%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU023+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 2.54s 2.78s
% Output : Proof 2.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU023+1 : TPTP v9.0.0. Released v3.2.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 05:56:55 EDT 2025
% 0.12/0.34 % CPUTime :
% 2.54/2.78 % SZS status Theorem
% 2.54/2.78 % SZS output start Proof
% 2.54/2.78 tff(apply_type, type, (
% 2.54/2.78 apply: ( $i * $i ) > $i)).
% 2.54/2.78 tff(tptp_fun_A_14_type, type, (
% 2.54/2.78 tptp_fun_A_14: $i)).
% 2.54/2.78 tff(tptp_fun_B_13_type, type, (
% 2.54/2.78 tptp_fun_B_13: $i)).
% 2.54/2.78 tff(function_inverse_type, type, (
% 2.54/2.78 function_inverse: $i > $i)).
% 2.54/2.78 tff(relation_composition_type, type, (
% 2.54/2.78 relation_composition: ( $i * $i ) > $i)).
% 2.54/2.78 tff(relation_type, type, (
% 2.54/2.78 relation: $i > $o)).
% 2.54/2.78 tff(function_type, type, (
% 2.54/2.78 function: $i > $o)).
% 2.54/2.78 tff(in_type, type, (
% 2.54/2.78 in: ( $i * $i ) > $o)).
% 2.54/2.78 tff(relation_dom_type, type, (
% 2.54/2.78 relation_dom: $i > $i)).
% 2.54/2.78 tff(one_to_one_type, type, (
% 2.54/2.78 one_to_one: $i > $o)).
% 2.54/2.78 tff(relation_rng_type, type, (
% 2.54/2.78 relation_rng: $i > $i)).
% 2.54/2.78 tff(tptp_fun_C_12_type, type, (
% 2.54/2.78 tptp_fun_C_12: ( $i * $i ) > $i)).
% 2.54/2.78 tff(tptp_fun_D_11_type, type, (
% 2.54/2.78 tptp_fun_D_11: ( $i * $i ) > $i)).
% 2.54/2.78 tff(1,plain,
% 2.54/2.78 ((~(((A!14 = apply(function_inverse(B!13), apply(B!13, A!14))) & (A!14 = apply(relation_composition(B!13, function_inverse(B!13)), A!14))) | (~(relation(B!13) & function(B!13))) | (~(one_to_one(B!13) & in(A!14, relation_dom(B!13)))))) <=> (~(((A!14 = apply(function_inverse(B!13), apply(B!13, A!14))) & (A!14 = apply(relation_composition(B!13, function_inverse(B!13)), A!14))) | (~(relation(B!13) & function(B!13))) | (~(one_to_one(B!13) & in(A!14, relation_dom(B!13))))))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(2,plain,
% 2.54/2.78 ((~![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))))))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(3,plain,
% 2.54/2.78 ((~![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))))))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(4,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')).
% 2.54/2.78 tff(5,plain,
% 2.54/2.78 (~![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)))))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[4, 3])).
% 2.54/2.78 tff(6,plain,
% 2.54/2.78 (~![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)))))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[5, 2])).
% 2.54/2.78 tff(7,plain,
% 2.54/2.78 (~![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)))))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[6, 2])).
% 2.54/2.78 tff(8,plain,
% 2.54/2.78 (~![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)))))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[7, 2])).
% 2.54/2.78 tff(9,plain,(
% 2.54/2.78 ~(((A!14 = apply(function_inverse(B!13), apply(B!13, A!14))) & (A!14 = apply(relation_composition(B!13, function_inverse(B!13)), A!14))) | (~(relation(B!13) & function(B!13))) | (~(one_to_one(B!13) & in(A!14, relation_dom(B!13)))))),
% 2.54/2.78 inference(skolemize,[status(sab)],[8])).
% 2.54/2.78 tff(10,plain,
% 2.54/2.78 (~(((A!14 = apply(function_inverse(B!13), apply(B!13, A!14))) & (A!14 = apply(relation_composition(B!13, function_inverse(B!13)), A!14))) | (~(relation(B!13) & function(B!13))) | (~(one_to_one(B!13) & in(A!14, relation_dom(B!13)))))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[9, 1])).
% 2.54/2.78 tff(11,plain,
% 2.54/2.78 (relation(B!13) & function(B!13)),
% 2.54/2.78 inference(or_elim,[status(thm)],[10])).
% 2.54/2.78 tff(12,plain,
% 2.54/2.78 (function(B!13)),
% 2.54/2.78 inference(and_elim,[status(thm)],[11])).
% 2.54/2.78 tff(13,plain,
% 2.54/2.78 (relation(B!13)),
% 2.54/2.78 inference(and_elim,[status(thm)],[11])).
% 2.54/2.78 tff(14,plain,
% 2.54/2.78 (^[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)))))))),
% 2.54/2.78 inference(bind,[status(th)],[])).
% 2.54/2.78 tff(15,plain,
% 2.54/2.78 (![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))))))),
% 2.54/2.78 inference(quant_intro,[status(thm)],[14])).
% 2.54/2.78 tff(16,plain,
% 2.54/2.78 (^[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))))))))),
% 2.54/2.78 inference(bind,[status(th)],[])).
% 2.54/2.78 tff(17,plain,
% 2.54/2.78 (![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))))))),
% 2.54/2.78 inference(quant_intro,[status(thm)],[16])).
% 2.54/2.78 tff(18,plain,
% 2.54/2.78 (![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))))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(19,plain,
% 2.54/2.78 (^[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)))))),
% 2.54/2.78 inference(bind,[status(th)],[])).
% 2.54/2.78 tff(20,plain,
% 2.54/2.78 (![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))))),
% 2.54/2.78 inference(quant_intro,[status(thm)],[19])).
% 2.54/2.78 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')).
% 2.54/2.78 tff(22,plain,
% 2.54/2.78 (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[21, 20])).
% 2.54/2.78 tff(23,plain,
% 2.54/2.78 (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[22, 18])).
% 2.54/2.78 tff(24,plain,(
% 2.54/2.78 ![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 2.54/2.78 inference(skolemize,[status(sab)],[23])).
% 2.54/2.78 tff(25,plain,
% 2.54/2.78 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[24, 17])).
% 2.54/2.78 tff(26,plain,
% 2.54/2.78 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[25, 15])).
% 2.54/2.78 tff(27,plain,
% 2.54/2.78 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | ((~function(B!13)) | (~relation(B!13)) | (~((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | (~function(B!13)) | (~relation(B!13)) | (~((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))))))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(28,plain,
% 2.54/2.78 (((~relation(B!13)) | (~function(B!13)) | (~((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13)))))) <=> ((~function(B!13)) | (~relation(B!13)) | (~((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))))))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(29,plain,
% 2.54/2.78 ((~((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))))) <=> (~((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13)))))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(30,plain,
% 2.54/2.78 (((~relation(B!13)) | (~function(B!13)) | (~((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13)))))) <=> ((~relation(B!13)) | (~function(B!13)) | (~((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))))))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[29])).
% 2.54/2.78 tff(31,plain,
% 2.54/2.78 (((~relation(B!13)) | (~function(B!13)) | (~((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13)))))) <=> ((~function(B!13)) | (~relation(B!13)) | (~((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))))))),
% 2.54/2.78 inference(transitivity,[status(thm)],[30, 28])).
% 2.54/2.78 tff(32,plain,
% 2.54/2.78 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | ((~relation(B!13)) | (~function(B!13)) | (~((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | ((~function(B!13)) | (~relation(B!13)) | (~((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13)))))))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[31])).
% 2.54/2.78 tff(33,plain,
% 2.54/2.78 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | ((~relation(B!13)) | (~function(B!13)) | (~((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | (~function(B!13)) | (~relation(B!13)) | (~((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))))))),
% 2.54/2.78 inference(transitivity,[status(thm)],[32, 27])).
% 2.54/2.78 tff(34,plain,
% 2.54/2.78 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | ((~relation(B!13)) | (~function(B!13)) | (~((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))))))),
% 2.54/2.78 inference(quant_inst,[status(thm)],[])).
% 2.54/2.78 tff(35,plain,
% 2.54/2.78 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | (~function(B!13)) | (~relation(B!13)) | (~((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13)))))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[34, 33])).
% 2.54/2.78 tff(36,plain,
% 2.54/2.78 (~((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[35, 26, 13, 12])).
% 2.54/2.78 tff(37,plain,
% 2.54/2.78 (((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13)))) | relation(function_inverse(B!13))),
% 2.54/2.78 inference(tautology,[status(thm)],[])).
% 2.54/2.78 tff(38,plain,
% 2.54/2.78 (relation(function_inverse(B!13))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[37, 36])).
% 2.54/2.78 tff(39,plain,
% 2.54/2.78 (((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13)))) | function(function_inverse(B!13))),
% 2.54/2.78 inference(tautology,[status(thm)],[])).
% 2.54/2.78 tff(40,plain,
% 2.54/2.78 (function(function_inverse(B!13))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[39, 36])).
% 2.54/2.78 tff(41,plain,
% 2.54/2.78 (^[A: $i, B: $i] : refl(((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))))),
% 2.54/2.78 inference(bind,[status(th)],[])).
% 2.54/2.78 tff(42,plain,
% 2.54/2.78 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))),
% 2.54/2.78 inference(quant_intro,[status(thm)],[41])).
% 2.54/2.78 tff(43,plain,
% 2.54/2.78 (^[A: $i, B: $i] : rewrite(((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))))),
% 2.54/2.78 inference(bind,[status(th)],[])).
% 2.54/2.78 tff(44,plain,
% 2.54/2.78 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))),
% 2.54/2.78 inference(quant_intro,[status(thm)],[43])).
% 2.54/2.78 tff(45,plain,
% 2.54/2.78 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))),
% 2.54/2.78 inference(transitivity,[status(thm)],[44, 42])).
% 2.54/2.78 tff(46,plain,
% 2.54/2.78 (^[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))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(C) & function(C)) <=> (~((~relation(C)) | (~function(C))))), ((~(relation(C) & function(C))) <=> (~(~((~relation(C)) | (~function(C))))))), rewrite((~(~((~relation(C)) | (~function(C))))) <=> ((~relation(C)) | (~function(C)))), ((~(relation(C) & function(C))) <=> ((~relation(C)) | (~function(C))))), (((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | ((~relation(C)) | (~function(C))) | (~in(A, relation_dom(B)))))), rewrite(((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | ((~relation(C)) | (~function(C))) | (~in(A, relation_dom(B)))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))), (((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))))), (![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))) <=> ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))), (((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))) <=> (((~relation(B)) | (~function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))))), rewrite((((~relation(B)) | (~function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))), (((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))))),
% 2.54/2.78 inference(bind,[status(th)],[])).
% 2.54/2.78 tff(47,plain,
% 2.54/2.78 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))),
% 2.54/2.78 inference(quant_intro,[status(thm)],[46])).
% 2.54/2.78 tff(48,plain,
% 2.54/2.78 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(49,plain,
% 2.54/2.78 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A)))) <=> ((~in(A, relation_dom(B))) | (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))), (((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))) <=> ((relation(C) & function(C)) => ((~in(A, relation_dom(B))) | (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))))), rewrite(((relation(C) & function(C)) => ((~in(A, relation_dom(B))) | (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))), (((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))))), (![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))) <=> ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))), (((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A)))))) <=> ((relation(B) & function(B)) => ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))))), rewrite(((relation(B) & function(B)) => ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))) <=> ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))), (((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A)))))) <=> ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))))),
% 2.54/2.78 inference(bind,[status(th)],[])).
% 2.54/2.78 tff(50,plain,
% 2.54/2.78 (![A: $i, B: $i] : ((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A)))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))),
% 2.54/2.78 inference(quant_intro,[status(thm)],[49])).
% 2.54/2.78 tff(51,axiom,(![A: $i, B: $i] : ((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t23_funct_1')).
% 2.54/2.78 tff(52,plain,
% 2.54/2.78 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[51, 50])).
% 2.54/2.78 tff(53,plain,
% 2.54/2.78 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[52, 48])).
% 2.54/2.78 tff(54,plain,(
% 2.54/2.78 ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))),
% 2.54/2.78 inference(skolemize,[status(sab)],[53])).
% 2.54/2.78 tff(55,plain,
% 2.54/2.78 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[54, 47])).
% 2.54/2.78 tff(56,plain,
% 2.54/2.78 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[55, 45])).
% 2.54/2.78 tff(57,plain,
% 2.54/2.78 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~function(B!13)) | (~relation(B!13)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14)))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | (~function(B!13)) | (~relation(B!13)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14)))))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(58,plain,
% 2.54/2.78 (((~relation(B!13)) | (~function(B!13)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14))))) <=> ((~function(B!13)) | (~relation(B!13)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14)))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(59,plain,
% 2.54/2.79 (^[C: $i] : rewrite(((apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14))) | (~in(A!14, relation_dom(B!13))) | (~relation(C)) | (~function(C))) <=> ((~relation(C)) | (~function(C)) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14)))))),
% 2.54/2.79 inference(bind,[status(th)],[])).
% 2.54/2.79 tff(60,plain,
% 2.54/2.79 (![C: $i] : ((apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14))) | (~in(A!14, relation_dom(B!13))) | (~relation(C)) | (~function(C))) <=> ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14))))),
% 2.54/2.79 inference(quant_intro,[status(thm)],[59])).
% 2.54/2.79 tff(61,plain,
% 2.54/2.79 (((~relation(B!13)) | (~function(B!13)) | ![C: $i] : ((apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14))) | (~in(A!14, relation_dom(B!13))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B!13)) | (~function(B!13)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14)))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[60])).
% 2.54/2.79 tff(62,plain,
% 2.54/2.79 (((~relation(B!13)) | (~function(B!13)) | ![C: $i] : ((apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14))) | (~in(A!14, relation_dom(B!13))) | (~relation(C)) | (~function(C)))) <=> ((~function(B!13)) | (~relation(B!13)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14)))))),
% 2.54/2.79 inference(transitivity,[status(thm)],[61, 58])).
% 2.54/2.79 tff(63,plain,
% 2.54/2.79 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~relation(B!13)) | (~function(B!13)) | ![C: $i] : ((apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14))) | (~in(A!14, relation_dom(B!13))) | (~relation(C)) | (~function(C))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~function(B!13)) | (~relation(B!13)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14))))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[62])).
% 2.54/2.79 tff(64,plain,
% 2.54/2.79 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~relation(B!13)) | (~function(B!13)) | ![C: $i] : ((apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14))) | (~in(A!14, relation_dom(B!13))) | (~relation(C)) | (~function(C))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | (~function(B!13)) | (~relation(B!13)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14)))))),
% 2.54/2.79 inference(transitivity,[status(thm)],[63, 57])).
% 2.54/2.79 tff(65,plain,
% 2.54/2.79 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~relation(B!13)) | (~function(B!13)) | ![C: $i] : ((apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14))) | (~in(A!14, relation_dom(B!13))) | (~relation(C)) | (~function(C))))),
% 2.54/2.79 inference(quant_inst,[status(thm)],[])).
% 2.54/2.79 tff(66,plain,
% 2.54/2.79 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | (~function(B!13)) | (~relation(B!13)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14))))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[65, 64])).
% 2.54/2.79 tff(67,plain,
% 2.54/2.79 (![C: $i] : ((~relation(C)) | (~function(C)) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[66, 56, 13, 12])).
% 2.54/2.79 tff(68,plain,
% 2.54/2.79 (one_to_one(B!13) & in(A!14, relation_dom(B!13))),
% 2.54/2.79 inference(or_elim,[status(thm)],[10])).
% 2.54/2.79 tff(69,plain,
% 2.54/2.79 (in(A!14, relation_dom(B!13))),
% 2.54/2.79 inference(and_elim,[status(thm)],[68])).
% 2.54/2.79 tff(70,plain,
% 2.54/2.79 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14))))) | ((~in(A!14, relation_dom(B!13))) | (~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (apply(relation_composition(B!13, function_inverse(B!13)), A!14) = apply(function_inverse(B!13), apply(B!13, A!14))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14))))) | (~in(A!14, relation_dom(B!13))) | (~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (apply(relation_composition(B!13, function_inverse(B!13)), A!14) = apply(function_inverse(B!13), apply(B!13, A!14))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(71,plain,
% 2.54/2.79 (((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, function_inverse(B!13)), A!14) = apply(function_inverse(B!13), apply(B!13, A!14)))) <=> ((~in(A!14, relation_dom(B!13))) | (~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (apply(relation_composition(B!13, function_inverse(B!13)), A!14) = apply(function_inverse(B!13), apply(B!13, A!14))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(72,plain,
% 2.54/2.79 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14))))) | ((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, function_inverse(B!13)), A!14) = apply(function_inverse(B!13), apply(B!13, A!14))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14))))) | ((~in(A!14, relation_dom(B!13))) | (~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (apply(relation_composition(B!13, function_inverse(B!13)), A!14) = apply(function_inverse(B!13), apply(B!13, A!14)))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[71])).
% 2.54/2.79 tff(73,plain,
% 2.54/2.79 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14))))) | ((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, function_inverse(B!13)), A!14) = apply(function_inverse(B!13), apply(B!13, A!14))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14))))) | (~in(A!14, relation_dom(B!13))) | (~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (apply(relation_composition(B!13, function_inverse(B!13)), A!14) = apply(function_inverse(B!13), apply(B!13, A!14))))),
% 2.54/2.79 inference(transitivity,[status(thm)],[72, 70])).
% 2.54/2.79 tff(74,plain,
% 2.54/2.79 ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14))))) | ((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, function_inverse(B!13)), A!14) = apply(function_inverse(B!13), apply(B!13, A!14))))),
% 2.54/2.79 inference(quant_inst,[status(thm)],[])).
% 2.54/2.79 tff(75,plain,
% 2.54/2.79 ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14))))) | (~in(A!14, relation_dom(B!13))) | (~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (apply(relation_composition(B!13, function_inverse(B!13)), A!14) = apply(function_inverse(B!13), apply(B!13, A!14)))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[74, 73])).
% 2.54/2.79 tff(76,plain,
% 2.54/2.79 ((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (apply(relation_composition(B!13, function_inverse(B!13)), A!14) = apply(function_inverse(B!13), apply(B!13, A!14)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[75, 69, 67])).
% 2.54/2.79 tff(77,plain,
% 2.54/2.79 (apply(relation_composition(B!13, function_inverse(B!13)), A!14) = apply(function_inverse(B!13), apply(B!13, A!14))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[76, 40, 38])).
% 2.54/2.79 tff(78,plain,
% 2.54/2.79 ((A!14 = apply(relation_composition(B!13, function_inverse(B!13)), A!14)) <=> (A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[77])).
% 2.54/2.79 tff(79,plain,
% 2.54/2.79 ((~(A!14 = apply(relation_composition(B!13, function_inverse(B!13)), A!14))) <=> (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[78])).
% 2.54/2.79 tff(80,assumption,(~(A!14 = apply(relation_composition(B!13, function_inverse(B!13)), A!14))), introduced(assumption)).
% 2.54/2.79 tff(81,plain,
% 2.54/2.79 (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[80, 79])).
% 2.54/2.79 tff(82,plain,
% 2.54/2.79 (((~in(apply(B!13, A!14), relation_rng(B!13))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14))))) | (A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))),
% 2.54/2.79 inference(tautology,[status(thm)],[])).
% 2.54/2.79 tff(83,plain,
% 2.54/2.79 ((~in(apply(B!13, A!14), relation_rng(B!13))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[82, 81])).
% 2.54/2.79 tff(84,plain,
% 2.54/2.79 ((~((~in(A!14, relation_dom(B!13))) | (~((~in(apply(B!13, A!14), relation_rng(B!13))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))))))) | (~in(A!14, relation_dom(B!13))) | (~((~in(apply(B!13, A!14), relation_rng(B!13))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14))))))),
% 2.54/2.79 inference(tautology,[status(thm)],[])).
% 2.54/2.79 tff(85,plain,
% 2.54/2.79 (~((~in(A!14, relation_dom(B!13))) | (~((~in(apply(B!13, A!14), relation_rng(B!13))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[84, 69, 83])).
% 2.54/2.79 tff(86,plain,
% 2.54/2.79 (((~(in(A!14, relation_dom(B!13)) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))) | (~in(apply(B!13, A!14), relation_rng(B!13))))) | (~((~in(A!14, relation_dom(B!13))) | (~((~in(apply(B!13, A!14), relation_rng(B!13))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14))))))))) | ((~in(A!14, relation_dom(B!13))) | (~((~in(apply(B!13, A!14), relation_rng(B!13))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))))))),
% 2.54/2.79 inference(tautology,[status(thm)],[])).
% 2.54/2.79 tff(87,plain,
% 2.54/2.79 ((~(in(A!14, relation_dom(B!13)) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))) | (~in(apply(B!13, A!14), relation_rng(B!13))))) | (~((~in(A!14, relation_dom(B!13))) | (~((~in(apply(B!13, A!14), relation_rng(B!13))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14))))))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[86, 85])).
% 2.54/2.79 tff(88,plain,
% 2.54/2.79 (one_to_one(B!13)),
% 2.54/2.79 inference(and_elim,[status(thm)],[68])).
% 2.54/2.79 tff(89,plain,
% 2.54/2.79 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))))) <=> (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))))))))), (((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))))))))))), rewrite(((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))))))), (((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))))))))), (![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))))) <=> ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))))))))))), (((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))))))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))))))))), rewrite(((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))))))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))))))))))), (((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))))))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))))))))))))),
% 2.54/2.79 inference(bind,[status(th)],[])).
% 2.54/2.79 tff(90,plain,
% 2.54/2.79 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))))))) <=> ![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))))))))))),
% 2.54/2.79 inference(quant_intro,[status(thm)],[89])).
% 2.54/2.79 tff(91,plain,
% 2.54/2.79 (^[A: $i] : refl(((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))))))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))))))))),
% 2.54/2.79 inference(bind,[status(th)],[])).
% 2.54/2.79 tff(92,plain,
% 2.54/2.79 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))))))) <=> ![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))))))),
% 2.54/2.79 inference(quant_intro,[status(thm)],[91])).
% 2.54/2.79 tff(93,plain,
% 2.54/2.79 (^[A: $i] : rewrite(((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))))))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))))))))),
% 2.54/2.79 inference(bind,[status(th)],[])).
% 2.54/2.79 tff(94,plain,
% 2.54/2.79 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))))))) <=> ![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))))))),
% 2.54/2.79 inference(quant_intro,[status(thm)],[93])).
% 2.54/2.79 tff(95,plain,
% 2.54/2.79 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))))))) <=> ![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))))))),
% 2.54/2.79 inference(transitivity,[status(thm)],[94, 92])).
% 2.54/2.79 tff(96,plain,
% 2.54/2.79 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(A) & function(A)) <=> (~((~relation(A)) | (~function(A))))), ((~(relation(A) & function(A))) <=> (~(~((~relation(A)) | (~function(A))))))), rewrite((~(~((~relation(A)) | (~function(A))))) <=> ((~relation(A)) | (~function(A)))), ((~(relation(A) & function(A))) <=> ((~relation(A)) | (~function(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(B) & function(B)) <=> (~((~relation(B)) | (~function(B))))), ((~(relation(B) & function(B))) <=> (~(~((~relation(B)) | (~function(B))))))), rewrite((~(~((~relation(B)) | (~function(B))))) <=> ((~relation(B)) | (~function(B)))), ((~(relation(B) & function(B))) <=> ((~relation(B)) | (~function(B))))), trans(monotonicity(rewrite(((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) <=> ((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))), trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) <=> (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))))), ((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) <=> (~(~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))))))), rewrite((~(~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))))) <=> ((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))), ((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) <=> ((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))))), rewrite((in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))) <=> (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))), (((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) <=> (((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))), rewrite((((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))) <=> ((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))), (((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) <=> ((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))), trans(monotonicity(trans(monotonicity(rewrite((in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))) <=> (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))), ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) <=> (~(~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))), rewrite((~(~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))) <=> ((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))), ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) <=> ((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))), rewrite((in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) <=> (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))))), (((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) <=> (((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))))))), rewrite((((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))))) <=> ((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))), (((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) <=> ((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))), ((((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) <=> (((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))) & ((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))), rewrite((((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))) & ((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))) <=> (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))), ((((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) <=> (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))))), ((~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))))) <=> (~(~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))))), rewrite((~(~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))) <=> ((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))), ((~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))))) <=> ((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))), (((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))))) <=> ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | ((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))))), rewrite(((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | ((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) <=> ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))), (((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))))) <=> ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))), ((((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))))))) <=> (((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))))) & ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))))), rewrite((((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))))) & ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) <=> (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))))), ((((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))))))) <=> (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))))))), (((~(relation(B) & function(B))) | (((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))))))) <=> (((~relation(B)) | (~function(B))) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))))))), rewrite((((~relation(B)) | (~function(B))) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))))))), (((~(relation(B) & function(B))) | (((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))))))))), (![B: $i] : ((~(relation(B) & function(B))) | (((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))))))) <=> ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))))))), (((~(relation(A) & function(A))) | (~one_to_one(A)) | ![B: $i] : ((~(relation(B) & function(B))) | (((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))))))))) <=> (((~relation(A)) | (~function(A))) | (~one_to_one(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))))))))), rewrite((((~relation(A)) | (~function(A))) | (~one_to_one(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))))))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))))))), (((~(relation(A) & function(A))) | (~one_to_one(A)) | ![B: $i] : ((~(relation(B) & function(B))) | (((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))))))))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))))))))),
% 2.54/2.80 inference(bind,[status(th)],[])).
% 2.54/2.80 tff(97,plain,
% 2.54/2.80 (![A: $i] : ((~(relation(A) & function(A))) | (~one_to_one(A)) | ![B: $i] : ((~(relation(B) & function(B))) | (((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))))))))) <=> ![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))))))),
% 2.54/2.80 inference(quant_intro,[status(thm)],[96])).
% 2.54/2.80 tff(98,plain,
% 2.54/2.80 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite(((~(relation(B) & function(B))) | (((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | ((~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))))))))) <=> ((~(relation(B) & function(B))) | (((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))))))))), (![B: $i] : ((~(relation(B) & function(B))) | (((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | ((~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))))))))) <=> ![B: $i] : ((~(relation(B) & function(B))) | (((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))))))))), (((~(relation(A) & function(A))) | ![B: $i] : ((~(relation(B) & function(B))) | (((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | ((~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))))))))) | (~one_to_one(A))) <=> ((~(relation(A) & function(A))) | ![B: $i] : ((~(relation(B) & function(B))) | (((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))))))) | (~one_to_one(A))))), rewrite(((~(relation(A) & function(A))) | ![B: $i] : ((~(relation(B) & function(B))) | (((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))))))) | (~one_to_one(A))) <=> ((~(relation(A) & function(A))) | (~one_to_one(A)) | ![B: $i] : ((~(relation(B) & function(B))) | (((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))))))))), (((~(relation(A) & function(A))) | ![B: $i] : ((~(relation(B) & function(B))) | (((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | ((~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))))))))) | (~one_to_one(A))) <=> ((~(relation(A) & function(A))) | (~one_to_one(A)) | ![B: $i] : ((~(relation(B) & function(B))) | (((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))))))))))),
% 2.54/2.80 inference(bind,[status(th)],[])).
% 2.54/2.80 tff(99,plain,
% 2.54/2.80 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((~(relation(B) & function(B))) | (((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | ((~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))))))))) | (~one_to_one(A))) <=> ![A: $i] : ((~(relation(A) & function(A))) | (~one_to_one(A)) | ![B: $i] : ((~(relation(B) & function(B))) | (((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))))))))),
% 2.54/2.80 inference(quant_intro,[status(thm)],[98])).
% 2.54/2.80 tff(100,plain,
% 2.54/2.80 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((~(relation(B) & function(B))) | ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C)))))))) | (~one_to_one(A))) <=> ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((~(relation(B) & function(B))) | ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C)))))))) | (~one_to_one(A)))),
% 2.54/2.80 inference(rewrite,[status(thm)],[])).
% 2.54/2.80 tff(101,plain,
% 2.54/2.80 (^[A: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite(((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((in(C, relation_rng(A)) & (D = apply(B, C))) => (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((in(D, relation_dom(A)) & (C = apply(A, D))) => (in(C, relation_rng(A)) & (D = apply(B, C))))))) <=> ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C)))))))), (((relation(B) & function(B)) => ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((in(C, relation_rng(A)) & (D = apply(B, C))) => (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((in(D, relation_dom(A)) & (C = apply(A, D))) => (in(C, relation_rng(A)) & (D = apply(B, C)))))))) <=> ((relation(B) & function(B)) => ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C)))))))))), rewrite(((relation(B) & function(B)) => ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C)))))))) <=> ((~(relation(B) & function(B))) | ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))))), (((relation(B) & function(B)) => ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((in(C, relation_rng(A)) & (D = apply(B, C))) => (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((in(D, relation_dom(A)) & (C = apply(A, D))) => (in(C, relation_rng(A)) & (D = apply(B, C)))))))) <=> ((~(relation(B) & function(B))) | ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))))))), (![B: $i] : ((relation(B) & function(B)) => ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((in(C, relation_rng(A)) & (D = apply(B, C))) => (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((in(D, relation_dom(A)) & (C = apply(A, D))) => (in(C, relation_rng(A)) & (D = apply(B, C)))))))) <=> ![B: $i] : ((~(relation(B) & function(B))) | ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C)))))))))), ((one_to_one(A) => ![B: $i] : ((relation(B) & function(B)) => ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((in(C, relation_rng(A)) & (D = apply(B, C))) => (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((in(D, relation_dom(A)) & (C = apply(A, D))) => (in(C, relation_rng(A)) & (D = apply(B, C))))))))) <=> (one_to_one(A) => ![B: $i] : ((~(relation(B) & function(B))) | ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))))))), rewrite((one_to_one(A) => ![B: $i] : ((~(relation(B) & function(B))) | ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))))) <=> ((~one_to_one(A)) | ![B: $i] : ((~(relation(B) & function(B))) | ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C)))))))))), ((one_to_one(A) => ![B: $i] : ((relation(B) & function(B)) => ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((in(C, relation_rng(A)) & (D = apply(B, C))) => (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((in(D, relation_dom(A)) & (C = apply(A, D))) => (in(C, relation_rng(A)) & (D = apply(B, C))))))))) <=> ((~one_to_one(A)) | ![B: $i] : ((~(relation(B) & function(B))) | ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))))))), (((relation(A) & function(A)) => (one_to_one(A) => ![B: $i] : ((relation(B) & function(B)) => ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((in(C, relation_rng(A)) & (D = apply(B, C))) => (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((in(D, relation_dom(A)) & (C = apply(A, D))) => (in(C, relation_rng(A)) & (D = apply(B, C)))))))))) <=> ((relation(A) & function(A)) => ((~one_to_one(A)) | ![B: $i] : ((~(relation(B) & function(B))) | ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C)))))))))))), rewrite(((relation(A) & function(A)) => ((~one_to_one(A)) | ![B: $i] : ((~(relation(B) & function(B))) | ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C)))))))))) <=> ((~(relation(A) & function(A))) | ![B: $i] : ((~(relation(B) & function(B))) | ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C)))))))) | (~one_to_one(A)))), (((relation(A) & function(A)) => (one_to_one(A) => ![B: $i] : ((relation(B) & function(B)) => ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((in(C, relation_rng(A)) & (D = apply(B, C))) => (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((in(D, relation_dom(A)) & (C = apply(A, D))) => (in(C, relation_rng(A)) & (D = apply(B, C)))))))))) <=> ((~(relation(A) & function(A))) | ![B: $i] : ((~(relation(B) & function(B))) | ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C)))))))) | (~one_to_one(A)))))),
% 2.54/2.80 inference(bind,[status(th)],[])).
% 2.54/2.80 tff(102,plain,
% 2.54/2.80 (![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => ![B: $i] : ((relation(B) & function(B)) => ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((in(C, relation_rng(A)) & (D = apply(B, C))) => (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((in(D, relation_dom(A)) & (C = apply(A, D))) => (in(C, relation_rng(A)) & (D = apply(B, C)))))))))) <=> ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((~(relation(B) & function(B))) | ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C)))))))) | (~one_to_one(A)))),
% 2.54/2.80 inference(quant_intro,[status(thm)],[101])).
% 2.54/2.80 tff(103,axiom,(![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => ![B: $i] : ((relation(B) & function(B)) => ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((in(C, relation_rng(A)) & (D = apply(B, C))) => (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((in(D, relation_dom(A)) & (C = apply(A, D))) => (in(C, relation_rng(A)) & (D = apply(B, C))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t54_funct_1')).
% 2.54/2.80 tff(104,plain,
% 2.54/2.80 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((~(relation(B) & function(B))) | ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C)))))))) | (~one_to_one(A)))),
% 2.54/2.80 inference(modus_ponens,[status(thm)],[103, 102])).
% 2.54/2.80 tff(105,plain,
% 2.54/2.80 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((~(relation(B) & function(B))) | ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C)))))))) | (~one_to_one(A)))),
% 2.54/2.80 inference(modus_ponens,[status(thm)],[104, 100])).
% 2.54/2.80 tff(106,plain,(
% 2.54/2.80 ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((~(relation(B) & function(B))) | (((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | ((~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))))))))) | (~one_to_one(A)))),
% 2.54/2.80 inference(skolemize,[status(sab)],[105])).
% 2.54/2.80 tff(107,plain,
% 2.54/2.80 (![A: $i] : ((~(relation(A) & function(A))) | (~one_to_one(A)) | ![B: $i] : ((~(relation(B) & function(B))) | (((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))))))))),
% 2.54/2.80 inference(modus_ponens,[status(thm)],[106, 99])).
% 2.54/2.80 tff(108,plain,
% 2.54/2.80 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))))))),
% 2.54/2.80 inference(modus_ponens,[status(thm)],[107, 97])).
% 2.54/2.80 tff(109,plain,
% 2.54/2.80 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))))))),
% 2.54/2.80 inference(modus_ponens,[status(thm)],[108, 95])).
% 2.54/2.80 tff(110,plain,
% 2.54/2.80 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))))))))))),
% 2.54/2.80 inference(modus_ponens,[status(thm)],[109, 90])).
% 2.54/2.80 tff(111,plain,
% 2.54/2.80 (((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))))))))))) | ((~function(B!13)) | (~relation(B!13)) | (~one_to_one(B!13)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!13))) | (B = function_inverse(B!13)) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))))))))))))))))))) <=> ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))))))))))) | (~function(B!13)) | (~relation(B!13)) | (~one_to_one(B!13)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!13))) | (B = function_inverse(B!13)) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))))))))))))))))))),
% 2.54/2.80 inference(rewrite,[status(thm)],[])).
% 2.54/2.80 tff(112,plain,
% 2.54/2.80 (((~one_to_one(B!13)) | (~relation(B!13)) | (~function(B!13)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!13))) | (B = function_inverse(B!13)) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13)))))))))))))))))) <=> ((~function(B!13)) | (~relation(B!13)) | (~one_to_one(B!13)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!13))) | (B = function_inverse(B!13)) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))))))))))))))))))),
% 2.54/2.80 inference(rewrite,[status(thm)],[])).
% 2.54/2.80 tff(113,plain,
% 2.54/2.80 (^[B: $i] : trans(monotonicity(rewrite((~((~((B = function_inverse(B!13)) | (~(relation_dom(B) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))) | (~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~((~in(C, relation_rng(B!13))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D)))))))))))))) <=> (~((~((~(relation_dom(B) = relation_rng(B!13))) | (B = function_inverse(B!13)) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))))))))))))))))), (((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!13)) | (~(relation_dom(B) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))) | (~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~((~in(C, relation_rng(B!13))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!13))) | (B = function_inverse(B!13)) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))))))))))))))))))), rewrite(((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!13))) | (B = function_inverse(B!13)) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))))))))))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!13))) | (B = function_inverse(B!13)) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13)))))))))))))))))), (((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!13)) | (~(relation_dom(B) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))) | (~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~((~in(C, relation_rng(B!13))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!13))) | (B = function_inverse(B!13)) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13)))))))))))))))))))),
% 2.64/2.80 inference(bind,[status(th)],[])).
% 2.64/2.80 tff(114,plain,
% 2.64/2.80 (![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!13)) | (~(relation_dom(B) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))) | (~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~((~in(C, relation_rng(B!13))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))))))))))) <=> ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!13))) | (B = function_inverse(B!13)) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13)))))))))))))))))),
% 2.64/2.81 inference(quant_intro,[status(thm)],[113])).
% 2.64/2.81 tff(115,plain,
% 2.64/2.81 (((~one_to_one(B!13)) | (~relation(B!13)) | (~function(B!13)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!13)) | (~(relation_dom(B) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))) | (~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~((~in(C, relation_rng(B!13))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D)))))))))))))))) <=> ((~one_to_one(B!13)) | (~relation(B!13)) | (~function(B!13)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!13))) | (B = function_inverse(B!13)) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))))))))))))))))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[114])).
% 2.64/2.81 tff(116,plain,
% 2.64/2.81 (((~one_to_one(B!13)) | (~relation(B!13)) | (~function(B!13)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!13)) | (~(relation_dom(B) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))) | (~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~((~in(C, relation_rng(B!13))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D)))))))))))))))) <=> ((~function(B!13)) | (~relation(B!13)) | (~one_to_one(B!13)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!13))) | (B = function_inverse(B!13)) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))))))))))))))))))),
% 2.64/2.81 inference(transitivity,[status(thm)],[115, 112])).
% 2.64/2.81 tff(117,plain,
% 2.64/2.81 (((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))))))))))) | ((~one_to_one(B!13)) | (~relation(B!13)) | (~function(B!13)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!13)) | (~(relation_dom(B) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))) | (~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~((~in(C, relation_rng(B!13))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))))))))))))) <=> ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))))))))))) | ((~function(B!13)) | (~relation(B!13)) | (~one_to_one(B!13)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!13))) | (B = function_inverse(B!13)) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13)))))))))))))))))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[116])).
% 2.64/2.81 tff(118,plain,
% 2.64/2.81 (((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))))))))))) | ((~one_to_one(B!13)) | (~relation(B!13)) | (~function(B!13)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!13)) | (~(relation_dom(B) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))) | (~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~((~in(C, relation_rng(B!13))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))))))))))))) <=> ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))))))))))) | (~function(B!13)) | (~relation(B!13)) | (~one_to_one(B!13)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!13))) | (B = function_inverse(B!13)) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))))))))))))))))))),
% 2.64/2.81 inference(transitivity,[status(thm)],[117, 111])).
% 2.64/2.81 tff(119,plain,
% 2.64/2.81 ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))))))))))) | ((~one_to_one(B!13)) | (~relation(B!13)) | (~function(B!13)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!13)) | (~(relation_dom(B) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))) | (~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~((~in(C, relation_rng(B!13))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))))))))))))),
% 2.64/2.81 inference(quant_inst,[status(thm)],[])).
% 2.64/2.81 tff(120,plain,
% 2.64/2.81 ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))))))))))) | (~function(B!13)) | (~relation(B!13)) | (~one_to_one(B!13)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!13))) | (B = function_inverse(B!13)) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13)))))))))))))))))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[119, 118])).
% 2.64/2.81 tff(121,plain,
% 2.64/2.81 (![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!13))) | (B = function_inverse(B!13)) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13)))))))))))))))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[120, 110, 13, 12, 88])).
% 2.64/2.81 tff(122,plain,
% 2.64/2.81 (((~![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!13))) | (B = function_inverse(B!13)) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13)))))))))))))))))) | ((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (~((~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C)))))))))))))) <=> ((~![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!13))) | (B = function_inverse(B!13)) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13)))))))))))))))))) | (~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (~((~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C)))))))))))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(123,plain,
% 2.64/2.81 (((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (~((~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C))))))))))))) <=> ((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (~((~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C)))))))))))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(124,plain,
% 2.64/2.81 ((~((~((~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (function_inverse(B!13) = function_inverse(B!13)) | (~((~in(tptp_fun_C_12(function_inverse(B!13), B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(function_inverse(B!13), B!13) = apply(function_inverse(B!13), tptp_fun_C_12(function_inverse(B!13), B!13)))) | (~((~in(tptp_fun_D_11(function_inverse(B!13), B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(function_inverse(B!13), B!13) = apply(B!13, tptp_fun_D_11(function_inverse(B!13), B!13)))))))) | (~((~(tptp_fun_C_12(function_inverse(B!13), B!13) = apply(B!13, tptp_fun_D_11(function_inverse(B!13), B!13)))) | (~in(tptp_fun_D_11(function_inverse(B!13), B!13), relation_dom(B!13))) | (~((~in(tptp_fun_C_12(function_inverse(B!13), B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(function_inverse(B!13), B!13) = apply(function_inverse(B!13), tptp_fun_C_12(function_inverse(B!13), B!13)))))))))) | (~((~(function_inverse(B!13) = function_inverse(B!13))) | (~((~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(function_inverse(B!13), C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(function_inverse(B!13), C))) | (~in(C, relation_rng(B!13)))))))))))))))) <=> (~((~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C))))))))))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(125,plain,
% 2.64/2.81 (((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (~((~((~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (function_inverse(B!13) = function_inverse(B!13)) | (~((~in(tptp_fun_C_12(function_inverse(B!13), B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(function_inverse(B!13), B!13) = apply(function_inverse(B!13), tptp_fun_C_12(function_inverse(B!13), B!13)))) | (~((~in(tptp_fun_D_11(function_inverse(B!13), B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(function_inverse(B!13), B!13) = apply(B!13, tptp_fun_D_11(function_inverse(B!13), B!13)))))))) | (~((~(tptp_fun_C_12(function_inverse(B!13), B!13) = apply(B!13, tptp_fun_D_11(function_inverse(B!13), B!13)))) | (~in(tptp_fun_D_11(function_inverse(B!13), B!13), relation_dom(B!13))) | (~((~in(tptp_fun_C_12(function_inverse(B!13), B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(function_inverse(B!13), B!13) = apply(function_inverse(B!13), tptp_fun_C_12(function_inverse(B!13), B!13)))))))))) | (~((~(function_inverse(B!13) = function_inverse(B!13))) | (~((~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(function_inverse(B!13), C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(function_inverse(B!13), C))) | (~in(C, relation_rng(B!13))))))))))))))))) <=> ((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (~((~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C)))))))))))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[124])).
% 2.64/2.81 tff(126,plain,
% 2.64/2.81 (((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (~((~((~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (function_inverse(B!13) = function_inverse(B!13)) | (~((~in(tptp_fun_C_12(function_inverse(B!13), B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(function_inverse(B!13), B!13) = apply(function_inverse(B!13), tptp_fun_C_12(function_inverse(B!13), B!13)))) | (~((~in(tptp_fun_D_11(function_inverse(B!13), B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(function_inverse(B!13), B!13) = apply(B!13, tptp_fun_D_11(function_inverse(B!13), B!13)))))))) | (~((~(tptp_fun_C_12(function_inverse(B!13), B!13) = apply(B!13, tptp_fun_D_11(function_inverse(B!13), B!13)))) | (~in(tptp_fun_D_11(function_inverse(B!13), B!13), relation_dom(B!13))) | (~((~in(tptp_fun_C_12(function_inverse(B!13), B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(function_inverse(B!13), B!13) = apply(function_inverse(B!13), tptp_fun_C_12(function_inverse(B!13), B!13)))))))))) | (~((~(function_inverse(B!13) = function_inverse(B!13))) | (~((~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(function_inverse(B!13), C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(function_inverse(B!13), C))) | (~in(C, relation_rng(B!13))))))))))))))))) <=> ((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (~((~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C)))))))))))))),
% 2.64/2.81 inference(transitivity,[status(thm)],[125, 123])).
% 2.64/2.81 tff(127,plain,
% 2.64/2.81 (((~![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!13))) | (B = function_inverse(B!13)) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13)))))))))))))))))) | ((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (~((~((~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (function_inverse(B!13) = function_inverse(B!13)) | (~((~in(tptp_fun_C_12(function_inverse(B!13), B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(function_inverse(B!13), B!13) = apply(function_inverse(B!13), tptp_fun_C_12(function_inverse(B!13), B!13)))) | (~((~in(tptp_fun_D_11(function_inverse(B!13), B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(function_inverse(B!13), B!13) = apply(B!13, tptp_fun_D_11(function_inverse(B!13), B!13)))))))) | (~((~(tptp_fun_C_12(function_inverse(B!13), B!13) = apply(B!13, tptp_fun_D_11(function_inverse(B!13), B!13)))) | (~in(tptp_fun_D_11(function_inverse(B!13), B!13), relation_dom(B!13))) | (~((~in(tptp_fun_C_12(function_inverse(B!13), B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(function_inverse(B!13), B!13) = apply(function_inverse(B!13), tptp_fun_C_12(function_inverse(B!13), B!13)))))))))) | (~((~(function_inverse(B!13) = function_inverse(B!13))) | (~((~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(function_inverse(B!13), C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(function_inverse(B!13), C))) | (~in(C, relation_rng(B!13)))))))))))))))))) <=> ((~![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!13))) | (B = function_inverse(B!13)) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13)))))))))))))))))) | ((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (~((~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C))))))))))))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[126])).
% 2.64/2.81 tff(128,plain,
% 2.64/2.81 (((~![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!13))) | (B = function_inverse(B!13)) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13)))))))))))))))))) | ((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (~((~((~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (function_inverse(B!13) = function_inverse(B!13)) | (~((~in(tptp_fun_C_12(function_inverse(B!13), B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(function_inverse(B!13), B!13) = apply(function_inverse(B!13), tptp_fun_C_12(function_inverse(B!13), B!13)))) | (~((~in(tptp_fun_D_11(function_inverse(B!13), B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(function_inverse(B!13), B!13) = apply(B!13, tptp_fun_D_11(function_inverse(B!13), B!13)))))))) | (~((~(tptp_fun_C_12(function_inverse(B!13), B!13) = apply(B!13, tptp_fun_D_11(function_inverse(B!13), B!13)))) | (~in(tptp_fun_D_11(function_inverse(B!13), B!13), relation_dom(B!13))) | (~((~in(tptp_fun_C_12(function_inverse(B!13), B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(function_inverse(B!13), B!13) = apply(function_inverse(B!13), tptp_fun_C_12(function_inverse(B!13), B!13)))))))))) | (~((~(function_inverse(B!13) = function_inverse(B!13))) | (~((~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(function_inverse(B!13), C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(function_inverse(B!13), C))) | (~in(C, relation_rng(B!13)))))))))))))))))) <=> ((~![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!13))) | (B = function_inverse(B!13)) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13)))))))))))))))))) | (~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (~((~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C)))))))))))))),
% 2.64/2.82 inference(transitivity,[status(thm)],[127, 122])).
% 2.64/2.82 tff(129,plain,
% 2.64/2.82 ((~![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!13))) | (B = function_inverse(B!13)) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13)))))))))))))))))) | ((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (~((~((~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (function_inverse(B!13) = function_inverse(B!13)) | (~((~in(tptp_fun_C_12(function_inverse(B!13), B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(function_inverse(B!13), B!13) = apply(function_inverse(B!13), tptp_fun_C_12(function_inverse(B!13), B!13)))) | (~((~in(tptp_fun_D_11(function_inverse(B!13), B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(function_inverse(B!13), B!13) = apply(B!13, tptp_fun_D_11(function_inverse(B!13), B!13)))))))) | (~((~(tptp_fun_C_12(function_inverse(B!13), B!13) = apply(B!13, tptp_fun_D_11(function_inverse(B!13), B!13)))) | (~in(tptp_fun_D_11(function_inverse(B!13), B!13), relation_dom(B!13))) | (~((~in(tptp_fun_C_12(function_inverse(B!13), B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(function_inverse(B!13), B!13) = apply(function_inverse(B!13), tptp_fun_C_12(function_inverse(B!13), B!13)))))))))) | (~((~(function_inverse(B!13) = function_inverse(B!13))) | (~((~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(function_inverse(B!13), C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(function_inverse(B!13), C))) | (~in(C, relation_rng(B!13)))))))))))))))))),
% 2.64/2.82 inference(quant_inst,[status(thm)],[])).
% 2.64/2.82 tff(130,plain,
% 2.64/2.82 ((~![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!13))) | (B = function_inverse(B!13)) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13)))))))))))))))))) | (~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (~((~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C))))))))))))),
% 2.64/2.82 inference(modus_ponens,[status(thm)],[129, 128])).
% 2.64/2.82 tff(131,plain,
% 2.64/2.82 (~((~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C)))))))))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[130, 121, 38, 40])).
% 2.64/2.82 tff(132,plain,
% 2.64/2.82 (((~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C))))))))))) | ![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C)))))))))),
% 2.64/2.82 inference(tautology,[status(thm)],[])).
% 2.64/2.82 tff(133,plain,
% 2.64/2.82 (![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C)))))))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[132, 131])).
% 2.64/2.82 tff(134,plain,
% 2.64/2.82 (((~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C)))))))))) | (~((~(in(A!14, relation_dom(B!13)) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))) | (~in(apply(B!13, A!14), relation_rng(B!13))))) | (~((~in(A!14, relation_dom(B!13))) | (~((~in(apply(B!13, A!14), relation_rng(B!13))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14))))))))))) <=> ((~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C)))))))))) | (~((~(in(A!14, relation_dom(B!13)) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))) | (~in(apply(B!13, A!14), relation_rng(B!13))))) | (~((~in(A!14, relation_dom(B!13))) | (~((~in(apply(B!13, A!14), relation_rng(B!13))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))))))))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(135,plain,
% 2.64/2.82 ((~((~((~in(apply(B!13, A!14), relation_rng(B!13))) | (~((~in(A!14, relation_dom(B!13))) | (~(apply(B!13, A!14) = apply(B!13, A!14))))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))))) | (~((~in(A!14, relation_dom(B!13))) | (~(apply(B!13, A!14) = apply(B!13, A!14))) | (~((~in(apply(B!13, A!14), relation_rng(B!13))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))))))))) <=> (~((~(in(A!14, relation_dom(B!13)) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))) | (~in(apply(B!13, A!14), relation_rng(B!13))))) | (~((~in(A!14, relation_dom(B!13))) | (~((~in(apply(B!13, A!14), relation_rng(B!13))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14))))))))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(136,plain,
% 2.64/2.82 (((~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C)))))))))) | (~((~((~in(apply(B!13, A!14), relation_rng(B!13))) | (~((~in(A!14, relation_dom(B!13))) | (~(apply(B!13, A!14) = apply(B!13, A!14))))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))))) | (~((~in(A!14, relation_dom(B!13))) | (~(apply(B!13, A!14) = apply(B!13, A!14))) | (~((~in(apply(B!13, A!14), relation_rng(B!13))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14))))))))))) <=> ((~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C)))))))))) | (~((~(in(A!14, relation_dom(B!13)) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))) | (~in(apply(B!13, A!14), relation_rng(B!13))))) | (~((~in(A!14, relation_dom(B!13))) | (~((~in(apply(B!13, A!14), relation_rng(B!13))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))))))))))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[135])).
% 2.64/2.82 tff(137,plain,
% 2.64/2.82 (((~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C)))))))))) | (~((~((~in(apply(B!13, A!14), relation_rng(B!13))) | (~((~in(A!14, relation_dom(B!13))) | (~(apply(B!13, A!14) = apply(B!13, A!14))))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))))) | (~((~in(A!14, relation_dom(B!13))) | (~(apply(B!13, A!14) = apply(B!13, A!14))) | (~((~in(apply(B!13, A!14), relation_rng(B!13))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14))))))))))) <=> ((~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C)))))))))) | (~((~(in(A!14, relation_dom(B!13)) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))) | (~in(apply(B!13, A!14), relation_rng(B!13))))) | (~((~in(A!14, relation_dom(B!13))) | (~((~in(apply(B!13, A!14), relation_rng(B!13))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))))))))))),
% 2.64/2.82 inference(transitivity,[status(thm)],[136, 134])).
% 2.64/2.82 tff(138,plain,
% 2.64/2.82 ((~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C)))))))))) | (~((~((~in(apply(B!13, A!14), relation_rng(B!13))) | (~((~in(A!14, relation_dom(B!13))) | (~(apply(B!13, A!14) = apply(B!13, A!14))))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))))) | (~((~in(A!14, relation_dom(B!13))) | (~(apply(B!13, A!14) = apply(B!13, A!14))) | (~((~in(apply(B!13, A!14), relation_rng(B!13))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14))))))))))),
% 2.64/2.82 inference(quant_inst,[status(thm)],[])).
% 2.64/2.82 tff(139,plain,
% 2.64/2.82 ((~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C)))))))))) | (~((~(in(A!14, relation_dom(B!13)) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))) | (~in(apply(B!13, A!14), relation_rng(B!13))))) | (~((~in(A!14, relation_dom(B!13))) | (~((~in(apply(B!13, A!14), relation_rng(B!13))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14))))))))))),
% 2.64/2.82 inference(modus_ponens,[status(thm)],[138, 137])).
% 2.64/2.82 tff(140,plain,
% 2.64/2.82 ($false),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[139, 133, 87])).
% 2.64/2.82 tff(141,plain,(A!14 = apply(relation_composition(B!13, function_inverse(B!13)), A!14)), inference(lemma,lemma(discharge,[]))).
% 2.64/2.82 tff(142,plain,
% 2.64/2.82 (A!14 = apply(function_inverse(B!13), apply(B!13, A!14))),
% 2.64/2.82 inference(transitivity,[status(thm)],[141, 77])).
% 2.64/2.82 tff(143,plain,
% 2.64/2.82 ((~(~((~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))) | (~(A!14 = apply(relation_composition(B!13, function_inverse(B!13)), A!14)))))) <=> ((~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))) | (~(A!14 = apply(relation_composition(B!13, function_inverse(B!13)), A!14))))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(144,plain,
% 2.64/2.84 (((A!14 = apply(function_inverse(B!13), apply(B!13, A!14))) & (A!14 = apply(relation_composition(B!13, function_inverse(B!13)), A!14))) <=> (~((~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))) | (~(A!14 = apply(relation_composition(B!13, function_inverse(B!13)), A!14)))))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(145,plain,
% 2.64/2.84 ((~((A!14 = apply(function_inverse(B!13), apply(B!13, A!14))) & (A!14 = apply(relation_composition(B!13, function_inverse(B!13)), A!14)))) <=> (~(~((~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))) | (~(A!14 = apply(relation_composition(B!13, function_inverse(B!13)), A!14))))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[144])).
% 2.64/2.84 tff(146,plain,
% 2.64/2.84 ((~((A!14 = apply(function_inverse(B!13), apply(B!13, A!14))) & (A!14 = apply(relation_composition(B!13, function_inverse(B!13)), A!14)))) <=> ((~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))) | (~(A!14 = apply(relation_composition(B!13, function_inverse(B!13)), A!14))))),
% 2.64/2.84 inference(transitivity,[status(thm)],[145, 143])).
% 2.64/2.84 tff(147,plain,
% 2.64/2.84 (~((A!14 = apply(function_inverse(B!13), apply(B!13, A!14))) & (A!14 = apply(relation_composition(B!13, function_inverse(B!13)), A!14)))),
% 2.64/2.84 inference(or_elim,[status(thm)],[10])).
% 2.64/2.84 tff(148,plain,
% 2.64/2.84 ((~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))) | (~(A!14 = apply(relation_composition(B!13, function_inverse(B!13)), A!14)))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[147, 146])).
% 2.64/2.84 tff(149,plain,
% 2.64/2.84 (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[148, 141])).
% 2.64/2.84 tff(150,plain,
% 2.64/2.84 ($false),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[149, 142])).
% 2.64/2.84 % SZS output end Proof
% 2.64/2.84 % E exiting
%------------------------------------------------------------------------------