TSTP Solution File: SEU027+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU027+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 07:27:19 EDT 2022
% Result : Timeout 291.87s 187.96s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU027+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n012.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Sep 3 09:01:34 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 291.87/187.96 % SZS status Theorem
% 291.87/187.96 % SZS output start Proof
% 291.87/187.96 tff(apply_type, type, (
% 291.87/187.96 apply: ( $i * $i ) > $i)).
% 291.87/187.96 tff(tptp_fun_C_18_type, type, (
% 291.87/187.96 tptp_fun_C_18: ( $i * $i ) > $i)).
% 291.87/187.96 tff(tptp_fun_A_16_type, type, (
% 291.87/187.96 tptp_fun_A_16: $i)).
% 291.87/187.96 tff(tptp_fun_B_17_type, type, (
% 291.87/187.96 tptp_fun_B_17: $i)).
% 291.87/187.96 tff(tptp_fun_C_1_type, type, (
% 291.87/187.96 tptp_fun_C_1: ( $i * $i ) > $i)).
% 291.87/187.96 tff(relation_dom_type, type, (
% 291.87/187.96 relation_dom: $i > $i)).
% 291.87/187.96 tff(in_type, type, (
% 291.87/187.96 in: ( $i * $i ) > $o)).
% 291.87/187.96 tff(tptp_fun_D_2_type, type, (
% 291.87/187.96 tptp_fun_D_2: ( $i * $i ) > $i)).
% 291.87/187.96 tff(relation_rng_type, type, (
% 291.87/187.96 relation_rng: $i > $i)).
% 291.87/187.96 tff(function_inverse_type, type, (
% 291.87/187.96 function_inverse: $i > $i)).
% 291.87/187.96 tff(tptp_fun_D_0_type, type, (
% 291.87/187.96 tptp_fun_D_0: ( $i * $i ) > $i)).
% 291.87/187.96 tff(function_type, type, (
% 291.87/187.96 function: $i > $o)).
% 291.87/187.96 tff(one_to_one_type, type, (
% 291.87/187.96 one_to_one: $i > $o)).
% 291.87/187.96 tff(relation_type, type, (
% 291.87/187.96 relation: $i > $o)).
% 291.87/187.96 tff(tptp_fun_C_15_type, type, (
% 291.87/187.96 tptp_fun_C_15: ( $i * $i ) > $i)).
% 291.87/187.96 tff(tptp_fun_D_14_type, type, (
% 291.87/187.96 tptp_fun_D_14: ( $i * $i ) > $i)).
% 291.87/187.96 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)).
% 291.87/187.96 tff(2,plain,
% 291.87/187.96 (((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))))),
% 291.87/187.96 inference(rewrite,[status(thm)],[])).
% 291.87/187.96 tff(3,plain,
% 291.87/187.96 (((~(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))))),
% 291.87/187.96 inference(rewrite,[status(thm)],[])).
% 291.87/187.96 tff(4,plain,
% 291.87/187.96 ((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))))),
% 291.87/187.97 inference(rewrite,[status(thm)],[])).
% 291.87/187.97 tff(5,plain,
% 291.87/187.97 ((~(~(relation(B!17) & function(B!17)))) <=> (relation(B!17) & function(B!17))),
% 291.87/187.97 inference(rewrite,[status(thm)],[])).
% 291.87/187.97 tff(6,plain,
% 291.87/187.97 (((~(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)))))),
% 291.87/187.97 inference(monotonicity,[status(thm)],[5, 4])).
% 291.87/187.97 tff(7,plain,
% 291.87/187.97 (((~(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))))),
% 291.87/187.97 inference(transitivity,[status(thm)],[6, 3])).
% 291.87/187.97 tff(8,plain,
% 291.87/187.97 ((~(~(relation(A!16) & function(A!16)))) <=> (relation(A!16) & function(A!16))),
% 291.87/187.97 inference(rewrite,[status(thm)],[])).
% 291.87/187.97 tff(9,plain,
% 291.87/187.97 (((~(~(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)))))),
% 291.87/187.97 inference(monotonicity,[status(thm)],[8, 7])).
% 291.87/187.97 tff(10,plain,
% 291.87/187.97 (((~(~(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))))),
% 291.87/187.97 inference(transitivity,[status(thm)],[9, 2])).
% 291.87/187.97 tff(11,plain,
% 291.87/187.97 ((~![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))))))))),
% 291.87/187.97 inference(rewrite,[status(thm)],[])).
% 291.87/187.97 tff(12,plain,
% 291.87/187.97 ((~![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))))))))),
% 291.87/187.97 inference(rewrite,[status(thm)],[])).
% 291.87/187.97 tff(13,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/sandbox2/benchmark/theBenchmark.p','t60_funct_1')).
% 291.87/187.97 tff(14,plain,
% 291.87/187.97 (~![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)))))))),
% 291.87/187.97 inference(modus_ponens,[status(thm)],[13, 12])).
% 291.87/187.97 tff(15,plain,
% 291.87/187.97 (~![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)))))))),
% 291.87/187.97 inference(modus_ponens,[status(thm)],[14, 11])).
% 291.87/187.97 tff(16,plain,
% 291.87/187.97 (~![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)))))))),
% 291.87/187.97 inference(modus_ponens,[status(thm)],[15, 11])).
% 291.87/187.97 tff(17,plain,
% 291.87/187.97 (~![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)))))))),
% 291.87/187.97 inference(modus_ponens,[status(thm)],[16, 11])).
% 291.87/187.97 tff(18,plain,
% 291.87/187.97 (~![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)))))))),
% 291.87/187.97 inference(modus_ponens,[status(thm)],[17, 11])).
% 291.87/187.97 tff(19,plain,
% 291.87/187.97 (~![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)))))))),
% 291.87/187.97 inference(modus_ponens,[status(thm)],[18, 11])).
% 291.87/187.97 tff(20,plain,
% 291.87/187.97 (~![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)))))))),
% 291.87/187.97 inference(modus_ponens,[status(thm)],[19, 11])).
% 291.87/187.97 tff(21,plain,
% 291.87/187.97 (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)))),
% 291.87/187.97 inference(modus_ponens,[status(thm)],[20, 10])).
% 291.87/187.97 tff(22,plain,
% 291.87/187.97 (function(A!16)),
% 291.87/187.97 inference(and_elim,[status(thm)],[21])).
% 291.87/187.97 tff(23,plain,
% 291.87/187.97 (relation(A!16)),
% 291.87/187.97 inference(and_elim,[status(thm)],[21])).
% 291.87/187.97 tff(24,plain,
% 291.87/187.97 (^[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))))))))))))))),
% 291.87/187.97 inference(bind,[status(th)],[])).
% 291.87/187.97 tff(25,plain,
% 291.87/187.97 (![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))))))))))))),
% 291.87/187.97 inference(quant_intro,[status(thm)],[24])).
% 291.87/187.97 tff(26,plain,
% 291.87/187.97 (^[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))))))))))))))),
% 291.87/187.97 inference(bind,[status(th)],[])).
% 291.87/187.97 tff(27,plain,
% 291.87/187.97 (![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)))))))))))))),
% 291.87/187.97 inference(quant_intro,[status(thm)],[26])).
% 291.87/187.97 tff(28,plain,
% 291.87/187.97 (^[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))))))))))))))),
% 291.87/187.97 inference(bind,[status(th)],[])).
% 291.87/187.97 tff(29,plain,
% 291.87/187.97 (![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)))))))))))))),
% 291.87/187.97 inference(quant_intro,[status(thm)],[28])).
% 291.87/187.97 tff(30,plain,
% 291.87/187.97 (![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)))))))))))))),
% 291.87/187.97 inference(transitivity,[status(thm)],[29, 27])).
% 291.87/187.97 tff(31,plain,
% 291.87/187.97 (^[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)))))))))))))))),
% 291.87/187.97 inference(bind,[status(th)],[])).
% 291.87/187.97 tff(32,plain,
% 291.87/187.97 (![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)))))))))))))),
% 291.87/187.97 inference(quant_intro,[status(thm)],[31])).
% 291.87/187.97 tff(33,plain,
% 291.87/187.97 (![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))))))),
% 291.87/187.97 inference(rewrite,[status(thm)],[])).
% 291.87/187.97 tff(34,plain,
% 291.87/187.97 (^[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)))))))),
% 291.87/187.97 inference(bind,[status(th)],[])).
% 291.87/187.97 tff(35,plain,
% 291.87/187.97 (![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))))))),
% 291.87/187.97 inference(quant_intro,[status(thm)],[34])).
% 291.87/187.97 tff(36,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/sandbox2/benchmark/theBenchmark.p','d5_funct_1')).
% 291.87/187.97 tff(37,plain,
% 291.87/187.97 (![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))))))),
% 291.87/187.97 inference(modus_ponens,[status(thm)],[36, 35])).
% 291.87/187.97 tff(38,plain,
% 291.87/187.97 (![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))))))),
% 291.87/187.97 inference(modus_ponens,[status(thm)],[37, 33])).
% 291.87/187.97 tff(39,plain,(
% 291.87/187.97 ![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)))))))))),
% 291.87/187.97 inference(skolemize,[status(sab)],[38])).
% 291.87/187.97 tff(40,plain,
% 291.87/187.97 (![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)))))))))))))),
% 291.87/187.97 inference(modus_ponens,[status(thm)],[39, 32])).
% 291.87/187.97 tff(41,plain,
% 291.87/187.97 (![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)))))))))))))),
% 291.87/187.97 inference(modus_ponens,[status(thm)],[40, 30])).
% 291.87/187.97 tff(42,plain,
% 291.87/187.97 (![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))))))))))))),
% 291.87/187.97 inference(modus_ponens,[status(thm)],[41, 25])).
% 291.87/187.97 tff(43,plain,
% 291.87/187.97 (((~![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))))))))))))) | (~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))))))))))))),
% 291.87/187.97 inference(rewrite,[status(thm)],[])).
% 291.87/187.97 tff(44,plain,
% 291.87/187.97 ((~![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))))))))))))),
% 291.87/187.97 inference(quant_inst,[status(thm)],[])).
% 291.87/187.97 tff(45,plain,
% 291.87/187.97 ((~![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)))))))))))),
% 291.87/187.98 inference(modus_ponens,[status(thm)],[44, 43])).
% 291.87/187.98 tff(46,plain,
% 291.87/187.98 (![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)))))))))))),
% 291.87/187.98 inference(unit_resolution,[status(thm)],[45, 42, 23, 22])).
% 291.87/187.98 tff(47,plain,
% 291.87/187.98 (((~![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)))))))))))))),
% 291.87/187.98 inference(rewrite,[status(thm)],[])).
% 291.87/187.98 tff(48,plain,
% 291.87/187.98 ((~((~((~(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))))))))))))),
% 291.87/187.98 inference(rewrite,[status(thm)],[])).
% 291.87/187.98 tff(49,plain,
% 291.87/187.98 (((~![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)))))))))))))),
% 291.87/187.98 inference(monotonicity,[status(thm)],[48])).
% 291.87/187.98 tff(50,plain,
% 291.87/187.98 (((~![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)))))))))))))),
% 291.93/187.98 inference(transitivity,[status(thm)],[49, 47])).
% 291.93/187.98 tff(51,plain,
% 291.93/187.98 ((~![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))))))))))))),
% 291.93/187.98 inference(quant_inst,[status(thm)],[])).
% 291.93/187.98 tff(52,plain,
% 291.93/187.98 ((~![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A!16))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A!16), relation_dom(A!16))) | (~(C = apply(A!16, tptp_fun_D_0(C, A!16)))))))) | (~(in(C, B) | (~in(D, relation_dom(A!16))) | (~(C = apply(A!16, D))))))))) | (~((B = relation_rng(A!16)) | (~((~(in(tptp_fun_C_1(B, A!16), B) | (~((~in(tptp_fun_D_2(B, A!16), relation_dom(A!16))) | (~(tptp_fun_C_1(B, A!16) = apply(A!16, tptp_fun_D_2(B, A!16)))))))) | (~((~in(tptp_fun_C_1(B, A!16), B)) | (~in(D_19, relation_dom(A!16))) | (~(tptp_fun_C_1(B, A!16) = apply(A!16, D_19)))))))))))) | (~((~((~(relation_dom(B!17) = relation_rng(A!16))) | (~((~((~in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))))))) | (~(in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17)) | (~in(tptp_fun_C_18(B!17, A!16), relation_dom(A!16))) | (~(tptp_fun_C_18(function_inverse(A!16), B!17) = apply(A!16, tptp_fun_C_18(B!17, A!16)))))))))) | (~((relation_dom(B!17) = relation_rng(A!16)) | (~((~(in(tptp_fun_C_1(relation_dom(B!17), A!16), relation_dom(B!17)) | (~((~in(tptp_fun_D_2(relation_dom(B!17), A!16), relation_dom(A!16))) | (~(tptp_fun_C_1(relation_dom(B!17), A!16) = apply(A!16, tptp_fun_D_2(relation_dom(B!17), A!16)))))))) | (~((~in(tptp_fun_C_18(B!17, A!16), relation_dom(A!16))) | (~in(tptp_fun_C_1(relation_dom(B!17), A!16), relation_dom(B!17))) | (~(tptp_fun_C_1(relation_dom(B!17), A!16) = apply(A!16, tptp_fun_C_18(B!17, A!16))))))))))))),
% 291.93/187.98 inference(modus_ponens,[status(thm)],[51, 50])).
% 291.93/187.98 tff(53,plain,
% 291.93/187.98 ($false),
% 291.93/187.98 inference(unit_resolution,[status(thm)],[52, 46, 1])).
% 291.93/187.98 tff(54,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,[]))).
% 291.93/187.98 tff(55,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)).
% 291.93/187.98 tff(56,plain,
% 291.93/187.98 (((~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)))),
% 291.93/187.98 inference(tautology,[status(thm)],[])).
% 291.93/187.98 tff(57,plain,
% 291.93/187.98 (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))),
% 291.93/187.98 inference(unit_resolution,[status(thm)],[56, 55])).
% 291.93/187.98 tff(58,plain,
% 291.93/187.98 (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)),
% 291.93/187.98 inference(symmetry,[status(thm)],[57])).
% 291.93/187.98 tff(59,plain,
% 291.93/187.98 (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))),
% 291.93/187.98 inference(monotonicity,[status(thm)],[58])).
% 291.93/187.98 tff(60,plain,
% 291.93/187.98 (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))),
% 291.93/187.98 inference(symmetry,[status(thm)],[59])).
% 291.93/187.98 tff(61,plain,
% 291.93/187.98 (^[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)))))))),
% 291.93/187.98 inference(bind,[status(th)],[])).
% 291.93/187.98 tff(62,plain,
% 291.93/187.98 (![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))))))),
% 291.93/187.98 inference(quant_intro,[status(thm)],[61])).
% 291.93/187.98 tff(63,plain,
% 291.93/187.98 (^[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))))))))),
% 291.93/187.98 inference(bind,[status(th)],[])).
% 291.93/187.98 tff(64,plain,
% 291.93/187.98 (![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))))))),
% 291.93/187.98 inference(quant_intro,[status(thm)],[63])).
% 291.93/187.98 tff(65,plain,
% 291.93/187.98 (![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))))),
% 291.93/187.98 inference(rewrite,[status(thm)],[])).
% 291.93/187.98 tff(66,plain,
% 291.93/187.98 (^[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)))))),
% 291.93/187.98 inference(bind,[status(th)],[])).
% 291.93/187.98 tff(67,plain,
% 291.93/187.98 (![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))))),
% 291.93/187.98 inference(quant_intro,[status(thm)],[66])).
% 291.93/187.98 tff(68,axiom,(![A: $i] : ((relation(A) & function(A)) => (relation(function_inverse(A)) & function(function_inverse(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k2_funct_1')).
% 291.93/187.98 tff(69,plain,
% 291.93/187.98 (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 291.93/187.98 inference(modus_ponens,[status(thm)],[68, 67])).
% 291.93/187.98 tff(70,plain,
% 291.93/187.98 (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 291.93/187.98 inference(modus_ponens,[status(thm)],[69, 65])).
% 291.93/187.98 tff(71,plain,(
% 291.93/187.98 ![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 291.93/187.98 inference(skolemize,[status(sab)],[70])).
% 291.93/187.98 tff(72,plain,
% 291.93/187.98 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 291.93/187.98 inference(modus_ponens,[status(thm)],[71, 64])).
% 291.93/187.98 tff(73,plain,
% 291.93/187.98 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 291.93/187.98 inference(modus_ponens,[status(thm)],[72, 62])).
% 291.93/187.98 tff(74,plain,
% 291.93/187.98 (((~![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))))))) | (~relation(A!16)) | (~function(A!16)) | (~((~relation(function_inverse(A!16))) | (~function(function_inverse(A!16))))))),
% 291.93/187.98 inference(rewrite,[status(thm)],[])).
% 291.93/187.98 tff(75,plain,
% 291.93/187.98 ((~![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))))))),
% 291.93/187.98 inference(quant_inst,[status(thm)],[])).
% 291.93/187.98 tff(76,plain,
% 291.93/187.98 ((~![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)))))),
% 291.93/187.98 inference(modus_ponens,[status(thm)],[75, 74])).
% 291.93/187.98 tff(77,plain,
% 291.93/187.98 (~((~relation(function_inverse(A!16))) | (~function(function_inverse(A!16))))),
% 291.93/187.98 inference(unit_resolution,[status(thm)],[76, 73, 23, 22])).
% 291.93/187.98 tff(78,plain,
% 291.93/187.98 (((~relation(function_inverse(A!16))) | (~function(function_inverse(A!16)))) | function(function_inverse(A!16))),
% 291.93/187.98 inference(tautology,[status(thm)],[])).
% 291.93/187.98 tff(79,plain,
% 291.93/187.98 (function(function_inverse(A!16))),
% 291.93/187.98 inference(unit_resolution,[status(thm)],[78, 77])).
% 291.93/187.98 tff(80,plain,
% 291.93/187.98 (((~relation(function_inverse(A!16))) | (~function(function_inverse(A!16)))) | relation(function_inverse(A!16))),
% 291.93/187.98 inference(tautology,[status(thm)],[])).
% 291.93/187.98 tff(81,plain,
% 291.93/187.98 (relation(function_inverse(A!16))),
% 291.93/187.98 inference(unit_resolution,[status(thm)],[80, 77])).
% 291.93/187.98 tff(82,plain,
% 291.93/187.98 (one_to_one(A!16)),
% 291.93/187.98 inference(and_elim,[status(thm)],[21])).
% 291.93/187.98 tff(83,plain,
% 291.93/187.98 (^[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))))))))))))))))))))),
% 291.93/187.98 inference(bind,[status(th)],[])).
% 291.93/187.98 tff(84,plain,
% 291.93/187.98 (![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))))))))))))))))))),
% 291.93/187.98 inference(quant_intro,[status(thm)],[83])).
% 291.93/187.98 tff(85,plain,
% 291.93/187.98 (^[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)))))))))))))),
% 291.93/187.99 inference(bind,[status(th)],[])).
% 291.93/187.99 tff(86,plain,
% 291.93/187.99 (![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))))))))))))),
% 291.93/187.99 inference(quant_intro,[status(thm)],[85])).
% 291.93/187.99 tff(87,plain,
% 291.93/187.99 (^[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)))))))))))))),
% 291.93/187.99 inference(bind,[status(th)],[])).
% 291.93/187.99 tff(88,plain,
% 291.93/187.99 (![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))))))))))))),
% 291.93/187.99 inference(quant_intro,[status(thm)],[87])).
% 291.93/187.99 tff(89,plain,
% 291.93/187.99 (![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))))))))))))),
% 291.93/187.99 inference(transitivity,[status(thm)],[88, 86])).
% 291.93/187.99 tff(90,plain,
% 291.93/187.99 (^[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))))))))))))))),
% 291.93/187.99 inference(bind,[status(th)],[])).
% 291.93/187.99 tff(91,plain,
% 291.93/187.99 (![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))))))))))))),
% 291.93/187.99 inference(quant_intro,[status(thm)],[90])).
% 291.93/187.99 tff(92,plain,
% 291.93/187.99 (^[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)))))))))))))),
% 291.93/187.99 inference(bind,[status(th)],[])).
% 291.93/187.99 tff(93,plain,
% 291.93/187.99 (![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)))))))))))),
% 291.93/187.99 inference(quant_intro,[status(thm)],[92])).
% 291.93/187.99 tff(94,plain,
% 291.93/187.99 (![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)))),
% 291.93/187.99 inference(rewrite,[status(thm)],[])).
% 291.93/187.99 tff(95,plain,
% 291.93/187.99 (^[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)))))),
% 291.93/187.99 inference(bind,[status(th)],[])).
% 291.93/187.99 tff(96,plain,
% 291.93/187.99 (![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)))),
% 291.93/187.99 inference(quant_intro,[status(thm)],[95])).
% 291.93/187.99 tff(97,axiom,(![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => ![B: $i] : ((relation(B) & function(B)) => ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((in(C, relation_rng(A)) & (D = apply(B, C))) => (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((in(D, relation_dom(A)) & (C = apply(A, D))) => (in(C, relation_rng(A)) & (D = apply(B, C))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t54_funct_1')).
% 291.93/187.99 tff(98,plain,
% 291.93/187.99 (![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)))),
% 291.93/187.99 inference(modus_ponens,[status(thm)],[97, 96])).
% 291.93/187.99 tff(99,plain,
% 291.93/187.99 (![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)))),
% 291.93/187.99 inference(modus_ponens,[status(thm)],[98, 94])).
% 291.93/187.99 tff(100,plain,(
% 291.93/187.99 ![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)))),
% 291.93/187.99 inference(skolemize,[status(sab)],[99])).
% 291.93/187.99 tff(101,plain,
% 291.93/187.99 (![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)))))))))))),
% 291.93/187.99 inference(modus_ponens,[status(thm)],[100, 93])).
% 291.93/187.99 tff(102,plain,
% 291.93/187.99 (![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))))))))))))),
% 291.93/187.99 inference(modus_ponens,[status(thm)],[101, 91])).
% 291.93/187.99 tff(103,plain,
% 291.93/187.99 (![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))))))))))))),
% 291.93/187.99 inference(modus_ponens,[status(thm)],[102, 89])).
% 291.93/187.99 tff(104,plain,
% 291.93/187.99 (![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))))))))))))))))))),
% 291.93/187.99 inference(modus_ponens,[status(thm)],[103, 84])).
% 291.93/187.99 tff(105,plain,
% 291.93/187.99 (((~![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))))))))))))))))))) | ((~relation(A!16)) | (~function(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)))))))) | (~((~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)))))))))) | (~((~(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))))))))))))))))))) | (~relation(A!16)) | (~function(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)))))))) | (~((~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)))))))))) | (~((~(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))))))))))))))))))),
% 291.93/187.99 inference(rewrite,[status(thm)],[])).
% 291.93/187.99 tff(106,plain,
% 291.93/187.99 (((~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_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)))))))))) | (~((~(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(A!16)) | (~function(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)))))))) | (~((~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)))))))))) | (~((~(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))))))))))))))))))),
% 291.93/188.00 inference(rewrite,[status(thm)],[])).
% 291.93/188.00 tff(107,plain,
% 291.93/188.00 (^[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)))))))) | (~((~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)))))))))) | (~((~(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)))))))) | (~((~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)))))))))) | (~((~(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)))))))) | (~((~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)))))))))) | (~((~(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_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)))))))))) | (~((~(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)))))))) | (~((~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)))))))))) | (~((~(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)))))))))))))))))))),
% 291.93/188.00 inference(bind,[status(th)],[])).
% 291.93/188.00 tff(108,plain,
% 291.93/188.00 (![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)))))))) | (~((~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)))))))))) | (~((~(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)))))))))))))))))),
% 291.93/188.00 inference(quant_intro,[status(thm)],[107])).
% 291.93/188.00 tff(109,plain,
% 291.93/188.00 (((~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)))))))) | (~((~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)))))))))) | (~((~(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))))))))))))))))))),
% 291.93/188.00 inference(monotonicity,[status(thm)],[108])).
% 291.93/188.00 tff(110,plain,
% 291.93/188.00 (((~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)))))))))))))))))) <=> ((~relation(A!16)) | (~function(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)))))))) | (~((~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)))))))))) | (~((~(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))))))))))))))))))),
% 291.93/188.00 inference(transitivity,[status(thm)],[109, 106])).
% 291.93/188.00 tff(111,plain,
% 291.93/188.00 (((~![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))))))))))))))))))) | ((~relation(A!16)) | (~function(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)))))))) | (~((~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)))))))))) | (~((~(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)))))))))))))))))))),
% 291.93/188.00 inference(monotonicity,[status(thm)],[110])).
% 291.93/188.00 tff(112,plain,
% 291.93/188.00 (((~![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))))))))))))))))))) | (~relation(A!16)) | (~function(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)))))))) | (~((~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)))))))))) | (~((~(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))))))))))))))))))),
% 291.93/188.00 inference(transitivity,[status(thm)],[111, 105])).
% 291.93/188.00 tff(113,plain,
% 291.93/188.00 ((~![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))))))))))))))))))),
% 291.93/188.00 inference(quant_inst,[status(thm)],[])).
% 291.93/188.00 tff(114,plain,
% 291.93/188.00 ((~![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))))))))))))))))))) | (~relation(A!16)) | (~function(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)))))))) | (~((~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)))))))))) | (~((~(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)))))))))))))))))),
% 291.93/188.00 inference(modus_ponens,[status(thm)],[113, 112])).
% 291.93/188.00 tff(115,plain,
% 291.93/188.00 (![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_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)))))))))) | (~((~(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)))))))))))))))))),
% 291.93/188.00 inference(unit_resolution,[status(thm)],[114, 104, 23, 22, 82])).
% 291.93/188.00 tff(116,plain,
% 291.93/188.00 (((~![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_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)))))))))) | (~((~(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)))))))) | (~((~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)))))))))) | (~((~(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)))))))))))))),
% 291.93/188.00 inference(rewrite,[status(thm)],[])).
% 291.93/188.00 tff(117,plain,
% 291.93/188.00 (((~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)))))))))))))),
% 291.93/188.00 inference(rewrite,[status(thm)],[])).
% 291.93/188.00 tff(118,plain,
% 291.93/188.00 ((~((~((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)))))))) | (~((~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)))) | (~((~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))))))))))))),
% 291.93/188.00 inference(rewrite,[status(thm)],[])).
% 291.93/188.00 tff(119,plain,
% 291.93/188.00 (((~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)))))))) | (~((~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)))) | (~((~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)))))))))))))),
% 291.93/188.00 inference(monotonicity,[status(thm)],[118])).
% 291.93/188.00 tff(120,plain,
% 291.93/188.00 (((~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)))))))) | (~((~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)))) | (~((~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)))))))))))))),
% 291.93/188.01 inference(transitivity,[status(thm)],[119, 117])).
% 291.93/188.01 tff(121,plain,
% 291.93/188.01 (((~![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_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)))))))))) | (~((~(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)))))))) | (~((~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)))) | (~((~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)))))))) | (~((~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)))))))))) | (~((~(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))))))))))))))),
% 291.93/188.01 inference(monotonicity,[status(thm)],[120])).
% 291.93/188.01 tff(122,plain,
% 291.93/188.01 (((~![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_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)))))))))) | (~((~(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)))))))) | (~((~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)))) | (~((~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)))))))) | (~((~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)))))))))) | (~((~(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)))))))))))))),
% 291.93/188.01 inference(transitivity,[status(thm)],[121, 116])).
% 291.93/188.01 tff(123,plain,
% 291.93/188.01 ((~![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_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)))))))))) | (~((~(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)))))))) | (~((~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)))) | (~((~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)))))))))))))))))),
% 291.93/188.01 inference(quant_inst,[status(thm)],[])).
% 291.93/188.01 tff(124,plain,
% 291.93/188.01 ((~![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_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)))))))))) | (~((~(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))))))))))))),
% 291.93/188.01 inference(modus_ponens,[status(thm)],[123, 122])).
% 291.93/188.01 tff(125,plain,
% 291.93/188.01 (~((~(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)))))))))))),
% 291.93/188.01 inference(unit_resolution,[status(thm)],[124, 115, 81, 79])).
% 291.93/188.01 tff(126,plain,
% 291.93/188.01 (((~(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))),
% 291.93/188.01 inference(tautology,[status(thm)],[])).
% 291.93/188.01 tff(127,plain,
% 291.93/188.01 (relation_dom(function_inverse(A!16)) = relation_rng(A!16)),
% 291.93/188.01 inference(unit_resolution,[status(thm)],[126, 125])).
% 291.93/188.01 tff(128,plain,
% 291.93/188.01 (relation_rng(A!16) = relation_dom(function_inverse(A!16))),
% 291.93/188.01 inference(symmetry,[status(thm)],[127])).
% 291.93/188.01 tff(129,plain,
% 291.93/188.01 (relation_rng(A!16) = relation_dom(B!17)),
% 291.93/188.01 inference(and_elim,[status(thm)],[21])).
% 291.93/188.01 tff(130,plain,
% 291.93/188.01 (relation_dom(B!17) = relation_rng(A!16)),
% 291.93/188.01 inference(symmetry,[status(thm)],[129])).
% 291.93/188.01 tff(131,plain,
% 291.93/188.01 (relation_dom(B!17) = relation_dom(function_inverse(A!16))),
% 291.93/188.01 inference(transitivity,[status(thm)],[130, 128])).
% 291.93/188.01 tff(132,plain,
% 291.93/188.01 (^[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)))))),
% 291.93/188.01 inference(bind,[status(th)],[])).
% 291.93/188.01 tff(133,plain,
% 291.93/188.01 (![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))))),
% 291.93/188.01 inference(quant_intro,[status(thm)],[132])).
% 291.93/188.01 tff(134,plain,
% 291.93/188.01 (^[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)))))),
% 291.93/188.01 inference(bind,[status(th)],[])).
% 291.93/188.01 tff(135,plain,
% 291.93/188.01 (![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))))),
% 291.93/188.01 inference(quant_intro,[status(thm)],[134])).
% 291.93/188.01 tff(136,plain,
% 291.93/188.01 (![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))))),
% 291.93/188.01 inference(transitivity,[status(thm)],[135, 133])).
% 291.93/188.01 tff(137,plain,
% 291.93/188.01 (^[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))))))),
% 291.93/188.01 inference(bind,[status(th)],[])).
% 291.93/188.01 tff(138,plain,
% 291.93/188.01 (![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))))),
% 291.93/188.01 inference(quant_intro,[status(thm)],[137])).
% 291.93/188.01 tff(139,plain,
% 291.93/188.01 (^[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))))))))),
% 291.93/188.01 inference(bind,[status(th)],[])).
% 291.93/188.01 tff(140,plain,
% 291.93/188.01 (![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)))))))),
% 291.93/188.01 inference(quant_intro,[status(thm)],[139])).
% 291.93/188.01 tff(141,plain,
% 291.93/188.01 (![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)))))))),
% 291.93/188.01 inference(rewrite,[status(thm)],[])).
% 291.93/188.01 tff(142,plain,
% 291.93/188.01 (^[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)))))))))),
% 291.93/188.01 inference(bind,[status(th)],[])).
% 291.93/188.01 tff(143,plain,
% 291.93/188.01 (![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)))))))),
% 291.93/188.01 inference(quant_intro,[status(thm)],[142])).
% 291.93/188.01 tff(144,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/sandbox2/benchmark/theBenchmark.p','t9_funct_1')).
% 291.93/188.01 tff(145,plain,
% 291.93/188.01 (![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)))))))),
% 291.93/188.01 inference(modus_ponens,[status(thm)],[144, 143])).
% 291.93/188.01 tff(146,plain,
% 291.93/188.01 (![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)))))))),
% 291.93/188.01 inference(modus_ponens,[status(thm)],[145, 141])).
% 291.93/188.01 tff(147,plain,(
% 291.93/188.01 ![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))))))))),
% 291.93/188.01 inference(skolemize,[status(sab)],[146])).
% 291.93/188.01 tff(148,plain,
% 291.93/188.01 (![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)))))))),
% 291.93/188.01 inference(modus_ponens,[status(thm)],[147, 140])).
% 291.93/188.01 tff(149,plain,
% 291.93/188.01 (![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))))),
% 291.93/188.01 inference(modus_ponens,[status(thm)],[148, 138])).
% 291.93/188.01 tff(150,plain,
% 291.93/188.01 (![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))))),
% 291.93/188.01 inference(modus_ponens,[status(thm)],[149, 136])).
% 291.93/188.01 tff(151,plain,
% 291.93/188.01 (function(B!17)),
% 291.93/188.01 inference(and_elim,[status(thm)],[21])).
% 291.93/188.01 tff(152,plain,
% 291.93/188.01 (relation(B!17)),
% 291.93/188.01 inference(and_elim,[status(thm)],[21])).
% 291.93/188.01 tff(153,plain,
% 291.93/188.01 (((~![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] : ((~relation(B)) | (~function(B)) | (~(relation_dom(B!17) = relation_dom(B))) | (B!17 = 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))))) | (~relation(B!17)) | (~function(B!17)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~(relation_dom(B!17) = relation_dom(B))) | (B!17 = 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)))))))),
% 291.93/188.01 inference(rewrite,[status(thm)],[])).
% 291.93/188.01 tff(154,plain,
% 291.93/188.01 (((~relation(B!17)) | (~function(B!17)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~(relation_dom(B!17) = relation_dom(B))) | (B!17 = 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!17)) | (~function(B!17)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~(relation_dom(B!17) = relation_dom(B))) | (B!17 = 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)))))))),
% 291.93/188.01 inference(rewrite,[status(thm)],[])).
% 291.93/188.01 tff(155,plain,
% 291.93/188.01 (^[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)) | (~(relation_dom(B!17) = relation_dom(B))) | (B!17 = 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)))))))),
% 291.93/188.01 inference(bind,[status(th)],[])).
% 291.93/188.01 tff(156,plain,
% 291.93/188.01 (![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)) | (~(relation_dom(B!17) = relation_dom(B))) | (B!17 = 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))))))),
% 291.93/188.01 inference(quant_intro,[status(thm)],[155])).
% 291.93/188.01 tff(157,plain,
% 291.93/188.01 (((~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)) | (~(relation_dom(B!17) = relation_dom(B))) | (B!17 = 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)))))))),
% 291.93/188.01 inference(monotonicity,[status(thm)],[156])).
% 291.93/188.01 tff(158,plain,
% 291.93/188.01 (((~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)) | (~(relation_dom(B!17) = relation_dom(B))) | (B!17 = 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)))))))),
% 291.93/188.01 inference(transitivity,[status(thm)],[157, 154])).
% 291.93/188.01 tff(159,plain,
% 291.93/188.01 (((~![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))))) | ((~relation(B!17)) | (~function(B!17)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~(relation_dom(B!17) = relation_dom(B))) | (B!17 = 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))))))))),
% 291.93/188.01 inference(monotonicity,[status(thm)],[158])).
% 291.93/188.01 tff(160,plain,
% 291.93/188.01 (((~![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))))) | (~relation(B!17)) | (~function(B!17)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~(relation_dom(B!17) = relation_dom(B))) | (B!17 = 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)))))))),
% 291.93/188.01 inference(transitivity,[status(thm)],[159, 153])).
% 291.93/188.01 tff(161,plain,
% 291.93/188.01 ((~![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))))),
% 291.93/188.01 inference(quant_inst,[status(thm)],[])).
% 291.93/188.01 tff(162,plain,
% 291.93/188.01 ((~![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] : ((~relation(B)) | (~function(B)) | (~(relation_dom(B!17) = relation_dom(B))) | (B!17 = 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))))))),
% 291.93/188.01 inference(modus_ponens,[status(thm)],[161, 160])).
% 291.93/188.01 tff(163,plain,
% 291.93/188.01 (![B: $i] : ((~relation(B)) | (~function(B)) | (~(relation_dom(B!17) = relation_dom(B))) | (B!17 = 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))))))),
% 291.93/188.01 inference(unit_resolution,[status(thm)],[162, 152, 151, 150])).
% 291.93/188.01 tff(164,plain,
% 291.93/188.01 (~(B!17 = function_inverse(A!16))),
% 291.93/188.01 inference(and_elim,[status(thm)],[21])).
% 291.93/188.01 tff(165,plain,
% 291.93/188.01 (((~![B: $i] : ((~relation(B)) | (~function(B)) | (~(relation_dom(B!17) = relation_dom(B))) | (B!17 = 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)) | (~(relation_dom(B!17) = relation_dom(B))) | (B!17 = 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))))))),
% 291.93/188.01 inference(rewrite,[status(thm)],[])).
% 291.93/188.01 tff(166,plain,
% 291.93/188.01 (((~relation(function_inverse(A!16))) | (~function(function_inverse(A!16))) | (~(relation_dom(B!17) = relation_dom(function_inverse(A!16)))) | (B!17 = 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))))))),
% 291.93/188.02 inference(rewrite,[status(thm)],[])).
% 291.93/188.02 tff(167,plain,
% 291.93/188.02 (((~![B: $i] : ((~relation(B)) | (~function(B)) | (~(relation_dom(B!17) = relation_dom(B))) | (B!17 = 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))) | (~(relation_dom(B!17) = relation_dom(function_inverse(A!16)))) | (B!17 = 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)) | (~(relation_dom(B!17) = relation_dom(B))) | (B!17 = 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)))))))),
% 291.93/188.02 inference(monotonicity,[status(thm)],[166])).
% 291.93/188.02 tff(168,plain,
% 291.93/188.02 (((~![B: $i] : ((~relation(B)) | (~function(B)) | (~(relation_dom(B!17) = relation_dom(B))) | (B!17 = 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))) | (~(relation_dom(B!17) = relation_dom(function_inverse(A!16)))) | (B!17 = 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)) | (~(relation_dom(B!17) = relation_dom(B))) | (B!17 = 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))))))),
% 291.93/188.02 inference(transitivity,[status(thm)],[167, 165])).
% 291.93/188.02 tff(169,plain,
% 291.93/188.02 ((~![B: $i] : ((~relation(B)) | (~function(B)) | (~(relation_dom(B!17) = relation_dom(B))) | (B!17 = 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))) | (~(relation_dom(B!17) = relation_dom(function_inverse(A!16)))) | (B!17 = 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))))))),
% 291.93/188.02 inference(quant_inst,[status(thm)],[])).
% 291.93/188.02 tff(170,plain,
% 291.93/188.02 ((~![B: $i] : ((~relation(B)) | (~function(B)) | (~(relation_dom(B!17) = relation_dom(B))) | (B!17 = 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)))))),
% 291.93/188.02 inference(modus_ponens,[status(thm)],[169, 168])).
% 291.93/188.02 tff(171,plain,
% 291.93/188.02 ((~(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)))))),
% 291.93/188.02 inference(unit_resolution,[status(thm)],[170, 164, 163, 81, 79])).
% 291.93/188.02 tff(172,plain,
% 291.93/188.02 (~((~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))))),
% 291.93/188.02 inference(unit_resolution,[status(thm)],[171, 131])).
% 291.93/188.02 tff(173,plain,
% 291.93/188.02 (((~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))),
% 291.93/188.02 inference(tautology,[status(thm)],[])).
% 291.93/188.02 tff(174,plain,
% 291.93/188.02 (in(tptp_fun_C_18(function_inverse(A!16), B!17), relation_dom(B!17))),
% 291.93/188.02 inference(unit_resolution,[status(thm)],[173, 172])).
% 291.93/188.02 tff(175,plain,
% 291.93/188.02 (in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_dom(B!17))),
% 291.93/188.02 inference(modus_ponens,[status(thm)],[174, 60])).
% 291.93/188.02 tff(176,plain,
% 291.93/188.02 ((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))))),
% 291.93/188.02 inference(commutativity,[status(thm)],[])).
% 291.93/188.02 tff(177,plain,
% 291.93/188.02 ((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))),
% 291.93/188.02 inference(symmetry,[status(thm)],[176])).
% 291.93/188.02 tff(178,plain,
% 291.93/188.02 (((~(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)))))))))),
% 291.93/188.02 inference(tautology,[status(thm)],[])).
% 291.93/188.02 tff(179,plain,
% 291.93/188.02 (![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)))))))))),
% 291.93/188.02 inference(unit_resolution,[status(thm)],[178, 125])).
% 291.93/188.02 tff(180,plain,
% 291.93/188.02 (((~![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))))))))))))),
% 291.93/188.02 inference(rewrite,[status(thm)],[])).
% 291.93/188.02 tff(181,plain,
% 291.93/188.02 ((~((~((~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)))))))))))),
% 291.93/188.02 inference(rewrite,[status(thm)],[])).
% 291.93/188.02 tff(182,plain,
% 291.93/188.02 (((~![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))))))))))))),
% 291.93/188.02 inference(monotonicity,[status(thm)],[181])).
% 291.93/188.02 tff(183,plain,
% 291.93/188.02 (((~![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))))))))))))),
% 291.93/188.02 inference(transitivity,[status(thm)],[182, 180])).
% 291.93/188.02 tff(184,plain,
% 291.93/188.02 ((~![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)))))))))))),
% 291.93/188.02 inference(quant_inst,[status(thm)],[])).
% 291.93/188.02 tff(185,plain,
% 291.93/188.02 ((~![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)))))))))))),
% 291.93/188.02 inference(modus_ponens,[status(thm)],[184, 183])).
% 291.93/188.02 tff(186,plain,
% 291.93/188.02 (~((~(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))))))))))),
% 291.93/188.02 inference(unit_resolution,[status(thm)],[185, 179])).
% 291.93/188.02 tff(187,plain,
% 291.93/188.02 (((~(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))))))))),
% 291.93/188.02 inference(tautology,[status(thm)],[])).
% 291.93/188.02 tff(188,plain,
% 291.93/188.02 ((~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)))))))),
% 291.93/188.02 inference(unit_resolution,[status(thm)],[187, 186])).
% 291.93/188.02 tff(189,plain,
% 291.93/188.02 (((~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))),
% 291.93/188.02 inference(tautology,[status(thm)],[])).
% 291.93/188.02 tff(190,plain,
% 291.93/188.02 (in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))),
% 291.93/188.02 inference(unit_resolution,[status(thm)],[189, 55])).
% 291.93/188.02 tff(191,plain,
% 291.93/188.02 ((~((~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)))))))),
% 291.93/188.02 inference(tautology,[status(thm)],[])).
% 291.93/188.02 tff(192,plain,
% 291.93/188.02 ((~((~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)))))))),
% 291.93/188.02 inference(unit_resolution,[status(thm)],[191, 190])).
% 291.93/188.02 tff(193,plain,
% 291.93/188.02 (~((~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))))))),
% 291.93/188.02 inference(unit_resolution,[status(thm)],[192, 188])).
% 291.93/188.02 tff(194,plain,
% 291.93/188.02 (((~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))))),
% 291.93/188.02 inference(tautology,[status(thm)],[])).
% 291.93/188.02 tff(195,plain,
% 291.93/188.02 (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)))),
% 291.93/188.02 inference(unit_resolution,[status(thm)],[194, 193])).
% 291.93/188.02 tff(196,plain,
% 291.93/188.02 (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)),
% 291.93/188.02 inference(symmetry,[status(thm)],[195])).
% 291.93/188.02 tff(197,plain,
% 291.93/188.02 (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)))),
% 291.93/188.02 inference(monotonicity,[status(thm)],[57])).
% 291.93/188.02 tff(198,plain,
% 291.93/188.02 (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)),
% 291.93/188.02 inference(transitivity,[status(thm)],[197, 196])).
% 291.93/188.02 tff(199,plain,
% 291.93/188.02 (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))),
% 291.93/188.02 inference(monotonicity,[status(thm)],[58])).
% 291.93/188.02 tff(200,plain,
% 291.93/188.02 (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)))),
% 291.93/188.02 inference(symmetry,[status(thm)],[199])).
% 291.93/188.02 tff(201,plain,
% 291.93/188.02 ((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))),
% 291.93/188.02 inference(monotonicity,[status(thm)],[200, 198])).
% 291.93/188.02 tff(202,plain,
% 291.93/188.02 ((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))))),
% 291.93/188.02 inference(transitivity,[status(thm)],[201, 176])).
% 291.93/188.02 tff(203,plain,
% 291.93/188.02 ((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))),
% 291.93/188.02 inference(transitivity,[status(thm)],[202, 177])).
% 291.93/188.02 tff(204,plain,
% 291.93/188.02 ((~(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)))),
% 291.93/188.02 inference(monotonicity,[status(thm)],[203])).
% 291.93/188.02 tff(205,plain,
% 291.93/188.02 (((~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))))),
% 291.93/188.02 inference(tautology,[status(thm)],[])).
% 291.93/188.02 tff(206,plain,
% 291.93/188.02 (~(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)))),
% 291.93/188.02 inference(unit_resolution,[status(thm)],[205, 172])).
% 291.93/188.02 tff(207,plain,
% 291.93/188.02 (~(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))),
% 291.93/188.02 inference(modus_ponens,[status(thm)],[206, 204])).
% 291.93/188.02 tff(208,plain,
% 291.93/188.02 (^[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)))))),
% 291.93/188.02 inference(bind,[status(th)],[])).
% 291.93/188.02 tff(209,plain,
% 291.93/188.02 (![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))))),
% 291.93/188.02 inference(quant_intro,[status(thm)],[208])).
% 291.93/188.02 tff(210,plain,
% 291.93/188.02 (^[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))))))),
% 291.93/188.02 inference(bind,[status(th)],[])).
% 291.93/188.02 tff(211,plain,
% 291.93/188.02 (![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))))),
% 291.93/188.02 inference(quant_intro,[status(thm)],[210])).
% 291.93/188.02 tff(212,plain,
% 291.93/188.02 (![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)))),
% 291.93/188.02 inference(and_elim,[status(thm)],[21])).
% 291.93/188.02 tff(213,plain,
% 291.93/188.02 (![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))))),
% 291.93/188.02 inference(modus_ponens,[status(thm)],[212, 211])).
% 291.93/188.02 tff(214,plain,
% 291.93/188.02 (![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))))),
% 291.93/188.02 inference(modus_ponens,[status(thm)],[213, 209])).
% 291.93/188.02 tff(215,plain,
% 291.93/188.02 (((~![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: $i] : (((apply(A!16, C) = D) <=> (apply(B!17, D) = C)) | (~in(C, relation_dom(A!16))) | (~in(D, relation_dom(B!17))))) | (~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_dom(B!17))) | (apply(B!17, apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) = tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))),
% 291.93/188.03 inference(rewrite,[status(thm)],[])).
% 291.93/188.03 tff(216,plain,
% 291.93/188.03 (((apply(B!17, apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) = tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)) | (~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_dom(B!17)))) <=> ((~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_dom(B!17))) | (apply(B!17, apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) = tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)))),
% 291.93/188.03 inference(rewrite,[status(thm)],[])).
% 291.93/188.03 tff(217,plain,
% 291.93/188.03 (($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))),
% 291.93/188.03 inference(rewrite,[status(thm)],[])).
% 291.93/188.03 tff(218,plain,
% 291.93/188.03 ((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))) <=> $true),
% 291.93/188.03 inference(rewrite,[status(thm)],[])).
% 291.93/188.03 tff(219,plain,
% 291.93/188.03 (((apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)) = apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) <=> (apply(B!17, apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) = tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) <=> ($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)))),
% 291.93/188.03 inference(monotonicity,[status(thm)],[218])).
% 291.93/188.03 tff(220,plain,
% 291.93/188.03 (((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))),
% 291.93/188.03 inference(transitivity,[status(thm)],[219, 217])).
% 291.93/188.03 tff(221,plain,
% 291.93/188.03 ((((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))))),
% 291.93/188.03 inference(monotonicity,[status(thm)],[220])).
% 291.93/188.03 tff(222,plain,
% 291.93/188.03 ((((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)))),
% 291.93/188.03 inference(transitivity,[status(thm)],[221, 216])).
% 291.93/188.03 tff(223,plain,
% 291.93/188.03 (((~![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))))),
% 291.93/188.03 inference(monotonicity,[status(thm)],[222])).
% 291.93/188.03 tff(224,plain,
% 291.93/188.03 (((~![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)))),
% 291.93/188.03 inference(transitivity,[status(thm)],[223, 215])).
% 291.93/188.03 tff(225,plain,
% 291.93/188.03 ((~![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))))),
% 291.93/188.03 inference(quant_inst,[status(thm)],[])).
% 291.93/188.03 tff(226,plain,
% 291.93/188.03 ((~![C: $i, D: $i] : (((apply(A!16, C) = D) <=> (apply(B!17, D) = C)) | (~in(C, relation_dom(A!16))) | (~in(D, relation_dom(B!17))))) | (~in(tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16), relation_dom(A!16))) | (~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_dom(B!17))) | (apply(B!17, apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) = tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))),
% 291.93/188.03 inference(modus_ponens,[status(thm)],[225, 224])).
% 291.93/188.03 tff(227,plain,
% 291.93/188.03 ((~in(apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16)), relation_dom(B!17))) | (apply(B!17, apply(A!16, tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))) = tptp_fun_D_0(tptp_fun_C_18(function_inverse(A!16), B!17), A!16))),
% 291.93/188.03 inference(unit_resolution,[status(thm)],[226, 214, 190])).
% 291.93/188.03 tff(228,plain,
% 291.93/188.03 ($false),
% 291.93/188.03 inference(unit_resolution,[status(thm)],[227, 207, 175])).
% 291.93/188.03 tff(229,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,[]))).
% 291.93/188.03 tff(230,plain,
% 291.93/188.03 ((~((~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))))))),
% 291.93/188.03 inference(tautology,[status(thm)],[])).
% 291.93/188.03 tff(231,plain,
% 291.93/188.03 (~((~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)))))))),
% 291.93/188.03 inference(unit_resolution,[status(thm)],[230, 174, 229])).
% 291.93/188.03 tff(232,plain,
% 291.93/188.03 (((~((~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)))))))),
% 291.93/188.03 inference(tautology,[status(thm)],[])).
% 291.93/188.03 tff(233,plain,
% 291.93/188.03 ((~((~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))))))),
% 291.93/188.03 inference(unit_resolution,[status(thm)],[232, 231])).
% 291.93/188.03 tff(234,plain,
% 291.93/188.03 ((~((~(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))))))))),
% 291.93/188.03 inference(tautology,[status(thm)],[])).
% 291.93/188.03 tff(235,plain,
% 291.93/188.03 (~((~(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)))))))))),
% 291.93/188.03 inference(unit_resolution,[status(thm)],[234, 130, 233])).
% 291.93/188.03 tff(236,plain,
% 291.93/188.03 (((~((~(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)))))))))),
% 291.93/188.03 inference(tautology,[status(thm)],[])).
% 291.93/188.03 tff(237,plain,
% 291.93/188.03 ((~((~(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))))))))))),
% 292.03/188.09 inference(unit_resolution,[status(thm)],[236, 235])).
% 292.03/188.09 tff(238,plain,
% 292.03/188.09 ($false),
% 292.03/188.09 inference(unit_resolution,[status(thm)],[237, 54])).
% 292.03/188.09 % SZS output end Proof
%------------------------------------------------------------------------------