%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU027+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:48 AM UTC 2025
% Result : Theorem 195.14s 195.28s
% Output : Proof 195.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SEU027+1 : TPTP v9.0.0. Released v3.2.0.
% 0.11/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n010.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 05:58:56 EDT 2025
% 0.11/0.33 % CPUTime :
% 195.14/195.28 % SZS status Theorem
% 195.14/195.28 % SZS output start Proof
% 195.14/195.28 tff(apply_type, type, (
% 195.14/195.28 apply: ( $i * $i ) > $i)).
% 195.14/195.28 tff(tptp_fun_C_18_type, type, (
% 195.14/195.28 tptp_fun_C_18: ( $i * $i ) > $i)).
% 195.14/195.28 tff(tptp_fun_A_16_type, type, (
% 195.14/195.28 tptp_fun_A_16: $i)).
% 195.14/195.28 tff(tptp_fun_B_17_type, type, (
% 195.14/195.28 tptp_fun_B_17: $i)).
% 195.14/195.28 tff(tptp_fun_C_1_type, type, (
% 195.14/195.28 tptp_fun_C_1: ( $i * $i ) > $i)).
% 195.14/195.28 tff(relation_dom_type, type, (
% 195.14/195.28 relation_dom: $i > $i)).
% 195.14/195.28 tff(in_type, type, (
% 195.14/195.28 in: ( $i * $i ) > $o)).
% 195.14/195.28 tff(tptp_fun_D_2_type, type, (
% 195.14/195.28 tptp_fun_D_2: ( $i * $i ) > $i)).
% 195.14/195.28 tff(relation_rng_type, type, (
% 195.14/195.28 relation_rng: $i > $i)).
% 195.14/195.28 tff(function_inverse_type, type, (
% 195.14/195.28 function_inverse: $i > $i)).
% 195.14/195.28 tff(tptp_fun_D_0_type, type, (
% 195.14/195.28 tptp_fun_D_0: ( $i * $i ) > $i)).
% 195.14/195.28 tff(function_type, type, (
% 195.14/195.28 function: $i > $o)).
% 195.14/195.28 tff(one_to_one_type, type, (
% 195.14/195.28 one_to_one: $i > $o)).
% 195.14/195.28 tff(relation_type, type, (
% 195.14/195.28 relation: $i > $o)).
% 195.14/195.28 tff(tptp_fun_C_15_type, type, (
% 195.14/195.28 tptp_fun_C_15: ( $i * $i ) > $i)).
% 195.14/195.28 tff(tptp_fun_D_14_type, type, (
% 195.14/195.28 tptp_fun_D_14: ( $i * $i ) > $i)).
% 195.14/195.28 tff(1,assumption,((~((~(relation_dom(B!17) = relation_rng(A!16))) | (~((~((~in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))))))) | (~(in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17)) | (~in(tptp_fun_C_18(B!17, A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_C_18(B!17, A!16)))))))))) | (~((relation_dom(B!17) = relation_rng(A!16)) | (~((~(in(tptp_fun_C_1(relation_dom(B!17), A!16), relation_dom(B!17)) | (~((~in(tptp_fun_D_2(relation_dom(B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_1(relation_dom(B!17), A!16) = apply(A!16, tptp_fun_D_2(relation_dom(B!17), A!16)))))))) | (~((~in(tptp_fun_C_18(B!17, A!16), relation_dom(A!16))) | (~in(tptp_fun_C_1(relation_dom(B!17), A!16), relation_dom(B!17))) | (~(tptp_fun_C_1(relation_dom(B!17), A!16) = apply(A!16, tptp_fun_C_18(B!17, A!16))))))))))), introduced(assumption)).
% 195.14/195.28 tff(2,plain,
% 195.14/195.28 (((relation(A!16) & function(A!16)) & ((~(B!17 = function_inverse(A!16))) & relation(B!17) & function(B!17) & one_to_one(A!16) & (relation_dom(A!16) = relation_rng(B!17)) & (relation_rng(A!16) = relation_dom(B!17)) & ![C: $i, D: $i] : ((~(in(C, relation_dom(A!16)) & in(D, relation_dom(B!17)))) | ((apply(A!16, C) = D) <=> (apply(B!17, D) = C))))) <=> (relation(A!16) & function(A!16) & (~(B!17 = function_inverse(A!16))) & relation(B!17) & function(B!17) & one_to_one(A!16) & (relation_dom(A!16) = relation_rng(B!17)) & (relation_rng(A!16) = relation_dom(B!17)) & ![C: $i, D: $i] : ((~(in(C, relation_dom(A!16)) & in(D, relation_dom(B!17)))) | ((apply(A!16, C) = D) <=> (apply(B!17, D) = C))))),
% 195.14/195.28 inference(rewrite,[status(thm)],[])).
% 195.14/195.28 tff(3,plain,
% 195.14/195.28 (((~(B!17 = function_inverse(A!16))) & (relation(B!17) & function(B!17)) & (one_to_one(A!16) & (relation_dom(A!16) = relation_rng(B!17)) & (relation_rng(A!16) = relation_dom(B!17)) & ![C: $i, D: $i] : ((~(in(C, relation_dom(A!16)) & in(D, relation_dom(B!17)))) | ((apply(A!16, C) = D) <=> (apply(B!17, D) = C))))) <=> ((~(B!17 = function_inverse(A!16))) & relation(B!17) & function(B!17) & one_to_one(A!16) & (relation_dom(A!16) = relation_rng(B!17)) & (relation_rng(A!16) = relation_dom(B!17)) & ![C: $i, D: $i] : ((~(in(C, relation_dom(A!16)) & in(D, relation_dom(B!17)))) | ((apply(A!16, C) = D) <=> (apply(B!17, D) = C))))),
% 195.14/195.28 inference(rewrite,[status(thm)],[])).
% 195.14/195.28 tff(4,plain,
% 195.14/195.28 ((one_to_one(A!16) & (relation_dom(A!16) = relation_rng(B!17)) & (relation_rng(A!16) = relation_dom(B!17)) & ![C: $i, D: $i] : ((~(in(C, relation_dom(A!16)) & in(D, relation_dom(B!17)))) | ((apply(A!16, C) = D) <=> (apply(B!17, D) = C)))) <=> (one_to_one(A!16) & (relation_dom(A!16) = relation_rng(B!17)) & (relation_rng(A!16) = relation_dom(B!17)) & ![C: $i, D: $i] : ((~(in(C, relation_dom(A!16)) & in(D, relation_dom(B!17)))) | ((apply(A!16, C) = D) <=> (apply(B!17, D) = C))))),
% 195.14/195.28 inference(rewrite,[status(thm)],[])).
% 195.14/195.28 tff(5,plain,
% 195.14/195.28 (((~(B!17 = function_inverse(A!16))) & (relation(B!17) & function(B!17)) & (one_to_one(A!16) & (relation_dom(A!16) = relation_rng(B!17)) & (relation_rng(A!16) = relation_dom(B!17)) & ![C: $i, D: $i] : ((~(in(C, relation_dom(A!16)) & in(D, relation_dom(B!17)))) | ((apply(A!16, C) = D) <=> (apply(B!17, D) = C))))) <=> ((~(B!17 = function_inverse(A!16))) & (relation(B!17) & function(B!17)) & (one_to_one(A!16) & (relation_dom(A!16) = relation_rng(B!17)) & (relation_rng(A!16) = relation_dom(B!17)) & ![C: $i, D: $i] : ((~(in(C, relation_dom(A!16)) & in(D, relation_dom(B!17)))) | ((apply(A!16, C) = D) <=> (apply(B!17, D) = C)))))),
% 195.14/195.28 inference(monotonicity,[status(thm)],[4])).
% 195.14/195.28 tff(6,plain,
% 195.14/195.28 (((~(B!17 = function_inverse(A!16))) & (relation(B!17) & function(B!17)) & (one_to_one(A!16) & (relation_dom(A!16) = relation_rng(B!17)) & (relation_rng(A!16) = relation_dom(B!17)) & ![C: $i, D: $i] : ((~(in(C, relation_dom(A!16)) & in(D, relation_dom(B!17)))) | ((apply(A!16, C) = D) <=> (apply(B!17, D) = C))))) <=> ((~(B!17 = function_inverse(A!16))) & relation(B!17) & function(B!17) & one_to_one(A!16) & (relation_dom(A!16) = relation_rng(B!17)) & (relation_rng(A!16) = relation_dom(B!17)) & ![C: $i, D: $i] : ((~(in(C, relation_dom(A!16)) & in(D, relation_dom(B!17)))) | ((apply(A!16, C) = D) <=> (apply(B!17, D) = C))))),
% 195.14/195.28 inference(transitivity,[status(thm)],[5, 3])).
% 195.14/195.28 tff(7,plain,
% 195.14/195.28 (((relation(A!16) & function(A!16)) & ((~(B!17 = function_inverse(A!16))) & (relation(B!17) & function(B!17)) & (one_to_one(A!16) & (relation_dom(A!16) = relation_rng(B!17)) & (relation_rng(A!16) = relation_dom(B!17)) & ![C: $i, D: $i] : ((~(in(C, relation_dom(A!16)) & in(D, relation_dom(B!17)))) | ((apply(A!16, C) = D) <=> (apply(B!17, D) = C)))))) <=> ((relation(A!16) & function(A!16)) & ((~(B!17 = function_inverse(A!16))) & relation(B!17) & function(B!17) & one_to_one(A!16) & (relation_dom(A!16) = relation_rng(B!17)) & (relation_rng(A!16) = relation_dom(B!17)) & ![C: $i, D: $i] : ((~(in(C, relation_dom(A!16)) & in(D, relation_dom(B!17)))) | ((apply(A!16, C) = D) <=> (apply(B!17, D) = C)))))),
% 195.14/195.28 inference(monotonicity,[status(thm)],[6])).
% 195.14/195.28 tff(8,plain,
% 195.14/195.28 (((relation(A!16) & function(A!16)) & ((~(B!17 = function_inverse(A!16))) & (relation(B!17) & function(B!17)) & (one_to_one(A!16) & (relation_dom(A!16) = relation_rng(B!17)) & (relation_rng(A!16) = relation_dom(B!17)) & ![C: $i, D: $i] : ((~(in(C, relation_dom(A!16)) & in(D, relation_dom(B!17)))) | ((apply(A!16, C) = D) <=> (apply(B!17, D) = C)))))) <=> (relation(A!16) & function(A!16) & (~(B!17 = function_inverse(A!16))) & relation(B!17) & function(B!17) & one_to_one(A!16) & (relation_dom(A!16) = relation_rng(B!17)) & (relation_rng(A!16) = relation_dom(B!17)) & ![C: $i, D: $i] : ((~(in(C, relation_dom(A!16)) & in(D, relation_dom(B!17)))) | ((apply(A!16, C) = D) <=> (apply(B!17, D) = C))))),
% 195.14/195.28 inference(transitivity,[status(thm)],[7, 2])).
% 195.14/195.28 tff(9,plain,
% 195.14/195.28 ((~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_dom(A) = relation_rng(B)) & (relation_rng(A) = relation_dom(B)) & ![C: $i, D: $i] : ((~(in(C, relation_dom(A)) & in(D, relation_dom(B)))) | ((apply(A, C) = D) <=> (apply(B, D) = C)))))))) <=> (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_dom(A) = relation_rng(B)) & (relation_rng(A) = relation_dom(B)) & ![C: $i, D: $i] : ((~(in(C, relation_dom(A)) & in(D, relation_dom(B)))) | ((apply(A, C) = D) <=> (apply(B, D) = C))))))))),
% 195.14/195.28 inference(rewrite,[status(thm)],[])).
% 195.14/195.28 tff(10,plain,
% 195.14/195.28 ((~![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => ((((one_to_one(A) & (relation_dom(A) = relation_rng(B))) & (relation_rng(A) = relation_dom(B))) & ![C: $i, D: $i] : ((in(C, relation_dom(A)) & in(D, relation_dom(B))) => ((apply(A, C) = D) <=> (apply(B, D) = C)))) => (B = function_inverse(A)))))) <=> (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_dom(A) = relation_rng(B)) & (relation_rng(A) = relation_dom(B)) & ![C: $i, D: $i] : ((~(in(C, relation_dom(A)) & in(D, relation_dom(B)))) | ((apply(A, C) = D) <=> (apply(B, D) = C))))))))),
% 195.14/195.28 inference(rewrite,[status(thm)],[])).
% 195.14/195.28 tff(11,axiom,(~![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => ((((one_to_one(A) & (relation_dom(A) = relation_rng(B))) & (relation_rng(A) = relation_dom(B))) & ![C: $i, D: $i] : ((in(C, relation_dom(A)) & in(D, relation_dom(B))) => ((apply(A, C) = D) <=> (apply(B, D) = C)))) => (B = function_inverse(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t60_funct_1')).
% 195.14/195.28 tff(12,plain,
% 195.14/195.28 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_dom(A) = relation_rng(B)) & (relation_rng(A) = relation_dom(B)) & ![C: $i, D: $i] : ((~(in(C, relation_dom(A)) & in(D, relation_dom(B)))) | ((apply(A, C) = D) <=> (apply(B, D) = C)))))))),
% 195.14/195.28 inference(modus_ponens,[status(thm)],[11, 10])).
% 195.14/195.28 tff(13,plain,
% 195.14/195.28 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_dom(A) = relation_rng(B)) & (relation_rng(A) = relation_dom(B)) & ![C: $i, D: $i] : ((~(in(C, relation_dom(A)) & in(D, relation_dom(B)))) | ((apply(A, C) = D) <=> (apply(B, D) = C)))))))),
% 195.14/195.28 inference(modus_ponens,[status(thm)],[12, 9])).
% 195.14/195.28 tff(14,plain,
% 195.14/195.28 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_dom(A) = relation_rng(B)) & (relation_rng(A) = relation_dom(B)) & ![C: $i, D: $i] : ((~(in(C, relation_dom(A)) & in(D, relation_dom(B)))) | ((apply(A, C) = D) <=> (apply(B, D) = C)))))))),
% 195.14/195.28 inference(modus_ponens,[status(thm)],[13, 9])).
% 195.14/195.28 tff(15,plain,
% 195.14/195.28 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_dom(A) = relation_rng(B)) & (relation_rng(A) = relation_dom(B)) & ![C: $i, D: $i] : ((~(in(C, relation_dom(A)) & in(D, relation_dom(B)))) | ((apply(A, C) = D) <=> (apply(B, D) = C)))))))),
% 195.14/195.28 inference(modus_ponens,[status(thm)],[14, 9])).
% 195.14/195.28 tff(16,plain,
% 195.14/195.28 (relation(A!16) & function(A!16) & (~(B!17 = function_inverse(A!16))) & relation(B!17) & function(B!17) & one_to_one(A!16) & (relation_dom(A!16) = relation_rng(B!17)) & (relation_rng(A!16) = relation_dom(B!17)) & ![C: $i, D: $i] : ((~(in(C, relation_dom(A!16)) & in(D, relation_dom(B!17)))) | ((apply(A!16, C) = D) <=> (apply(B!17, D) = C)))),
% 195.14/195.28 inference(modus_ponens,[status(thm)],[15, 8])).
% 195.14/195.28 tff(17,plain,
% 195.14/195.28 (function(A!16)),
% 195.14/195.28 inference(and_elim,[status(thm)],[16])).
% 195.14/195.28 tff(18,plain,
% 195.14/195.28 (relation(A!16)),
% 195.14/195.28 inference(and_elim,[status(thm)],[16])).
% 195.14/195.28 tff(19,plain,
% 195.14/195.28 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i, D_19: $i, C: $i, D: $i] : rewrite((~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19)))))))))))) <=> (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19))))))))))))), (![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19)))))))))))) <=> ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19))))))))))))), (((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19))))))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19)))))))))))))), rewrite(((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19)))))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19))))))))))))), (((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19))))))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19))))))))))))))),
% 195.14/195.29 inference(bind,[status(th)],[])).
% 195.14/195.29 tff(20,plain,
% 195.14/195.29 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19))))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19))))))))))))),
% 195.14/195.29 inference(quant_intro,[status(thm)],[19])).
% 195.14/195.29 tff(21,plain,
% 195.14/195.29 (^[A: $i] : refl(((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19))))))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19))))))))))))))),
% 195.14/195.29 inference(bind,[status(th)],[])).
% 195.14/195.29 tff(22,plain,
% 195.14/195.29 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19))))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19)))))))))))))),
% 195.14/195.29 inference(quant_intro,[status(thm)],[21])).
% 195.14/195.29 tff(23,plain,
% 195.14/195.29 (^[A: $i] : rewrite(((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D))))))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19))))))))))))))),
% 195.14/195.29 inference(bind,[status(th)],[])).
% 195.14/195.29 tff(24,plain,
% 195.14/195.29 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D))))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19)))))))))))))),
% 195.14/195.29 inference(quant_intro,[status(thm)],[23])).
% 195.14/195.29 tff(25,plain,
% 195.14/195.29 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D))))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19)))))))))))))),
% 195.14/195.29 inference(transitivity,[status(thm)],[24, 22])).
% 195.14/195.29 tff(26,plain,
% 195.14/195.29 (^[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(rewrite(((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_0(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_0(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) <=> ((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))), trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))) <=> (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))))), ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) <=> (in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))))))), rewrite((in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))))) <=> (in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))), ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) <=> (in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))))))), rewrite(((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D))))) <=> ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))), (((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D)))))) <=> ((in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))))), rewrite(((in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))) <=> (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D))))))))), (((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D)))))) <=> (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))))))), (((B = relation_rng(A)) | ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D))))))) <=> ((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D))))))))))), rewrite(((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D))))))))) <=> ((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))))))), (((B = relation_rng(A)) | ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D))))))) <=> ((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D))))))))))), ((((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_0(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_0(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D)))))))) <=> (((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) & ((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))))))))), rewrite((((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) & ((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))))))) <=> (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D))))))))))))), ((((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_0(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_0(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D)))))))) <=> (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D))))))))))))))), (![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_0(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_0(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D)))))))) <=> ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))))))))))), (((~(relation(A) & function(A))) | ![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_0(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_0(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D))))))))) <=> (((~relation(A)) | (~function(A))) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D))))))))))))))), rewrite((((~relation(A)) | (~function(A))) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D))))))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))))))))))), (((~(relation(A) & function(A))) | ![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_0(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_0(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))))))))))))),
% 195.14/195.29 inference(bind,[status(th)],[])).
% 195.14/195.29 tff(27,plain,
% 195.14/195.29 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_0(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_0(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))))))))))),
% 195.14/195.29 inference(quant_intro,[status(thm)],[26])).
% 195.14/195.29 tff(28,plain,
% 195.14/195.29 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D)))))) <=> ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D))))))),
% 195.14/195.29 inference(rewrite,[status(thm)],[])).
% 195.14/195.29 tff(29,plain,
% 195.14/195.29 (^[A: $i] : rewrite(((relation(A) & function(A)) => ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D)))))) <=> ((~(relation(A) & function(A))) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D)))))))),
% 195.14/195.29 inference(bind,[status(th)],[])).
% 195.14/195.29 tff(30,plain,
% 195.14/195.29 (![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D)))))) <=> ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D))))))),
% 195.14/195.29 inference(quant_intro,[status(thm)],[29])).
% 195.14/195.29 tff(31,axiom,(![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d5_funct_1')).
% 195.14/195.29 tff(32,plain,
% 195.14/195.29 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D))))))),
% 195.14/195.29 inference(modus_ponens,[status(thm)],[31, 30])).
% 195.14/195.29 tff(33,plain,
% 195.14/195.29 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D))))))),
% 195.14/195.29 inference(modus_ponens,[status(thm)],[32, 28])).
% 195.14/195.29 tff(34,plain,(
% 195.14/195.29 ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_0(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_0(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D)))))))))),
% 195.14/195.29 inference(skolemize,[status(sab)],[33])).
% 195.14/195.29 tff(35,plain,
% 195.14/195.29 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))))))))))),
% 195.14/195.29 inference(modus_ponens,[status(thm)],[34, 27])).
% 195.14/195.29 tff(36,plain,
% 195.14/195.29 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19)))))))))))))),
% 195.14/195.29 inference(modus_ponens,[status(thm)],[35, 25])).
% 195.14/195.29 tff(37,plain,
% 195.14/195.29 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19))))))))))))),
% 195.14/195.29 inference(modus_ponens,[status(thm)],[36, 20])).
% 195.14/195.29 tff(38,plain,
% 195.14/195.29 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19))))))))))))) | ((~function(A!16)) | (~relation(A!16)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A!16))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A!16), relation_dom(A!16))) | (~(C = apply(A!16, tptp_fun_D_0(C, A!16)))))))) | (~(in(C, B) | (~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))))) | (~((B = relation_rng(A!16)) | (~((~(in(tptp_fun_C_1(B, A!16), B) | (~((~in(tptp_fun_D_2(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_1(B, A!16) = apply(A!16, tptp_fun_D_2(B, A!16)))))))) | (~((~in(tptp_fun_C_1(B, A!16), B)) | (~in(D_19, relation_dom(A!16))) | (~(tptp_fun_C_1(B, A!16) = apply(A!16, D_19))))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19))))))))))))) | (~function(A!16)) | (~relation(A!16)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A!16))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A!16), relation_dom(A!16))) | (~(C = apply(A!16, tptp_fun_D_0(C, A!16)))))))) | (~(in(C, B) | (~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))))) | (~((B = relation_rng(A!16)) | (~((~(in(tptp_fun_C_1(B, A!16), B) | (~((~in(tptp_fun_D_2(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_1(B, A!16) = apply(A!16, tptp_fun_D_2(B, A!16)))))))) | (~((~in(tptp_fun_C_1(B, A!16), B)) | (~in(D_19, relation_dom(A!16))) | (~(tptp_fun_C_1(B, A!16) = apply(A!16, D_19))))))))))))),
% 195.14/195.29 inference(rewrite,[status(thm)],[])).
% 195.14/195.29 tff(39,plain,
% 195.14/195.29 (((~relation(A!16)) | (~function(A!16)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A!16))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A!16), relation_dom(A!16))) | (~(C = apply(A!16, tptp_fun_D_0(C, A!16)))))))) | (~(in(C, B) | (~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))))) | (~((B = relation_rng(A!16)) | (~((~(in(tptp_fun_C_1(B, A!16), B) | (~((~in(tptp_fun_D_2(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_1(B, A!16) = apply(A!16, tptp_fun_D_2(B, A!16)))))))) | (~((~in(tptp_fun_C_1(B, A!16), B)) | (~in(D_19, relation_dom(A!16))) | (~(tptp_fun_C_1(B, A!16) = apply(A!16, D_19)))))))))))) <=> ((~function(A!16)) | (~relation(A!16)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A!16))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A!16), relation_dom(A!16))) | (~(C = apply(A!16, tptp_fun_D_0(C, A!16)))))))) | (~(in(C, B) | (~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))))) | (~((B = relation_rng(A!16)) | (~((~(in(tptp_fun_C_1(B, A!16), B) | (~((~in(tptp_fun_D_2(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_1(B, A!16) = apply(A!16, tptp_fun_D_2(B, A!16)))))))) | (~((~in(tptp_fun_C_1(B, A!16), B)) | (~in(D_19, relation_dom(A!16))) | (~(tptp_fun_C_1(B, A!16) = apply(A!16, D_19))))))))))))),
% 195.14/195.29 inference(rewrite,[status(thm)],[])).
% 195.14/195.29 tff(40,plain,
% 195.14/195.29 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19))))))))))))) | ((~relation(A!16)) | (~function(A!16)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A!16))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A!16), relation_dom(A!16))) | (~(C = apply(A!16, tptp_fun_D_0(C, A!16)))))))) | (~(in(C, B) | (~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))))) | (~((B = relation_rng(A!16)) | (~((~(in(tptp_fun_C_1(B, A!16), B) | (~((~in(tptp_fun_D_2(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_1(B, A!16) = apply(A!16, tptp_fun_D_2(B, A!16)))))))) | (~((~in(tptp_fun_C_1(B, A!16), B)) | (~in(D_19, relation_dom(A!16))) | (~(tptp_fun_C_1(B, A!16) = apply(A!16, D_19))))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19))))))))))))) | ((~function(A!16)) | (~relation(A!16)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A!16))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A!16), relation_dom(A!16))) | (~(C = apply(A!16, tptp_fun_D_0(C, A!16)))))))) | (~(in(C, B) | (~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))))) | (~((B = relation_rng(A!16)) | (~((~(in(tptp_fun_C_1(B, A!16), B) | (~((~in(tptp_fun_D_2(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_1(B, A!16) = apply(A!16, tptp_fun_D_2(B, A!16)))))))) | (~((~in(tptp_fun_C_1(B, A!16), B)) | (~in(D_19, relation_dom(A!16))) | (~(tptp_fun_C_1(B, A!16) = apply(A!16, D_19)))))))))))))),
% 195.14/195.29 inference(monotonicity,[status(thm)],[39])).
% 195.14/195.29 tff(41,plain,
% 195.14/195.29 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19))))))))))))) | ((~relation(A!16)) | (~function(A!16)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A!16))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A!16), relation_dom(A!16))) | (~(C = apply(A!16, tptp_fun_D_0(C, A!16)))))))) | (~(in(C, B) | (~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))))) | (~((B = relation_rng(A!16)) | (~((~(in(tptp_fun_C_1(B, A!16), B) | (~((~in(tptp_fun_D_2(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_1(B, A!16) = apply(A!16, tptp_fun_D_2(B, A!16)))))))) | (~((~in(tptp_fun_C_1(B, A!16), B)) | (~in(D_19, relation_dom(A!16))) | (~(tptp_fun_C_1(B, A!16) = apply(A!16, D_19))))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19))))))))))))) | (~function(A!16)) | (~relation(A!16)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A!16))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A!16), relation_dom(A!16))) | (~(C = apply(A!16, tptp_fun_D_0(C, A!16)))))))) | (~(in(C, B) | (~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))))) | (~((B = relation_rng(A!16)) | (~((~(in(tptp_fun_C_1(B, A!16), B) | (~((~in(tptp_fun_D_2(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_1(B, A!16) = apply(A!16, tptp_fun_D_2(B, A!16)))))))) | (~((~in(tptp_fun_C_1(B, A!16), B)) | (~in(D_19, relation_dom(A!16))) | (~(tptp_fun_C_1(B, A!16) = apply(A!16, D_19))))))))))))),
% 195.14/195.29 inference(transitivity,[status(thm)],[40, 38])).
% 195.14/195.29 tff(42,plain,
% 195.14/195.29 ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19))))))))))))) | ((~relation(A!16)) | (~function(A!16)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A!16))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A!16), relation_dom(A!16))) | (~(C = apply(A!16, tptp_fun_D_0(C, A!16)))))))) | (~(in(C, B) | (~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))))) | (~((B = relation_rng(A!16)) | (~((~(in(tptp_fun_C_1(B, A!16), B) | (~((~in(tptp_fun_D_2(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_1(B, A!16) = apply(A!16, tptp_fun_D_2(B, A!16)))))))) | (~((~in(tptp_fun_C_1(B, A!16), B)) | (~in(D_19, relation_dom(A!16))) | (~(tptp_fun_C_1(B, A!16) = apply(A!16, D_19))))))))))))),
% 195.14/195.29 inference(quant_inst,[status(thm)],[])).
% 195.14/195.29 tff(43,plain,
% 195.14/195.29 ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19))))))))))))) | (~function(A!16)) | (~relation(A!16)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A!16))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A!16), relation_dom(A!16))) | (~(C = apply(A!16, tptp_fun_D_0(C, A!16)))))))) | (~(in(C, B) | (~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))))) | (~((B = relation_rng(A!16)) | (~((~(in(tptp_fun_C_1(B, A!16), B) | (~((~in(tptp_fun_D_2(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_1(B, A!16) = apply(A!16, tptp_fun_D_2(B, A!16)))))))) | (~((~in(tptp_fun_C_1(B, A!16), B)) | (~in(D_19, relation_dom(A!16))) | (~(tptp_fun_C_1(B, A!16) = apply(A!16, D_19)))))))))))),
% 195.14/195.29 inference(modus_ponens,[status(thm)],[42, 41])).
% 195.14/195.29 tff(44,plain,
% 195.14/195.29 (![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A!16))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A!16), relation_dom(A!16))) | (~(C = apply(A!16, tptp_fun_D_0(C, A!16)))))))) | (~(in(C, B) | (~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))))) | (~((B = relation_rng(A!16)) | (~((~(in(tptp_fun_C_1(B, A!16), B) | (~((~in(tptp_fun_D_2(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_1(B, A!16) = apply(A!16, tptp_fun_D_2(B, A!16)))))))) | (~((~in(tptp_fun_C_1(B, A!16), B)) | (~in(D_19, relation_dom(A!16))) | (~(tptp_fun_C_1(B, A!16) = apply(A!16, D_19)))))))))))),
% 195.14/195.29 inference(unit_resolution,[status(thm)],[43, 37, 18, 17])).
% 195.14/195.29 tff(45,plain,
% 195.14/195.29 (((~![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A!16))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A!16), relation_dom(A!16))) | (~(C = apply(A!16, tptp_fun_D_0(C, A!16)))))))) | (~(in(C, B) | (~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))))) | (~((B = relation_rng(A!16)) | (~((~(in(tptp_fun_C_1(B, A!16), B) | (~((~in(tptp_fun_D_2(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_1(B, A!16) = apply(A!16, tptp_fun_D_2(B, A!16)))))))) | (~((~in(tptp_fun_C_1(B, A!16), B)) | (~in(D_19, relation_dom(A!16))) | (~(tptp_fun_C_1(B, A!16) = apply(A!16, D_19)))))))))))) | (~((~((~(relation_dom(B!17) = relation_rng(A!16))) | (~((~((~in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))))))) | (~(in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17)) | (~in(tptp_fun_C_18(B!17, A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_C_18(B!17, A!16)))))))))) | (~((relation_dom(B!17) = relation_rng(A!16)) | (~((~(in(tptp_fun_C_1(relation_dom(B!17), A!16), relation_dom(B!17)) | (~((~in(tptp_fun_D_2(relation_dom(B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_1(relation_dom(B!17), A!16) = apply(A!16, tptp_fun_D_2(relation_dom(B!17), A!16)))))))) | (~((~in(tptp_fun_C_18(B!17, A!16), relation_dom(A!16))) | (~in(tptp_fun_C_1(relation_dom(B!17), A!16), relation_dom(B!17))) | (~(tptp_fun_C_1(relation_dom(B!17), A!16) = apply(A!16, tptp_fun_C_18(B!17, A!16))))))))))))) <=> ((~![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A!16))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A!16), relation_dom(A!16))) | (~(C = apply(A!16, tptp_fun_D_0(C, A!16)))))))) | (~(in(C, B) | (~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))))) | (~((B = relation_rng(A!16)) | (~((~(in(tptp_fun_C_1(B, A!16), B) | (~((~in(tptp_fun_D_2(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_1(B, A!16) = apply(A!16, tptp_fun_D_2(B, A!16)))))))) | (~((~in(tptp_fun_C_1(B, A!16), B)) | (~in(D_19, relation_dom(A!16))) | (~(tptp_fun_C_1(B, A!16) = apply(A!16, D_19)))))))))))) | (~((~((~(relation_dom(B!17) = relation_rng(A!16))) | (~((~((~in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))))))) | (~(in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17)) | (~in(tptp_fun_C_18(B!17, A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_C_18(B!17, A!16)))))))))) | (~((relation_dom(B!17) = relation_rng(A!16)) | (~((~(in(tptp_fun_C_1(relation_dom(B!17), A!16), relation_dom(B!17)) | (~((~in(tptp_fun_D_2(relation_dom(B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_1(relation_dom(B!17), A!16) = apply(A!16, tptp_fun_D_2(relation_dom(B!17), A!16)))))))) | (~((~in(tptp_fun_C_18(B!17, A!16), relation_dom(A!16))) | (~in(tptp_fun_C_1(relation_dom(B!17), A!16), relation_dom(B!17))) | (~(tptp_fun_C_1(relation_dom(B!17), A!16) = apply(A!16, tptp_fun_C_18(B!17, A!16)))))))))))))),
% 195.16/195.30 inference(rewrite,[status(thm)],[])).
% 195.16/195.30 tff(46,plain,
% 195.16/195.30 ((~((~((~(relation_dom(B!17) = relation_rng(A!16))) | (~((~((~in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))))))) | (~(in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17)) | (~in(tptp_fun_C_18(B!17, A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_C_18(B!17, A!16)))))))))) | (~((relation_dom(B!17) = relation_rng(A!16)) | (~((~(in(tptp_fun_C_1(relation_dom(B!17), A!16), relation_dom(B!17)) | (~((~in(tptp_fun_D_2(relation_dom(B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_1(relation_dom(B!17), A!16) = apply(A!16, tptp_fun_D_2(relation_dom(B!17), A!16)))))))) | (~((~in(tptp_fun_C_1(relation_dom(B!17), A!16), relation_dom(B!17))) | (~in(tptp_fun_C_18(B!17, A!16), relation_dom(A!16))) | (~(tptp_fun_C_1(relation_dom(B!17), A!16) = apply(A!16, tptp_fun_C_18(B!17, A!16)))))))))))) <=> (~((~((~(relation_dom(B!17) = relation_rng(A!16))) | (~((~((~in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))))))) | (~(in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17)) | (~in(tptp_fun_C_18(B!17, A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_C_18(B!17, A!16)))))))))) | (~((relation_dom(B!17) = relation_rng(A!16)) | (~((~(in(tptp_fun_C_1(relation_dom(B!17), A!16), relation_dom(B!17)) | (~((~in(tptp_fun_D_2(relation_dom(B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_1(relation_dom(B!17), A!16) = apply(A!16, tptp_fun_D_2(relation_dom(B!17), A!16)))))))) | (~((~in(tptp_fun_C_18(B!17, A!16), relation_dom(A!16))) | (~in(tptp_fun_C_1(relation_dom(B!17), A!16), relation_dom(B!17))) | (~(tptp_fun_C_1(relation_dom(B!17), A!16) = apply(A!16, tptp_fun_C_18(B!17, A!16))))))))))))),
% 195.16/195.30 inference(rewrite,[status(thm)],[])).
% 195.16/195.30 tff(47,plain,
% 195.16/195.30 (((~![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A!16))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A!16), relation_dom(A!16))) | (~(C = apply(A!16, tptp_fun_D_0(C, A!16)))))))) | (~(in(C, B) | (~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))))) | (~((B = relation_rng(A!16)) | (~((~(in(tptp_fun_C_1(B, A!16), B) | (~((~in(tptp_fun_D_2(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_1(B, A!16) = apply(A!16, tptp_fun_D_2(B, A!16)))))))) | (~((~in(tptp_fun_C_1(B, A!16), B)) | (~in(D_19, relation_dom(A!16))) | (~(tptp_fun_C_1(B, A!16) = apply(A!16, D_19)))))))))))) | (~((~((~(relation_dom(B!17) = relation_rng(A!16))) | (~((~((~in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))))))) | (~(in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17)) | (~in(tptp_fun_C_18(B!17, A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_C_18(B!17, A!16)))))))))) | (~((relation_dom(B!17) = relation_rng(A!16)) | (~((~(in(tptp_fun_C_1(relation_dom(B!17), A!16), relation_dom(B!17)) | (~((~in(tptp_fun_D_2(relation_dom(B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_1(relation_dom(B!17), A!16) = apply(A!16, tptp_fun_D_2(relation_dom(B!17), A!16)))))))) | (~((~in(tptp_fun_C_1(relation_dom(B!17), A!16), relation_dom(B!17))) | (~in(tptp_fun_C_18(B!17, A!16), relation_dom(A!16))) | (~(tptp_fun_C_1(relation_dom(B!17), A!16) = apply(A!16, tptp_fun_C_18(B!17, A!16))))))))))))) <=> ((~![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A!16))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A!16), relation_dom(A!16))) | (~(C = apply(A!16, tptp_fun_D_0(C, A!16)))))))) | (~(in(C, B) | (~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))))) | (~((B = relation_rng(A!16)) | (~((~(in(tptp_fun_C_1(B, A!16), B) | (~((~in(tptp_fun_D_2(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_1(B, A!16) = apply(A!16, tptp_fun_D_2(B, A!16)))))))) | (~((~in(tptp_fun_C_1(B, A!16), B)) | (~in(D_19, relation_dom(A!16))) | (~(tptp_fun_C_1(B, A!16) = apply(A!16, D_19)))))))))))) | (~((~((~(relation_dom(B!17) = relation_rng(A!16))) | (~((~((~in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))))))) | (~(in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17)) | (~in(tptp_fun_C_18(B!17, A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_C_18(B!17, A!16)))))))))) | (~((relation_dom(B!17) = relation_rng(A!16)) | (~((~(in(tptp_fun_C_1(relation_dom(B!17), A!16), relation_dom(B!17)) | (~((~in(tptp_fun_D_2(relation_dom(B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_1(relation_dom(B!17), A!16) = apply(A!16, tptp_fun_D_2(relation_dom(B!17), A!16)))))))) | (~((~in(tptp_fun_C_18(B!17, A!16), relation_dom(A!16))) | (~in(tptp_fun_C_1(relation_dom(B!17), A!16), relation_dom(B!17))) | (~(tptp_fun_C_1(relation_dom(B!17), A!16) = apply(A!16, tptp_fun_C_18(B!17, A!16)))))))))))))),
% 195.16/195.30 inference(monotonicity,[status(thm)],[46])).
% 195.16/195.30 tff(48,plain,
% 195.16/195.30 (((~![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A!16))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A!16), relation_dom(A!16))) | (~(C = apply(A!16, tptp_fun_D_0(C, A!16)))))))) | (~(in(C, B) | (~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))))) | (~((B = relation_rng(A!16)) | (~((~(in(tptp_fun_C_1(B, A!16), B) | (~((~in(tptp_fun_D_2(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_1(B, A!16) = apply(A!16, tptp_fun_D_2(B, A!16)))))))) | (~((~in(tptp_fun_C_1(B, A!16), B)) | (~in(D_19, relation_dom(A!16))) | (~(tptp_fun_C_1(B, A!16) = apply(A!16, D_19)))))))))))) | (~((~((~(relation_dom(B!17) = relation_rng(A!16))) | (~((~((~in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))))))) | (~(in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17)) | (~in(tptp_fun_C_18(B!17, A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_C_18(B!17, A!16)))))))))) | (~((relation_dom(B!17) = relation_rng(A!16)) | (~((~(in(tptp_fun_C_1(relation_dom(B!17), A!16), relation_dom(B!17)) | (~((~in(tptp_fun_D_2(relation_dom(B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_1(relation_dom(B!17), A!16) = apply(A!16, tptp_fun_D_2(relation_dom(B!17), A!16)))))))) | (~((~in(tptp_fun_C_1(relation_dom(B!17), A!16), relation_dom(B!17))) | (~in(tptp_fun_C_18(B!17, A!16), relation_dom(A!16))) | (~(tptp_fun_C_1(relation_dom(B!17), A!16) = apply(A!16, tptp_fun_C_18(B!17, A!16))))))))))))) <=> ((~![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A!16))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A!16), relation_dom(A!16))) | (~(C = apply(A!16, tptp_fun_D_0(C, A!16)))))))) | (~(in(C, B) | (~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))))) | (~((B = relation_rng(A!16)) | (~((~(in(tptp_fun_C_1(B, A!16), B) | (~((~in(tptp_fun_D_2(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_1(B, A!16) = apply(A!16, tptp_fun_D_2(B, A!16)))))))) | (~((~in(tptp_fun_C_1(B, A!16), B)) | (~in(D_19, relation_dom(A!16))) | (~(tptp_fun_C_1(B, A!16) = apply(A!16, D_19)))))))))))) | (~((~((~(relation_dom(B!17) = relation_rng(A!16))) | (~((~((~in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))))))) | (~(in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17)) | (~in(tptp_fun_C_18(B!17, A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_C_18(B!17, A!16)))))))))) | (~((relation_dom(B!17) = relation_rng(A!16)) | (~((~(in(tptp_fun_C_1(relation_dom(B!17), A!16), relation_dom(B!17)) | (~((~in(tptp_fun_D_2(relation_dom(B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_1(relation_dom(B!17), A!16) = apply(A!16, tptp_fun_D_2(relation_dom(B!17), A!16)))))))) | (~((~in(tptp_fun_C_18(B!17, A!16), relation_dom(A!16))) | (~in(tptp_fun_C_1(relation_dom(B!17), A!16), relation_dom(B!17))) | (~(tptp_fun_C_1(relation_dom(B!17), A!16) = apply(A!16, tptp_fun_C_18(B!17, A!16)))))))))))))),
% 195.16/195.30 inference(transitivity,[status(thm)],[47, 45])).
% 195.16/195.30 tff(49,plain,
% 195.16/195.30 ((~![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A!16))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A!16), relation_dom(A!16))) | (~(C = apply(A!16, tptp_fun_D_0(C, A!16)))))))) | (~(in(C, B) | (~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))))) | (~((B = relation_rng(A!16)) | (~((~(in(tptp_fun_C_1(B, A!16), B) | (~((~in(tptp_fun_D_2(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_1(B, A!16) = apply(A!16, tptp_fun_D_2(B, A!16)))))))) | (~((~in(tptp_fun_C_1(B, A!16), B)) | (~in(D_19, relation_dom(A!16))) | (~(tptp_fun_C_1(B, A!16) = apply(A!16, D_19)))))))))))) | (~((~((~(relation_dom(B!17) = relation_rng(A!16))) | (~((~((~in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))))))) | (~(in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17)) | (~in(tptp_fun_C_18(B!17, A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_C_18(B!17, A!16)))))))))) | (~((relation_dom(B!17) = relation_rng(A!16)) | (~((~(in(tptp_fun_C_1(relation_dom(B!17), A!16), relation_dom(B!17)) | (~((~in(tptp_fun_D_2(relation_dom(B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_1(relation_dom(B!17), A!16) = apply(A!16, tptp_fun_D_2(relation_dom(B!17), A!16)))))))) | (~((~in(tptp_fun_C_1(relation_dom(B!17), A!16), relation_dom(B!17))) | (~in(tptp_fun_C_18(B!17, A!16), relation_dom(A!16))) | (~(tptp_fun_C_1(relation_dom(B!17), A!16) = apply(A!16, tptp_fun_C_18(B!17, A!16))))))))))))),
% 195.16/195.30 inference(quant_inst,[status(thm)],[])).
% 195.16/195.30 tff(50,plain,
% 195.16/195.30 ((~![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A!16))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A!16), relation_dom(A!16))) | (~(C = apply(A!16, tptp_fun_D_0(C, A!16)))))))) | (~(in(C, B) | (~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))))) | (~((B = relation_rng(A!16)) | (~((~(in(tptp_fun_C_1(B, A!16), B) | (~((~in(tptp_fun_D_2(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_1(B, A!16) = apply(A!16, tptp_fun_D_2(B, A!16)))))))) | (~((~in(tptp_fun_C_1(B, A!16), B)) | (~in(D_19, relation_dom(A!16))) | (~(tptp_fun_C_1(B, A!16) = apply(A!16, D_19)))))))))))) | (~((~((~(relation_dom(B!17) = relation_rng(A!16))) | (~((~((~in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))))))) | (~(in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17)) | (~in(tptp_fun_C_18(B!17, A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_C_18(B!17, A!16)))))))))) | (~((relation_dom(B!17) = relation_rng(A!16)) | (~((~(in(tptp_fun_C_1(relation_dom(B!17), A!16), relation_dom(B!17)) | (~((~in(tptp_fun_D_2(relation_dom(B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_1(relation_dom(B!17), A!16) = apply(A!16, tptp_fun_D_2(relation_dom(B!17), A!16)))))))) | (~((~in(tptp_fun_C_18(B!17, A!16), relation_dom(A!16))) | (~in(tptp_fun_C_1(relation_dom(B!17), A!16), relation_dom(B!17))) | (~(tptp_fun_C_1(relation_dom(B!17), A!16) = apply(A!16, tptp_fun_C_18(B!17, A!16))))))))))))),
% 195.16/195.30 inference(modus_ponens,[status(thm)],[49, 48])).
% 195.16/195.30 tff(51,plain,
% 195.16/195.30 ($false),
% 195.16/195.30 inference(unit_resolution,[status(thm)],[50, 44, 1])).
% 195.16/195.30 tff(52,plain,(~((~((~(relation_dom(B!17) = relation_rng(A!16))) | (~((~((~in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))))))) | (~(in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17)) | (~in(tptp_fun_C_18(B!17, A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_C_18(B!17, A!16)))))))))) | (~((relation_dom(B!17) = relation_rng(A!16)) | (~((~(in(tptp_fun_C_1(relation_dom(B!17), A!16), relation_dom(B!17)) | (~((~in(tptp_fun_D_2(relation_dom(B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_1(relation_dom(B!17), A!16) = apply(A!16, tptp_fun_D_2(relation_dom(B!17), A!16)))))))) | (~((~in(tptp_fun_C_18(B!17, A!16), relation_dom(A!16))) | (~in(tptp_fun_C_1(relation_dom(B!17), A!16), relation_dom(B!17))) | (~(tptp_fun_C_1(relation_dom(B!17), A!16) = apply(A!16, tptp_fun_C_18(B!17, A!16)))))))))))), inference(lemma,lemma(discharge,[]))).
% 195.16/195.30 tff(53,assumption,(~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))))), introduced(assumption)).
% 195.16/195.30 tff(54,plain,
% 195.16/195.30 (((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))))) | (tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))),
% 195.16/195.30 inference(tautology,[status(thm)],[])).
% 195.16/195.30 tff(55,plain,
% 195.16/195.30 (tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))),
% 195.16/195.30 inference(unit_resolution,[status(thm)],[54, 53])).
% 195.16/195.30 tff(56,plain,
% 195.16/195.30 (apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)) = tptp_fun_C_18(function_inverse(A!16), B!17)),
% 195.16/195.30 inference(symmetry,[status(thm)],[55])).
% 195.16/195.30 tff(57,plain,
% 195.16/195.30 (in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_dom(B!17)) <=> in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17))),
% 195.16/195.30 inference(monotonicity,[status(thm)],[56])).
% 195.16/195.30 tff(58,plain,
% 195.16/195.30 (in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17)) <=> in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_dom(B!17))),
% 195.16/195.30 inference(symmetry,[status(thm)],[57])).
% 195.16/195.30 tff(59,plain,
% 195.16/195.30 (^[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)))))))),
% 195.16/195.30 inference(bind,[status(th)],[])).
% 195.16/195.30 tff(60,plain,
% 195.16/195.30 (![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))))))),
% 195.16/195.30 inference(quant_intro,[status(thm)],[59])).
% 195.16/195.30 tff(61,plain,
% 195.16/195.30 (^[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))))))))),
% 195.16/195.30 inference(bind,[status(th)],[])).
% 195.16/195.30 tff(62,plain,
% 195.16/195.30 (![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))))))),
% 195.16/195.30 inference(quant_intro,[status(thm)],[61])).
% 195.16/195.30 tff(63,plain,
% 195.16/195.30 (![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))))),
% 195.16/195.30 inference(rewrite,[status(thm)],[])).
% 195.16/195.30 tff(64,plain,
% 195.16/195.30 (^[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)))))),
% 195.16/195.30 inference(bind,[status(th)],[])).
% 195.16/195.30 tff(65,plain,
% 195.16/195.30 (![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))))),
% 195.16/195.30 inference(quant_intro,[status(thm)],[64])).
% 195.16/195.30 tff(66,axiom,(![A: $i] : ((relation(A) & function(A)) => (relation(function_inverse(A)) & function(function_inverse(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k2_funct_1')).
% 195.16/195.30 tff(67,plain,
% 195.16/195.30 (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 195.16/195.30 inference(modus_ponens,[status(thm)],[66, 65])).
% 195.16/195.30 tff(68,plain,
% 195.16/195.30 (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 195.16/195.30 inference(modus_ponens,[status(thm)],[67, 63])).
% 195.16/195.30 tff(69,plain,(
% 195.16/195.30 ![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 195.16/195.30 inference(skolemize,[status(sab)],[68])).
% 195.16/195.30 tff(70,plain,
% 195.16/195.30 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 195.16/195.30 inference(modus_ponens,[status(thm)],[69, 62])).
% 195.16/195.30 tff(71,plain,
% 195.16/195.30 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 195.16/195.30 inference(modus_ponens,[status(thm)],[70, 60])).
% 195.16/195.30 tff(72,plain,
% 195.16/195.30 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | ((~function(A!16)) | (~relation(A!16)) | (~((~relation(function_inverse(A!16))) | (~function(function_inverse(A!16))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | (~function(A!16)) | (~relation(A!16)) | (~((~relation(function_inverse(A!16))) | (~function(function_inverse(A!16))))))),
% 195.16/195.30 inference(rewrite,[status(thm)],[])).
% 195.16/195.30 tff(73,plain,
% 195.16/195.30 (((~relation(A!16)) | (~function(A!16)) | (~((~relation(function_inverse(A!16))) | (~function(function_inverse(A!16)))))) <=> ((~function(A!16)) | (~relation(A!16)) | (~((~relation(function_inverse(A!16))) | (~function(function_inverse(A!16))))))),
% 195.16/195.30 inference(rewrite,[status(thm)],[])).
% 195.16/195.30 tff(74,plain,
% 195.16/195.30 ((~((~relation(function_inverse(A!16))) | (~function(function_inverse(A!16))))) <=> (~((~relation(function_inverse(A!16))) | (~function(function_inverse(A!16)))))),
% 195.16/195.30 inference(rewrite,[status(thm)],[])).
% 195.16/195.30 tff(75,plain,
% 195.16/195.30 (((~relation(A!16)) | (~function(A!16)) | (~((~relation(function_inverse(A!16))) | (~function(function_inverse(A!16)))))) <=> ((~relation(A!16)) | (~function(A!16)) | (~((~relation(function_inverse(A!16))) | (~function(function_inverse(A!16))))))),
% 195.16/195.30 inference(monotonicity,[status(thm)],[74])).
% 195.16/195.30 tff(76,plain,
% 195.16/195.30 (((~relation(A!16)) | (~function(A!16)) | (~((~relation(function_inverse(A!16))) | (~function(function_inverse(A!16)))))) <=> ((~function(A!16)) | (~relation(A!16)) | (~((~relation(function_inverse(A!16))) | (~function(function_inverse(A!16))))))),
% 195.16/195.30 inference(transitivity,[status(thm)],[75, 73])).
% 195.16/195.30 tff(77,plain,
% 195.16/195.30 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | ((~relation(A!16)) | (~function(A!16)) | (~((~relation(function_inverse(A!16))) | (~function(function_inverse(A!16))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | ((~function(A!16)) | (~relation(A!16)) | (~((~relation(function_inverse(A!16))) | (~function(function_inverse(A!16)))))))),
% 195.16/195.30 inference(monotonicity,[status(thm)],[76])).
% 195.16/195.30 tff(78,plain,
% 195.16/195.30 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | ((~relation(A!16)) | (~function(A!16)) | (~((~relation(function_inverse(A!16))) | (~function(function_inverse(A!16))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | (~function(A!16)) | (~relation(A!16)) | (~((~relation(function_inverse(A!16))) | (~function(function_inverse(A!16))))))),
% 195.16/195.30 inference(transitivity,[status(thm)],[77, 72])).
% 195.16/195.30 tff(79,plain,
% 195.16/195.30 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | ((~relation(A!16)) | (~function(A!16)) | (~((~relation(function_inverse(A!16))) | (~function(function_inverse(A!16))))))),
% 195.16/195.30 inference(quant_inst,[status(thm)],[])).
% 195.16/195.30 tff(80,plain,
% 195.16/195.30 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | (~function(A!16)) | (~relation(A!16)) | (~((~relation(function_inverse(A!16))) | (~function(function_inverse(A!16)))))),
% 195.16/195.30 inference(modus_ponens,[status(thm)],[79, 78])).
% 195.16/195.30 tff(81,plain,
% 195.16/195.30 (~((~relation(function_inverse(A!16))) | (~function(function_inverse(A!16))))),
% 195.16/195.30 inference(unit_resolution,[status(thm)],[80, 71, 18, 17])).
% 195.16/195.30 tff(82,plain,
% 195.16/195.30 (((~relation(function_inverse(A!16))) | (~function(function_inverse(A!16)))) | function(function_inverse(A!16))),
% 195.16/195.30 inference(tautology,[status(thm)],[])).
% 195.16/195.30 tff(83,plain,
% 195.16/195.30 (function(function_inverse(A!16))),
% 195.16/195.30 inference(unit_resolution,[status(thm)],[82, 81])).
% 195.16/195.30 tff(84,plain,
% 195.16/195.30 (((~relation(function_inverse(A!16))) | (~function(function_inverse(A!16)))) | relation(function_inverse(A!16))),
% 195.16/195.30 inference(tautology,[status(thm)],[])).
% 195.16/195.30 tff(85,plain,
% 195.16/195.30 (relation(function_inverse(A!16))),
% 195.16/195.30 inference(unit_resolution,[status(thm)],[84, 81])).
% 195.16/195.30 tff(86,plain,
% 195.16/195.30 (one_to_one(A!16)),
% 195.16/195.30 inference(and_elim,[status(thm)],[16])).
% 195.16/195.30 tff(87,plain,
% 195.16/195.30 (^[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(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_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))))) <=> (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_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(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 = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_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(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))) | (~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_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(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))) | (~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_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(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 = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_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(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 = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))))))))) <=> ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_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(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)) | ![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_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_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))) | (~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_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(D, relation_dom(A))) | (~(C = apply(A, D))) | (~((~in(C, relation_rng(A))) | (~(D = apply(B, C)))))))))))))))))))), 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_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_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(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)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_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(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)) | ![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_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_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))) | (~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_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(D, relation_dom(A))) | (~(C = apply(A, D))) | (~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))))))))))))))))))),
% 195.16/195.30 inference(bind,[status(th)],[])).
% 195.16/195.30 tff(88,plain,
% 195.16/195.30 (![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(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_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_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))) | (~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_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(D, relation_dom(A))) | (~(C = apply(A, D))) | (~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))))))))))))))))),
% 195.16/195.31 inference(quant_intro,[status(thm)],[87])).
% 195.16/195.31 tff(89,plain,
% 195.16/195.31 (^[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(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_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_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_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))))))))),
% 195.16/195.31 inference(bind,[status(th)],[])).
% 195.16/195.31 tff(90,plain,
% 195.16/195.31 (![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(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_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_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(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_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))))))))))),
% 195.16/195.31 inference(quant_intro,[status(thm)],[89])).
% 195.16/195.31 tff(91,plain,
% 195.16/195.31 (^[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(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_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_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_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))))))))),
% 195.16/195.31 inference(bind,[status(th)],[])).
% 195.16/195.31 tff(92,plain,
% 195.16/195.31 (![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(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_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_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(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_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))))))))))),
% 195.16/195.31 inference(quant_intro,[status(thm)],[91])).
% 195.16/195.31 tff(93,plain,
% 195.16/195.31 (![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(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_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_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(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_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))))))))))),
% 195.16/195.31 inference(transitivity,[status(thm)],[92, 90])).
% 195.16/195.31 tff(94,plain,
% 195.16/195.31 (^[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(D, relation_dom(A))) | (~(C = apply(A, D))) | (~((~in(C, relation_rng(A))) | (~(D = apply(B, C)))))))))))))), trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((in(tptp_fun_C_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) <=> (~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))))), ((~(in(tptp_fun_C_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))) <=> (~(~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))))))), rewrite((~(~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))))) <=> ((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))), ((~(in(tptp_fun_C_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))) <=> ((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))))), rewrite((in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))) <=> (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))))), (((~(in(tptp_fun_C_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))) | (in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) <=> (((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))))))), rewrite((((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))))) <=> ((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))), (((~(in(tptp_fun_C_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))) | (in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) <=> ((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))))))), trans(monotonicity(trans(monotonicity(rewrite((in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))) <=> (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))))), ((~(in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) <=> (~(~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))))))), rewrite((~(~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))))) <=> ((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))), ((~(in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) <=> ((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))))), rewrite((in(tptp_fun_C_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) <=> (~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))))), (((~(in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) | (in(tptp_fun_C_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))) <=> (((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) | (~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))))))), rewrite((((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) | (~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))))) <=> ((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))), (((~(in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) | (in(tptp_fun_C_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))) <=> ((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))))), ((((~(in(tptp_fun_C_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))) | (in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) & ((~(in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) | (in(tptp_fun_C_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) <=> (((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))))) & ((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))), rewrite((((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))))) & ((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))) <=> (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))))))), ((((~(in(tptp_fun_C_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))) | (in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) & ((~(in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) | (in(tptp_fun_C_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) <=> (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))))), ((~(((~(in(tptp_fun_C_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))) | (in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) & ((~(in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) | (in(tptp_fun_C_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))))) <=> (~(~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))))))))), rewrite((~(~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))))))) <=> ((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))), ((~(((~(in(tptp_fun_C_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))) | (in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) & ((~(in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) | (in(tptp_fun_C_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))))) <=> ((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))))))), (((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))) | (in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) & ((~(in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) | (in(tptp_fun_C_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))))) <=> ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | ((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))))), rewrite(((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | ((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) <=> ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))), (((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))) | (in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) & ((~(in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) | (in(tptp_fun_C_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))))) <=> ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_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(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_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))) | (in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) & ((~(in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) | (in(tptp_fun_C_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(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_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(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(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_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_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(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_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_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(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_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))) | (in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) & ((~(in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) | (in(tptp_fun_C_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(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_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_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_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))) | (in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) & ((~(in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) | (in(tptp_fun_C_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(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_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(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(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_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_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_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_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_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))) | (in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) & ((~(in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) | (in(tptp_fun_C_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(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_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_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_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))) | (in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) & ((~(in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) | (in(tptp_fun_C_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(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_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_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(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_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))) | (in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) & ((~(in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) | (in(tptp_fun_C_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(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_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(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(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_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_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_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_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(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_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))) | (in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) & ((~(in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) | (in(tptp_fun_C_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(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_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))))))))))))),
% 195.17/195.31 inference(bind,[status(th)],[])).
% 195.17/195.31 tff(95,plain,
% 195.17/195.31 (![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_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))) | (in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) & ((~(in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) | (in(tptp_fun_C_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(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(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_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))))))))))),
% 195.17/195.31 inference(quant_intro,[status(thm)],[94])).
% 195.17/195.31 tff(96,plain,
% 195.17/195.31 (^[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_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))) | (in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) & ((~(in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) | (in(tptp_fun_C_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(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_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))) | (in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) & ((~(in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) | (in(tptp_fun_C_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(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_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))) | (in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) & ((~(in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) | (in(tptp_fun_C_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(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_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))) | (in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) & ((~(in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) | (in(tptp_fun_C_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(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_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))) | (in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) & ((~(in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) | (in(tptp_fun_C_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(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_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))) | (in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) & ((~(in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) | (in(tptp_fun_C_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(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_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))) | (in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) & ((~(in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) | (in(tptp_fun_C_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(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_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))) | (in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) & ((~(in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) | (in(tptp_fun_C_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(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_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))) | (in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) & ((~(in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) | (in(tptp_fun_C_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(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_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))) | (in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) & ((~(in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) | (in(tptp_fun_C_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))))))))))),
% 195.17/195.31 inference(bind,[status(th)],[])).
% 195.17/195.31 tff(97,plain,
% 195.17/195.31 (![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_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))) | (in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) & ((~(in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) | (in(tptp_fun_C_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(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_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))) | (in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) & ((~(in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) | (in(tptp_fun_C_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))))))))),
% 195.17/195.31 inference(quant_intro,[status(thm)],[96])).
% 195.17/195.31 tff(98,plain,
% 195.17/195.31 (![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)))),
% 195.17/195.31 inference(rewrite,[status(thm)],[])).
% 195.17/195.31 tff(99,plain,
% 195.17/195.31 (^[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)))))),
% 195.17/195.31 inference(bind,[status(th)],[])).
% 195.17/195.31 tff(100,plain,
% 195.17/195.31 (![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)))),
% 195.17/195.31 inference(quant_intro,[status(thm)],[99])).
% 195.17/195.31 tff(101,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/sandbox/benchmark/theBenchmark.p','t54_funct_1')).
% 195.17/195.32 tff(102,plain,
% 195.17/195.32 (![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)))),
% 195.17/195.32 inference(modus_ponens,[status(thm)],[101, 100])).
% 195.17/195.32 tff(103,plain,
% 195.17/195.32 (![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)))),
% 195.17/195.32 inference(modus_ponens,[status(thm)],[102, 98])).
% 195.17/195.32 tff(104,plain,(
% 195.17/195.32 ![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_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))) | (in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) & ((~(in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) | (in(tptp_fun_C_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))))))))) | (~one_to_one(A)))),
% 195.17/195.32 inference(skolemize,[status(sab)],[103])).
% 195.17/195.32 tff(105,plain,
% 195.17/195.32 (![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_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A))))) | (in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) & ((~(in(tptp_fun_D_14(B, A), relation_dom(A)) & (tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))) | (in(tptp_fun_C_15(B, A), relation_rng(A)) & (tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))))))))),
% 195.17/195.32 inference(modus_ponens,[status(thm)],[104, 97])).
% 195.17/195.32 tff(106,plain,
% 195.17/195.32 (![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(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_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))))))))))),
% 195.17/195.32 inference(modus_ponens,[status(thm)],[105, 95])).
% 195.17/195.32 tff(107,plain,
% 195.17/195.32 (![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(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_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A))))))))))))),
% 195.17/195.32 inference(modus_ponens,[status(thm)],[106, 93])).
% 195.17/195.32 tff(108,plain,
% 195.17/195.32 (![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_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_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(D, relation_dom(A))) | (~(C = apply(A, D))) | (~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))))))))))))))))),
% 195.17/195.32 inference(modus_ponens,[status(thm)],[107, 88])).
% 195.17/195.32 tff(109,plain,
% 195.17/195.32 (((~![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_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_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(D, relation_dom(A))) | (~(C = apply(A, D))) | (~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))))))))))))))))) | ((~function(A!16)) | (~relation(A!16)) | (~one_to_one(A!16)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A!16)) | (~(relation_dom(B) = relation_rng(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))) | (~((~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))))))) | (~((~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))) | (~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))))))))) | (~((~(B = function_inverse(A!16))) | (~((~(relation_dom(B) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16))))))))))))))))))) <=> ((~![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_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_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(D, relation_dom(A))) | (~(C = apply(A, D))) | (~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))))))))))))))))) | (~function(A!16)) | (~relation(A!16)) | (~one_to_one(A!16)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A!16)) | (~(relation_dom(B) = relation_rng(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))) | (~((~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))))))) | (~((~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))) | (~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))))))))) | (~((~(B = function_inverse(A!16))) | (~((~(relation_dom(B) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16))))))))))))))))))),
% 195.17/195.32 inference(rewrite,[status(thm)],[])).
% 195.17/195.32 tff(110,plain,
% 195.17/195.32 (((~one_to_one(A!16)) | (~relation(A!16)) | (~function(A!16)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A!16)) | (~(relation_dom(B) = relation_rng(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))) | (~((~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))))))) | (~((~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))) | (~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))))))))) | (~((~(B = function_inverse(A!16))) | (~((~(relation_dom(B) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16)))))))))))))))))) <=> ((~function(A!16)) | (~relation(A!16)) | (~one_to_one(A!16)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A!16)) | (~(relation_dom(B) = relation_rng(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))) | (~((~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))))))) | (~((~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))) | (~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))))))))) | (~((~(B = function_inverse(A!16))) | (~((~(relation_dom(B) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16))))))))))))))))))),
% 195.17/195.32 inference(rewrite,[status(thm)],[])).
% 195.17/195.32 tff(111,plain,
% 195.17/195.32 (^[B: $i] : trans(monotonicity(rewrite((~((~((B = function_inverse(A!16)) | (~(relation_dom(B) = relation_rng(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))) | (~((~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))))))) | (~((~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))))) | (~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))))))) | (~((~(B = function_inverse(A!16))) | (~((~(relation_dom(B) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!16))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~in(C, relation_rng(A!16))) | (~(D = apply(B, C)))))))))))))))) <=> (~((~((B = function_inverse(A!16)) | (~(relation_dom(B) = relation_rng(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))) | (~((~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))))))) | (~((~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))) | (~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))))))))) | (~((~(B = function_inverse(A!16))) | (~((~(relation_dom(B) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16))))))))))))))))), (((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A!16)) | (~(relation_dom(B) = relation_rng(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))) | (~((~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))))))) | (~((~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))))) | (~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))))))) | (~((~(B = function_inverse(A!16))) | (~((~(relation_dom(B) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!16))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~in(C, relation_rng(A!16))) | (~(D = apply(B, C))))))))))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A!16)) | (~(relation_dom(B) = relation_rng(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))) | (~((~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))))))) | (~((~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))) | (~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))))))))) | (~((~(B = function_inverse(A!16))) | (~((~(relation_dom(B) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16))))))))))))))))))), rewrite(((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A!16)) | (~(relation_dom(B) = relation_rng(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))) | (~((~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))))))) | (~((~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))) | (~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))))))))) | (~((~(B = function_inverse(A!16))) | (~((~(relation_dom(B) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16))))))))))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A!16)) | (~(relation_dom(B) = relation_rng(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))) | (~((~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))))))) | (~((~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))) | (~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))))))))) | (~((~(B = function_inverse(A!16))) | (~((~(relation_dom(B) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16)))))))))))))))))), (((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A!16)) | (~(relation_dom(B) = relation_rng(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))) | (~((~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))))))) | (~((~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))))) | (~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))))))) | (~((~(B = function_inverse(A!16))) | (~((~(relation_dom(B) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!16))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~in(C, relation_rng(A!16))) | (~(D = apply(B, C))))))))))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A!16)) | (~(relation_dom(B) = relation_rng(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))) | (~((~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))))))) | (~((~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))) | (~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))))))))) | (~((~(B = function_inverse(A!16))) | (~((~(relation_dom(B) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16)))))))))))))))))))),
% 195.17/195.32 inference(bind,[status(th)],[])).
% 195.17/195.32 tff(112,plain,
% 195.17/195.32 (![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A!16)) | (~(relation_dom(B) = relation_rng(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))) | (~((~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))))))) | (~((~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))))) | (~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))))))) | (~((~(B = function_inverse(A!16))) | (~((~(relation_dom(B) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!16))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~in(C, relation_rng(A!16))) | (~(D = apply(B, C))))))))))))))))) <=> ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A!16)) | (~(relation_dom(B) = relation_rng(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))) | (~((~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))))))) | (~((~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))) | (~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))))))))) | (~((~(B = function_inverse(A!16))) | (~((~(relation_dom(B) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16)))))))))))))))))),
% 195.17/195.32 inference(quant_intro,[status(thm)],[111])).
% 195.17/195.32 tff(113,plain,
% 195.17/195.32 (((~one_to_one(A!16)) | (~relation(A!16)) | (~function(A!16)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A!16)) | (~(relation_dom(B) = relation_rng(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))) | (~((~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))))))) | (~((~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))))) | (~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))))))) | (~((~(B = function_inverse(A!16))) | (~((~(relation_dom(B) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!16))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~in(C, relation_rng(A!16))) | (~(D = apply(B, C)))))))))))))))))) <=> ((~one_to_one(A!16)) | (~relation(A!16)) | (~function(A!16)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A!16)) | (~(relation_dom(B) = relation_rng(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))) | (~((~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))))))) | (~((~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))) | (~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))))))))) | (~((~(B = function_inverse(A!16))) | (~((~(relation_dom(B) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16))))))))))))))))))),
% 195.17/195.32 inference(monotonicity,[status(thm)],[112])).
% 195.17/195.32 tff(114,plain,
% 195.17/195.32 (((~one_to_one(A!16)) | (~relation(A!16)) | (~function(A!16)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A!16)) | (~(relation_dom(B) = relation_rng(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))) | (~((~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))))))) | (~((~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))))) | (~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))))))) | (~((~(B = function_inverse(A!16))) | (~((~(relation_dom(B) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!16))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~in(C, relation_rng(A!16))) | (~(D = apply(B, C)))))))))))))))))) <=> ((~function(A!16)) | (~relation(A!16)) | (~one_to_one(A!16)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A!16)) | (~(relation_dom(B) = relation_rng(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))) | (~((~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))))))) | (~((~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))) | (~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))))))))) | (~((~(B = function_inverse(A!16))) | (~((~(relation_dom(B) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16))))))))))))))))))),
% 195.17/195.32 inference(transitivity,[status(thm)],[113, 110])).
% 195.17/195.32 tff(115,plain,
% 195.17/195.32 (((~![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_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_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(D, relation_dom(A))) | (~(C = apply(A, D))) | (~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))))))))))))))))) | ((~one_to_one(A!16)) | (~relation(A!16)) | (~function(A!16)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A!16)) | (~(relation_dom(B) = relation_rng(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))) | (~((~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))))))) | (~((~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))))) | (~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))))))) | (~((~(B = function_inverse(A!16))) | (~((~(relation_dom(B) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!16))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~in(C, relation_rng(A!16))) | (~(D = apply(B, C))))))))))))))))))) <=> ((~![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_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_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(D, relation_dom(A))) | (~(C = apply(A, D))) | (~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))))))))))))))))) | ((~function(A!16)) | (~relation(A!16)) | (~one_to_one(A!16)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A!16)) | (~(relation_dom(B) = relation_rng(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))) | (~((~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))))))) | (~((~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))) | (~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))))))))) | (~((~(B = function_inverse(A!16))) | (~((~(relation_dom(B) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16)))))))))))))))))))),
% 195.17/195.32 inference(monotonicity,[status(thm)],[114])).
% 195.17/195.32 tff(116,plain,
% 195.17/195.32 (((~![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_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_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(D, relation_dom(A))) | (~(C = apply(A, D))) | (~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))))))))))))))))) | ((~one_to_one(A!16)) | (~relation(A!16)) | (~function(A!16)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A!16)) | (~(relation_dom(B) = relation_rng(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))) | (~((~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))))))) | (~((~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))))) | (~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))))))) | (~((~(B = function_inverse(A!16))) | (~((~(relation_dom(B) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!16))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~in(C, relation_rng(A!16))) | (~(D = apply(B, C))))))))))))))))))) <=> ((~![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_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_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(D, relation_dom(A))) | (~(C = apply(A, D))) | (~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))))))))))))))))) | (~function(A!16)) | (~relation(A!16)) | (~one_to_one(A!16)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A!16)) | (~(relation_dom(B) = relation_rng(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))) | (~((~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))))))) | (~((~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))) | (~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))))))))) | (~((~(B = function_inverse(A!16))) | (~((~(relation_dom(B) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16))))))))))))))))))),
% 195.17/195.32 inference(transitivity,[status(thm)],[115, 109])).
% 195.17/195.32 tff(117,plain,
% 195.17/195.32 ((~![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_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_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(D, relation_dom(A))) | (~(C = apply(A, D))) | (~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))))))))))))))))) | ((~one_to_one(A!16)) | (~relation(A!16)) | (~function(A!16)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A!16)) | (~(relation_dom(B) = relation_rng(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))) | (~((~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))))))) | (~((~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))))) | (~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))))))) | (~((~(B = function_inverse(A!16))) | (~((~(relation_dom(B) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!16))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~in(C, relation_rng(A!16))) | (~(D = apply(B, C))))))))))))))))))),
% 195.17/195.33 inference(quant_inst,[status(thm)],[])).
% 195.17/195.33 tff(118,plain,
% 195.17/195.33 ((~![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_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))) | (~((~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_14(B, A)))))))) | (~((~((~in(tptp_fun_C_15(B, A), relation_rng(A))) | (~(tptp_fun_D_14(B, A) = apply(B, tptp_fun_C_15(B, A)))))) | (~in(tptp_fun_D_14(B, A), relation_dom(A))) | (~(tptp_fun_C_15(B, A) = apply(A, tptp_fun_D_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(D, relation_dom(A))) | (~(C = apply(A, D))) | (~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))))))))))))))))) | (~function(A!16)) | (~relation(A!16)) | (~one_to_one(A!16)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A!16)) | (~(relation_dom(B) = relation_rng(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))) | (~((~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))))))) | (~((~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))) | (~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))))))))) | (~((~(B = function_inverse(A!16))) | (~((~(relation_dom(B) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16)))))))))))))))))),
% 195.17/195.33 inference(modus_ponens,[status(thm)],[117, 116])).
% 195.17/195.33 tff(119,plain,
% 195.17/195.33 (![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A!16)) | (~(relation_dom(B) = relation_rng(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))) | (~((~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))))))) | (~((~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))) | (~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))))))))) | (~((~(B = function_inverse(A!16))) | (~((~(relation_dom(B) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16)))))))))))))))))),
% 195.17/195.33 inference(unit_resolution,[status(thm)],[118, 108, 18, 17, 86])).
% 195.17/195.33 tff(120,plain,
% 195.17/195.33 (((~![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A!16)) | (~(relation_dom(B) = relation_rng(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))) | (~((~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))))))) | (~((~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))) | (~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))))))))) | (~((~(B = function_inverse(A!16))) | (~((~(relation_dom(B) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16)))))))))))))))))) | ((~relation(function_inverse(A!16))) | (~function(function_inverse(A!16))) | (~((~(relation_dom(function_inverse(A!16)) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))) | (~(D = apply(function_inverse(A!16), C))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~in(C, relation_rng(A!16))) | (~(D = apply(function_inverse(A!16), C)))))))))))))) <=> ((~![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A!16)) | (~(relation_dom(B) = relation_rng(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))) | (~((~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))))))) | (~((~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))) | (~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))))))))) | (~((~(B = function_inverse(A!16))) | (~((~(relation_dom(B) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16)))))))))))))))))) | (~relation(function_inverse(A!16))) | (~function(function_inverse(A!16))) | (~((~(relation_dom(function_inverse(A!16)) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))) | (~(D = apply(function_inverse(A!16), C))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~in(C, relation_rng(A!16))) | (~(D = apply(function_inverse(A!16), C)))))))))))))),
% 195.17/195.33 inference(rewrite,[status(thm)],[])).
% 195.17/195.33 tff(121,plain,
% 195.17/195.33 (((~relation(function_inverse(A!16))) | (~function(function_inverse(A!16))) | (~((~(relation_dom(function_inverse(A!16)) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))) | (~(D = apply(function_inverse(A!16), C))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~in(C, relation_rng(A!16))) | (~(D = apply(function_inverse(A!16), C))))))))))))) <=> ((~relation(function_inverse(A!16))) | (~function(function_inverse(A!16))) | (~((~(relation_dom(function_inverse(A!16)) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))) | (~(D = apply(function_inverse(A!16), C))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~in(C, relation_rng(A!16))) | (~(D = apply(function_inverse(A!16), C)))))))))))))),
% 195.17/195.33 inference(rewrite,[status(thm)],[])).
% 195.17/195.33 tff(122,plain,
% 195.17/195.33 ((~((~((function_inverse(A!16) = function_inverse(A!16)) | (~(relation_dom(function_inverse(A!16)) = relation_rng(A!16))) | (~((~in(tptp_fun_C_15(function_inverse(A!16), A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(function_inverse(A!16), A!16) = apply(function_inverse(A!16), tptp_fun_C_15(function_inverse(A!16), A!16)))) | (~((~in(tptp_fun_D_14(function_inverse(A!16), A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(function_inverse(A!16), A!16) = apply(A!16, tptp_fun_D_14(function_inverse(A!16), A!16)))))))) | (~((~(tptp_fun_C_15(function_inverse(A!16), A!16) = apply(A!16, tptp_fun_D_14(function_inverse(A!16), A!16)))) | (~in(tptp_fun_D_14(function_inverse(A!16), A!16), relation_dom(A!16))) | (~((~in(tptp_fun_C_15(function_inverse(A!16), A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(function_inverse(A!16), A!16) = apply(function_inverse(A!16), tptp_fun_C_15(function_inverse(A!16), A!16)))))))))) | (~((~(function_inverse(A!16) = function_inverse(A!16))) | (~((~(relation_dom(function_inverse(A!16)) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~(D = apply(function_inverse(A!16), C))) | (~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~(D = apply(function_inverse(A!16), C))) | (~in(C, relation_rng(A!16)))))))))))))))) <=> (~((~(relation_dom(function_inverse(A!16)) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))) | (~(D = apply(function_inverse(A!16), C))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~in(C, relation_rng(A!16))) | (~(D = apply(function_inverse(A!16), C))))))))))))),
% 195.17/195.33 inference(rewrite,[status(thm)],[])).
% 195.17/195.33 tff(123,plain,
% 195.17/195.33 (((~relation(function_inverse(A!16))) | (~function(function_inverse(A!16))) | (~((~((function_inverse(A!16) = function_inverse(A!16)) | (~(relation_dom(function_inverse(A!16)) = relation_rng(A!16))) | (~((~in(tptp_fun_C_15(function_inverse(A!16), A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(function_inverse(A!16), A!16) = apply(function_inverse(A!16), tptp_fun_C_15(function_inverse(A!16), A!16)))) | (~((~in(tptp_fun_D_14(function_inverse(A!16), A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(function_inverse(A!16), A!16) = apply(A!16, tptp_fun_D_14(function_inverse(A!16), A!16)))))))) | (~((~(tptp_fun_C_15(function_inverse(A!16), A!16) = apply(A!16, tptp_fun_D_14(function_inverse(A!16), A!16)))) | (~in(tptp_fun_D_14(function_inverse(A!16), A!16), relation_dom(A!16))) | (~((~in(tptp_fun_C_15(function_inverse(A!16), A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(function_inverse(A!16), A!16) = apply(function_inverse(A!16), tptp_fun_C_15(function_inverse(A!16), A!16)))))))))) | (~((~(function_inverse(A!16) = function_inverse(A!16))) | (~((~(relation_dom(function_inverse(A!16)) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~(D = apply(function_inverse(A!16), C))) | (~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~(D = apply(function_inverse(A!16), C))) | (~in(C, relation_rng(A!16))))))))))))))))) <=> ((~relation(function_inverse(A!16))) | (~function(function_inverse(A!16))) | (~((~(relation_dom(function_inverse(A!16)) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))) | (~(D = apply(function_inverse(A!16), C))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~in(C, relation_rng(A!16))) | (~(D = apply(function_inverse(A!16), C)))))))))))))),
% 195.17/195.33 inference(monotonicity,[status(thm)],[122])).
% 195.17/195.33 tff(124,plain,
% 195.17/195.33 (((~relation(function_inverse(A!16))) | (~function(function_inverse(A!16))) | (~((~((function_inverse(A!16) = function_inverse(A!16)) | (~(relation_dom(function_inverse(A!16)) = relation_rng(A!16))) | (~((~in(tptp_fun_C_15(function_inverse(A!16), A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(function_inverse(A!16), A!16) = apply(function_inverse(A!16), tptp_fun_C_15(function_inverse(A!16), A!16)))) | (~((~in(tptp_fun_D_14(function_inverse(A!16), A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(function_inverse(A!16), A!16) = apply(A!16, tptp_fun_D_14(function_inverse(A!16), A!16)))))))) | (~((~(tptp_fun_C_15(function_inverse(A!16), A!16) = apply(A!16, tptp_fun_D_14(function_inverse(A!16), A!16)))) | (~in(tptp_fun_D_14(function_inverse(A!16), A!16), relation_dom(A!16))) | (~((~in(tptp_fun_C_15(function_inverse(A!16), A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(function_inverse(A!16), A!16) = apply(function_inverse(A!16), tptp_fun_C_15(function_inverse(A!16), A!16)))))))))) | (~((~(function_inverse(A!16) = function_inverse(A!16))) | (~((~(relation_dom(function_inverse(A!16)) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~(D = apply(function_inverse(A!16), C))) | (~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~(D = apply(function_inverse(A!16), C))) | (~in(C, relation_rng(A!16))))))))))))))))) <=> ((~relation(function_inverse(A!16))) | (~function(function_inverse(A!16))) | (~((~(relation_dom(function_inverse(A!16)) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))) | (~(D = apply(function_inverse(A!16), C))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~in(C, relation_rng(A!16))) | (~(D = apply(function_inverse(A!16), C)))))))))))))),
% 195.17/195.33 inference(transitivity,[status(thm)],[123, 121])).
% 195.17/195.33 tff(125,plain,
% 195.17/195.33 (((~![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A!16)) | (~(relation_dom(B) = relation_rng(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))) | (~((~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))))))) | (~((~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))) | (~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))))))))) | (~((~(B = function_inverse(A!16))) | (~((~(relation_dom(B) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16)))))))))))))))))) | ((~relation(function_inverse(A!16))) | (~function(function_inverse(A!16))) | (~((~((function_inverse(A!16) = function_inverse(A!16)) | (~(relation_dom(function_inverse(A!16)) = relation_rng(A!16))) | (~((~in(tptp_fun_C_15(function_inverse(A!16), A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(function_inverse(A!16), A!16) = apply(function_inverse(A!16), tptp_fun_C_15(function_inverse(A!16), A!16)))) | (~((~in(tptp_fun_D_14(function_inverse(A!16), A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(function_inverse(A!16), A!16) = apply(A!16, tptp_fun_D_14(function_inverse(A!16), A!16)))))))) | (~((~(tptp_fun_C_15(function_inverse(A!16), A!16) = apply(A!16, tptp_fun_D_14(function_inverse(A!16), A!16)))) | (~in(tptp_fun_D_14(function_inverse(A!16), A!16), relation_dom(A!16))) | (~((~in(tptp_fun_C_15(function_inverse(A!16), A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(function_inverse(A!16), A!16) = apply(function_inverse(A!16), tptp_fun_C_15(function_inverse(A!16), A!16)))))))))) | (~((~(function_inverse(A!16) = function_inverse(A!16))) | (~((~(relation_dom(function_inverse(A!16)) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~(D = apply(function_inverse(A!16), C))) | (~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~(D = apply(function_inverse(A!16), C))) | (~in(C, relation_rng(A!16)))))))))))))))))) <=> ((~![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A!16)) | (~(relation_dom(B) = relation_rng(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))) | (~((~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))))))) | (~((~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))) | (~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))))))))) | (~((~(B = function_inverse(A!16))) | (~((~(relation_dom(B) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16)))))))))))))))))) | ((~relation(function_inverse(A!16))) | (~function(function_inverse(A!16))) | (~((~(relation_dom(function_inverse(A!16)) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))) | (~(D = apply(function_inverse(A!16), C))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~in(C, relation_rng(A!16))) | (~(D = apply(function_inverse(A!16), C))))))))))))))),
% 195.17/195.33 inference(monotonicity,[status(thm)],[124])).
% 195.17/195.33 tff(126,plain,
% 195.17/195.33 (((~![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A!16)) | (~(relation_dom(B) = relation_rng(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))) | (~((~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))))))) | (~((~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))) | (~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))))))))) | (~((~(B = function_inverse(A!16))) | (~((~(relation_dom(B) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16)))))))))))))))))) | ((~relation(function_inverse(A!16))) | (~function(function_inverse(A!16))) | (~((~((function_inverse(A!16) = function_inverse(A!16)) | (~(relation_dom(function_inverse(A!16)) = relation_rng(A!16))) | (~((~in(tptp_fun_C_15(function_inverse(A!16), A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(function_inverse(A!16), A!16) = apply(function_inverse(A!16), tptp_fun_C_15(function_inverse(A!16), A!16)))) | (~((~in(tptp_fun_D_14(function_inverse(A!16), A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(function_inverse(A!16), A!16) = apply(A!16, tptp_fun_D_14(function_inverse(A!16), A!16)))))))) | (~((~(tptp_fun_C_15(function_inverse(A!16), A!16) = apply(A!16, tptp_fun_D_14(function_inverse(A!16), A!16)))) | (~in(tptp_fun_D_14(function_inverse(A!16), A!16), relation_dom(A!16))) | (~((~in(tptp_fun_C_15(function_inverse(A!16), A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(function_inverse(A!16), A!16) = apply(function_inverse(A!16), tptp_fun_C_15(function_inverse(A!16), A!16)))))))))) | (~((~(function_inverse(A!16) = function_inverse(A!16))) | (~((~(relation_dom(function_inverse(A!16)) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~(D = apply(function_inverse(A!16), C))) | (~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~(D = apply(function_inverse(A!16), C))) | (~in(C, relation_rng(A!16)))))))))))))))))) <=> ((~![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A!16)) | (~(relation_dom(B) = relation_rng(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))) | (~((~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))))))) | (~((~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))) | (~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))))))))) | (~((~(B = function_inverse(A!16))) | (~((~(relation_dom(B) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16)))))))))))))))))) | (~relation(function_inverse(A!16))) | (~function(function_inverse(A!16))) | (~((~(relation_dom(function_inverse(A!16)) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))) | (~(D = apply(function_inverse(A!16), C))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~in(C, relation_rng(A!16))) | (~(D = apply(function_inverse(A!16), C)))))))))))))),
% 195.17/195.33 inference(transitivity,[status(thm)],[125, 120])).
% 195.17/195.33 tff(127,plain,
% 195.17/195.33 ((~![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A!16)) | (~(relation_dom(B) = relation_rng(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))) | (~((~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))))))) | (~((~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))) | (~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))))))))) | (~((~(B = function_inverse(A!16))) | (~((~(relation_dom(B) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16)))))))))))))))))) | ((~relation(function_inverse(A!16))) | (~function(function_inverse(A!16))) | (~((~((function_inverse(A!16) = function_inverse(A!16)) | (~(relation_dom(function_inverse(A!16)) = relation_rng(A!16))) | (~((~in(tptp_fun_C_15(function_inverse(A!16), A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(function_inverse(A!16), A!16) = apply(function_inverse(A!16), tptp_fun_C_15(function_inverse(A!16), A!16)))) | (~((~in(tptp_fun_D_14(function_inverse(A!16), A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(function_inverse(A!16), A!16) = apply(A!16, tptp_fun_D_14(function_inverse(A!16), A!16)))))))) | (~((~(tptp_fun_C_15(function_inverse(A!16), A!16) = apply(A!16, tptp_fun_D_14(function_inverse(A!16), A!16)))) | (~in(tptp_fun_D_14(function_inverse(A!16), A!16), relation_dom(A!16))) | (~((~in(tptp_fun_C_15(function_inverse(A!16), A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(function_inverse(A!16), A!16) = apply(function_inverse(A!16), tptp_fun_C_15(function_inverse(A!16), A!16)))))))))) | (~((~(function_inverse(A!16) = function_inverse(A!16))) | (~((~(relation_dom(function_inverse(A!16)) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~(D = apply(function_inverse(A!16), C))) | (~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~(D = apply(function_inverse(A!16), C))) | (~in(C, relation_rng(A!16)))))))))))))))))),
% 195.17/195.33 inference(quant_inst,[status(thm)],[])).
% 195.17/195.33 tff(128,plain,
% 195.17/195.33 ((~![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A!16)) | (~(relation_dom(B) = relation_rng(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))) | (~((~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))))))) | (~((~(tptp_fun_C_15(B, A!16) = apply(A!16, tptp_fun_D_14(B, A!16)))) | (~in(tptp_fun_D_14(B, A!16), relation_dom(A!16))) | (~((~in(tptp_fun_C_15(B, A!16), relation_rng(A!16))) | (~(tptp_fun_D_14(B, A!16) = apply(B, tptp_fun_C_15(B, A!16)))))))))) | (~((~(B = function_inverse(A!16))) | (~((~(relation_dom(B) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(A!16)))))))))))))))))) | (~relation(function_inverse(A!16))) | (~function(function_inverse(A!16))) | (~((~(relation_dom(function_inverse(A!16)) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))) | (~(D = apply(function_inverse(A!16), C))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~in(C, relation_rng(A!16))) | (~(D = apply(function_inverse(A!16), C))))))))))))),
% 195.17/195.33 inference(modus_ponens,[status(thm)],[127, 126])).
% 195.17/195.33 tff(129,plain,
% 195.17/195.33 (~((~(relation_dom(function_inverse(A!16)) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))) | (~(D = apply(function_inverse(A!16), C))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~in(C, relation_rng(A!16))) | (~(D = apply(function_inverse(A!16), C)))))))))))),
% 195.17/195.33 inference(unit_resolution,[status(thm)],[128, 119, 85, 83])).
% 195.17/195.33 tff(130,plain,
% 195.17/195.33 (((~(relation_dom(function_inverse(A!16)) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))) | (~(D = apply(function_inverse(A!16), C))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~in(C, relation_rng(A!16))) | (~(D = apply(function_inverse(A!16), C))))))))))) | (relation_dom(function_inverse(A!16)) = relation_rng(A!16))),
% 195.17/195.33 inference(tautology,[status(thm)],[])).
% 195.17/195.33 tff(131,plain,
% 195.17/195.33 (relation_dom(function_inverse(A!16)) = relation_rng(A!16)),
% 195.17/195.33 inference(unit_resolution,[status(thm)],[130, 129])).
% 195.17/195.33 tff(132,plain,
% 195.17/195.33 (relation_rng(A!16) = relation_dom(function_inverse(A!16))),
% 195.17/195.33 inference(symmetry,[status(thm)],[131])).
% 195.17/195.33 tff(133,plain,
% 195.17/195.33 (relation_rng(A!16) = relation_dom(B!17)),
% 195.17/195.33 inference(and_elim,[status(thm)],[16])).
% 195.17/195.33 tff(134,plain,
% 195.17/195.33 (relation_dom(B!17) = relation_rng(A!16)),
% 195.17/195.33 inference(symmetry,[status(thm)],[133])).
% 195.17/195.33 tff(135,plain,
% 195.17/195.33 (relation_dom(B!17) = relation_dom(function_inverse(A!16))),
% 195.17/195.33 inference(transitivity,[status(thm)],[134, 132])).
% 195.17/195.33 tff(136,plain,
% 195.17/195.33 (^[A: $i] : refl(((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))) | (~relation(B)) | (~function(B)))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))) | (~relation(B)) | (~function(B)))))),
% 195.17/195.33 inference(bind,[status(th)],[])).
% 195.17/195.33 tff(137,plain,
% 195.17/195.33 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))) | (~relation(B)) | (~function(B)))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))) | (~relation(B)) | (~function(B))))),
% 195.17/195.33 inference(quant_intro,[status(thm)],[136])).
% 195.17/195.33 tff(138,plain,
% 195.17/195.33 (^[A: $i] : rewrite(((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))) | (~relation(B)) | (~function(B)))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))) | (~relation(B)) | (~function(B)))))),
% 195.17/195.33 inference(bind,[status(th)],[])).
% 195.17/195.33 tff(139,plain,
% 195.17/195.33 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))) | (~relation(B)) | (~function(B)))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))) | (~relation(B)) | (~function(B))))),
% 195.17/195.33 inference(quant_intro,[status(thm)],[138])).
% 195.17/195.33 tff(140,plain,
% 195.17/195.33 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))) | (~relation(B)) | (~function(B)))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))) | (~relation(B)) | (~function(B))))),
% 195.17/195.33 inference(transitivity,[status(thm)],[139, 137])).
% 195.17/195.33 tff(141,plain,
% 195.17/195.33 (^[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))))), (((A = B) | (~(relation(B) & function(B))) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A)))))) <=> ((A = B) | ((~relation(B)) | (~function(B))) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A)))))))), rewrite(((A = B) | ((~relation(B)) | (~function(B))) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A)))))) <=> ((A = B) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))) | (~relation(B)) | (~function(B)))), (((A = B) | (~(relation(B) & function(B))) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A)))))) <=> ((A = B) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))) | (~relation(B)) | (~function(B)))))), (![B: $i] : ((A = B) | (~(relation(B) & function(B))) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A)))))) <=> ![B: $i] : ((A = B) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))) | (~relation(B)) | (~function(B))))), (((~(relation(A) & function(A))) | ![B: $i] : ((A = B) | (~(relation(B) & function(B))) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))))) <=> (((~relation(A)) | (~function(A))) | ![B: $i] : ((A = B) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))) | (~relation(B)) | (~function(B)))))), rewrite((((~relation(A)) | (~function(A))) | ![B: $i] : ((A = B) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))) | (~relation(B)) | (~function(B)))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))) | (~relation(B)) | (~function(B))))), (((~(relation(A) & function(A))) | ![B: $i] : ((A = B) | (~(relation(B) & function(B))) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))) | (~relation(B)) | (~function(B))))))),
% 195.17/195.33 inference(bind,[status(th)],[])).
% 195.17/195.33 tff(142,plain,
% 195.17/195.33 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((A = B) | (~(relation(B) & function(B))) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))) | (~relation(B)) | (~function(B))))),
% 195.17/195.33 inference(quant_intro,[status(thm)],[141])).
% 195.17/195.33 tff(143,plain,
% 195.17/195.33 (^[A: $i] : rewrite(((~(relation(A) & function(A))) | ![B: $i] : ((A = B) | (~(relation(B) & function(B))) | ((~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A)))))))) <=> ((~(relation(A) & function(A))) | ![B: $i] : ((A = B) | (~(relation(B) & function(B))) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))))))),
% 195.17/195.33 inference(bind,[status(th)],[])).
% 195.17/195.33 tff(144,plain,
% 195.17/195.33 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((A = B) | (~(relation(B) & function(B))) | ((~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A)))))))) <=> ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((A = B) | (~(relation(B) & function(B))) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A)))))))),
% 195.17/195.33 inference(quant_intro,[status(thm)],[143])).
% 195.17/195.33 tff(145,plain,
% 195.17/195.33 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((A = B) | (~(relation(B) & function(B))) | (~((relation_dom(A) = relation_dom(B)) & ![C: $i] : ((~in(C, relation_dom(A))) | (apply(A, C) = apply(B, C))))))) <=> ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((A = B) | (~(relation(B) & function(B))) | (~((relation_dom(A) = relation_dom(B)) & ![C: $i] : ((~in(C, relation_dom(A))) | (apply(A, C) = apply(B, C)))))))),
% 195.17/195.33 inference(rewrite,[status(thm)],[])).
% 195.17/195.33 tff(146,plain,
% 195.17/195.33 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((relation_dom(A) = relation_dom(B)) & ![C: $i] : (in(C, relation_dom(A)) => (apply(A, C) = apply(B, C)))) <=> ((relation_dom(A) = relation_dom(B)) & ![C: $i] : ((~in(C, relation_dom(A))) | (apply(A, C) = apply(B, C))))), ((((relation_dom(A) = relation_dom(B)) & ![C: $i] : (in(C, relation_dom(A)) => (apply(A, C) = apply(B, C)))) => (A = B)) <=> (((relation_dom(A) = relation_dom(B)) & ![C: $i] : ((~in(C, relation_dom(A))) | (apply(A, C) = apply(B, C)))) => (A = B)))), rewrite((((relation_dom(A) = relation_dom(B)) & ![C: $i] : ((~in(C, relation_dom(A))) | (apply(A, C) = apply(B, C)))) => (A = B)) <=> ((~((relation_dom(A) = relation_dom(B)) & ![C: $i] : ((~in(C, relation_dom(A))) | (apply(A, C) = apply(B, C))))) | (A = B))), ((((relation_dom(A) = relation_dom(B)) & ![C: $i] : (in(C, relation_dom(A)) => (apply(A, C) = apply(B, C)))) => (A = B)) <=> ((~((relation_dom(A) = relation_dom(B)) & ![C: $i] : ((~in(C, relation_dom(A))) | (apply(A, C) = apply(B, C))))) | (A = B)))), (((relation(B) & function(B)) => (((relation_dom(A) = relation_dom(B)) & ![C: $i] : (in(C, relation_dom(A)) => (apply(A, C) = apply(B, C)))) => (A = B))) <=> ((relation(B) & function(B)) => ((~((relation_dom(A) = relation_dom(B)) & ![C: $i] : ((~in(C, relation_dom(A))) | (apply(A, C) = apply(B, C))))) | (A = B))))), rewrite(((relation(B) & function(B)) => ((~((relation_dom(A) = relation_dom(B)) & ![C: $i] : ((~in(C, relation_dom(A))) | (apply(A, C) = apply(B, C))))) | (A = B))) <=> ((A = B) | (~(relation(B) & function(B))) | (~((relation_dom(A) = relation_dom(B)) & ![C: $i] : ((~in(C, relation_dom(A))) | (apply(A, C) = apply(B, C))))))), (((relation(B) & function(B)) => (((relation_dom(A) = relation_dom(B)) & ![C: $i] : (in(C, relation_dom(A)) => (apply(A, C) = apply(B, C)))) => (A = B))) <=> ((A = B) | (~(relation(B) & function(B))) | (~((relation_dom(A) = relation_dom(B)) & ![C: $i] : ((~in(C, relation_dom(A))) | (apply(A, C) = apply(B, C))))))))), (![B: $i] : ((relation(B) & function(B)) => (((relation_dom(A) = relation_dom(B)) & ![C: $i] : (in(C, relation_dom(A)) => (apply(A, C) = apply(B, C)))) => (A = B))) <=> ![B: $i] : ((A = B) | (~(relation(B) & function(B))) | (~((relation_dom(A) = relation_dom(B)) & ![C: $i] : ((~in(C, relation_dom(A))) | (apply(A, C) = apply(B, C)))))))), (((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => (((relation_dom(A) = relation_dom(B)) & ![C: $i] : (in(C, relation_dom(A)) => (apply(A, C) = apply(B, C)))) => (A = B)))) <=> ((relation(A) & function(A)) => ![B: $i] : ((A = B) | (~(relation(B) & function(B))) | (~((relation_dom(A) = relation_dom(B)) & ![C: $i] : ((~in(C, relation_dom(A))) | (apply(A, C) = apply(B, C))))))))), rewrite(((relation(A) & function(A)) => ![B: $i] : ((A = B) | (~(relation(B) & function(B))) | (~((relation_dom(A) = relation_dom(B)) & ![C: $i] : ((~in(C, relation_dom(A))) | (apply(A, C) = apply(B, C))))))) <=> ((~(relation(A) & function(A))) | ![B: $i] : ((A = B) | (~(relation(B) & function(B))) | (~((relation_dom(A) = relation_dom(B)) & ![C: $i] : ((~in(C, relation_dom(A))) | (apply(A, C) = apply(B, C)))))))), (((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => (((relation_dom(A) = relation_dom(B)) & ![C: $i] : (in(C, relation_dom(A)) => (apply(A, C) = apply(B, C)))) => (A = B)))) <=> ((~(relation(A) & function(A))) | ![B: $i] : ((A = B) | (~(relation(B) & function(B))) | (~((relation_dom(A) = relation_dom(B)) & ![C: $i] : ((~in(C, relation_dom(A))) | (apply(A, C) = apply(B, C)))))))))),
% 195.17/195.34 inference(bind,[status(th)],[])).
% 195.17/195.34 tff(147,plain,
% 195.17/195.34 (![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => (((relation_dom(A) = relation_dom(B)) & ![C: $i] : (in(C, relation_dom(A)) => (apply(A, C) = apply(B, C)))) => (A = B)))) <=> ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((A = B) | (~(relation(B) & function(B))) | (~((relation_dom(A) = relation_dom(B)) & ![C: $i] : ((~in(C, relation_dom(A))) | (apply(A, C) = apply(B, C)))))))),
% 195.17/195.34 inference(quant_intro,[status(thm)],[146])).
% 195.17/195.34 tff(148,axiom,(![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => (((relation_dom(A) = relation_dom(B)) & ![C: $i] : (in(C, relation_dom(A)) => (apply(A, C) = apply(B, C)))) => (A = B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t9_funct_1')).
% 195.17/195.34 tff(149,plain,
% 195.17/195.34 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((A = B) | (~(relation(B) & function(B))) | (~((relation_dom(A) = relation_dom(B)) & ![C: $i] : ((~in(C, relation_dom(A))) | (apply(A, C) = apply(B, C)))))))),
% 195.17/195.34 inference(modus_ponens,[status(thm)],[148, 147])).
% 195.17/195.34 tff(150,plain,
% 195.17/195.34 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((A = B) | (~(relation(B) & function(B))) | (~((relation_dom(A) = relation_dom(B)) & ![C: $i] : ((~in(C, relation_dom(A))) | (apply(A, C) = apply(B, C)))))))),
% 195.17/195.34 inference(modus_ponens,[status(thm)],[149, 145])).
% 195.17/195.34 tff(151,plain,(
% 195.17/195.34 ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((A = B) | (~(relation(B) & function(B))) | ((~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))))))),
% 195.17/195.34 inference(skolemize,[status(sab)],[150])).
% 195.17/195.34 tff(152,plain,
% 195.17/195.34 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((A = B) | (~(relation(B) & function(B))) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A)))))))),
% 195.17/195.34 inference(modus_ponens,[status(thm)],[151, 144])).
% 195.17/195.34 tff(153,plain,
% 195.17/195.34 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))) | (~relation(B)) | (~function(B))))),
% 195.17/195.34 inference(modus_ponens,[status(thm)],[152, 142])).
% 195.17/195.34 tff(154,plain,
% 195.17/195.34 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))) | (~relation(B)) | (~function(B))))),
% 195.17/195.34 inference(modus_ponens,[status(thm)],[153, 140])).
% 195.17/195.34 tff(155,plain,
% 195.17/195.34 (function(B!17)),
% 195.17/195.34 inference(and_elim,[status(thm)],[16])).
% 195.17/195.34 tff(156,plain,
% 195.17/195.34 (relation(B!17)),
% 195.17/195.34 inference(and_elim,[status(thm)],[16])).
% 195.17/195.34 tff(157,plain,
% 195.17/195.34 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))) | (~relation(B)) | (~function(B))))) | ((~function(B!17)) | (~relation(B!17)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (B!17 = B) | (~(relation_dom(B!17) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, B!17), relation_dom(B!17))) | (apply(B!17, tptp_fun_C_18(B, B!17)) = apply(B, tptp_fun_C_18(B, B!17)))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))) | (~relation(B)) | (~function(B))))) | (~function(B!17)) | (~relation(B!17)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (B!17 = B) | (~(relation_dom(B!17) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, B!17), relation_dom(B!17))) | (apply(B!17, tptp_fun_C_18(B, B!17)) = apply(B, tptp_fun_C_18(B, B!17)))))))),
% 195.17/195.34 inference(rewrite,[status(thm)],[])).
% 195.17/195.34 tff(158,plain,
% 195.17/195.34 (((~relation(B!17)) | (~function(B!17)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (B!17 = B) | (~(relation_dom(B!17) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, B!17), relation_dom(B!17))) | (apply(B!17, tptp_fun_C_18(B, B!17)) = apply(B, tptp_fun_C_18(B, B!17))))))) <=> ((~function(B!17)) | (~relation(B!17)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (B!17 = B) | (~(relation_dom(B!17) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, B!17), relation_dom(B!17))) | (apply(B!17, tptp_fun_C_18(B, B!17)) = apply(B, tptp_fun_C_18(B, B!17)))))))),
% 195.17/195.34 inference(rewrite,[status(thm)],[])).
% 195.17/195.34 tff(159,plain,
% 195.17/195.34 (^[B: $i] : rewrite(((B!17 = B) | (~(relation_dom(B!17) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, B!17), relation_dom(B!17))) | (apply(B!17, tptp_fun_C_18(B, B!17)) = apply(B, tptp_fun_C_18(B, B!17))))) | (~relation(B)) | (~function(B))) <=> ((~relation(B)) | (~function(B)) | (B!17 = B) | (~(relation_dom(B!17) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, B!17), relation_dom(B!17))) | (apply(B!17, tptp_fun_C_18(B, B!17)) = apply(B, tptp_fun_C_18(B, B!17)))))))),
% 195.17/195.34 inference(bind,[status(th)],[])).
% 195.17/195.34 tff(160,plain,
% 195.17/195.34 (![B: $i] : ((B!17 = B) | (~(relation_dom(B!17) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, B!17), relation_dom(B!17))) | (apply(B!17, tptp_fun_C_18(B, B!17)) = apply(B, tptp_fun_C_18(B, B!17))))) | (~relation(B)) | (~function(B))) <=> ![B: $i] : ((~relation(B)) | (~function(B)) | (B!17 = B) | (~(relation_dom(B!17) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, B!17), relation_dom(B!17))) | (apply(B!17, tptp_fun_C_18(B, B!17)) = apply(B, tptp_fun_C_18(B, B!17))))))),
% 195.17/195.34 inference(quant_intro,[status(thm)],[159])).
% 195.17/195.34 tff(161,plain,
% 195.17/195.34 (((~relation(B!17)) | (~function(B!17)) | ![B: $i] : ((B!17 = B) | (~(relation_dom(B!17) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, B!17), relation_dom(B!17))) | (apply(B!17, tptp_fun_C_18(B, B!17)) = apply(B, tptp_fun_C_18(B, B!17))))) | (~relation(B)) | (~function(B)))) <=> ((~relation(B!17)) | (~function(B!17)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (B!17 = B) | (~(relation_dom(B!17) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, B!17), relation_dom(B!17))) | (apply(B!17, tptp_fun_C_18(B, B!17)) = apply(B, tptp_fun_C_18(B, B!17)))))))),
% 195.17/195.34 inference(monotonicity,[status(thm)],[160])).
% 195.17/195.34 tff(162,plain,
% 195.17/195.34 (((~relation(B!17)) | (~function(B!17)) | ![B: $i] : ((B!17 = B) | (~(relation_dom(B!17) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, B!17), relation_dom(B!17))) | (apply(B!17, tptp_fun_C_18(B, B!17)) = apply(B, tptp_fun_C_18(B, B!17))))) | (~relation(B)) | (~function(B)))) <=> ((~function(B!17)) | (~relation(B!17)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (B!17 = B) | (~(relation_dom(B!17) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, B!17), relation_dom(B!17))) | (apply(B!17, tptp_fun_C_18(B, B!17)) = apply(B, tptp_fun_C_18(B, B!17)))))))),
% 195.17/195.34 inference(transitivity,[status(thm)],[161, 158])).
% 195.17/195.34 tff(163,plain,
% 195.17/195.34 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))) | (~relation(B)) | (~function(B))))) | ((~relation(B!17)) | (~function(B!17)) | ![B: $i] : ((B!17 = B) | (~(relation_dom(B!17) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, B!17), relation_dom(B!17))) | (apply(B!17, tptp_fun_C_18(B, B!17)) = apply(B, tptp_fun_C_18(B, B!17))))) | (~relation(B)) | (~function(B))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))) | (~relation(B)) | (~function(B))))) | ((~function(B!17)) | (~relation(B!17)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (B!17 = B) | (~(relation_dom(B!17) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, B!17), relation_dom(B!17))) | (apply(B!17, tptp_fun_C_18(B, B!17)) = apply(B, tptp_fun_C_18(B, B!17))))))))),
% 195.17/195.34 inference(monotonicity,[status(thm)],[162])).
% 195.17/195.34 tff(164,plain,
% 195.17/195.34 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))) | (~relation(B)) | (~function(B))))) | ((~relation(B!17)) | (~function(B!17)) | ![B: $i] : ((B!17 = B) | (~(relation_dom(B!17) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, B!17), relation_dom(B!17))) | (apply(B!17, tptp_fun_C_18(B, B!17)) = apply(B, tptp_fun_C_18(B, B!17))))) | (~relation(B)) | (~function(B))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))) | (~relation(B)) | (~function(B))))) | (~function(B!17)) | (~relation(B!17)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (B!17 = B) | (~(relation_dom(B!17) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, B!17), relation_dom(B!17))) | (apply(B!17, tptp_fun_C_18(B, B!17)) = apply(B, tptp_fun_C_18(B, B!17)))))))),
% 195.17/195.34 inference(transitivity,[status(thm)],[163, 157])).
% 195.17/195.34 tff(165,plain,
% 195.17/195.34 ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))) | (~relation(B)) | (~function(B))))) | ((~relation(B!17)) | (~function(B!17)) | ![B: $i] : ((B!17 = B) | (~(relation_dom(B!17) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, B!17), relation_dom(B!17))) | (apply(B!17, tptp_fun_C_18(B, B!17)) = apply(B, tptp_fun_C_18(B, B!17))))) | (~relation(B)) | (~function(B))))),
% 195.17/195.34 inference(quant_inst,[status(thm)],[])).
% 195.17/195.34 tff(166,plain,
% 195.17/195.34 ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))) | (~relation(B)) | (~function(B))))) | (~function(B!17)) | (~relation(B!17)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (B!17 = B) | (~(relation_dom(B!17) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, B!17), relation_dom(B!17))) | (apply(B!17, tptp_fun_C_18(B, B!17)) = apply(B, tptp_fun_C_18(B, B!17))))))),
% 195.17/195.34 inference(modus_ponens,[status(thm)],[165, 164])).
% 195.17/195.34 tff(167,plain,
% 195.17/195.34 (![B: $i] : ((~relation(B)) | (~function(B)) | (B!17 = B) | (~(relation_dom(B!17) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, B!17), relation_dom(B!17))) | (apply(B!17, tptp_fun_C_18(B, B!17)) = apply(B, tptp_fun_C_18(B, B!17))))))),
% 195.17/195.34 inference(unit_resolution,[status(thm)],[166, 156, 155, 154])).
% 195.17/195.34 tff(168,plain,
% 195.17/195.34 (~(B!17 = function_inverse(A!16))),
% 195.17/195.34 inference(and_elim,[status(thm)],[16])).
% 195.17/195.34 tff(169,plain,
% 195.17/195.34 (((~![B: $i] : ((~relation(B)) | (~function(B)) | (B!17 = B) | (~(relation_dom(B!17) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, B!17), relation_dom(B!17))) | (apply(B!17, tptp_fun_C_18(B, B!17)) = apply(B, tptp_fun_C_18(B, B!17))))))) | ((B!17 = function_inverse(A!16)) | (~relation(function_inverse(A!16))) | (~function(function_inverse(A!16))) | (~(relation_dom(B!17) = relation_dom(function_inverse(A!16)))) | (~((~in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17))) | (apply(B!17, tptp_fun_C_18(function_inverse(A!16), B!17)) = apply(function_inverse(A!16), tptp_fun_C_18(function_inverse(A!16), B!17))))))) <=> ((~![B: $i] : ((~relation(B)) | (~function(B)) | (B!17 = B) | (~(relation_dom(B!17) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, B!17), relation_dom(B!17))) | (apply(B!17, tptp_fun_C_18(B, B!17)) = apply(B, tptp_fun_C_18(B, B!17))))))) | (B!17 = function_inverse(A!16)) | (~relation(function_inverse(A!16))) | (~function(function_inverse(A!16))) | (~(relation_dom(B!17) = relation_dom(function_inverse(A!16)))) | (~((~in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17))) | (apply(B!17, tptp_fun_C_18(function_inverse(A!16), B!17)) = apply(function_inverse(A!16), tptp_fun_C_18(function_inverse(A!16), B!17))))))),
% 195.17/195.34 inference(rewrite,[status(thm)],[])).
% 195.17/195.34 tff(170,plain,
% 195.17/195.34 (((~relation(function_inverse(A!16))) | (~function(function_inverse(A!16))) | (B!17 = function_inverse(A!16)) | (~(relation_dom(B!17) = relation_dom(function_inverse(A!16)))) | (~((~in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17))) | (apply(B!17, tptp_fun_C_18(function_inverse(A!16), B!17)) = apply(function_inverse(A!16), tptp_fun_C_18(function_inverse(A!16), B!17)))))) <=> ((B!17 = function_inverse(A!16)) | (~relation(function_inverse(A!16))) | (~function(function_inverse(A!16))) | (~(relation_dom(B!17) = relation_dom(function_inverse(A!16)))) | (~((~in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17))) | (apply(B!17, tptp_fun_C_18(function_inverse(A!16), B!17)) = apply(function_inverse(A!16), tptp_fun_C_18(function_inverse(A!16), B!17))))))),
% 195.17/195.34 inference(rewrite,[status(thm)],[])).
% 195.17/195.34 tff(171,plain,
% 195.17/195.34 (((~![B: $i] : ((~relation(B)) | (~function(B)) | (B!17 = B) | (~(relation_dom(B!17) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, B!17), relation_dom(B!17))) | (apply(B!17, tptp_fun_C_18(B, B!17)) = apply(B, tptp_fun_C_18(B, B!17))))))) | ((~relation(function_inverse(A!16))) | (~function(function_inverse(A!16))) | (B!17 = function_inverse(A!16)) | (~(relation_dom(B!17) = relation_dom(function_inverse(A!16)))) | (~((~in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17))) | (apply(B!17, tptp_fun_C_18(function_inverse(A!16), B!17)) = apply(function_inverse(A!16), tptp_fun_C_18(function_inverse(A!16), B!17))))))) <=> ((~![B: $i] : ((~relation(B)) | (~function(B)) | (B!17 = B) | (~(relation_dom(B!17) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, B!17), relation_dom(B!17))) | (apply(B!17, tptp_fun_C_18(B, B!17)) = apply(B, tptp_fun_C_18(B, B!17))))))) | ((B!17 = function_inverse(A!16)) | (~relation(function_inverse(A!16))) | (~function(function_inverse(A!16))) | (~(relation_dom(B!17) = relation_dom(function_inverse(A!16)))) | (~((~in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17))) | (apply(B!17, tptp_fun_C_18(function_inverse(A!16), B!17)) = apply(function_inverse(A!16), tptp_fun_C_18(function_inverse(A!16), B!17)))))))),
% 195.17/195.34 inference(monotonicity,[status(thm)],[170])).
% 195.17/195.34 tff(172,plain,
% 195.17/195.34 (((~![B: $i] : ((~relation(B)) | (~function(B)) | (B!17 = B) | (~(relation_dom(B!17) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, B!17), relation_dom(B!17))) | (apply(B!17, tptp_fun_C_18(B, B!17)) = apply(B, tptp_fun_C_18(B, B!17))))))) | ((~relation(function_inverse(A!16))) | (~function(function_inverse(A!16))) | (B!17 = function_inverse(A!16)) | (~(relation_dom(B!17) = relation_dom(function_inverse(A!16)))) | (~((~in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17))) | (apply(B!17, tptp_fun_C_18(function_inverse(A!16), B!17)) = apply(function_inverse(A!16), tptp_fun_C_18(function_inverse(A!16), B!17))))))) <=> ((~![B: $i] : ((~relation(B)) | (~function(B)) | (B!17 = B) | (~(relation_dom(B!17) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, B!17), relation_dom(B!17))) | (apply(B!17, tptp_fun_C_18(B, B!17)) = apply(B, tptp_fun_C_18(B, B!17))))))) | (B!17 = function_inverse(A!16)) | (~relation(function_inverse(A!16))) | (~function(function_inverse(A!16))) | (~(relation_dom(B!17) = relation_dom(function_inverse(A!16)))) | (~((~in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17))) | (apply(B!17, tptp_fun_C_18(function_inverse(A!16), B!17)) = apply(function_inverse(A!16), tptp_fun_C_18(function_inverse(A!16), B!17))))))),
% 195.17/195.34 inference(transitivity,[status(thm)],[171, 169])).
% 195.17/195.34 tff(173,plain,
% 195.17/195.34 ((~![B: $i] : ((~relation(B)) | (~function(B)) | (B!17 = B) | (~(relation_dom(B!17) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, B!17), relation_dom(B!17))) | (apply(B!17, tptp_fun_C_18(B, B!17)) = apply(B, tptp_fun_C_18(B, B!17))))))) | ((~relation(function_inverse(A!16))) | (~function(function_inverse(A!16))) | (B!17 = function_inverse(A!16)) | (~(relation_dom(B!17) = relation_dom(function_inverse(A!16)))) | (~((~in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17))) | (apply(B!17, tptp_fun_C_18(function_inverse(A!16), B!17)) = apply(function_inverse(A!16), tptp_fun_C_18(function_inverse(A!16), B!17))))))),
% 195.17/195.34 inference(quant_inst,[status(thm)],[])).
% 195.17/195.34 tff(174,plain,
% 195.17/195.34 ((~![B: $i] : ((~relation(B)) | (~function(B)) | (B!17 = B) | (~(relation_dom(B!17) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, B!17), relation_dom(B!17))) | (apply(B!17, tptp_fun_C_18(B, B!17)) = apply(B, tptp_fun_C_18(B, B!17))))))) | (B!17 = function_inverse(A!16)) | (~relation(function_inverse(A!16))) | (~function(function_inverse(A!16))) | (~(relation_dom(B!17) = relation_dom(function_inverse(A!16)))) | (~((~in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17))) | (apply(B!17, tptp_fun_C_18(function_inverse(A!16), B!17)) = apply(function_inverse(A!16), tptp_fun_C_18(function_inverse(A!16), B!17)))))),
% 195.17/195.34 inference(modus_ponens,[status(thm)],[173, 172])).
% 195.17/195.34 tff(175,plain,
% 195.17/195.34 ((~(relation_dom(B!17) = relation_dom(function_inverse(A!16)))) | (~((~in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17))) | (apply(B!17, tptp_fun_C_18(function_inverse(A!16), B!17)) = apply(function_inverse(A!16), tptp_fun_C_18(function_inverse(A!16), B!17)))))),
% 195.17/195.34 inference(unit_resolution,[status(thm)],[174, 168, 167, 85, 83])).
% 195.17/195.34 tff(176,plain,
% 195.17/195.34 (~((~in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17))) | (apply(B!17, tptp_fun_C_18(function_inverse(A!16), B!17)) = apply(function_inverse(A!16), tptp_fun_C_18(function_inverse(A!16), B!17))))),
% 195.17/195.34 inference(unit_resolution,[status(thm)],[175, 135])).
% 195.17/195.34 tff(177,plain,
% 195.17/195.34 (((~in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17))) | (apply(B!17, tptp_fun_C_18(function_inverse(A!16), B!17)) = apply(function_inverse(A!16), tptp_fun_C_18(function_inverse(A!16), B!17)))) | in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17))),
% 195.17/195.34 inference(tautology,[status(thm)],[])).
% 195.17/195.34 tff(178,plain,
% 195.17/195.34 (in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17))),
% 195.17/195.34 inference(unit_resolution,[status(thm)],[177, 176])).
% 195.17/195.34 tff(179,plain,
% 195.17/195.34 (in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_dom(B!17))),
% 195.17/195.34 inference(modus_ponens,[status(thm)],[178, 58])).
% 195.17/195.34 tff(180,plain,
% 195.17/195.34 ((apply(B!17, apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) = tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)) <=> (tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16) = apply(B!17, apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))))),
% 195.17/195.34 inference(commutativity,[status(thm)],[])).
% 195.17/195.34 tff(181,plain,
% 195.17/195.34 ((tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16) = apply(B!17, apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))) <=> (apply(B!17, apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) = tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))),
% 195.17/195.34 inference(symmetry,[status(thm)],[180])).
% 195.17/195.34 tff(182,plain,
% 195.17/195.34 (((~(relation_dom(function_inverse(A!16)) = relation_rng(A!16))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))) | (~(D = apply(function_inverse(A!16), C))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~in(C, relation_rng(A!16))) | (~(D = apply(function_inverse(A!16), C))))))))))) | ![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))) | (~(D = apply(function_inverse(A!16), C))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~in(C, relation_rng(A!16))) | (~(D = apply(function_inverse(A!16), C)))))))))),
% 195.17/195.34 inference(tautology,[status(thm)],[])).
% 195.17/195.34 tff(183,plain,
% 195.17/195.34 (![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))) | (~(D = apply(function_inverse(A!16), C))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~in(C, relation_rng(A!16))) | (~(D = apply(function_inverse(A!16), C)))))))))),
% 195.17/195.34 inference(unit_resolution,[status(thm)],[182, 129])).
% 195.17/195.34 tff(184,plain,
% 195.17/195.34 (((~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))) | (~(D = apply(function_inverse(A!16), C))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~in(C, relation_rng(A!16))) | (~(D = apply(function_inverse(A!16), C)))))))))) | (~((~(in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16)) | (~(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16) = apply(function_inverse(A!16), apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))))) | (~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_rng(A!16))))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~((~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_rng(A!16))) | (~(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16) = apply(function_inverse(A!16), apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))))))))))) <=> ((~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))) | (~(D = apply(function_inverse(A!16), C))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~in(C, relation_rng(A!16))) | (~(D = apply(function_inverse(A!16), C)))))))))) | (~((~(in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16)) | (~(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16) = apply(function_inverse(A!16), apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))))) | (~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_rng(A!16))))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~((~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_rng(A!16))) | (~(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16) = apply(function_inverse(A!16), apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))))))))))))),
% 195.17/195.34 inference(rewrite,[status(thm)],[])).
% 195.17/195.34 tff(185,plain,
% 195.17/195.34 ((~((~((~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_rng(A!16))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))))) | (~(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16) = apply(function_inverse(A!16), apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))))))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))) | (~((~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_rng(A!16))) | (~(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16) = apply(function_inverse(A!16), apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))))))))))) <=> (~((~(in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16)) | (~(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16) = apply(function_inverse(A!16), apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))))) | (~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_rng(A!16))))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~((~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_rng(A!16))) | (~(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16) = apply(function_inverse(A!16), apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))))))))))),
% 195.17/195.34 inference(rewrite,[status(thm)],[])).
% 195.17/195.34 tff(186,plain,
% 195.17/195.34 (((~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))) | (~(D = apply(function_inverse(A!16), C))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~in(C, relation_rng(A!16))) | (~(D = apply(function_inverse(A!16), C)))))))))) | (~((~((~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_rng(A!16))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))))) | (~(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16) = apply(function_inverse(A!16), apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))))))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))) | (~((~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_rng(A!16))) | (~(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16) = apply(function_inverse(A!16), apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))))))))))) <=> ((~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))) | (~(D = apply(function_inverse(A!16), C))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~in(C, relation_rng(A!16))) | (~(D = apply(function_inverse(A!16), C)))))))))) | (~((~(in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16)) | (~(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16) = apply(function_inverse(A!16), apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))))) | (~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_rng(A!16))))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~((~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_rng(A!16))) | (~(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16) = apply(function_inverse(A!16), apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))))))))))))),
% 195.17/195.34 inference(monotonicity,[status(thm)],[185])).
% 195.17/195.34 tff(187,plain,
% 195.17/195.34 (((~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))) | (~(D = apply(function_inverse(A!16), C))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~in(C, relation_rng(A!16))) | (~(D = apply(function_inverse(A!16), C)))))))))) | (~((~((~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_rng(A!16))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))))) | (~(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16) = apply(function_inverse(A!16), apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))))))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))) | (~((~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_rng(A!16))) | (~(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16) = apply(function_inverse(A!16), apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))))))))))) <=> ((~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))) | (~(D = apply(function_inverse(A!16), C))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~in(C, relation_rng(A!16))) | (~(D = apply(function_inverse(A!16), C)))))))))) | (~((~(in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16)) | (~(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16) = apply(function_inverse(A!16), apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))))) | (~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_rng(A!16))))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~((~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_rng(A!16))) | (~(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16) = apply(function_inverse(A!16), apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))))))))))))),
% 195.17/195.34 inference(transitivity,[status(thm)],[186, 184])).
% 195.17/195.34 tff(188,plain,
% 195.17/195.34 ((~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))) | (~(D = apply(function_inverse(A!16), C))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~in(C, relation_rng(A!16))) | (~(D = apply(function_inverse(A!16), C)))))))))) | (~((~((~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_rng(A!16))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))))) | (~(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16) = apply(function_inverse(A!16), apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))))))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))) | (~((~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_rng(A!16))) | (~(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16) = apply(function_inverse(A!16), apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))))))))))),
% 195.17/195.35 inference(quant_inst,[status(thm)],[])).
% 195.17/195.35 tff(189,plain,
% 195.17/195.35 ((~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A!16))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))) | (~(D = apply(function_inverse(A!16), C))))) | (~((~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))) | (~((~in(C, relation_rng(A!16))) | (~(D = apply(function_inverse(A!16), C)))))))))) | (~((~(in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16)) | (~(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16) = apply(function_inverse(A!16), apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))))) | (~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_rng(A!16))))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~((~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_rng(A!16))) | (~(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16) = apply(function_inverse(A!16), apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))))))))))),
% 195.17/195.35 inference(modus_ponens,[status(thm)],[188, 187])).
% 195.17/195.35 tff(190,plain,
% 195.17/195.35 (~((~(in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16)) | (~(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16) = apply(function_inverse(A!16), apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))))) | (~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_rng(A!16))))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~((~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_rng(A!16))) | (~(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16) = apply(function_inverse(A!16), apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))))))))))),
% 195.17/195.35 inference(unit_resolution,[status(thm)],[189, 183])).
% 195.17/195.35 tff(191,plain,
% 195.17/195.35 (((~(in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16)) | (~(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16) = apply(function_inverse(A!16), apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))))) | (~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_rng(A!16))))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~((~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_rng(A!16))) | (~(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16) = apply(function_inverse(A!16), apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))))))))) | ((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~((~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_rng(A!16))) | (~(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16) = apply(function_inverse(A!16), apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))))))))),
% 195.17/195.35 inference(tautology,[status(thm)],[])).
% 195.17/195.35 tff(192,plain,
% 195.17/195.35 ((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~((~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_rng(A!16))) | (~(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16) = apply(function_inverse(A!16), apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))))))),
% 195.17/195.35 inference(unit_resolution,[status(thm)],[191, 190])).
% 195.17/195.35 tff(193,plain,
% 195.17/195.35 (((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))))) | in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))),
% 195.17/195.35 inference(tautology,[status(thm)],[])).
% 195.17/195.35 tff(194,plain,
% 195.17/195.35 (in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))),
% 195.17/195.35 inference(unit_resolution,[status(thm)],[193, 53])).
% 195.17/195.35 tff(195,plain,
% 195.17/195.35 ((~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~((~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_rng(A!16))) | (~(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16) = apply(function_inverse(A!16), apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))))))))) | (~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~((~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_rng(A!16))) | (~(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16) = apply(function_inverse(A!16), apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))))))),
% 195.17/195.35 inference(tautology,[status(thm)],[])).
% 195.17/195.35 tff(196,plain,
% 195.17/195.35 ((~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~((~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_rng(A!16))) | (~(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16) = apply(function_inverse(A!16), apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))))))))) | (~((~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_rng(A!16))) | (~(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16) = apply(function_inverse(A!16), apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))))))),
% 195.17/195.35 inference(unit_resolution,[status(thm)],[195, 194])).
% 195.17/195.35 tff(197,plain,
% 195.17/195.35 (~((~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_rng(A!16))) | (~(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16) = apply(function_inverse(A!16), apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))))))),
% 195.17/195.35 inference(unit_resolution,[status(thm)],[196, 192])).
% 195.17/195.35 tff(198,plain,
% 195.17/195.35 (((~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_rng(A!16))) | (~(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16) = apply(function_inverse(A!16), apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))))) | (tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16) = apply(function_inverse(A!16), apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))))),
% 195.17/195.35 inference(tautology,[status(thm)],[])).
% 195.17/195.35 tff(199,plain,
% 195.17/195.35 (tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16) = apply(function_inverse(A!16), apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))),
% 195.17/195.35 inference(unit_resolution,[status(thm)],[198, 197])).
% 195.17/195.35 tff(200,plain,
% 195.17/195.35 (apply(function_inverse(A!16), apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) = tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)),
% 195.17/195.35 inference(symmetry,[status(thm)],[199])).
% 195.17/195.35 tff(201,plain,
% 195.17/195.35 (apply(function_inverse(A!16), tptp_fun_C_18(function_inverse(A!16), B!17)) = apply(function_inverse(A!16), apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))),
% 195.17/195.35 inference(monotonicity,[status(thm)],[55])).
% 195.17/195.35 tff(202,plain,
% 195.17/195.35 (apply(function_inverse(A!16), tptp_fun_C_18(function_inverse(A!16), B!17)) = tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)),
% 195.17/195.35 inference(transitivity,[status(thm)],[201, 200])).
% 195.17/195.35 tff(203,plain,
% 195.17/195.35 (apply(B!17, apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) = apply(B!17, tptp_fun_C_18(function_inverse(A!16), B!17))),
% 195.17/195.35 inference(monotonicity,[status(thm)],[56])).
% 195.17/195.35 tff(204,plain,
% 195.17/195.35 (apply(B!17, tptp_fun_C_18(function_inverse(A!16), B!17)) = apply(B!17, apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))),
% 195.17/195.35 inference(symmetry,[status(thm)],[203])).
% 195.17/195.35 tff(205,plain,
% 195.17/195.35 ((apply(B!17, tptp_fun_C_18(function_inverse(A!16), B!17)) = apply(function_inverse(A!16), tptp_fun_C_18(function_inverse(A!16), B!17))) <=> (apply(B!17, apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) = tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))),
% 195.17/195.35 inference(monotonicity,[status(thm)],[204, 202])).
% 195.17/195.35 tff(206,plain,
% 195.17/195.35 ((apply(B!17, tptp_fun_C_18(function_inverse(A!16), B!17)) = apply(function_inverse(A!16), tptp_fun_C_18(function_inverse(A!16), B!17))) <=> (tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16) = apply(B!17, apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))))),
% 195.17/195.35 inference(transitivity,[status(thm)],[205, 180])).
% 195.17/195.35 tff(207,plain,
% 195.17/195.35 ((apply(B!17, tptp_fun_C_18(function_inverse(A!16), B!17)) = apply(function_inverse(A!16), tptp_fun_C_18(function_inverse(A!16), B!17))) <=> (apply(B!17, apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) = tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))),
% 195.17/195.35 inference(transitivity,[status(thm)],[206, 181])).
% 195.17/195.35 tff(208,plain,
% 195.17/195.35 ((~(apply(B!17, tptp_fun_C_18(function_inverse(A!16), B!17)) = apply(function_inverse(A!16), tptp_fun_C_18(function_inverse(A!16), B!17)))) <=> (~(apply(B!17, apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) = tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))),
% 195.17/195.35 inference(monotonicity,[status(thm)],[207])).
% 195.17/195.35 tff(209,plain,
% 195.17/195.35 (((~in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17))) | (apply(B!17, tptp_fun_C_18(function_inverse(A!16), B!17)) = apply(function_inverse(A!16), tptp_fun_C_18(function_inverse(A!16), B!17)))) | (~(apply(B!17, tptp_fun_C_18(function_inverse(A!16), B!17)) = apply(function_inverse(A!16), tptp_fun_C_18(function_inverse(A!16), B!17))))),
% 195.17/195.35 inference(tautology,[status(thm)],[])).
% 195.17/195.35 tff(210,plain,
% 195.17/195.35 (~(apply(B!17, tptp_fun_C_18(function_inverse(A!16), B!17)) = apply(function_inverse(A!16), tptp_fun_C_18(function_inverse(A!16), B!17)))),
% 195.17/195.35 inference(unit_resolution,[status(thm)],[209, 176])).
% 195.17/195.35 tff(211,plain,
% 195.17/195.35 (~(apply(B!17, apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) = tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))),
% 195.17/195.35 inference(modus_ponens,[status(thm)],[210, 208])).
% 195.17/195.35 tff(212,plain,
% 195.17/195.35 (^[C: $i, D: $i] : refl((((apply(A!16, C) = D) <=> (apply(B!17, D) = C)) | (~in(C, relation_dom(A!16))) | (~in(D, relation_dom(B!17)))) <=> (((apply(A!16, C) = D) <=> (apply(B!17, D) = C)) | (~in(C, relation_dom(A!16))) | (~in(D, relation_dom(B!17)))))),
% 195.17/195.35 inference(bind,[status(th)],[])).
% 195.17/195.35 tff(213,plain,
% 195.17/195.35 (![C: $i, D: $i] : (((apply(A!16, C) = D) <=> (apply(B!17, D) = C)) | (~in(C, relation_dom(A!16))) | (~in(D, relation_dom(B!17)))) <=> ![C: $i, D: $i] : (((apply(A!16, C) = D) <=> (apply(B!17, D) = C)) | (~in(C, relation_dom(A!16))) | (~in(D, relation_dom(B!17))))),
% 195.17/195.35 inference(quant_intro,[status(thm)],[212])).
% 195.17/195.35 tff(214,plain,
% 195.17/195.35 (^[C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((in(C, relation_dom(A!16)) & in(D, relation_dom(B!17))) <=> (~((~in(C, relation_dom(A!16))) | (~in(D, relation_dom(B!17)))))), ((~(in(C, relation_dom(A!16)) & in(D, relation_dom(B!17)))) <=> (~(~((~in(C, relation_dom(A!16))) | (~in(D, relation_dom(B!17)))))))), rewrite((~(~((~in(C, relation_dom(A!16))) | (~in(D, relation_dom(B!17)))))) <=> ((~in(C, relation_dom(A!16))) | (~in(D, relation_dom(B!17))))), ((~(in(C, relation_dom(A!16)) & in(D, relation_dom(B!17)))) <=> ((~in(C, relation_dom(A!16))) | (~in(D, relation_dom(B!17)))))), (((~(in(C, relation_dom(A!16)) & in(D, relation_dom(B!17)))) | ((apply(A!16, C) = D) <=> (apply(B!17, D) = C))) <=> (((~in(C, relation_dom(A!16))) | (~in(D, relation_dom(B!17)))) | ((apply(A!16, C) = D) <=> (apply(B!17, D) = C))))), rewrite((((~in(C, relation_dom(A!16))) | (~in(D, relation_dom(B!17)))) | ((apply(A!16, C) = D) <=> (apply(B!17, D) = C))) <=> (((apply(A!16, C) = D) <=> (apply(B!17, D) = C)) | (~in(C, relation_dom(A!16))) | (~in(D, relation_dom(B!17))))), (((~(in(C, relation_dom(A!16)) & in(D, relation_dom(B!17)))) | ((apply(A!16, C) = D) <=> (apply(B!17, D) = C))) <=> (((apply(A!16, C) = D) <=> (apply(B!17, D) = C)) | (~in(C, relation_dom(A!16))) | (~in(D, relation_dom(B!17))))))),
% 195.17/195.35 inference(bind,[status(th)],[])).
% 195.17/195.35 tff(215,plain,
% 195.17/195.35 (![C: $i, D: $i] : ((~(in(C, relation_dom(A!16)) & in(D, relation_dom(B!17)))) | ((apply(A!16, C) = D) <=> (apply(B!17, D) = C))) <=> ![C: $i, D: $i] : (((apply(A!16, C) = D) <=> (apply(B!17, D) = C)) | (~in(C, relation_dom(A!16))) | (~in(D, relation_dom(B!17))))),
% 195.17/195.35 inference(quant_intro,[status(thm)],[214])).
% 195.17/195.35 tff(216,plain,
% 195.17/195.35 (![C: $i, D: $i] : ((~(in(C, relation_dom(A!16)) & in(D, relation_dom(B!17)))) | ((apply(A!16, C) = D) <=> (apply(B!17, D) = C)))),
% 195.17/195.35 inference(and_elim,[status(thm)],[16])).
% 195.17/195.35 tff(217,plain,
% 195.17/195.35 (![C: $i, D: $i] : (((apply(A!16, C) = D) <=> (apply(B!17, D) = C)) | (~in(C, relation_dom(A!16))) | (~in(D, relation_dom(B!17))))),
% 195.17/195.35 inference(modus_ponens,[status(thm)],[216, 215])).
% 195.17/195.35 tff(218,plain,
% 195.17/195.35 (![C: $i, D: $i] : (((apply(A!16, C) = D) <=> (apply(B!17, D) = C)) | (~in(C, relation_dom(A!16))) | (~in(D, relation_dom(B!17))))),
% 195.17/195.35 inference(modus_ponens,[status(thm)],[217, 213])).
% 195.17/195.35 tff(219,plain,
% 195.17/195.35 (((~![C: $i, D: $i] : (((apply(A!16, C) = D) <=> (apply(B!17, D) = C)) | (~in(C, relation_dom(A!16))) | (~in(D, relation_dom(B!17))))) | ((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_dom(B!17))) | (apply(B!17, apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) = tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))) <=> ((~![C: $i, D: $i] : (((apply(A!16, C) = D) <=> (apply(B!17, D) = C)) | (~in(C, relation_dom(A!16))) | (~in(D, relation_dom(B!17))))) | (~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_dom(B!17))) | (apply(B!17, apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) = tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))),
% 195.17/195.35 inference(rewrite,[status(thm)],[])).
% 195.17/195.35 tff(220,plain,
% 195.17/195.35 (((apply(B!17, apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) = tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)) | (~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_dom(B!17)))) <=> ((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_dom(B!17))) | (apply(B!17, apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) = tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))),
% 195.17/195.35 inference(rewrite,[status(thm)],[])).
% 195.17/195.35 tff(221,plain,
% 195.17/195.35 (($true <=> (apply(B!17, apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) = tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) <=> (apply(B!17, apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) = tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))),
% 195.17/195.35 inference(rewrite,[status(thm)],[])).
% 195.17/195.35 tff(222,plain,
% 195.17/195.35 ((apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) <=> $true),
% 195.17/195.35 inference(rewrite,[status(thm)],[])).
% 195.17/195.35 tff(223,plain,
% 195.17/195.35 (((apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) <=> (apply(B!17, apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) = tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) <=> ($true <=> (apply(B!17, apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) = tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))),
% 195.17/195.35 inference(monotonicity,[status(thm)],[222])).
% 195.17/195.35 tff(224,plain,
% 195.17/195.35 (((apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) <=> (apply(B!17, apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) = tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) <=> (apply(B!17, apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) = tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))),
% 195.17/195.35 inference(transitivity,[status(thm)],[223, 221])).
% 195.17/195.35 tff(225,plain,
% 195.17/195.35 ((((apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) <=> (apply(B!17, apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) = tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) | (~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_dom(B!17)))) <=> ((apply(B!17, apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) = tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)) | (~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_dom(B!17))))),
% 195.17/195.35 inference(monotonicity,[status(thm)],[224])).
% 195.17/195.35 tff(226,plain,
% 195.17/195.35 ((((apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) <=> (apply(B!17, apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) = tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) | (~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_dom(B!17)))) <=> ((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_dom(B!17))) | (apply(B!17, apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) = tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))),
% 195.17/195.35 inference(transitivity,[status(thm)],[225, 220])).
% 195.17/195.35 tff(227,plain,
% 195.17/195.35 (((~![C: $i, D: $i] : (((apply(A!16, C) = D) <=> (apply(B!17, D) = C)) | (~in(C, relation_dom(A!16))) | (~in(D, relation_dom(B!17))))) | (((apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) <=> (apply(B!17, apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) = tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) | (~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_dom(B!17))))) <=> ((~![C: $i, D: $i] : (((apply(A!16, C) = D) <=> (apply(B!17, D) = C)) | (~in(C, relation_dom(A!16))) | (~in(D, relation_dom(B!17))))) | ((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_dom(B!17))) | (apply(B!17, apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) = tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))))),
% 195.17/195.35 inference(monotonicity,[status(thm)],[226])).
% 195.17/195.35 tff(228,plain,
% 195.17/195.35 (((~![C: $i, D: $i] : (((apply(A!16, C) = D) <=> (apply(B!17, D) = C)) | (~in(C, relation_dom(A!16))) | (~in(D, relation_dom(B!17))))) | (((apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) <=> (apply(B!17, apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) = tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) | (~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_dom(B!17))))) <=> ((~![C: $i, D: $i] : (((apply(A!16, C) = D) <=> (apply(B!17, D) = C)) | (~in(C, relation_dom(A!16))) | (~in(D, relation_dom(B!17))))) | (~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_dom(B!17))) | (apply(B!17, apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) = tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))),
% 195.17/195.35 inference(transitivity,[status(thm)],[227, 219])).
% 195.17/195.35 tff(229,plain,
% 195.17/195.35 ((~![C: $i, D: $i] : (((apply(A!16, C) = D) <=> (apply(B!17, D) = C)) | (~in(C, relation_dom(A!16))) | (~in(D, relation_dom(B!17))))) | (((apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) <=> (apply(B!17, apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) = tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) | (~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_dom(B!17))))),
% 195.17/195.35 inference(quant_inst,[status(thm)],[])).
% 195.17/195.35 tff(230,plain,
% 195.17/195.35 ((~![C: $i, D: $i] : (((apply(A!16, C) = D) <=> (apply(B!17, D) = C)) | (~in(C, relation_dom(A!16))) | (~in(D, relation_dom(B!17))))) | (~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_dom(B!17))) | (apply(B!17, apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) = tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))),
% 195.17/195.35 inference(modus_ponens,[status(thm)],[229, 228])).
% 195.17/195.35 tff(231,plain,
% 195.17/195.35 ((~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_dom(B!17))) | (apply(B!17, apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) = tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))),
% 195.17/195.35 inference(unit_resolution,[status(thm)],[230, 218, 194])).
% 195.17/195.35 tff(232,plain,
% 195.17/195.35 ($false),
% 195.17/195.35 inference(unit_resolution,[status(thm)],[231, 211, 179])).
% 195.17/195.35 tff(233,plain,((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))))), inference(lemma,lemma(discharge,[]))).
% 195.17/195.35 tff(234,plain,
% 195.17/195.36 ((~((~in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))))))) | (~in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))))))),
% 195.17/195.36 inference(tautology,[status(thm)],[])).
% 195.17/195.36 tff(235,plain,
% 195.17/195.36 (~((~in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))))))),
% 195.17/195.36 inference(unit_resolution,[status(thm)],[234, 178, 233])).
% 195.17/195.36 tff(236,plain,
% 195.17/195.36 (((~((~in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))))))) | (~(in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17)) | (~in(tptp_fun_C_18(B!17, A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_C_18(B!17, A!16))))))) | ((~in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))))))),
% 195.17/195.36 inference(tautology,[status(thm)],[])).
% 195.17/195.36 tff(237,plain,
% 195.17/195.36 ((~((~in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))))))) | (~(in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17)) | (~in(tptp_fun_C_18(B!17, A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_C_18(B!17, A!16))))))),
% 195.17/195.36 inference(unit_resolution,[status(thm)],[236, 235])).
% 195.17/195.36 tff(238,plain,
% 195.17/195.36 ((~((~(relation_dom(B!17) = relation_rng(A!16))) | (~((~((~in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))))))) | (~(in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17)) | (~in(tptp_fun_C_18(B!17, A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_C_18(B!17, A!16)))))))))) | (~(relation_dom(B!17) = relation_rng(A!16))) | (~((~((~in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))))))) | (~(in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17)) | (~in(tptp_fun_C_18(B!17, A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_C_18(B!17, A!16))))))))),
% 195.17/195.36 inference(tautology,[status(thm)],[])).
% 195.17/195.36 tff(239,plain,
% 195.17/195.36 (~((~(relation_dom(B!17) = relation_rng(A!16))) | (~((~((~in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))))))) | (~(in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17)) | (~in(tptp_fun_C_18(B!17, A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_C_18(B!17, A!16)))))))))),
% 195.26/195.47 inference(unit_resolution,[status(thm)],[238, 134, 237])).
% 195.26/195.47 tff(240,plain,
% 195.26/195.47 (((~((~(relation_dom(B!17) = relation_rng(A!16))) | (~((~((~in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))))))) | (~(in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17)) | (~in(tptp_fun_C_18(B!17, A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_C_18(B!17, A!16)))))))))) | (~((relation_dom(B!17) = relation_rng(A!16)) | (~((~(in(tptp_fun_C_1(relation_dom(B!17), A!16), relation_dom(B!17)) | (~((~in(tptp_fun_D_2(relation_dom(B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_1(relation_dom(B!17), A!16) = apply(A!16, tptp_fun_D_2(relation_dom(B!17), A!16)))))))) | (~((~in(tptp_fun_C_18(B!17, A!16), relation_dom(A!16))) | (~in(tptp_fun_C_1(relation_dom(B!17), A!16), relation_dom(B!17))) | (~(tptp_fun_C_1(relation_dom(B!17), A!16) = apply(A!16, tptp_fun_C_18(B!17, A!16))))))))))) | ((~(relation_dom(B!17) = relation_rng(A!16))) | (~((~((~in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))))))) | (~(in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17)) | (~in(tptp_fun_C_18(B!17, A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_C_18(B!17, A!16)))))))))),
% 195.26/195.47 inference(tautology,[status(thm)],[])).
% 195.26/195.47 tff(241,plain,
% 195.26/195.47 ((~((~(relation_dom(B!17) = relation_rng(A!16))) | (~((~((~in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))))))) | (~(in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17)) | (~in(tptp_fun_C_18(B!17, A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_C_18(B!17, A!16)))))))))) | (~((relation_dom(B!17) = relation_rng(A!16)) | (~((~(in(tptp_fun_C_1(relation_dom(B!17), A!16), relation_dom(B!17)) | (~((~in(tptp_fun_D_2(relation_dom(B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_1(relation_dom(B!17), A!16) = apply(A!16, tptp_fun_D_2(relation_dom(B!17), A!16)))))))) | (~((~in(tptp_fun_C_18(B!17, A!16), relation_dom(A!16))) | (~in(tptp_fun_C_1(relation_dom(B!17), A!16), relation_dom(B!17))) | (~(tptp_fun_C_1(relation_dom(B!17), A!16) = apply(A!16, tptp_fun_C_18(B!17, A!16))))))))))),
% 195.26/195.47 inference(unit_resolution,[status(thm)],[240, 239])).
% 195.26/195.47 tff(242,plain,
% 195.26/195.47 ($false),
% 195.26/195.47 inference(unit_resolution,[status(thm)],[241, 52])).
% 195.26/195.47 % SZS output end Proof
% 195.26/195.47 % E exiting
%------------------------------------------------------------------------------