%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU221+3 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:27:17 AM UTC 2025
% Result : Theorem 0.21s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU221+3 : TPTP v9.0.0. Released v3.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 06:22:40 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.41 % SZS status Theorem
% 0.21/0.41 % SZS output start Proof
% 0.21/0.41 tff(tptp_fun_C_0_type, type, (
% 0.21/0.41 tptp_fun_C_0: $i > $i)).
% 0.21/0.41 tff(function_inverse_type, type, (
% 0.21/0.41 function_inverse: $i > $i)).
% 0.21/0.41 tff(tptp_fun_A_15_type, type, (
% 0.21/0.41 tptp_fun_A_15: $i)).
% 0.21/0.41 tff(tptp_fun_B_1_type, type, (
% 0.21/0.41 tptp_fun_B_1: $i > $i)).
% 0.21/0.41 tff(apply_type, type, (
% 0.21/0.41 apply: ( $i * $i ) > $i)).
% 0.21/0.41 tff(in_type, type, (
% 0.21/0.41 in: ( $i * $i ) > $o)).
% 0.21/0.41 tff(relation_dom_type, type, (
% 0.21/0.41 relation_dom: $i > $i)).
% 0.21/0.41 tff(one_to_one_type, type, (
% 0.21/0.41 one_to_one: $i > $o)).
% 0.21/0.41 tff(relation_type, type, (
% 0.21/0.41 relation: $i > $o)).
% 0.21/0.41 tff(function_type, type, (
% 0.21/0.41 function: $i > $o)).
% 0.21/0.41 tff(relation_composition_type, type, (
% 0.21/0.41 relation_composition: ( $i * $i ) > $i)).
% 0.21/0.41 tff(relation_rng_type, type, (
% 0.21/0.41 relation_rng: $i > $i)).
% 0.21/0.41 tff(tptp_fun_C_14_type, type, (
% 0.21/0.41 tptp_fun_C_14: ( $i * $i ) > $i)).
% 0.21/0.41 tff(tptp_fun_D_13_type, type, (
% 0.21/0.41 tptp_fun_D_13: ( $i * $i ) > $i)).
% 0.21/0.41 tff(1,plain,
% 0.21/0.41 ((~(one_to_one(function_inverse(A!15)) | (~(relation(A!15) & function(A!15))) | (~one_to_one(A!15)))) <=> (~(one_to_one(function_inverse(A!15)) | (~(relation(A!15) & function(A!15))) | (~one_to_one(A!15))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(2,plain,
% 0.21/0.41 ((~![A: $i] : (one_to_one(function_inverse(A)) | (~(relation(A) & function(A))) | (~one_to_one(A)))) <=> (~![A: $i] : (one_to_one(function_inverse(A)) | (~(relation(A) & function(A))) | (~one_to_one(A))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(3,plain,
% 0.21/0.41 ((~![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => one_to_one(function_inverse(A))))) <=> (~![A: $i] : (one_to_one(function_inverse(A)) | (~(relation(A) & function(A))) | (~one_to_one(A))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(4,axiom,(~![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => one_to_one(function_inverse(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t62_funct_1')).
% 0.21/0.41 tff(5,plain,
% 0.21/0.41 (~![A: $i] : (one_to_one(function_inverse(A)) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.41 tff(6,plain,
% 0.21/0.41 (~![A: $i] : (one_to_one(function_inverse(A)) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.21/0.41 tff(7,plain,
% 0.21/0.41 (~![A: $i] : (one_to_one(function_inverse(A)) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.41 tff(8,plain,
% 0.21/0.41 (~![A: $i] : (one_to_one(function_inverse(A)) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.21/0.41 tff(9,plain,(
% 0.21/0.41 ~(one_to_one(function_inverse(A!15)) | (~(relation(A!15) & function(A!15))) | (~one_to_one(A!15)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[8])).
% 0.21/0.41 tff(10,plain,
% 0.21/0.41 (~(one_to_one(function_inverse(A!15)) | (~(relation(A!15) & function(A!15))) | (~one_to_one(A!15)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.21/0.41 tff(11,plain,
% 0.21/0.41 (relation(A!15) & function(A!15)),
% 0.21/0.41 inference(or_elim,[status(thm)],[10])).
% 0.21/0.41 tff(12,plain,
% 0.21/0.41 (function(A!15)),
% 0.21/0.41 inference(and_elim,[status(thm)],[11])).
% 0.21/0.41 tff(13,plain,
% 0.21/0.41 (relation(A!15)),
% 0.21/0.41 inference(and_elim,[status(thm)],[11])).
% 0.21/0.41 tff(14,plain,
% 0.21/0.41 (^[A: $i] : refl(((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A)))))) <=> ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A)))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(15,plain,
% 0.21/0.41 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A)))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[14])).
% 0.21/0.41 tff(16,plain,
% 0.21/0.41 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(A) & function(A)) <=> (~((~relation(A)) | (~function(A))))), ((~(relation(A) & function(A))) <=> (~(~((~relation(A)) | (~function(A))))))), rewrite((~(~((~relation(A)) | (~function(A))))) <=> ((~relation(A)) | (~function(A)))), ((~(relation(A) & function(A))) <=> ((~relation(A)) | (~function(A))))), rewrite((relation(function_inverse(A)) & function(function_inverse(A))) <=> (~((~relation(function_inverse(A))) | (~function(function_inverse(A)))))), (((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A)))) <=> (((~relation(A)) | (~function(A))) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A)))))))), rewrite((((~relation(A)) | (~function(A))) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A)))))) <=> ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))), (((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A)))) <=> ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(17,plain,
% 0.21/0.41 (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A)))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[16])).
% 0.21/0.41 tff(18,plain,
% 0.21/0.41 (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A)))) <=> ![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(19,plain,
% 0.21/0.41 (^[A: $i] : rewrite(((relation(A) & function(A)) => (relation(function_inverse(A)) & function(function_inverse(A)))) <=> ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(20,plain,
% 0.21/0.41 (![A: $i] : ((relation(A) & function(A)) => (relation(function_inverse(A)) & function(function_inverse(A)))) <=> ![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[19])).
% 0.21/0.41 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')).
% 0.21/0.41 tff(22,plain,
% 0.21/0.41 (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.21/0.41 tff(23,plain,
% 0.21/0.41 (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.21/0.41 tff(24,plain,(
% 0.21/0.41 ![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 0.21/0.41 inference(skolemize,[status(sab)],[23])).
% 0.21/0.41 tff(25,plain,
% 0.21/0.41 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.21/0.41 tff(26,plain,
% 0.21/0.41 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[25, 15])).
% 0.21/0.41 tff(27,plain,
% 0.21/0.41 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | ((~function(A!15)) | (~relation(A!15)) | (~((~relation(function_inverse(A!15))) | (~function(function_inverse(A!15))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | (~function(A!15)) | (~relation(A!15)) | (~((~relation(function_inverse(A!15))) | (~function(function_inverse(A!15))))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(28,plain,
% 0.21/0.41 (((~relation(A!15)) | (~function(A!15)) | (~((~relation(function_inverse(A!15))) | (~function(function_inverse(A!15)))))) <=> ((~function(A!15)) | (~relation(A!15)) | (~((~relation(function_inverse(A!15))) | (~function(function_inverse(A!15))))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(29,plain,
% 0.21/0.41 ((~((~relation(function_inverse(A!15))) | (~function(function_inverse(A!15))))) <=> (~((~relation(function_inverse(A!15))) | (~function(function_inverse(A!15)))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(30,plain,
% 0.21/0.41 (((~relation(A!15)) | (~function(A!15)) | (~((~relation(function_inverse(A!15))) | (~function(function_inverse(A!15)))))) <=> ((~relation(A!15)) | (~function(A!15)) | (~((~relation(function_inverse(A!15))) | (~function(function_inverse(A!15))))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[29])).
% 0.21/0.41 tff(31,plain,
% 0.21/0.41 (((~relation(A!15)) | (~function(A!15)) | (~((~relation(function_inverse(A!15))) | (~function(function_inverse(A!15)))))) <=> ((~function(A!15)) | (~relation(A!15)) | (~((~relation(function_inverse(A!15))) | (~function(function_inverse(A!15))))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[30, 28])).
% 0.21/0.41 tff(32,plain,
% 0.21/0.41 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | ((~relation(A!15)) | (~function(A!15)) | (~((~relation(function_inverse(A!15))) | (~function(function_inverse(A!15))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | ((~function(A!15)) | (~relation(A!15)) | (~((~relation(function_inverse(A!15))) | (~function(function_inverse(A!15)))))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[31])).
% 0.21/0.41 tff(33,plain,
% 0.21/0.41 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | ((~relation(A!15)) | (~function(A!15)) | (~((~relation(function_inverse(A!15))) | (~function(function_inverse(A!15))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | (~function(A!15)) | (~relation(A!15)) | (~((~relation(function_inverse(A!15))) | (~function(function_inverse(A!15))))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[32, 27])).
% 0.21/0.41 tff(34,plain,
% 0.21/0.41 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | ((~relation(A!15)) | (~function(A!15)) | (~((~relation(function_inverse(A!15))) | (~function(function_inverse(A!15))))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(35,plain,
% 0.21/0.41 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | (~function(A!15)) | (~relation(A!15)) | (~((~relation(function_inverse(A!15))) | (~function(function_inverse(A!15)))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.21/0.41 tff(36,plain,
% 0.21/0.41 (~((~relation(function_inverse(A!15))) | (~function(function_inverse(A!15))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[35, 26, 13, 12])).
% 0.21/0.41 tff(37,plain,
% 0.21/0.41 (((~relation(function_inverse(A!15))) | (~function(function_inverse(A!15)))) | relation(function_inverse(A!15))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(38,plain,
% 0.21/0.41 (relation(function_inverse(A!15))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.21/0.41 tff(39,plain,
% 0.21/0.41 (((~relation(function_inverse(A!15))) | (~function(function_inverse(A!15)))) | function(function_inverse(A!15))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(40,plain,
% 0.21/0.41 (function(function_inverse(A!15))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[39, 36])).
% 0.21/0.41 tff(41,plain,
% 0.21/0.41 (^[A: $i] : refl(((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))))))))) <=> ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))))))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(42,plain,
% 0.21/0.41 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[41])).
% 0.21/0.41 tff(43,plain,
% 0.21/0.41 (^[A: $i] : rewrite(((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))))))))) <=> ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))))))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(44,plain,
% 0.21/0.41 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[43])).
% 0.21/0.41 tff(45,plain,
% 0.21/0.41 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[44, 42])).
% 0.21/0.41 tff(46,plain,
% 0.21/0.41 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(A) & function(A)) <=> (~((~relation(A)) | (~function(A))))), ((~(relation(A) & function(A))) <=> (~(~((~relation(A)) | (~function(A))))))), rewrite((~(~((~relation(A)) | (~function(A))))) <=> ((~relation(A)) | (~function(A)))), ((~(relation(A) & function(A))) <=> ((~relation(A)) | (~function(A))))), trans(monotonicity(rewrite(((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) <=> ((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))), rewrite((one_to_one(A) | (~((~(in(tptp_fun_B_1(A), relation_dom(A)) & in(tptp_fun_C_0(A), relation_dom(A)) & (apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))) | (tptp_fun_B_1(A) = tptp_fun_C_0(A))))) <=> (one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))), ((((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) & (one_to_one(A) | (~((~(in(tptp_fun_B_1(A), relation_dom(A)) & in(tptp_fun_C_0(A), relation_dom(A)) & (apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))) | (tptp_fun_B_1(A) = tptp_fun_C_0(A)))))) <=> (((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C))))) & (one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))), rewrite((((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C))))) & (one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))) <=> (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))))))))), ((((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) & (one_to_one(A) | (~((~(in(tptp_fun_B_1(A), relation_dom(A)) & in(tptp_fun_C_0(A), relation_dom(A)) & (apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))) | (tptp_fun_B_1(A) = tptp_fun_C_0(A)))))) <=> (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))), (((~(relation(A) & function(A))) | (((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) & (one_to_one(A) | (~((~(in(tptp_fun_B_1(A), relation_dom(A)) & in(tptp_fun_C_0(A), relation_dom(A)) & (apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))) | (tptp_fun_B_1(A) = tptp_fun_C_0(A))))))) <=> (((~relation(A)) | (~function(A))) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))))))))))), rewrite((((~relation(A)) | (~function(A))) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))))))))) <=> ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))), (((~(relation(A) & function(A))) | (((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) & (one_to_one(A) | (~((~(in(tptp_fun_B_1(A), relation_dom(A)) & in(tptp_fun_C_0(A), relation_dom(A)) & (apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))) | (tptp_fun_B_1(A) = tptp_fun_C_0(A))))))) <=> ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(47,plain,
% 0.21/0.41 (![A: $i] : ((~(relation(A) & function(A))) | (((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) & (one_to_one(A) | (~((~(in(tptp_fun_B_1(A), relation_dom(A)) & in(tptp_fun_C_0(A), relation_dom(A)) & (apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))) | (tptp_fun_B_1(A) = tptp_fun_C_0(A))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[46])).
% 0.21/0.41 tff(48,plain,
% 0.21/0.41 (![A: $i] : ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C)))) <=> ![A: $i] : ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(49,plain,
% 0.21/0.41 (^[A: $i] : trans(monotonicity(rewrite((one_to_one(A) <=> ![B: $i, C: $i] : (((in(B, relation_dom(A)) & in(C, relation_dom(A))) & (apply(A, B) = apply(A, C))) => (B = C))) <=> (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C)))), (((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : (((in(B, relation_dom(A)) & in(C, relation_dom(A))) & (apply(A, B) = apply(A, C))) => (B = C)))) <=> ((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C)))))), rewrite(((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C)))) <=> ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))), (((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : (((in(B, relation_dom(A)) & in(C, relation_dom(A))) & (apply(A, B) = apply(A, C))) => (B = C)))) <=> ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(50,plain,
% 0.21/0.41 (![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : (((in(B, relation_dom(A)) & in(C, relation_dom(A))) & (apply(A, B) = apply(A, C))) => (B = C)))) <=> ![A: $i] : ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[49])).
% 0.21/0.42 tff(51,axiom,(![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : (((in(B, relation_dom(A)) & in(C, relation_dom(A))) & (apply(A, B) = apply(A, C))) => (B = C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d8_funct_1')).
% 0.21/0.42 tff(52,plain,
% 0.21/0.42 (![A: $i] : ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.21/0.42 tff(53,plain,
% 0.21/0.42 (![A: $i] : ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.21/0.42 tff(54,plain,(
% 0.21/0.42 ![A: $i] : ((~(relation(A) & function(A))) | (((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) & (one_to_one(A) | (~((~(in(tptp_fun_B_1(A), relation_dom(A)) & in(tptp_fun_C_0(A), relation_dom(A)) & (apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))) | (tptp_fun_B_1(A) = tptp_fun_C_0(A)))))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[53])).
% 0.21/0.42 tff(55,plain,
% 0.21/0.42 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.21/0.42 tff(56,plain,
% 0.21/0.42 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[55, 45])).
% 0.21/0.42 tff(57,plain,
% 0.21/0.42 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))) | ((~relation(function_inverse(A!15))) | (~function(function_inverse(A!15))) | (~((~((~one_to_one(function_inverse(A!15))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(function_inverse(A!15)))) | (~in(C, relation_dom(function_inverse(A!15)))) | (~(apply(function_inverse(A!15), B) = apply(function_inverse(A!15), C)))))) | (~(one_to_one(function_inverse(A!15)) | (~((~(apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15))) = apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15))))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (tptp_fun_B_1(function_inverse(A!15)) = tptp_fun_C_0(function_inverse(A!15))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))) | (~relation(function_inverse(A!15))) | (~function(function_inverse(A!15))) | (~((~((~one_to_one(function_inverse(A!15))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(function_inverse(A!15)))) | (~in(C, relation_dom(function_inverse(A!15)))) | (~(apply(function_inverse(A!15), B) = apply(function_inverse(A!15), C)))))) | (~(one_to_one(function_inverse(A!15)) | (~((~(apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15))) = apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15))))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (tptp_fun_B_1(function_inverse(A!15)) = tptp_fun_C_0(function_inverse(A!15))))))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(58,plain,
% 0.21/0.42 (((~relation(function_inverse(A!15))) | (~function(function_inverse(A!15))) | (~((~((~one_to_one(function_inverse(A!15))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(function_inverse(A!15)))) | (~in(C, relation_dom(function_inverse(A!15)))) | (~(apply(function_inverse(A!15), B) = apply(function_inverse(A!15), C)))))) | (~(one_to_one(function_inverse(A!15)) | (~((~(apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15))) = apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15))))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (tptp_fun_B_1(function_inverse(A!15)) = tptp_fun_C_0(function_inverse(A!15)))))))))) <=> ((~relation(function_inverse(A!15))) | (~function(function_inverse(A!15))) | (~((~((~one_to_one(function_inverse(A!15))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(function_inverse(A!15)))) | (~in(C, relation_dom(function_inverse(A!15)))) | (~(apply(function_inverse(A!15), B) = apply(function_inverse(A!15), C)))))) | (~(one_to_one(function_inverse(A!15)) | (~((~(apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15))) = apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15))))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (tptp_fun_B_1(function_inverse(A!15)) = tptp_fun_C_0(function_inverse(A!15))))))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(59,plain,
% 0.21/0.42 ((~((~((~one_to_one(function_inverse(A!15))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(function_inverse(A!15)))) | (~in(C, relation_dom(function_inverse(A!15)))) | (~(apply(function_inverse(A!15), B) = apply(function_inverse(A!15), C)))))) | (~(one_to_one(function_inverse(A!15)) | (~((tptp_fun_B_1(function_inverse(A!15)) = tptp_fun_C_0(function_inverse(A!15))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (~(apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15))) = apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15))))))))))) <=> (~((~((~one_to_one(function_inverse(A!15))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(function_inverse(A!15)))) | (~in(C, relation_dom(function_inverse(A!15)))) | (~(apply(function_inverse(A!15), B) = apply(function_inverse(A!15), C)))))) | (~(one_to_one(function_inverse(A!15)) | (~((~(apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15))) = apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15))))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (tptp_fun_B_1(function_inverse(A!15)) = tptp_fun_C_0(function_inverse(A!15)))))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(60,plain,
% 0.21/0.42 (((~relation(function_inverse(A!15))) | (~function(function_inverse(A!15))) | (~((~((~one_to_one(function_inverse(A!15))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(function_inverse(A!15)))) | (~in(C, relation_dom(function_inverse(A!15)))) | (~(apply(function_inverse(A!15), B) = apply(function_inverse(A!15), C)))))) | (~(one_to_one(function_inverse(A!15)) | (~((tptp_fun_B_1(function_inverse(A!15)) = tptp_fun_C_0(function_inverse(A!15))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (~(apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15))) = apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15)))))))))))) <=> ((~relation(function_inverse(A!15))) | (~function(function_inverse(A!15))) | (~((~((~one_to_one(function_inverse(A!15))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(function_inverse(A!15)))) | (~in(C, relation_dom(function_inverse(A!15)))) | (~(apply(function_inverse(A!15), B) = apply(function_inverse(A!15), C)))))) | (~(one_to_one(function_inverse(A!15)) | (~((~(apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15))) = apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15))))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (tptp_fun_B_1(function_inverse(A!15)) = tptp_fun_C_0(function_inverse(A!15))))))))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[59])).
% 0.21/0.42 tff(61,plain,
% 0.21/0.42 (((~relation(function_inverse(A!15))) | (~function(function_inverse(A!15))) | (~((~((~one_to_one(function_inverse(A!15))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(function_inverse(A!15)))) | (~in(C, relation_dom(function_inverse(A!15)))) | (~(apply(function_inverse(A!15), B) = apply(function_inverse(A!15), C)))))) | (~(one_to_one(function_inverse(A!15)) | (~((tptp_fun_B_1(function_inverse(A!15)) = tptp_fun_C_0(function_inverse(A!15))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (~(apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15))) = apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15)))))))))))) <=> ((~relation(function_inverse(A!15))) | (~function(function_inverse(A!15))) | (~((~((~one_to_one(function_inverse(A!15))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(function_inverse(A!15)))) | (~in(C, relation_dom(function_inverse(A!15)))) | (~(apply(function_inverse(A!15), B) = apply(function_inverse(A!15), C)))))) | (~(one_to_one(function_inverse(A!15)) | (~((~(apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15))) = apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15))))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (tptp_fun_B_1(function_inverse(A!15)) = tptp_fun_C_0(function_inverse(A!15))))))))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[60, 58])).
% 0.21/0.42 tff(62,plain,
% 0.21/0.42 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))) | ((~relation(function_inverse(A!15))) | (~function(function_inverse(A!15))) | (~((~((~one_to_one(function_inverse(A!15))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(function_inverse(A!15)))) | (~in(C, relation_dom(function_inverse(A!15)))) | (~(apply(function_inverse(A!15), B) = apply(function_inverse(A!15), C)))))) | (~(one_to_one(function_inverse(A!15)) | (~((tptp_fun_B_1(function_inverse(A!15)) = tptp_fun_C_0(function_inverse(A!15))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (~(apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15))) = apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15))))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))) | ((~relation(function_inverse(A!15))) | (~function(function_inverse(A!15))) | (~((~((~one_to_one(function_inverse(A!15))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(function_inverse(A!15)))) | (~in(C, relation_dom(function_inverse(A!15)))) | (~(apply(function_inverse(A!15), B) = apply(function_inverse(A!15), C)))))) | (~(one_to_one(function_inverse(A!15)) | (~((~(apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15))) = apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15))))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (tptp_fun_B_1(function_inverse(A!15)) = tptp_fun_C_0(function_inverse(A!15)))))))))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[61])).
% 0.21/0.42 tff(63,plain,
% 0.21/0.42 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))) | ((~relation(function_inverse(A!15))) | (~function(function_inverse(A!15))) | (~((~((~one_to_one(function_inverse(A!15))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(function_inverse(A!15)))) | (~in(C, relation_dom(function_inverse(A!15)))) | (~(apply(function_inverse(A!15), B) = apply(function_inverse(A!15), C)))))) | (~(one_to_one(function_inverse(A!15)) | (~((tptp_fun_B_1(function_inverse(A!15)) = tptp_fun_C_0(function_inverse(A!15))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (~(apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15))) = apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15))))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))) | (~relation(function_inverse(A!15))) | (~function(function_inverse(A!15))) | (~((~((~one_to_one(function_inverse(A!15))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(function_inverse(A!15)))) | (~in(C, relation_dom(function_inverse(A!15)))) | (~(apply(function_inverse(A!15), B) = apply(function_inverse(A!15), C)))))) | (~(one_to_one(function_inverse(A!15)) | (~((~(apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15))) = apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15))))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (tptp_fun_B_1(function_inverse(A!15)) = tptp_fun_C_0(function_inverse(A!15))))))))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[62, 57])).
% 0.21/0.42 tff(64,plain,
% 0.21/0.42 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))) | ((~relation(function_inverse(A!15))) | (~function(function_inverse(A!15))) | (~((~((~one_to_one(function_inverse(A!15))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(function_inverse(A!15)))) | (~in(C, relation_dom(function_inverse(A!15)))) | (~(apply(function_inverse(A!15), B) = apply(function_inverse(A!15), C)))))) | (~(one_to_one(function_inverse(A!15)) | (~((tptp_fun_B_1(function_inverse(A!15)) = tptp_fun_C_0(function_inverse(A!15))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (~(apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15))) = apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15))))))))))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(65,plain,
% 0.21/0.43 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))) | (~relation(function_inverse(A!15))) | (~function(function_inverse(A!15))) | (~((~((~one_to_one(function_inverse(A!15))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(function_inverse(A!15)))) | (~in(C, relation_dom(function_inverse(A!15)))) | (~(apply(function_inverse(A!15), B) = apply(function_inverse(A!15), C)))))) | (~(one_to_one(function_inverse(A!15)) | (~((~(apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15))) = apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15))))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (tptp_fun_B_1(function_inverse(A!15)) = tptp_fun_C_0(function_inverse(A!15)))))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.21/0.43 tff(66,plain,
% 0.21/0.43 ((~relation(function_inverse(A!15))) | (~function(function_inverse(A!15))) | (~((~((~one_to_one(function_inverse(A!15))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(function_inverse(A!15)))) | (~in(C, relation_dom(function_inverse(A!15)))) | (~(apply(function_inverse(A!15), B) = apply(function_inverse(A!15), C)))))) | (~(one_to_one(function_inverse(A!15)) | (~((~(apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15))) = apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15))))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (tptp_fun_B_1(function_inverse(A!15)) = tptp_fun_C_0(function_inverse(A!15)))))))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[65, 56])).
% 0.21/0.43 tff(67,plain,
% 0.21/0.43 (~((~((~one_to_one(function_inverse(A!15))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(function_inverse(A!15)))) | (~in(C, relation_dom(function_inverse(A!15)))) | (~(apply(function_inverse(A!15), B) = apply(function_inverse(A!15), C)))))) | (~(one_to_one(function_inverse(A!15)) | (~((~(apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15))) = apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15))))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (tptp_fun_B_1(function_inverse(A!15)) = tptp_fun_C_0(function_inverse(A!15))))))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[66, 40, 38])).
% 0.21/0.43 tff(68,plain,
% 0.21/0.43 (((~((~one_to_one(function_inverse(A!15))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(function_inverse(A!15)))) | (~in(C, relation_dom(function_inverse(A!15)))) | (~(apply(function_inverse(A!15), B) = apply(function_inverse(A!15), C)))))) | (~(one_to_one(function_inverse(A!15)) | (~((~(apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15))) = apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15))))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (tptp_fun_B_1(function_inverse(A!15)) = tptp_fun_C_0(function_inverse(A!15)))))))) | (one_to_one(function_inverse(A!15)) | (~((~(apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15))) = apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15))))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (tptp_fun_B_1(function_inverse(A!15)) = tptp_fun_C_0(function_inverse(A!15))))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(69,plain,
% 0.21/0.43 (one_to_one(function_inverse(A!15)) | (~((~(apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15))) = apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15))))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (tptp_fun_B_1(function_inverse(A!15)) = tptp_fun_C_0(function_inverse(A!15)))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.21/0.43 tff(70,plain,
% 0.21/0.43 (~one_to_one(function_inverse(A!15))),
% 0.21/0.43 inference(or_elim,[status(thm)],[10])).
% 0.21/0.43 tff(71,plain,
% 0.21/0.43 ((~(one_to_one(function_inverse(A!15)) | (~((~(apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15))) = apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15))))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (tptp_fun_B_1(function_inverse(A!15)) = tptp_fun_C_0(function_inverse(A!15))))))) | one_to_one(function_inverse(A!15)) | (~((~(apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15))) = apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15))))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (tptp_fun_B_1(function_inverse(A!15)) = tptp_fun_C_0(function_inverse(A!15)))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(72,plain,
% 0.21/0.43 ((~(one_to_one(function_inverse(A!15)) | (~((~(apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15))) = apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15))))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (tptp_fun_B_1(function_inverse(A!15)) = tptp_fun_C_0(function_inverse(A!15))))))) | (~((~(apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15))) = apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15))))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (tptp_fun_B_1(function_inverse(A!15)) = tptp_fun_C_0(function_inverse(A!15)))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.21/0.43 tff(73,plain,
% 0.21/0.43 (~((~(apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15))) = apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15))))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (tptp_fun_B_1(function_inverse(A!15)) = tptp_fun_C_0(function_inverse(A!15))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[72, 69])).
% 0.21/0.43 tff(74,plain,
% 0.21/0.43 (((~(apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15))) = apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15))))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (tptp_fun_B_1(function_inverse(A!15)) = tptp_fun_C_0(function_inverse(A!15)))) | (apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15))) = apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(75,plain,
% 0.21/0.43 (apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15))) = apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.21/0.43 tff(76,plain,
% 0.21/0.43 (apply(A!15, apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15)))) = apply(A!15, apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[75])).
% 0.21/0.43 tff(77,plain,
% 0.21/0.43 (apply(A!15, apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15)))) = apply(A!15, apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15))))),
% 0.21/0.43 inference(symmetry,[status(thm)],[76])).
% 0.21/0.43 tff(78,plain,
% 0.21/0.43 (one_to_one(A!15)),
% 0.21/0.43 inference(or_elim,[status(thm)],[10])).
% 0.21/0.43 tff(79,plain,
% 0.21/0.43 (^[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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))))) <=> (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))))))))) <=> ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(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))))))))))))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(80,plain,
% 0.21/0.43 (![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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(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))))))))))))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[79])).
% 0.21/0.43 tff(81,plain,
% 0.21/0.43 (^[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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(82,plain,
% 0.21/0.43 (![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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))))))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[81])).
% 0.21/0.44 tff(83,plain,
% 0.21/0.44 (^[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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(84,plain,
% 0.21/0.44 (![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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))))))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[83])).
% 0.21/0.44 tff(85,plain,
% 0.21/0.44 (![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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))))))))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[84, 82])).
% 0.21/0.44 tff(86,plain,
% 0.21/0.44 (^[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_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) <=> (~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))))), ((~(in(tptp_fun_C_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))) <=> (~(~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))))))), rewrite((~(~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))))) <=> ((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))), ((~(in(tptp_fun_C_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))) <=> ((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))))), rewrite((in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))) <=> (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))))), (((~(in(tptp_fun_C_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))) | (in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) <=> (((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))))))), rewrite((((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))))) <=> ((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))), (((~(in(tptp_fun_C_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))) | (in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) <=> ((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))))))), trans(monotonicity(trans(monotonicity(rewrite((in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))) <=> (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))))), ((~(in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) <=> (~(~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))))))), rewrite((~(~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))))) <=> ((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))), ((~(in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) <=> ((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))))), rewrite((in(tptp_fun_C_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) <=> (~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))))), (((~(in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) | (in(tptp_fun_C_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))) <=> (((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) | (~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))))))), rewrite((((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) | (~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))))) <=> ((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))), (((~(in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) | (in(tptp_fun_C_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))) <=> ((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))))), ((((~(in(tptp_fun_C_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))) | (in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) & ((~(in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) | (in(tptp_fun_C_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) <=> (((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))))) & ((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))), rewrite((((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))))) & ((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))) <=> (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))))))), ((((~(in(tptp_fun_C_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))) | (in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) & ((~(in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) | (in(tptp_fun_C_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) <=> (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))))), ((~(((~(in(tptp_fun_C_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))) | (in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) & ((~(in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) | (in(tptp_fun_C_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))))) <=> (~(~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))))))))), rewrite((~(~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))))))) <=> ((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))), ((~(((~(in(tptp_fun_C_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))) | (in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) & ((~(in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) | (in(tptp_fun_C_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))))) <=> ((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))))))), (((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))) | (in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) & ((~(in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) | (in(tptp_fun_C_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))))) <=> ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | ((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))))), rewrite(((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | ((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) <=> ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))), (((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))) | (in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) & ((~(in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) | (in(tptp_fun_C_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))))) <=> ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(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_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))) | (in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) & ((~(in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) | (in(tptp_fun_C_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(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_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))) | (in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) & ((~(in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) | (in(tptp_fun_C_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(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_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))) | (in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) & ((~(in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) | (in(tptp_fun_C_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(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_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))) | (in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) & ((~(in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) | (in(tptp_fun_C_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(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_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))) | (in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) & ((~(in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) | (in(tptp_fun_C_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(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_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))) | (in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) & ((~(in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) | (in(tptp_fun_C_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(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_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))) | (in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) & ((~(in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) | (in(tptp_fun_C_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))))))))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(87,plain,
% 0.21/0.45 (![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_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))) | (in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) & ((~(in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) | (in(tptp_fun_C_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))))))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[86])).
% 0.21/0.45 tff(88,plain,
% 0.21/0.45 (^[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_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))) | (in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) & ((~(in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) | (in(tptp_fun_C_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(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_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))) | (in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) & ((~(in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) | (in(tptp_fun_C_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(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_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))) | (in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) & ((~(in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) | (in(tptp_fun_C_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(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_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))) | (in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) & ((~(in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) | (in(tptp_fun_C_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(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_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))) | (in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) & ((~(in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) | (in(tptp_fun_C_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(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_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))) | (in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) & ((~(in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) | (in(tptp_fun_C_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(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_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))) | (in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) & ((~(in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) | (in(tptp_fun_C_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(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_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))) | (in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) & ((~(in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) | (in(tptp_fun_C_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(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_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))) | (in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) & ((~(in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) | (in(tptp_fun_C_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(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_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))) | (in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) & ((~(in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) | (in(tptp_fun_C_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))))))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(89,plain,
% 0.21/0.45 (![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_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))) | (in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) & ((~(in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) | (in(tptp_fun_C_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(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_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))) | (in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) & ((~(in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) | (in(tptp_fun_C_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[88])).
% 0.21/0.45 tff(90,plain,
% 0.21/0.45 (![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)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(91,plain,
% 0.21/0.45 (^[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)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(92,plain,
% 0.21/0.45 (![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)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[91])).
% 0.21/0.45 tff(93,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')).
% 0.21/0.45 tff(94,plain,
% 0.21/0.45 (![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)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.21/0.45 tff(95,plain,
% 0.21/0.45 (![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)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[94, 90])).
% 0.21/0.45 tff(96,plain,(
% 0.21/0.45 ![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_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))) | (in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) & ((~(in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) | (in(tptp_fun_C_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))))))))) | (~one_to_one(A)))),
% 0.21/0.45 inference(skolemize,[status(sab)],[95])).
% 0.21/0.45 tff(97,plain,
% 0.21/0.45 (![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_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A))))) | (in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) & ((~(in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))) | (in(tptp_fun_C_14(B, A), relation_rng(A)) & (tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[96, 89])).
% 0.21/0.45 tff(98,plain,
% 0.21/0.45 (![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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))))))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[97, 87])).
% 0.21/0.45 tff(99,plain,
% 0.21/0.45 (![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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A))))))))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[98, 85])).
% 0.21/0.45 tff(100,plain,
% 0.21/0.45 (![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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(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))))))))))))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[99, 80])).
% 0.21/0.45 tff(101,plain,
% 0.21/0.45 (((~![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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(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!15)) | (~function(A!15)) | (~relation(A!15)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(A!15))) | (B = function_inverse(A!15)) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))) | (~((~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))))))) | (~((~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))) | (~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))))))))) | (~((~(B = function_inverse(A!15))) | (~((~(relation_dom(B) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15))))))))))))))))))) <=> ((~![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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(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!15)) | (~function(A!15)) | (~relation(A!15)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(A!15))) | (B = function_inverse(A!15)) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))) | (~((~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))))))) | (~((~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))) | (~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))))))))) | (~((~(B = function_inverse(A!15))) | (~((~(relation_dom(B) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15))))))))))))))))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(102,plain,
% 0.21/0.46 (((~one_to_one(A!15)) | (~relation(A!15)) | (~function(A!15)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(A!15))) | (B = function_inverse(A!15)) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))) | (~((~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))))))) | (~((~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))) | (~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))))))))) | (~((~(B = function_inverse(A!15))) | (~((~(relation_dom(B) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15)))))))))))))))))) <=> ((~one_to_one(A!15)) | (~function(A!15)) | (~relation(A!15)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(A!15))) | (B = function_inverse(A!15)) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))) | (~((~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))))))) | (~((~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))) | (~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))))))))) | (~((~(B = function_inverse(A!15))) | (~((~(relation_dom(B) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15))))))))))))))))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(103,plain,
% 0.21/0.46 (^[B: $i] : trans(monotonicity(rewrite((~((~((B = function_inverse(A!15)) | (~(relation_dom(B) = relation_rng(A!15))) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))) | (~((~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))))))) | (~((~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))))) | (~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))))))) | (~((~(B = function_inverse(A!15))) | (~((~(relation_dom(B) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!15))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))))) | (~((~((~in(C, relation_rng(A!15))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D)))))))))))))) <=> (~((~((~(relation_dom(B) = relation_rng(A!15))) | (B = function_inverse(A!15)) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))) | (~((~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))))))) | (~((~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))) | (~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))))))))) | (~((~(B = function_inverse(A!15))) | (~((~(relation_dom(B) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15))))))))))))))))), (((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A!15)) | (~(relation_dom(B) = relation_rng(A!15))) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))) | (~((~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))))))) | (~((~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))))) | (~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))))))) | (~((~(B = function_inverse(A!15))) | (~((~(relation_dom(B) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!15))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))))) | (~((~((~in(C, relation_rng(A!15))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))))))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(A!15))) | (B = function_inverse(A!15)) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))) | (~((~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))))))) | (~((~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))) | (~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))))))))) | (~((~(B = function_inverse(A!15))) | (~((~(relation_dom(B) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15))))))))))))))))))), rewrite(((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(A!15))) | (B = function_inverse(A!15)) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))) | (~((~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))))))) | (~((~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))) | (~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))))))))) | (~((~(B = function_inverse(A!15))) | (~((~(relation_dom(B) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15))))))))))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(A!15))) | (B = function_inverse(A!15)) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))) | (~((~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))))))) | (~((~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))) | (~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))))))))) | (~((~(B = function_inverse(A!15))) | (~((~(relation_dom(B) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15)))))))))))))))))), (((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A!15)) | (~(relation_dom(B) = relation_rng(A!15))) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))) | (~((~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))))))) | (~((~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))))) | (~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))))))) | (~((~(B = function_inverse(A!15))) | (~((~(relation_dom(B) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!15))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))))) | (~((~((~in(C, relation_rng(A!15))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))))))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(A!15))) | (B = function_inverse(A!15)) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))) | (~((~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))))))) | (~((~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))) | (~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))))))))) | (~((~(B = function_inverse(A!15))) | (~((~(relation_dom(B) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15)))))))))))))))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(104,plain,
% 0.21/0.46 (![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A!15)) | (~(relation_dom(B) = relation_rng(A!15))) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))) | (~((~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))))))) | (~((~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))))) | (~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))))))) | (~((~(B = function_inverse(A!15))) | (~((~(relation_dom(B) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!15))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))))) | (~((~((~in(C, relation_rng(A!15))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))))))))))))) <=> ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(A!15))) | (B = function_inverse(A!15)) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))) | (~((~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))))))) | (~((~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))) | (~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))))))))) | (~((~(B = function_inverse(A!15))) | (~((~(relation_dom(B) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15)))))))))))))))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[103])).
% 0.21/0.46 tff(105,plain,
% 0.21/0.46 (((~one_to_one(A!15)) | (~relation(A!15)) | (~function(A!15)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A!15)) | (~(relation_dom(B) = relation_rng(A!15))) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))) | (~((~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))))))) | (~((~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))))) | (~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))))))) | (~((~(B = function_inverse(A!15))) | (~((~(relation_dom(B) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!15))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))))) | (~((~((~in(C, relation_rng(A!15))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D)))))))))))))))) <=> ((~one_to_one(A!15)) | (~relation(A!15)) | (~function(A!15)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(A!15))) | (B = function_inverse(A!15)) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))) | (~((~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))))))) | (~((~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))) | (~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))))))))) | (~((~(B = function_inverse(A!15))) | (~((~(relation_dom(B) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15))))))))))))))))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[104])).
% 0.21/0.46 tff(106,plain,
% 0.21/0.46 (((~one_to_one(A!15)) | (~relation(A!15)) | (~function(A!15)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A!15)) | (~(relation_dom(B) = relation_rng(A!15))) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))) | (~((~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))))))) | (~((~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))))) | (~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))))))) | (~((~(B = function_inverse(A!15))) | (~((~(relation_dom(B) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!15))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))))) | (~((~((~in(C, relation_rng(A!15))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D)))))))))))))))) <=> ((~one_to_one(A!15)) | (~function(A!15)) | (~relation(A!15)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(A!15))) | (B = function_inverse(A!15)) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))) | (~((~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))))))) | (~((~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))) | (~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))))))))) | (~((~(B = function_inverse(A!15))) | (~((~(relation_dom(B) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15))))))))))))))))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[105, 102])).
% 0.21/0.46 tff(107,plain,
% 0.21/0.46 (((~![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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(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!15)) | (~relation(A!15)) | (~function(A!15)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A!15)) | (~(relation_dom(B) = relation_rng(A!15))) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))) | (~((~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))))))) | (~((~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))))) | (~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))))))) | (~((~(B = function_inverse(A!15))) | (~((~(relation_dom(B) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!15))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))))) | (~((~((~in(C, relation_rng(A!15))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A!15))) | (~(C = apply(A!15, 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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(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!15)) | (~function(A!15)) | (~relation(A!15)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(A!15))) | (B = function_inverse(A!15)) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))) | (~((~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))))))) | (~((~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))) | (~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))))))))) | (~((~(B = function_inverse(A!15))) | (~((~(relation_dom(B) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15)))))))))))))))))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[106])).
% 0.21/0.46 tff(108,plain,
% 0.21/0.46 (((~![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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(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!15)) | (~relation(A!15)) | (~function(A!15)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A!15)) | (~(relation_dom(B) = relation_rng(A!15))) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))) | (~((~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))))))) | (~((~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))))) | (~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))))))) | (~((~(B = function_inverse(A!15))) | (~((~(relation_dom(B) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!15))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))))) | (~((~((~in(C, relation_rng(A!15))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A!15))) | (~(C = apply(A!15, 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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(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!15)) | (~function(A!15)) | (~relation(A!15)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(A!15))) | (B = function_inverse(A!15)) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))) | (~((~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))))))) | (~((~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))) | (~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))))))))) | (~((~(B = function_inverse(A!15))) | (~((~(relation_dom(B) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15))))))))))))))))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[107, 101])).
% 0.21/0.46 tff(109,plain,
% 0.21/0.46 ((~![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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(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!15)) | (~relation(A!15)) | (~function(A!15)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A!15)) | (~(relation_dom(B) = relation_rng(A!15))) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))) | (~((~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))))))) | (~((~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))))) | (~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))))))) | (~((~(B = function_inverse(A!15))) | (~((~(relation_dom(B) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!15))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))))) | (~((~((~in(C, relation_rng(A!15))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))))))))))))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(110,plain,
% 0.21/0.47 ((~![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_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~((~in(tptp_fun_C_14(B, A), relation_rng(A))) | (~(tptp_fun_D_13(B, A) = apply(B, tptp_fun_C_14(B, A)))))) | (~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_14(B, A) = apply(A, tptp_fun_D_13(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!15)) | (~function(A!15)) | (~relation(A!15)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(A!15))) | (B = function_inverse(A!15)) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))) | (~((~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))))))) | (~((~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))) | (~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))))))))) | (~((~(B = function_inverse(A!15))) | (~((~(relation_dom(B) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15)))))))))))))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.21/0.47 tff(111,plain,
% 0.21/0.47 (![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(A!15))) | (B = function_inverse(A!15)) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))) | (~((~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))))))) | (~((~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))) | (~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))))))))) | (~((~(B = function_inverse(A!15))) | (~((~(relation_dom(B) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15)))))))))))))))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[110, 100, 13, 12, 78])).
% 0.21/0.47 tff(112,plain,
% 0.21/0.47 (((~![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(A!15))) | (B = function_inverse(A!15)) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))) | (~((~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))))))) | (~((~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))) | (~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))))))))) | (~((~(B = function_inverse(A!15))) | (~((~(relation_dom(B) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15)))))))))))))))))) | ((~relation(function_inverse(A!15))) | (~function(function_inverse(A!15))) | (~((~(relation_dom(function_inverse(A!15)) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!15))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))) | (~(D = apply(function_inverse(A!15), C))))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))) | (~((~in(C, relation_rng(A!15))) | (~(D = apply(function_inverse(A!15), C)))))))))))))) <=> ((~![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(A!15))) | (B = function_inverse(A!15)) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))) | (~((~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))))))) | (~((~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))) | (~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))))))))) | (~((~(B = function_inverse(A!15))) | (~((~(relation_dom(B) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15)))))))))))))))))) | (~relation(function_inverse(A!15))) | (~function(function_inverse(A!15))) | (~((~(relation_dom(function_inverse(A!15)) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!15))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))) | (~(D = apply(function_inverse(A!15), C))))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))) | (~((~in(C, relation_rng(A!15))) | (~(D = apply(function_inverse(A!15), C)))))))))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(113,plain,
% 0.21/0.47 (((~relation(function_inverse(A!15))) | (~function(function_inverse(A!15))) | (~((~(relation_dom(function_inverse(A!15)) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!15))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))) | (~(D = apply(function_inverse(A!15), C))))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))) | (~((~in(C, relation_rng(A!15))) | (~(D = apply(function_inverse(A!15), C))))))))))))) <=> ((~relation(function_inverse(A!15))) | (~function(function_inverse(A!15))) | (~((~(relation_dom(function_inverse(A!15)) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!15))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))) | (~(D = apply(function_inverse(A!15), C))))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))) | (~((~in(C, relation_rng(A!15))) | (~(D = apply(function_inverse(A!15), C)))))))))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(114,plain,
% 0.21/0.47 ((~((~((~(relation_dom(function_inverse(A!15)) = relation_rng(A!15))) | (function_inverse(A!15) = function_inverse(A!15)) | (~((~in(tptp_fun_C_14(function_inverse(A!15), A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(function_inverse(A!15), A!15) = apply(function_inverse(A!15), tptp_fun_C_14(function_inverse(A!15), A!15)))) | (~((~in(tptp_fun_D_13(function_inverse(A!15), A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(function_inverse(A!15), A!15) = apply(A!15, tptp_fun_D_13(function_inverse(A!15), A!15)))))))) | (~((~(tptp_fun_C_14(function_inverse(A!15), A!15) = apply(A!15, tptp_fun_D_13(function_inverse(A!15), A!15)))) | (~in(tptp_fun_D_13(function_inverse(A!15), A!15), relation_dom(A!15))) | (~((~in(tptp_fun_C_14(function_inverse(A!15), A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(function_inverse(A!15), A!15) = apply(function_inverse(A!15), tptp_fun_C_14(function_inverse(A!15), A!15)))))))))) | (~((~(function_inverse(A!15) = function_inverse(A!15))) | (~((~(relation_dom(function_inverse(A!15)) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~(D = apply(function_inverse(A!15), C))) | (~in(C, relation_rng(A!15))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))) | (~((~(D = apply(function_inverse(A!15), C))) | (~in(C, relation_rng(A!15)))))))))))))))) <=> (~((~(relation_dom(function_inverse(A!15)) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!15))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))) | (~(D = apply(function_inverse(A!15), C))))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))) | (~((~in(C, relation_rng(A!15))) | (~(D = apply(function_inverse(A!15), C))))))))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(115,plain,
% 0.21/0.47 (((~relation(function_inverse(A!15))) | (~function(function_inverse(A!15))) | (~((~((~(relation_dom(function_inverse(A!15)) = relation_rng(A!15))) | (function_inverse(A!15) = function_inverse(A!15)) | (~((~in(tptp_fun_C_14(function_inverse(A!15), A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(function_inverse(A!15), A!15) = apply(function_inverse(A!15), tptp_fun_C_14(function_inverse(A!15), A!15)))) | (~((~in(tptp_fun_D_13(function_inverse(A!15), A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(function_inverse(A!15), A!15) = apply(A!15, tptp_fun_D_13(function_inverse(A!15), A!15)))))))) | (~((~(tptp_fun_C_14(function_inverse(A!15), A!15) = apply(A!15, tptp_fun_D_13(function_inverse(A!15), A!15)))) | (~in(tptp_fun_D_13(function_inverse(A!15), A!15), relation_dom(A!15))) | (~((~in(tptp_fun_C_14(function_inverse(A!15), A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(function_inverse(A!15), A!15) = apply(function_inverse(A!15), tptp_fun_C_14(function_inverse(A!15), A!15)))))))))) | (~((~(function_inverse(A!15) = function_inverse(A!15))) | (~((~(relation_dom(function_inverse(A!15)) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~(D = apply(function_inverse(A!15), C))) | (~in(C, relation_rng(A!15))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))) | (~((~(D = apply(function_inverse(A!15), C))) | (~in(C, relation_rng(A!15))))))))))))))))) <=> ((~relation(function_inverse(A!15))) | (~function(function_inverse(A!15))) | (~((~(relation_dom(function_inverse(A!15)) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!15))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))) | (~(D = apply(function_inverse(A!15), C))))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))) | (~((~in(C, relation_rng(A!15))) | (~(D = apply(function_inverse(A!15), C)))))))))))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[114])).
% 0.21/0.47 tff(116,plain,
% 0.21/0.47 (((~relation(function_inverse(A!15))) | (~function(function_inverse(A!15))) | (~((~((~(relation_dom(function_inverse(A!15)) = relation_rng(A!15))) | (function_inverse(A!15) = function_inverse(A!15)) | (~((~in(tptp_fun_C_14(function_inverse(A!15), A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(function_inverse(A!15), A!15) = apply(function_inverse(A!15), tptp_fun_C_14(function_inverse(A!15), A!15)))) | (~((~in(tptp_fun_D_13(function_inverse(A!15), A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(function_inverse(A!15), A!15) = apply(A!15, tptp_fun_D_13(function_inverse(A!15), A!15)))))))) | (~((~(tptp_fun_C_14(function_inverse(A!15), A!15) = apply(A!15, tptp_fun_D_13(function_inverse(A!15), A!15)))) | (~in(tptp_fun_D_13(function_inverse(A!15), A!15), relation_dom(A!15))) | (~((~in(tptp_fun_C_14(function_inverse(A!15), A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(function_inverse(A!15), A!15) = apply(function_inverse(A!15), tptp_fun_C_14(function_inverse(A!15), A!15)))))))))) | (~((~(function_inverse(A!15) = function_inverse(A!15))) | (~((~(relation_dom(function_inverse(A!15)) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~(D = apply(function_inverse(A!15), C))) | (~in(C, relation_rng(A!15))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))) | (~((~(D = apply(function_inverse(A!15), C))) | (~in(C, relation_rng(A!15))))))))))))))))) <=> ((~relation(function_inverse(A!15))) | (~function(function_inverse(A!15))) | (~((~(relation_dom(function_inverse(A!15)) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!15))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))) | (~(D = apply(function_inverse(A!15), C))))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))) | (~((~in(C, relation_rng(A!15))) | (~(D = apply(function_inverse(A!15), C)))))))))))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[115, 113])).
% 0.21/0.47 tff(117,plain,
% 0.21/0.47 (((~![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(A!15))) | (B = function_inverse(A!15)) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))) | (~((~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))))))) | (~((~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))) | (~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))))))))) | (~((~(B = function_inverse(A!15))) | (~((~(relation_dom(B) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15)))))))))))))))))) | ((~relation(function_inverse(A!15))) | (~function(function_inverse(A!15))) | (~((~((~(relation_dom(function_inverse(A!15)) = relation_rng(A!15))) | (function_inverse(A!15) = function_inverse(A!15)) | (~((~in(tptp_fun_C_14(function_inverse(A!15), A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(function_inverse(A!15), A!15) = apply(function_inverse(A!15), tptp_fun_C_14(function_inverse(A!15), A!15)))) | (~((~in(tptp_fun_D_13(function_inverse(A!15), A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(function_inverse(A!15), A!15) = apply(A!15, tptp_fun_D_13(function_inverse(A!15), A!15)))))))) | (~((~(tptp_fun_C_14(function_inverse(A!15), A!15) = apply(A!15, tptp_fun_D_13(function_inverse(A!15), A!15)))) | (~in(tptp_fun_D_13(function_inverse(A!15), A!15), relation_dom(A!15))) | (~((~in(tptp_fun_C_14(function_inverse(A!15), A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(function_inverse(A!15), A!15) = apply(function_inverse(A!15), tptp_fun_C_14(function_inverse(A!15), A!15)))))))))) | (~((~(function_inverse(A!15) = function_inverse(A!15))) | (~((~(relation_dom(function_inverse(A!15)) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~(D = apply(function_inverse(A!15), C))) | (~in(C, relation_rng(A!15))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))) | (~((~(D = apply(function_inverse(A!15), C))) | (~in(C, relation_rng(A!15)))))))))))))))))) <=> ((~![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(A!15))) | (B = function_inverse(A!15)) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))) | (~((~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))))))) | (~((~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))) | (~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))))))))) | (~((~(B = function_inverse(A!15))) | (~((~(relation_dom(B) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15)))))))))))))))))) | ((~relation(function_inverse(A!15))) | (~function(function_inverse(A!15))) | (~((~(relation_dom(function_inverse(A!15)) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!15))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))) | (~(D = apply(function_inverse(A!15), C))))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))) | (~((~in(C, relation_rng(A!15))) | (~(D = apply(function_inverse(A!15), C))))))))))))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[116])).
% 0.21/0.47 tff(118,plain,
% 0.21/0.47 (((~![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(A!15))) | (B = function_inverse(A!15)) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))) | (~((~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))))))) | (~((~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))) | (~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))))))))) | (~((~(B = function_inverse(A!15))) | (~((~(relation_dom(B) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15)))))))))))))))))) | ((~relation(function_inverse(A!15))) | (~function(function_inverse(A!15))) | (~((~((~(relation_dom(function_inverse(A!15)) = relation_rng(A!15))) | (function_inverse(A!15) = function_inverse(A!15)) | (~((~in(tptp_fun_C_14(function_inverse(A!15), A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(function_inverse(A!15), A!15) = apply(function_inverse(A!15), tptp_fun_C_14(function_inverse(A!15), A!15)))) | (~((~in(tptp_fun_D_13(function_inverse(A!15), A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(function_inverse(A!15), A!15) = apply(A!15, tptp_fun_D_13(function_inverse(A!15), A!15)))))))) | (~((~(tptp_fun_C_14(function_inverse(A!15), A!15) = apply(A!15, tptp_fun_D_13(function_inverse(A!15), A!15)))) | (~in(tptp_fun_D_13(function_inverse(A!15), A!15), relation_dom(A!15))) | (~((~in(tptp_fun_C_14(function_inverse(A!15), A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(function_inverse(A!15), A!15) = apply(function_inverse(A!15), tptp_fun_C_14(function_inverse(A!15), A!15)))))))))) | (~((~(function_inverse(A!15) = function_inverse(A!15))) | (~((~(relation_dom(function_inverse(A!15)) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~(D = apply(function_inverse(A!15), C))) | (~in(C, relation_rng(A!15))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))) | (~((~(D = apply(function_inverse(A!15), C))) | (~in(C, relation_rng(A!15)))))))))))))))))) <=> ((~![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(A!15))) | (B = function_inverse(A!15)) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))) | (~((~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))))))) | (~((~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))) | (~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))))))))) | (~((~(B = function_inverse(A!15))) | (~((~(relation_dom(B) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15)))))))))))))))))) | (~relation(function_inverse(A!15))) | (~function(function_inverse(A!15))) | (~((~(relation_dom(function_inverse(A!15)) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!15))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))) | (~(D = apply(function_inverse(A!15), C))))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))) | (~((~in(C, relation_rng(A!15))) | (~(D = apply(function_inverse(A!15), C)))))))))))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[117, 112])).
% 0.21/0.47 tff(119,plain,
% 0.21/0.47 ((~![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(A!15))) | (B = function_inverse(A!15)) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))) | (~((~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))))))) | (~((~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))) | (~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))))))))) | (~((~(B = function_inverse(A!15))) | (~((~(relation_dom(B) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15)))))))))))))))))) | ((~relation(function_inverse(A!15))) | (~function(function_inverse(A!15))) | (~((~((~(relation_dom(function_inverse(A!15)) = relation_rng(A!15))) | (function_inverse(A!15) = function_inverse(A!15)) | (~((~in(tptp_fun_C_14(function_inverse(A!15), A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(function_inverse(A!15), A!15) = apply(function_inverse(A!15), tptp_fun_C_14(function_inverse(A!15), A!15)))) | (~((~in(tptp_fun_D_13(function_inverse(A!15), A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(function_inverse(A!15), A!15) = apply(A!15, tptp_fun_D_13(function_inverse(A!15), A!15)))))))) | (~((~(tptp_fun_C_14(function_inverse(A!15), A!15) = apply(A!15, tptp_fun_D_13(function_inverse(A!15), A!15)))) | (~in(tptp_fun_D_13(function_inverse(A!15), A!15), relation_dom(A!15))) | (~((~in(tptp_fun_C_14(function_inverse(A!15), A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(function_inverse(A!15), A!15) = apply(function_inverse(A!15), tptp_fun_C_14(function_inverse(A!15), A!15)))))))))) | (~((~(function_inverse(A!15) = function_inverse(A!15))) | (~((~(relation_dom(function_inverse(A!15)) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~(D = apply(function_inverse(A!15), C))) | (~in(C, relation_rng(A!15))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))) | (~((~(D = apply(function_inverse(A!15), C))) | (~in(C, relation_rng(A!15)))))))))))))))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(120,plain,
% 0.21/0.47 ((~![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(A!15))) | (B = function_inverse(A!15)) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))) | (~((~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))))))) | (~((~(tptp_fun_C_14(B, A!15) = apply(A!15, tptp_fun_D_13(B, A!15)))) | (~in(tptp_fun_D_13(B, A!15), relation_dom(A!15))) | (~((~in(tptp_fun_C_14(B, A!15), relation_rng(A!15))) | (~(tptp_fun_D_13(B, A!15) = apply(B, tptp_fun_C_14(B, A!15)))))))))) | (~((~(B = function_inverse(A!15))) | (~((~(relation_dom(B) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!15)))))))))))))))))) | (~relation(function_inverse(A!15))) | (~function(function_inverse(A!15))) | (~((~(relation_dom(function_inverse(A!15)) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!15))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))) | (~(D = apply(function_inverse(A!15), C))))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))) | (~((~in(C, relation_rng(A!15))) | (~(D = apply(function_inverse(A!15), C))))))))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.21/0.48 tff(121,plain,
% 0.21/0.48 (~((~(relation_dom(function_inverse(A!15)) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!15))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))) | (~(D = apply(function_inverse(A!15), C))))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))) | (~((~in(C, relation_rng(A!15))) | (~(D = apply(function_inverse(A!15), C)))))))))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[120, 111, 38, 40])).
% 0.21/0.48 tff(122,plain,
% 0.21/0.48 (((~(relation_dom(function_inverse(A!15)) = relation_rng(A!15))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!15))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))))) | (~(D = apply(function_inverse(A!15), C))))) | (~((~in(D, relation_dom(A!15))) | (~(C = apply(A!15, D))) | (~((~in(C, relation_rng(A!15))) | (~(D = apply(function_inverse(A!15), C))))))))))) | (relation_dom(function_inverse(A!15)) = relation_rng(A!15))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(123,plain,
% 0.21/0.48 (relation_dom(function_inverse(A!15)) = relation_rng(A!15)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.21/0.48 tff(124,plain,
% 0.21/0.48 (in(tptp_fun_C_0(function_inverse(A!15)), relation_dom(function_inverse(A!15))) <=> in(tptp_fun_C_0(function_inverse(A!15)), relation_rng(A!15))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[123])).
% 0.21/0.48 tff(125,plain,
% 0.21/0.48 (((~(apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15))) = apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15))))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (tptp_fun_B_1(function_inverse(A!15)) = tptp_fun_C_0(function_inverse(A!15)))) | in(tptp_fun_C_0(function_inverse(A!15)), relation_dom(function_inverse(A!15)))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(126,plain,
% 0.21/0.48 (in(tptp_fun_C_0(function_inverse(A!15)), relation_dom(function_inverse(A!15)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[125, 73])).
% 0.21/0.48 tff(127,plain,
% 0.21/0.48 (in(tptp_fun_C_0(function_inverse(A!15)), relation_rng(A!15))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[126, 124])).
% 0.21/0.48 tff(128,plain,
% 0.21/0.48 (^[A: $i, B: $i] : refl(((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B)))) <=> ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B)))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(129,plain,
% 0.21/0.48 (![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B)))) <=> ![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[128])).
% 0.21/0.48 tff(130,plain,
% 0.21/0.48 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) <=> (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A)))))), trans(monotonicity(rewrite((relation(B) & function(B)) <=> (~((~relation(B)) | (~function(B))))), ((~(relation(B) & function(B))) <=> (~(~((~relation(B)) | (~function(B))))))), rewrite((~(~((~relation(B)) | (~function(B))))) <=> ((~relation(B)) | (~function(B)))), ((~(relation(B) & function(B))) <=> ((~relation(B)) | (~function(B))))), trans(monotonicity(rewrite((one_to_one(B) & in(A, relation_rng(B))) <=> (~((~one_to_one(B)) | (~in(A, relation_rng(B)))))), ((~(one_to_one(B) & in(A, relation_rng(B)))) <=> (~(~((~one_to_one(B)) | (~in(A, relation_rng(B)))))))), rewrite((~(~((~one_to_one(B)) | (~in(A, relation_rng(B)))))) <=> ((~one_to_one(B)) | (~in(A, relation_rng(B))))), ((~(one_to_one(B) & in(A, relation_rng(B)))) <=> ((~one_to_one(B)) | (~in(A, relation_rng(B)))))), ((((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B))))) <=> ((~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | ((~relation(B)) | (~function(B))) | ((~one_to_one(B)) | (~in(A, relation_rng(B))))))), rewrite(((~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | ((~relation(B)) | (~function(B))) | ((~one_to_one(B)) | (~in(A, relation_rng(B))))) <=> ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))), ((((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B))))) <=> ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(131,plain,
% 0.21/0.48 (![A: $i, B: $i] : (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B))))) <=> ![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[130])).
% 0.21/0.48 tff(132,plain,
% 0.21/0.48 (![A: $i, B: $i] : (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B))))) <=> ![A: $i, B: $i] : (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B)))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(133,plain,
% 0.21/0.48 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((one_to_one(B) & in(A, relation_rng(B))) => ((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A)))) <=> ((~(one_to_one(B) & in(A, relation_rng(B)))) | ((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))))), (((relation(B) & function(B)) => ((one_to_one(B) & in(A, relation_rng(B))) => ((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))))) <=> ((relation(B) & function(B)) => ((~(one_to_one(B) & in(A, relation_rng(B)))) | ((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))))))), rewrite(((relation(B) & function(B)) => ((~(one_to_one(B) & in(A, relation_rng(B)))) | ((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))))) <=> (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B)))))), (((relation(B) & function(B)) => ((one_to_one(B) & in(A, relation_rng(B))) => ((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))))) <=> (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B)))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(134,plain,
% 0.21/0.48 (![A: $i, B: $i] : ((relation(B) & function(B)) => ((one_to_one(B) & in(A, relation_rng(B))) => ((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))))) <=> ![A: $i, B: $i] : (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B)))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[133])).
% 0.21/0.48 tff(135,axiom,(![A: $i, B: $i] : ((relation(B) & function(B)) => ((one_to_one(B) & in(A, relation_rng(B))) => ((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t57_funct_1')).
% 0.21/0.48 tff(136,plain,
% 0.21/0.48 (![A: $i, B: $i] : (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B)))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.21/0.48 tff(137,plain,
% 0.21/0.48 (![A: $i, B: $i] : (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B)))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[136, 132])).
% 0.21/0.48 tff(138,plain,(
% 0.21/0.48 ![A: $i, B: $i] : (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B)))))),
% 0.21/0.48 inference(skolemize,[status(sab)],[137])).
% 0.21/0.48 tff(139,plain,
% 0.21/0.48 (![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[138, 131])).
% 0.21/0.48 tff(140,plain,
% 0.21/0.48 (![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[139, 129])).
% 0.21/0.48 tff(141,plain,
% 0.21/0.48 (((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))) | ((~one_to_one(A!15)) | (~function(A!15)) | (~relation(A!15)) | (~((~(tptp_fun_C_0(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15)))))) | (~(tptp_fun_C_0(function_inverse(A!15)) = apply(relation_composition(function_inverse(A!15), A!15), tptp_fun_C_0(function_inverse(A!15))))))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_rng(A!15))))) <=> ((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))) | (~one_to_one(A!15)) | (~function(A!15)) | (~relation(A!15)) | (~((~(tptp_fun_C_0(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15)))))) | (~(tptp_fun_C_0(function_inverse(A!15)) = apply(relation_composition(function_inverse(A!15), A!15), tptp_fun_C_0(function_inverse(A!15))))))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_rng(A!15))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(142,plain,
% 0.21/0.48 (((~one_to_one(A!15)) | (~relation(A!15)) | (~function(A!15)) | (~((~(tptp_fun_C_0(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15)))))) | (~(tptp_fun_C_0(function_inverse(A!15)) = apply(relation_composition(function_inverse(A!15), A!15), tptp_fun_C_0(function_inverse(A!15))))))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_rng(A!15)))) <=> ((~one_to_one(A!15)) | (~function(A!15)) | (~relation(A!15)) | (~((~(tptp_fun_C_0(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15)))))) | (~(tptp_fun_C_0(function_inverse(A!15)) = apply(relation_composition(function_inverse(A!15), A!15), tptp_fun_C_0(function_inverse(A!15))))))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_rng(A!15))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(143,plain,
% 0.21/0.48 ((~((~(tptp_fun_C_0(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15)))))) | (~(tptp_fun_C_0(function_inverse(A!15)) = apply(relation_composition(function_inverse(A!15), A!15), tptp_fun_C_0(function_inverse(A!15))))))) <=> (~((~(tptp_fun_C_0(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15)))))) | (~(tptp_fun_C_0(function_inverse(A!15)) = apply(relation_composition(function_inverse(A!15), A!15), tptp_fun_C_0(function_inverse(A!15)))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(144,plain,
% 0.21/0.48 (((~one_to_one(A!15)) | (~relation(A!15)) | (~function(A!15)) | (~((~(tptp_fun_C_0(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15)))))) | (~(tptp_fun_C_0(function_inverse(A!15)) = apply(relation_composition(function_inverse(A!15), A!15), tptp_fun_C_0(function_inverse(A!15))))))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_rng(A!15)))) <=> ((~one_to_one(A!15)) | (~relation(A!15)) | (~function(A!15)) | (~((~(tptp_fun_C_0(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15)))))) | (~(tptp_fun_C_0(function_inverse(A!15)) = apply(relation_composition(function_inverse(A!15), A!15), tptp_fun_C_0(function_inverse(A!15))))))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_rng(A!15))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[143])).
% 0.21/0.48 tff(145,plain,
% 0.21/0.48 (((~one_to_one(A!15)) | (~relation(A!15)) | (~function(A!15)) | (~((~(tptp_fun_C_0(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15)))))) | (~(tptp_fun_C_0(function_inverse(A!15)) = apply(relation_composition(function_inverse(A!15), A!15), tptp_fun_C_0(function_inverse(A!15))))))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_rng(A!15)))) <=> ((~one_to_one(A!15)) | (~function(A!15)) | (~relation(A!15)) | (~((~(tptp_fun_C_0(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15)))))) | (~(tptp_fun_C_0(function_inverse(A!15)) = apply(relation_composition(function_inverse(A!15), A!15), tptp_fun_C_0(function_inverse(A!15))))))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_rng(A!15))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[144, 142])).
% 0.21/0.48 tff(146,plain,
% 0.21/0.48 (((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))) | ((~one_to_one(A!15)) | (~relation(A!15)) | (~function(A!15)) | (~((~(tptp_fun_C_0(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15)))))) | (~(tptp_fun_C_0(function_inverse(A!15)) = apply(relation_composition(function_inverse(A!15), A!15), tptp_fun_C_0(function_inverse(A!15))))))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_rng(A!15))))) <=> ((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))) | ((~one_to_one(A!15)) | (~function(A!15)) | (~relation(A!15)) | (~((~(tptp_fun_C_0(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15)))))) | (~(tptp_fun_C_0(function_inverse(A!15)) = apply(relation_composition(function_inverse(A!15), A!15), tptp_fun_C_0(function_inverse(A!15))))))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_rng(A!15)))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[145])).
% 0.21/0.48 tff(147,plain,
% 0.21/0.48 (((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))) | ((~one_to_one(A!15)) | (~relation(A!15)) | (~function(A!15)) | (~((~(tptp_fun_C_0(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15)))))) | (~(tptp_fun_C_0(function_inverse(A!15)) = apply(relation_composition(function_inverse(A!15), A!15), tptp_fun_C_0(function_inverse(A!15))))))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_rng(A!15))))) <=> ((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))) | (~one_to_one(A!15)) | (~function(A!15)) | (~relation(A!15)) | (~((~(tptp_fun_C_0(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15)))))) | (~(tptp_fun_C_0(function_inverse(A!15)) = apply(relation_composition(function_inverse(A!15), A!15), tptp_fun_C_0(function_inverse(A!15))))))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_rng(A!15))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[146, 141])).
% 0.21/0.48 tff(148,plain,
% 0.21/0.48 ((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))) | ((~one_to_one(A!15)) | (~relation(A!15)) | (~function(A!15)) | (~((~(tptp_fun_C_0(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15)))))) | (~(tptp_fun_C_0(function_inverse(A!15)) = apply(relation_composition(function_inverse(A!15), A!15), tptp_fun_C_0(function_inverse(A!15))))))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_rng(A!15))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(149,plain,
% 0.21/0.48 ((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))) | (~one_to_one(A!15)) | (~function(A!15)) | (~relation(A!15)) | (~((~(tptp_fun_C_0(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15)))))) | (~(tptp_fun_C_0(function_inverse(A!15)) = apply(relation_composition(function_inverse(A!15), A!15), tptp_fun_C_0(function_inverse(A!15))))))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_rng(A!15)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.21/0.48 tff(150,plain,
% 0.21/0.48 ((~((~(tptp_fun_C_0(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15)))))) | (~(tptp_fun_C_0(function_inverse(A!15)) = apply(relation_composition(function_inverse(A!15), A!15), tptp_fun_C_0(function_inverse(A!15))))))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_rng(A!15)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[149, 140, 13, 12, 78])).
% 0.21/0.48 tff(151,plain,
% 0.21/0.48 (~((~(tptp_fun_C_0(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15)))))) | (~(tptp_fun_C_0(function_inverse(A!15)) = apply(relation_composition(function_inverse(A!15), A!15), tptp_fun_C_0(function_inverse(A!15))))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[150, 127])).
% 0.21/0.48 tff(152,plain,
% 0.21/0.48 (((~(tptp_fun_C_0(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15)))))) | (~(tptp_fun_C_0(function_inverse(A!15)) = apply(relation_composition(function_inverse(A!15), A!15), tptp_fun_C_0(function_inverse(A!15)))))) | (tptp_fun_C_0(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15)))))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(153,plain,
% 0.21/0.48 (tptp_fun_C_0(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[152, 151])).
% 0.21/0.48 tff(154,plain,
% 0.21/0.48 (tptp_fun_C_0(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[153, 77])).
% 0.21/0.48 tff(155,plain,
% 0.21/0.48 ((tptp_fun_B_1(function_inverse(A!15)) = tptp_fun_C_0(function_inverse(A!15))) <=> (tptp_fun_B_1(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15)))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[154])).
% 0.21/0.48 tff(156,plain,
% 0.21/0.48 ((tptp_fun_B_1(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15))))) <=> (tptp_fun_B_1(function_inverse(A!15)) = tptp_fun_C_0(function_inverse(A!15)))),
% 0.21/0.48 inference(symmetry,[status(thm)],[155])).
% 0.21/0.48 tff(157,plain,
% 0.21/0.48 (in(tptp_fun_B_1(function_inverse(A!15)), relation_dom(function_inverse(A!15))) <=> in(tptp_fun_B_1(function_inverse(A!15)), relation_rng(A!15))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[123])).
% 0.21/0.48 tff(158,plain,
% 0.21/0.48 (((~(apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15))) = apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15))))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (tptp_fun_B_1(function_inverse(A!15)) = tptp_fun_C_0(function_inverse(A!15)))) | in(tptp_fun_B_1(function_inverse(A!15)), relation_dom(function_inverse(A!15)))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(159,plain,
% 0.21/0.48 (in(tptp_fun_B_1(function_inverse(A!15)), relation_dom(function_inverse(A!15)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[158, 73])).
% 0.21/0.48 tff(160,plain,
% 0.21/0.48 (in(tptp_fun_B_1(function_inverse(A!15)), relation_rng(A!15))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[159, 157])).
% 0.21/0.48 tff(161,plain,
% 0.21/0.48 (((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))) | ((~one_to_one(A!15)) | (~function(A!15)) | (~relation(A!15)) | (~((~(tptp_fun_B_1(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15)))))) | (~(tptp_fun_B_1(function_inverse(A!15)) = apply(relation_composition(function_inverse(A!15), A!15), tptp_fun_B_1(function_inverse(A!15))))))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_rng(A!15))))) <=> ((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))) | (~one_to_one(A!15)) | (~function(A!15)) | (~relation(A!15)) | (~((~(tptp_fun_B_1(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15)))))) | (~(tptp_fun_B_1(function_inverse(A!15)) = apply(relation_composition(function_inverse(A!15), A!15), tptp_fun_B_1(function_inverse(A!15))))))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_rng(A!15))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(162,plain,
% 0.21/0.48 (((~one_to_one(A!15)) | (~relation(A!15)) | (~function(A!15)) | (~((~(tptp_fun_B_1(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15)))))) | (~(tptp_fun_B_1(function_inverse(A!15)) = apply(relation_composition(function_inverse(A!15), A!15), tptp_fun_B_1(function_inverse(A!15))))))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_rng(A!15)))) <=> ((~one_to_one(A!15)) | (~function(A!15)) | (~relation(A!15)) | (~((~(tptp_fun_B_1(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15)))))) | (~(tptp_fun_B_1(function_inverse(A!15)) = apply(relation_composition(function_inverse(A!15), A!15), tptp_fun_B_1(function_inverse(A!15))))))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_rng(A!15))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(163,plain,
% 0.21/0.48 ((~((~(tptp_fun_B_1(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15)))))) | (~(tptp_fun_B_1(function_inverse(A!15)) = apply(relation_composition(function_inverse(A!15), A!15), tptp_fun_B_1(function_inverse(A!15))))))) <=> (~((~(tptp_fun_B_1(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15)))))) | (~(tptp_fun_B_1(function_inverse(A!15)) = apply(relation_composition(function_inverse(A!15), A!15), tptp_fun_B_1(function_inverse(A!15)))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(164,plain,
% 0.21/0.48 (((~one_to_one(A!15)) | (~relation(A!15)) | (~function(A!15)) | (~((~(tptp_fun_B_1(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15)))))) | (~(tptp_fun_B_1(function_inverse(A!15)) = apply(relation_composition(function_inverse(A!15), A!15), tptp_fun_B_1(function_inverse(A!15))))))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_rng(A!15)))) <=> ((~one_to_one(A!15)) | (~relation(A!15)) | (~function(A!15)) | (~((~(tptp_fun_B_1(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15)))))) | (~(tptp_fun_B_1(function_inverse(A!15)) = apply(relation_composition(function_inverse(A!15), A!15), tptp_fun_B_1(function_inverse(A!15))))))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_rng(A!15))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[163])).
% 0.21/0.48 tff(165,plain,
% 0.21/0.48 (((~one_to_one(A!15)) | (~relation(A!15)) | (~function(A!15)) | (~((~(tptp_fun_B_1(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15)))))) | (~(tptp_fun_B_1(function_inverse(A!15)) = apply(relation_composition(function_inverse(A!15), A!15), tptp_fun_B_1(function_inverse(A!15))))))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_rng(A!15)))) <=> ((~one_to_one(A!15)) | (~function(A!15)) | (~relation(A!15)) | (~((~(tptp_fun_B_1(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15)))))) | (~(tptp_fun_B_1(function_inverse(A!15)) = apply(relation_composition(function_inverse(A!15), A!15), tptp_fun_B_1(function_inverse(A!15))))))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_rng(A!15))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[164, 162])).
% 0.21/0.48 tff(166,plain,
% 0.21/0.48 (((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))) | ((~one_to_one(A!15)) | (~relation(A!15)) | (~function(A!15)) | (~((~(tptp_fun_B_1(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15)))))) | (~(tptp_fun_B_1(function_inverse(A!15)) = apply(relation_composition(function_inverse(A!15), A!15), tptp_fun_B_1(function_inverse(A!15))))))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_rng(A!15))))) <=> ((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))) | ((~one_to_one(A!15)) | (~function(A!15)) | (~relation(A!15)) | (~((~(tptp_fun_B_1(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15)))))) | (~(tptp_fun_B_1(function_inverse(A!15)) = apply(relation_composition(function_inverse(A!15), A!15), tptp_fun_B_1(function_inverse(A!15))))))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_rng(A!15)))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[165])).
% 0.21/0.48 tff(167,plain,
% 0.21/0.48 (((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))) | ((~one_to_one(A!15)) | (~relation(A!15)) | (~function(A!15)) | (~((~(tptp_fun_B_1(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15)))))) | (~(tptp_fun_B_1(function_inverse(A!15)) = apply(relation_composition(function_inverse(A!15), A!15), tptp_fun_B_1(function_inverse(A!15))))))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_rng(A!15))))) <=> ((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))) | (~one_to_one(A!15)) | (~function(A!15)) | (~relation(A!15)) | (~((~(tptp_fun_B_1(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15)))))) | (~(tptp_fun_B_1(function_inverse(A!15)) = apply(relation_composition(function_inverse(A!15), A!15), tptp_fun_B_1(function_inverse(A!15))))))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_rng(A!15))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[166, 161])).
% 0.21/0.48 tff(168,plain,
% 0.21/0.48 ((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))) | ((~one_to_one(A!15)) | (~relation(A!15)) | (~function(A!15)) | (~((~(tptp_fun_B_1(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15)))))) | (~(tptp_fun_B_1(function_inverse(A!15)) = apply(relation_composition(function_inverse(A!15), A!15), tptp_fun_B_1(function_inverse(A!15))))))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_rng(A!15))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(169,plain,
% 0.21/0.48 ((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))) | (~one_to_one(A!15)) | (~function(A!15)) | (~relation(A!15)) | (~((~(tptp_fun_B_1(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15)))))) | (~(tptp_fun_B_1(function_inverse(A!15)) = apply(relation_composition(function_inverse(A!15), A!15), tptp_fun_B_1(function_inverse(A!15))))))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_rng(A!15)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.21/0.48 tff(170,plain,
% 0.21/0.48 ((~((~(tptp_fun_B_1(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15)))))) | (~(tptp_fun_B_1(function_inverse(A!15)) = apply(relation_composition(function_inverse(A!15), A!15), tptp_fun_B_1(function_inverse(A!15))))))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_rng(A!15)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[169, 140, 13, 12, 78])).
% 0.21/0.48 tff(171,plain,
% 0.21/0.48 (~((~(tptp_fun_B_1(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15)))))) | (~(tptp_fun_B_1(function_inverse(A!15)) = apply(relation_composition(function_inverse(A!15), A!15), tptp_fun_B_1(function_inverse(A!15))))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[170, 160])).
% 0.21/0.48 tff(172,plain,
% 0.21/0.48 (((~(tptp_fun_B_1(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15)))))) | (~(tptp_fun_B_1(function_inverse(A!15)) = apply(relation_composition(function_inverse(A!15), A!15), tptp_fun_B_1(function_inverse(A!15)))))) | (tptp_fun_B_1(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15)))))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(173,plain,
% 0.21/0.48 (tptp_fun_B_1(function_inverse(A!15)) = apply(A!15, apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[172, 171])).
% 0.21/0.48 tff(174,plain,
% 0.21/0.48 (tptp_fun_B_1(function_inverse(A!15)) = tptp_fun_C_0(function_inverse(A!15))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[173, 156])).
% 0.21/0.49 tff(175,plain,
% 0.21/0.49 (((~(apply(function_inverse(A!15), tptp_fun_B_1(function_inverse(A!15))) = apply(function_inverse(A!15), tptp_fun_C_0(function_inverse(A!15))))) | (~in(tptp_fun_C_0(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (~in(tptp_fun_B_1(function_inverse(A!15)), relation_dom(function_inverse(A!15)))) | (tptp_fun_B_1(function_inverse(A!15)) = tptp_fun_C_0(function_inverse(A!15)))) | (~(tptp_fun_B_1(function_inverse(A!15)) = tptp_fun_C_0(function_inverse(A!15))))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(176,plain,
% 0.21/0.49 (~(tptp_fun_B_1(function_inverse(A!15)) = tptp_fun_C_0(function_inverse(A!15)))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[175, 73])).
% 0.21/0.49 tff(177,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[176, 174])).
% 0.21/0.49 % SZS output end Proof
% 0.21/0.49 % E exiting
%------------------------------------------------------------------------------