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (~((~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(A!12, apply(function_inverse(A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))) | (~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[176, 175])).
% 1.31/1.50 tff(178,plain,
% 1.31/1.50 (~((~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(A!12, apply(function_inverse(A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))) | (~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[177, 168, 13, 12, 110, 155])).
% 1.31/1.50 tff(179,plain,
% 1.31/1.50 (((~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(A!12, apply(function_inverse(A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))) | (~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))) | (tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))),
% 1.31/1.50 inference(tautology,[status(thm)],[])).
% 1.31/1.50 tff(180,plain,
% 1.31/1.50 (tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[179, 178])).
% 1.31/1.50 tff(181,plain,
% 1.31/1.50 (apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))) = tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))),
% 1.31/1.50 inference(symmetry,[status(thm)],[180])).
% 1.31/1.50 tff(182,plain,
% 1.31/1.50 (((~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))) = tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))) | (~(apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))) = tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))),
% 1.31/1.50 inference(tautology,[status(thm)],[])).
% 1.31/1.50 tff(183,plain,
% 1.31/1.50 (~(apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))) = tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[182, 153])).
% 1.31/1.50 tff(184,plain,
% 1.31/1.50 ($false),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[183, 181])).
% 1.31/1.50 tff(185,plain,((~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))) = tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))), inference(lemma,lemma(discharge,[]))).
% 1.31/1.50 tff(186,plain,
% 1.31/1.50 (^[A: $i] : refl(((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A)))))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A)))))))),
% 1.31/1.50 inference(bind,[status(th)],[])).
% 1.31/1.50 tff(187,plain,
% 1.31/1.50 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A)))))) <=> ![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))))))),
% 1.31/1.50 inference(quant_intro,[status(thm)],[186])).
% 1.31/1.50 tff(188,plain,
% 1.31/1.50 (^[A: $i] : trans(monotonicity(rewrite(((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))) <=> (~((~(relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation_rng(relation_composition(function_inverse(A), A)) = 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_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ((~((~(relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))))) | ((~relation(A)) | (~function(A))) | (~one_to_one(A))))), rewrite(((~((~(relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))))) | ((~relation(A)) | (~function(A))) | (~one_to_one(A))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))))))), ((((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))))))))),
% 1.31/1.50 inference(bind,[status(th)],[])).
% 1.31/1.50 tff(189,plain,
% 1.31/1.50 (![A: $i] : (((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))))))),
% 1.31/1.50 inference(quant_intro,[status(thm)],[188])).
% 1.31/1.50 tff(190,plain,
% 1.31/1.50 (![A: $i] : (((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ![A: $i] : (((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(191,plain,
% 1.31/1.50 (^[A: $i] : trans(monotonicity(rewrite((one_to_one(A) => ((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A)))) <=> ((~one_to_one(A)) | ((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))))), (((relation(A) & function(A)) => (one_to_one(A) => ((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))))) <=> ((relation(A) & function(A)) => ((~one_to_one(A)) | ((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))))))), rewrite(((relation(A) & function(A)) => ((~one_to_one(A)) | ((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))))) <=> (((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation(A) & function(A))) | (~one_to_one(A)))), (((relation(A) & function(A)) => (one_to_one(A) => ((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))))) <=> (((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation(A) & function(A))) | (~one_to_one(A)))))),
% 1.31/1.50 inference(bind,[status(th)],[])).
% 1.31/1.50 tff(192,plain,
% 1.31/1.50 (![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => ((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))))) <=> ![A: $i] : (((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 1.31/1.50 inference(quant_intro,[status(thm)],[191])).
% 1.31/1.50 tff(193,axiom,(![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => ((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t59_funct_1')).
% 1.31/1.50 tff(194,plain,
% 1.31/1.50 (![A: $i] : (((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[193, 192])).
% 1.31/1.50 tff(195,plain,
% 1.31/1.50 (![A: $i] : (((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[194, 190])).
% 1.31/1.50 tff(196,plain,(
% 1.31/1.50 ![A: $i] : (((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 1.31/1.50 inference(skolemize,[status(sab)],[195])).
% 1.31/1.50 tff(197,plain,
% 1.31/1.50 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))))))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[196, 189])).
% 1.31/1.50 tff(198,plain,
% 1.31/1.50 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))))))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[197, 187])).
% 1.31/1.50 tff(199,plain,
% 1.31/1.50 (((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))))))) | ((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~(relation_rng(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))))))) <=> ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))))))) | (~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~(relation_rng(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))))))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(200,plain,
% 1.31/1.50 ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))))))) | ((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~(relation_rng(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))))))),
% 1.31/1.50 inference(quant_inst,[status(thm)],[])).
% 1.31/1.50 tff(201,plain,
% 1.31/1.50 ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))))))) | (~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~(relation_rng(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12)))))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[200, 199])).
% 1.31/1.50 tff(202,plain,
% 1.31/1.50 (~((~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~(relation_rng(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))))),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[201, 198, 13, 12, 110])).
% 1.31/1.50 tff(203,plain,
% 1.31/1.50 (((~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~(relation_rng(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12)))) | (relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))),
% 1.31/1.50 inference(tautology,[status(thm)],[])).
% 1.31/1.50 tff(204,plain,
% 1.31/1.50 (relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[203, 202])).
% 1.31/1.50 tff(205,plain,
% 1.31/1.50 ((~((relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12))) | (~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))) = tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))) | (relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12))) | (~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))) = tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))),
% 1.31/1.50 inference(tautology,[status(thm)],[])).
% 1.31/1.50 tff(206,plain,
% 1.31/1.50 ((~((relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12))) | (~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))) = tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))) | (relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12)))),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[205, 204, 185])).
% 1.31/1.50 tff(207,plain,
% 1.31/1.50 (relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12))),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[206, 152])).
% 1.31/1.50 tff(208,plain,
% 1.31/1.50 ((~(~((~(relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12)))) | (~(relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12))))))) <=> ((~(relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12)))) | (~(relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12)))))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(209,plain,
% 1.31/1.50 (((relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12))) & (relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12)))) <=> (~((~(relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12)))) | (~(relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12))))))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(210,plain,
% 1.31/1.50 ((~((relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12))) & (relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12))))) <=> (~(~((~(relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12)))) | (~(relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12)))))))),
% 1.31/1.50 inference(monotonicity,[status(thm)],[209])).
% 1.31/1.50 tff(211,plain,
% 1.31/1.50 ((~((relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12))) & (relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12))))) <=> ((~(relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12)))) | (~(relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12)))))),
% 1.31/1.50 inference(transitivity,[status(thm)],[210, 208])).
% 1.31/1.50 tff(212,plain,
% 1.31/1.50 (~((relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12))) & (relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12))))),
% 1.31/1.50 inference(or_elim,[status(thm)],[10])).
% 1.31/1.50 tff(213,plain,
% 1.31/1.50 ((~(relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12)))) | (~(relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12))))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[212, 211])).
% 1.31/1.50 tff(214,plain,
% 1.31/1.50 (~(relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12)))),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[213, 207])).
% 1.31/1.50 tff(215,plain,
% 1.31/1.50 ((~((relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12))) | (~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))) = tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))) | (relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12))) | (~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))) = tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))),
% 1.31/1.50 inference(tautology,[status(thm)],[])).
% 1.31/1.50 tff(216,plain,
% 1.31/1.50 ((~((relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12))) | (~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))) = tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))) | (~((~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))) = tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[215, 214, 129])).
% 1.31/1.50 tff(217,plain,
% 1.31/1.50 (~((~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))) = tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[216, 109])).
% 1.31/1.50 tff(218,plain,
% 1.31/1.50 (((~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))) = tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))) | in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))),
% 1.31/1.50 inference(tautology,[status(thm)],[])).
% 1.31/1.50 tff(219,plain,
% 1.31/1.50 (in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[218, 217])).
% 1.31/1.50 tff(220,plain,
% 1.31/1.50 (^[A: $i, B: $i] : refl(((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(function_inverse(B), apply(B, A)))) | (~(A = apply(relation_composition(B, function_inverse(B)), A))))) | (~in(A, relation_dom(B)))) <=> ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(function_inverse(B), apply(B, A)))) | (~(A = apply(relation_composition(B, function_inverse(B)), A))))) | (~in(A, relation_dom(B)))))),
% 1.31/1.50 inference(bind,[status(th)],[])).
% 1.31/1.50 tff(221,plain,
% 1.31/1.50 (![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(function_inverse(B), apply(B, A)))) | (~(A = apply(relation_composition(B, function_inverse(B)), A))))) | (~in(A, relation_dom(B)))) <=> ![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(function_inverse(B), apply(B, A)))) | (~(A = apply(relation_composition(B, function_inverse(B)), A))))) | (~in(A, relation_dom(B))))),
% 1.31/1.50 inference(quant_intro,[status(thm)],[220])).
% 1.31/1.50 tff(222,plain,
% 1.31/1.50 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))) <=> (~((~(A = apply(function_inverse(B), apply(B, A)))) | (~(A = apply(relation_composition(B, function_inverse(B)), A)))))), 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(B) & in(A, relation_dom(B))) <=> (~((~one_to_one(B)) | (~in(A, relation_dom(B)))))), ((~(one_to_one(B) & in(A, relation_dom(B)))) <=> (~(~((~one_to_one(B)) | (~in(A, relation_dom(B)))))))), rewrite((~(~((~one_to_one(B)) | (~in(A, relation_dom(B)))))) <=> ((~one_to_one(B)) | (~in(A, relation_dom(B))))), ((~(one_to_one(B) & in(A, relation_dom(B)))) <=> ((~one_to_one(B)) | (~in(A, relation_dom(B)))))), ((((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_dom(B))))) <=> ((~((~(A = apply(function_inverse(B), apply(B, A)))) | (~(A = apply(relation_composition(B, function_inverse(B)), A))))) | ((~relation(B)) | (~function(B))) | ((~one_to_one(B)) | (~in(A, relation_dom(B))))))), rewrite(((~((~(A = apply(function_inverse(B), apply(B, A)))) | (~(A = apply(relation_composition(B, function_inverse(B)), A))))) | ((~relation(B)) | (~function(B))) | ((~one_to_one(B)) | (~in(A, relation_dom(B))))) <=> ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(function_inverse(B), apply(B, A)))) | (~(A = apply(relation_composition(B, function_inverse(B)), A))))) | (~in(A, relation_dom(B))))), ((((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_dom(B))))) <=> ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(function_inverse(B), apply(B, A)))) | (~(A = apply(relation_composition(B, function_inverse(B)), A))))) | (~in(A, relation_dom(B))))))),
% 1.31/1.51 inference(bind,[status(th)],[])).
% 1.31/1.51 tff(223,plain,
% 1.31/1.51 (![A: $i, B: $i] : (((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_dom(B))))) <=> ![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(function_inverse(B), apply(B, A)))) | (~(A = apply(relation_composition(B, function_inverse(B)), A))))) | (~in(A, relation_dom(B))))),
% 1.31/1.51 inference(quant_intro,[status(thm)],[222])).
% 1.31/1.51 tff(224,plain,
% 1.31/1.51 (![A: $i, B: $i] : (((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_dom(B))))) <=> ![A: $i, B: $i] : (((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_dom(B)))))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(225,plain,
% 1.31/1.51 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((one_to_one(B) & in(A, relation_dom(B))) => ((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A)))) <=> ((~(one_to_one(B) & in(A, relation_dom(B)))) | ((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))))), (((relation(B) & function(B)) => ((one_to_one(B) & in(A, relation_dom(B))) => ((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))))) <=> ((relation(B) & function(B)) => ((~(one_to_one(B) & in(A, relation_dom(B)))) | ((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))))))), rewrite(((relation(B) & function(B)) => ((~(one_to_one(B) & in(A, relation_dom(B)))) | ((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))))) <=> (((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_dom(B)))))), (((relation(B) & function(B)) => ((one_to_one(B) & in(A, relation_dom(B))) => ((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))))) <=> (((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_dom(B)))))))),
% 1.31/1.51 inference(bind,[status(th)],[])).
% 1.31/1.51 tff(226,plain,
% 1.31/1.51 (![A: $i, B: $i] : ((relation(B) & function(B)) => ((one_to_one(B) & in(A, relation_dom(B))) => ((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))))) <=> ![A: $i, B: $i] : (((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_dom(B)))))),
% 1.31/1.51 inference(quant_intro,[status(thm)],[225])).
% 1.31/1.51 tff(227,axiom,(![A: $i, B: $i] : ((relation(B) & function(B)) => ((one_to_one(B) & in(A, relation_dom(B))) => ((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t56_funct_1')).
% 1.31/1.51 tff(228,plain,
% 1.31/1.51 (![A: $i, B: $i] : (((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_dom(B)))))),
% 1.31/1.51 inference(modus_ponens,[status(thm)],[227, 226])).
% 1.31/1.51 tff(229,plain,
% 1.31/1.51 (![A: $i, B: $i] : (((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_dom(B)))))),
% 1.31/1.51 inference(modus_ponens,[status(thm)],[228, 224])).
% 1.31/1.51 tff(230,plain,(
% 1.31/1.51 ![A: $i, B: $i] : (((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_dom(B)))))),
% 1.31/1.51 inference(skolemize,[status(sab)],[229])).
% 1.31/1.51 tff(231,plain,
% 1.31/1.51 (![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(function_inverse(B), apply(B, A)))) | (~(A = apply(relation_composition(B, function_inverse(B)), A))))) | (~in(A, relation_dom(B))))),
% 1.31/1.51 inference(modus_ponens,[status(thm)],[230, 223])).
% 1.31/1.51 tff(232,plain,
% 1.31/1.51 (![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(function_inverse(B), apply(B, A)))) | (~(A = apply(relation_composition(B, function_inverse(B)), A))))) | (~in(A, relation_dom(B))))),
% 1.31/1.51 inference(modus_ponens,[status(thm)],[231, 221])).
% 1.31/1.51 tff(233,plain,
% 1.31/1.51 (((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(function_inverse(B), apply(B, A)))) | (~(A = apply(relation_composition(B, function_inverse(B)), A))))) | (~in(A, relation_dom(B))))) | ((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (~((~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(function_inverse(A!12), apply(A!12, tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))) | (~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))))) <=> ((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(function_inverse(B), apply(B, A)))) | (~(A = apply(relation_composition(B, function_inverse(B)), A))))) | (~in(A, relation_dom(B))))) | (~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (~((~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(function_inverse(A!12), apply(A!12, tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))) | (~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(234,plain,
% 1.31/1.51 (((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(function_inverse(A!12), apply(A!12, tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))) | (~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))) | (~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12)))) <=> ((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (~((~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(function_inverse(A!12), apply(A!12, tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))) | (~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(235,plain,
% 1.31/1.51 ((~((~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(function_inverse(A!12), apply(A!12, tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))) | (~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))) <=> (~((~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(function_inverse(A!12), apply(A!12, tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))) | (~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(236,plain,
% 1.31/1.51 (((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(function_inverse(A!12), apply(A!12, tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))) | (~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))) | (~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12)))) <=> ((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(function_inverse(A!12), apply(A!12, tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))) | (~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))) | (~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))))),
% 1.31/1.51 inference(monotonicity,[status(thm)],[235])).
% 1.31/1.51 tff(237,plain,
% 1.31/1.51 (((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(function_inverse(A!12), apply(A!12, tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))) | (~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))) | (~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12)))) <=> ((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (~((~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(function_inverse(A!12), apply(A!12, tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))) | (~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))))),
% 1.31/1.51 inference(transitivity,[status(thm)],[236, 234])).
% 1.31/1.51 tff(238,plain,
% 1.31/1.51 (((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(function_inverse(B), apply(B, A)))) | (~(A = apply(relation_composition(B, function_inverse(B)), A))))) | (~in(A, relation_dom(B))))) | ((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(function_inverse(A!12), apply(A!12, tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))) | (~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))) | (~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))))) <=> ((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(function_inverse(B), apply(B, A)))) | (~(A = apply(relation_composition(B, function_inverse(B)), A))))) | (~in(A, relation_dom(B))))) | ((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (~((~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(function_inverse(A!12), apply(A!12, tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))) | (~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))))))),
% 1.31/1.51 inference(monotonicity,[status(thm)],[237])).
% 1.31/1.51 tff(239,plain,
% 1.31/1.51 (((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(function_inverse(B), apply(B, A)))) | (~(A = apply(relation_composition(B, function_inverse(B)), A))))) | (~in(A, relation_dom(B))))) | ((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(function_inverse(A!12), apply(A!12, tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))) | (~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))) | (~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))))) <=> ((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(function_inverse(B), apply(B, A)))) | (~(A = apply(relation_composition(B, function_inverse(B)), A))))) | (~in(A, relation_dom(B))))) | (~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (~((~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(function_inverse(A!12), apply(A!12, tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))) | (~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))))),
% 1.31/1.51 inference(transitivity,[status(thm)],[238, 233])).
% 1.31/1.51 tff(240,plain,
% 1.31/1.51 ((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(function_inverse(B), apply(B, A)))) | (~(A = apply(relation_composition(B, function_inverse(B)), A))))) | (~in(A, relation_dom(B))))) | ((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(function_inverse(A!12), apply(A!12, tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))) | (~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))) | (~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))))),
% 1.31/1.51 inference(quant_inst,[status(thm)],[])).
% 1.31/1.51 tff(241,plain,
% 1.31/1.51 ((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(function_inverse(B), apply(B, A)))) | (~(A = apply(relation_composition(B, function_inverse(B)), A))))) | (~in(A, relation_dom(B))))) | (~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (~((~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(function_inverse(A!12), apply(A!12, tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))) | (~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))))),
% 1.31/1.51 inference(modus_ponens,[status(thm)],[240, 239])).
% 1.31/1.51 tff(242,plain,
% 1.31/1.51 (~((~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(function_inverse(A!12), apply(A!12, tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))) | (~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[241, 232, 13, 12, 110, 219])).
% 1.31/1.51 tff(243,plain,
% 1.31/1.51 (((~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(function_inverse(A!12), apply(A!12, tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))) | (~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))) | (tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))),
% 1.31/1.51 inference(tautology,[status(thm)],[])).
% 1.31/1.51 tff(244,plain,
% 1.31/1.51 (tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[243, 242])).
% 1.31/1.51 tff(245,plain,
% 1.31/1.51 (apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))) = tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))),
% 1.31/1.51 inference(symmetry,[status(thm)],[244])).
% 1.31/1.51 tff(246,plain,
% 1.31/1.51 (((~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))) = tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))) | (~(apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))) = tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))),
% 1.31/1.52 inference(tautology,[status(thm)],[])).
% 1.31/1.52 tff(247,plain,
% 1.31/1.52 (~(apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))) = tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[246, 217])).
% 1.31/1.52 tff(248,plain,
% 1.31/1.52 ($false),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[247, 245])).
% 1.31/1.52 % SZS output end Proof
% 1.31/1.52 % E exiting
%------------------------------------------------------------------------------