%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SEU023+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n006.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   : Theorem 3.72s 2.63s
% Output   : Proof 3.81s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SEU023+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33  % Computer : n006.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Sat Sep  3 09:00:38 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.33  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33  Usage: tptp [options] [-file:]file
% 0.12/0.33    -h, -?       prints this message.
% 0.12/0.33    -smt2        print SMT-LIB2 benchmark.
% 0.12/0.33    -m, -model   generate model.
% 0.12/0.33    -p, -proof   generate proof.
% 0.12/0.33    -c, -core    generate unsat core of named formulas.
% 0.12/0.33    -st, -statistics display statistics.
% 0.12/0.33    -t:timeout   set timeout (in second).
% 0.12/0.33    -smt2status  display status in smt2 format instead of SZS.
% 0.12/0.33    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33    -<param>:<value> configuration parameter and value.
% 0.12/0.33    -o:<output-file> file to place output in.
% 3.72/2.63  % SZS status Theorem
% 3.72/2.63  % SZS output start Proof
% 3.72/2.63  tff(apply_type, type, (
% 3.72/2.63     apply: ( $i * $i ) > $i)).
% 3.72/2.63  tff(tptp_fun_A_14_type, type, (
% 3.72/2.63     tptp_fun_A_14: $i)).
% 3.72/2.63  tff(tptp_fun_B_13_type, type, (
% 3.72/2.63     tptp_fun_B_13: $i)).
% 3.72/2.63  tff(function_inverse_type, type, (
% 3.72/2.63     function_inverse: $i > $i)).
% 3.72/2.63  tff(relation_composition_type, type, (
% 3.72/2.63     relation_composition: ( $i * $i ) > $i)).
% 3.72/2.63  tff(relation_type, type, (
% 3.72/2.63     relation: $i > $o)).
% 3.72/2.63  tff(function_type, type, (
% 3.72/2.63     function: $i > $o)).
% 3.72/2.63  tff(in_type, type, (
% 3.72/2.63     in: ( $i * $i ) > $o)).
% 3.72/2.63  tff(relation_dom_type, type, (
% 3.72/2.63     relation_dom: $i > $i)).
% 3.72/2.63  tff(one_to_one_type, type, (
% 3.72/2.63     one_to_one: $i > $o)).
% 3.72/2.63  tff(relation_rng_type, type, (
% 3.72/2.63     relation_rng: $i > $i)).
% 3.72/2.63  tff(tptp_fun_C_12_type, type, (
% 3.72/2.63     tptp_fun_C_12: ( $i * $i ) > $i)).
% 3.72/2.63  tff(tptp_fun_D_11_type, type, (
% 3.72/2.63     tptp_fun_D_11: ( $i * $i ) > $i)).
% 3.72/2.63  tff(1,plain,
% 3.72/2.63      ((~(((A!14 = apply(function_inverse(B!13), apply(B!13, A!14))) & (A!14 = apply(relation_composition(B!13, function_inverse(B!13)), A!14))) | (~(relation(B!13) & function(B!13))) | (~(one_to_one(B!13) & in(A!14, relation_dom(B!13)))))) <=> (~(((A!14 = apply(function_inverse(B!13), apply(B!13, A!14))) & (A!14 = apply(relation_composition(B!13, function_inverse(B!13)), A!14))) | (~(relation(B!13) & function(B!13))) | (~(one_to_one(B!13) & in(A!14, relation_dom(B!13))))))),
% 3.72/2.63      inference(rewrite,[status(thm)],[])).
% 3.72/2.63  tff(2,plain,
% 3.72/2.63      ((~![A: $i, B: $i] : (((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_dom(B)))))) <=> (~![A: $i, B: $i] : (((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_dom(B))))))),
% 3.72/2.63      inference(rewrite,[status(thm)],[])).
% 3.72/2.63  tff(3,plain,
% 3.72/2.63      ((~![A: $i, B: $i] : ((relation(B) & function(B)) => ((one_to_one(B) & in(A, relation_dom(B))) => ((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A)))))) <=> (~![A: $i, B: $i] : (((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_dom(B))))))),
% 3.72/2.63      inference(rewrite,[status(thm)],[])).
% 3.72/2.63  tff(4,axiom,(~![A: $i, B: $i] : ((relation(B) & function(B)) => ((one_to_one(B) & in(A, relation_dom(B))) => ((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t56_funct_1')).
% 3.72/2.63  tff(5,plain,
% 3.72/2.63      (~![A: $i, B: $i] : (((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_dom(B)))))),
% 3.72/2.63      inference(modus_ponens,[status(thm)],[4, 3])).
% 3.72/2.63  tff(6,plain,
% 3.72/2.63      (~![A: $i, B: $i] : (((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_dom(B)))))),
% 3.72/2.63      inference(modus_ponens,[status(thm)],[5, 2])).
% 3.72/2.63  tff(7,plain,
% 3.72/2.63      (~![A: $i, B: $i] : (((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_dom(B)))))),
% 3.72/2.63      inference(modus_ponens,[status(thm)],[6, 2])).
% 3.72/2.63  tff(8,plain,
% 3.72/2.63      (~![A: $i, B: $i] : (((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_dom(B)))))),
% 3.72/2.63      inference(modus_ponens,[status(thm)],[7, 2])).
% 3.72/2.63  tff(9,plain,
% 3.72/2.63      (~![A: $i, B: $i] : (((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_dom(B)))))),
% 3.72/2.63      inference(modus_ponens,[status(thm)],[8, 2])).
% 3.72/2.63  tff(10,plain,
% 3.72/2.63      (~![A: $i, B: $i] : (((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_dom(B)))))),
% 3.72/2.63      inference(modus_ponens,[status(thm)],[9, 2])).
% 3.72/2.63  tff(11,plain,
% 3.72/2.63      (~![A: $i, B: $i] : (((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_dom(B)))))),
% 3.72/2.63      inference(modus_ponens,[status(thm)],[10, 2])).
% 3.72/2.63  tff(12,plain,(
% 3.72/2.63      ~(((A!14 = apply(function_inverse(B!13), apply(B!13, A!14))) & (A!14 = apply(relation_composition(B!13, function_inverse(B!13)), A!14))) | (~(relation(B!13) & function(B!13))) | (~(one_to_one(B!13) & in(A!14, relation_dom(B!13)))))),
% 3.72/2.63      inference(skolemize,[status(sab)],[11])).
% 3.72/2.63  tff(13,plain,
% 3.72/2.63      (~(((A!14 = apply(function_inverse(B!13), apply(B!13, A!14))) & (A!14 = apply(relation_composition(B!13, function_inverse(B!13)), A!14))) | (~(relation(B!13) & function(B!13))) | (~(one_to_one(B!13) & in(A!14, relation_dom(B!13)))))),
% 3.72/2.63      inference(modus_ponens,[status(thm)],[12, 1])).
% 3.72/2.63  tff(14,plain,
% 3.72/2.63      (relation(B!13) & function(B!13)),
% 3.72/2.63      inference(or_elim,[status(thm)],[13])).
% 3.72/2.63  tff(15,plain,
% 3.72/2.63      (function(B!13)),
% 3.72/2.63      inference(and_elim,[status(thm)],[14])).
% 3.72/2.63  tff(16,plain,
% 3.72/2.63      (relation(B!13)),
% 3.72/2.63      inference(and_elim,[status(thm)],[14])).
% 3.72/2.63  tff(17,plain,
% 3.72/2.63      (^[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)))))))),
% 3.72/2.63      inference(bind,[status(th)],[])).
% 3.72/2.63  tff(18,plain,
% 3.72/2.63      (![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))))))),
% 3.72/2.63      inference(quant_intro,[status(thm)],[17])).
% 3.72/2.63  tff(19,plain,
% 3.72/2.63      (^[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))))))))),
% 3.72/2.63      inference(bind,[status(th)],[])).
% 3.72/2.63  tff(20,plain,
% 3.72/2.63      (![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))))))),
% 3.72/2.63      inference(quant_intro,[status(thm)],[19])).
% 3.72/2.63  tff(21,plain,
% 3.72/2.63      (![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))))),
% 3.72/2.63      inference(rewrite,[status(thm)],[])).
% 3.72/2.63  tff(22,plain,
% 3.72/2.63      (^[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)))))),
% 3.72/2.63      inference(bind,[status(th)],[])).
% 3.72/2.63  tff(23,plain,
% 3.72/2.63      (![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))))),
% 3.72/2.63      inference(quant_intro,[status(thm)],[22])).
% 3.72/2.63  tff(24,axiom,(![A: $i] : ((relation(A) & function(A)) => (relation(function_inverse(A)) & function(function_inverse(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k2_funct_1')).
% 3.72/2.63  tff(25,plain,
% 3.72/2.63      (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 3.72/2.63      inference(modus_ponens,[status(thm)],[24, 23])).
% 3.72/2.63  tff(26,plain,
% 3.72/2.63      (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 3.72/2.63      inference(modus_ponens,[status(thm)],[25, 21])).
% 3.72/2.63  tff(27,plain,(
% 3.72/2.63      ![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 3.72/2.63      inference(skolemize,[status(sab)],[26])).
% 3.72/2.63  tff(28,plain,
% 3.72/2.63      (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 3.72/2.63      inference(modus_ponens,[status(thm)],[27, 20])).
% 3.72/2.63  tff(29,plain,
% 3.72/2.63      (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 3.72/2.63      inference(modus_ponens,[status(thm)],[28, 18])).
% 3.72/2.63  tff(30,plain,
% 3.72/2.63      (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | ((~relation(B!13)) | (~function(B!13)) | (~((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | (~relation(B!13)) | (~function(B!13)) | (~((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))))))),
% 3.72/2.63      inference(rewrite,[status(thm)],[])).
% 3.72/2.63  tff(31,plain,
% 3.72/2.63      ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | ((~relation(B!13)) | (~function(B!13)) | (~((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))))))),
% 3.72/2.63      inference(quant_inst,[status(thm)],[])).
% 3.72/2.63  tff(32,plain,
% 3.72/2.63      ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | (~relation(B!13)) | (~function(B!13)) | (~((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13)))))),
% 3.72/2.63      inference(modus_ponens,[status(thm)],[31, 30])).
% 3.72/2.63  tff(33,plain,
% 3.72/2.63      (~((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))))),
% 3.72/2.63      inference(unit_resolution,[status(thm)],[32, 29, 16, 15])).
% 3.72/2.63  tff(34,plain,
% 3.72/2.63      (((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13)))) | relation(function_inverse(B!13))),
% 3.72/2.63      inference(tautology,[status(thm)],[])).
% 3.72/2.63  tff(35,plain,
% 3.72/2.63      (relation(function_inverse(B!13))),
% 3.72/2.63      inference(unit_resolution,[status(thm)],[34, 33])).
% 3.72/2.63  tff(36,plain,
% 3.72/2.63      (((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13)))) | function(function_inverse(B!13))),
% 3.72/2.63      inference(tautology,[status(thm)],[])).
% 3.72/2.63  tff(37,plain,
% 3.72/2.63      (function(function_inverse(B!13))),
% 3.72/2.63      inference(unit_resolution,[status(thm)],[36, 33])).
% 3.72/2.63  tff(38,plain,
% 3.72/2.63      (^[A: $i, B: $i] : refl(((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))))),
% 3.72/2.63      inference(bind,[status(th)],[])).
% 3.72/2.63  tff(39,plain,
% 3.72/2.63      (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))),
% 3.72/2.63      inference(quant_intro,[status(thm)],[38])).
% 3.72/2.63  tff(40,plain,
% 3.72/2.63      (^[A: $i, B: $i] : rewrite(((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))))),
% 3.72/2.63      inference(bind,[status(th)],[])).
% 3.72/2.63  tff(41,plain,
% 3.72/2.63      (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))),
% 3.72/2.63      inference(quant_intro,[status(thm)],[40])).
% 3.72/2.63  tff(42,plain,
% 3.72/2.63      (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))),
% 3.72/2.63      inference(transitivity,[status(thm)],[41, 39])).
% 3.72/2.63  tff(43,plain,
% 3.72/2.63      (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(B) & function(B)) <=> (~((~relation(B)) | (~function(B))))), ((~(relation(B) & function(B))) <=> (~(~((~relation(B)) | (~function(B))))))), rewrite((~(~((~relation(B)) | (~function(B))))) <=> ((~relation(B)) | (~function(B)))), ((~(relation(B) & function(B))) <=> ((~relation(B)) | (~function(B))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(C) & function(C)) <=> (~((~relation(C)) | (~function(C))))), ((~(relation(C) & function(C))) <=> (~(~((~relation(C)) | (~function(C))))))), rewrite((~(~((~relation(C)) | (~function(C))))) <=> ((~relation(C)) | (~function(C)))), ((~(relation(C) & function(C))) <=> ((~relation(C)) | (~function(C))))), (((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | ((~relation(C)) | (~function(C))) | (~in(A, relation_dom(B)))))), rewrite(((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | ((~relation(C)) | (~function(C))) | (~in(A, relation_dom(B)))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))), (((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))))), (![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))) <=> ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))), (((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))) <=> (((~relation(B)) | (~function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))))), rewrite((((~relation(B)) | (~function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))), (((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))))),
% 3.72/2.63      inference(bind,[status(th)],[])).
% 3.72/2.63  tff(44,plain,
% 3.72/2.63      (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))),
% 3.72/2.63      inference(quant_intro,[status(thm)],[43])).
% 3.72/2.63  tff(45,plain,
% 3.72/2.63      (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))),
% 3.72/2.63      inference(rewrite,[status(thm)],[])).
% 3.72/2.63  tff(46,plain,
% 3.72/2.63      (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A)))) <=> ((~in(A, relation_dom(B))) | (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))), (((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))) <=> ((relation(C) & function(C)) => ((~in(A, relation_dom(B))) | (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))))), rewrite(((relation(C) & function(C)) => ((~in(A, relation_dom(B))) | (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))), (((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))))), (![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))) <=> ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))), (((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A)))))) <=> ((relation(B) & function(B)) => ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))))), rewrite(((relation(B) & function(B)) => ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))) <=> ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))), (((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A)))))) <=> ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))))),
% 3.72/2.63      inference(bind,[status(th)],[])).
% 3.72/2.63  tff(47,plain,
% 3.72/2.63      (![A: $i, B: $i] : ((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A)))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))),
% 3.72/2.63      inference(quant_intro,[status(thm)],[46])).
% 3.72/2.63  tff(48,axiom,(![A: $i, B: $i] : ((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t23_funct_1')).
% 3.72/2.63  tff(49,plain,
% 3.72/2.63      (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))),
% 3.72/2.63      inference(modus_ponens,[status(thm)],[48, 47])).
% 3.72/2.63  tff(50,plain,
% 3.72/2.63      (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))),
% 3.72/2.63      inference(modus_ponens,[status(thm)],[49, 45])).
% 3.72/2.63  tff(51,plain,(
% 3.72/2.63      ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))),
% 3.72/2.63      inference(skolemize,[status(sab)],[50])).
% 3.72/2.63  tff(52,plain,
% 3.72/2.63      (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))),
% 3.72/2.63      inference(modus_ponens,[status(thm)],[51, 44])).
% 3.72/2.63  tff(53,plain,
% 3.72/2.63      (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))),
% 3.72/2.63      inference(modus_ponens,[status(thm)],[52, 42])).
% 3.72/2.63  tff(54,plain,
% 3.72/2.63      (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~relation(B!13)) | (~function(B!13)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14)))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | (~relation(B!13)) | (~function(B!13)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14)))))),
% 3.72/2.63      inference(rewrite,[status(thm)],[])).
% 3.72/2.63  tff(55,plain,
% 3.72/2.63      (((~relation(B!13)) | (~function(B!13)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14))))) <=> ((~relation(B!13)) | (~function(B!13)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14)))))),
% 3.72/2.63      inference(rewrite,[status(thm)],[])).
% 3.72/2.63  tff(56,plain,
% 3.72/2.63      (^[C: $i] : rewrite(((apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14))) | (~in(A!14, relation_dom(B!13))) | (~relation(C)) | (~function(C))) <=> ((~relation(C)) | (~function(C)) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14)))))),
% 3.72/2.63      inference(bind,[status(th)],[])).
% 3.72/2.63  tff(57,plain,
% 3.72/2.63      (![C: $i] : ((apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14))) | (~in(A!14, relation_dom(B!13))) | (~relation(C)) | (~function(C))) <=> ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14))))),
% 3.72/2.63      inference(quant_intro,[status(thm)],[56])).
% 3.72/2.63  tff(58,plain,
% 3.72/2.63      (((~relation(B!13)) | (~function(B!13)) | ![C: $i] : ((apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14))) | (~in(A!14, relation_dom(B!13))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B!13)) | (~function(B!13)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14)))))),
% 3.72/2.63      inference(monotonicity,[status(thm)],[57])).
% 3.72/2.63  tff(59,plain,
% 3.72/2.63      (((~relation(B!13)) | (~function(B!13)) | ![C: $i] : ((apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14))) | (~in(A!14, relation_dom(B!13))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B!13)) | (~function(B!13)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14)))))),
% 3.72/2.63      inference(transitivity,[status(thm)],[58, 55])).
% 3.72/2.63  tff(60,plain,
% 3.72/2.63      (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~relation(B!13)) | (~function(B!13)) | ![C: $i] : ((apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14))) | (~in(A!14, relation_dom(B!13))) | (~relation(C)) | (~function(C))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~relation(B!13)) | (~function(B!13)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14))))))),
% 3.72/2.63      inference(monotonicity,[status(thm)],[59])).
% 3.72/2.63  tff(61,plain,
% 3.72/2.63      (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~relation(B!13)) | (~function(B!13)) | ![C: $i] : ((apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14))) | (~in(A!14, relation_dom(B!13))) | (~relation(C)) | (~function(C))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | (~relation(B!13)) | (~function(B!13)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14)))))),
% 3.72/2.63      inference(transitivity,[status(thm)],[60, 54])).
% 3.72/2.63  tff(62,plain,
% 3.72/2.63      ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~relation(B!13)) | (~function(B!13)) | ![C: $i] : ((apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14))) | (~in(A!14, relation_dom(B!13))) | (~relation(C)) | (~function(C))))),
% 3.72/2.63      inference(quant_inst,[status(thm)],[])).
% 3.72/2.63  tff(63,plain,
% 3.72/2.63      ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | (~relation(B!13)) | (~function(B!13)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14))))),
% 3.72/2.63      inference(modus_ponens,[status(thm)],[62, 61])).
% 3.72/2.63  tff(64,plain,
% 3.72/2.63      (![C: $i] : ((~relation(C)) | (~function(C)) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14))))),
% 3.72/2.63      inference(unit_resolution,[status(thm)],[63, 53, 16, 15])).
% 3.72/2.63  tff(65,plain,
% 3.72/2.63      (one_to_one(B!13) & in(A!14, relation_dom(B!13))),
% 3.72/2.63      inference(or_elim,[status(thm)],[13])).
% 3.72/2.63  tff(66,plain,
% 3.72/2.63      (in(A!14, relation_dom(B!13))),
% 3.72/2.63      inference(and_elim,[status(thm)],[65])).
% 3.72/2.63  tff(67,plain,
% 3.72/2.63      (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14))))) | ((~in(A!14, relation_dom(B!13))) | (~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (apply(relation_composition(B!13, function_inverse(B!13)), A!14) = apply(function_inverse(B!13), apply(B!13, A!14))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14))))) | (~in(A!14, relation_dom(B!13))) | (~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (apply(relation_composition(B!13, function_inverse(B!13)), A!14) = apply(function_inverse(B!13), apply(B!13, A!14))))),
% 3.72/2.64      inference(rewrite,[status(thm)],[])).
% 3.72/2.64  tff(68,plain,
% 3.72/2.64      (((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, function_inverse(B!13)), A!14) = apply(function_inverse(B!13), apply(B!13, A!14)))) <=> ((~in(A!14, relation_dom(B!13))) | (~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (apply(relation_composition(B!13, function_inverse(B!13)), A!14) = apply(function_inverse(B!13), apply(B!13, A!14))))),
% 3.72/2.64      inference(rewrite,[status(thm)],[])).
% 3.72/2.64  tff(69,plain,
% 3.72/2.64      (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14))))) | ((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, function_inverse(B!13)), A!14) = apply(function_inverse(B!13), apply(B!13, A!14))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14))))) | ((~in(A!14, relation_dom(B!13))) | (~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (apply(relation_composition(B!13, function_inverse(B!13)), A!14) = apply(function_inverse(B!13), apply(B!13, A!14)))))),
% 3.72/2.64      inference(monotonicity,[status(thm)],[68])).
% 3.72/2.64  tff(70,plain,
% 3.72/2.64      (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14))))) | ((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, function_inverse(B!13)), A!14) = apply(function_inverse(B!13), apply(B!13, A!14))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14))))) | (~in(A!14, relation_dom(B!13))) | (~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (apply(relation_composition(B!13, function_inverse(B!13)), A!14) = apply(function_inverse(B!13), apply(B!13, A!14))))),
% 3.72/2.64      inference(transitivity,[status(thm)],[69, 67])).
% 3.72/2.64  tff(71,plain,
% 3.72/2.64      ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14))))) | ((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, function_inverse(B!13)), A!14) = apply(function_inverse(B!13), apply(B!13, A!14))))),
% 3.72/2.64      inference(quant_inst,[status(thm)],[])).
% 3.72/2.64  tff(72,plain,
% 3.72/2.64      ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(A!14, relation_dom(B!13))) | (apply(relation_composition(B!13, C), A!14) = apply(C, apply(B!13, A!14))))) | (~in(A!14, relation_dom(B!13))) | (~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (apply(relation_composition(B!13, function_inverse(B!13)), A!14) = apply(function_inverse(B!13), apply(B!13, A!14)))),
% 3.72/2.64      inference(modus_ponens,[status(thm)],[71, 70])).
% 3.72/2.64  tff(73,plain,
% 3.72/2.64      ((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (apply(relation_composition(B!13, function_inverse(B!13)), A!14) = apply(function_inverse(B!13), apply(B!13, A!14)))),
% 3.72/2.64      inference(unit_resolution,[status(thm)],[72, 66, 64])).
% 3.72/2.64  tff(74,plain,
% 3.72/2.64      (apply(relation_composition(B!13, function_inverse(B!13)), A!14) = apply(function_inverse(B!13), apply(B!13, A!14))),
% 3.72/2.64      inference(unit_resolution,[status(thm)],[73, 37, 35])).
% 3.72/2.64  tff(75,plain,
% 3.72/2.64      ((A!14 = apply(relation_composition(B!13, function_inverse(B!13)), A!14)) <=> (A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))),
% 3.72/2.64      inference(monotonicity,[status(thm)],[74])).
% 3.72/2.64  tff(76,plain,
% 3.72/2.64      ((~(A!14 = apply(relation_composition(B!13, function_inverse(B!13)), A!14))) <=> (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14))))),
% 3.72/2.64      inference(monotonicity,[status(thm)],[75])).
% 3.72/2.64  tff(77,assumption,(~(A!14 = apply(relation_composition(B!13, function_inverse(B!13)), A!14))), introduced(assumption)).
% 3.72/2.64  tff(78,plain,
% 3.72/2.64      (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))),
% 3.72/2.64      inference(modus_ponens,[status(thm)],[77, 76])).
% 3.72/2.64  tff(79,plain,
% 3.72/2.64      (((~in(apply(B!13, A!14), relation_rng(B!13))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14))))) | (A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))),
% 3.72/2.64      inference(tautology,[status(thm)],[])).
% 3.72/2.64  tff(80,plain,
% 3.72/2.64      ((~in(apply(B!13, A!14), relation_rng(B!13))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14))))),
% 3.72/2.64      inference(unit_resolution,[status(thm)],[79, 78])).
% 3.72/2.64  tff(81,plain,
% 3.72/2.64      ((~((~in(A!14, relation_dom(B!13))) | (~((~in(apply(B!13, A!14), relation_rng(B!13))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))))))) | (~in(A!14, relation_dom(B!13))) | (~((~in(apply(B!13, A!14), relation_rng(B!13))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14))))))),
% 3.72/2.64      inference(tautology,[status(thm)],[])).
% 3.72/2.64  tff(82,plain,
% 3.72/2.64      (~((~in(A!14, relation_dom(B!13))) | (~((~in(apply(B!13, A!14), relation_rng(B!13))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))))))),
% 3.72/2.64      inference(unit_resolution,[status(thm)],[81, 66, 80])).
% 3.72/2.64  tff(83,plain,
% 3.72/2.64      (((~(in(A!14, relation_dom(B!13)) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))) | (~in(apply(B!13, A!14), relation_rng(B!13))))) | (~((~in(A!14, relation_dom(B!13))) | (~((~in(apply(B!13, A!14), relation_rng(B!13))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14))))))))) | ((~in(A!14, relation_dom(B!13))) | (~((~in(apply(B!13, A!14), relation_rng(B!13))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))))))),
% 3.72/2.64      inference(tautology,[status(thm)],[])).
% 3.72/2.64  tff(84,plain,
% 3.72/2.64      ((~(in(A!14, relation_dom(B!13)) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))) | (~in(apply(B!13, A!14), relation_rng(B!13))))) | (~((~in(A!14, relation_dom(B!13))) | (~((~in(apply(B!13, A!14), relation_rng(B!13))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14))))))))),
% 3.72/2.64      inference(unit_resolution,[status(thm)],[83, 82])).
% 3.72/2.64  tff(85,plain,
% 3.72/2.64      (one_to_one(B!13)),
% 3.72/2.64      inference(and_elim,[status(thm)],[65])).
% 3.72/2.64  tff(86,plain,
% 3.72/2.64      (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))))) <=> (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))))))))), (((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))))))))))), rewrite(((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))))))), (((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))))))))), (![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))))) <=> ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))))))))))), (((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))))))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))))))))), rewrite(((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))))))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))))))))))), (((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))))))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))))))))))))),
% 3.72/2.64      inference(bind,[status(th)],[])).
% 3.72/2.64  tff(87,plain,
% 3.72/2.64      (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))))))) <=> ![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))))))))))),
% 3.72/2.64      inference(quant_intro,[status(thm)],[86])).
% 3.72/2.64  tff(88,plain,
% 3.72/2.64      (^[A: $i] : refl(((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))))))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))))))))),
% 3.72/2.64      inference(bind,[status(th)],[])).
% 3.72/2.64  tff(89,plain,
% 3.72/2.64      (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))))))) <=> ![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))))))),
% 3.72/2.64      inference(quant_intro,[status(thm)],[88])).
% 3.72/2.64  tff(90,plain,
% 3.72/2.64      (^[A: $i] : rewrite(((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))))))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))))))))),
% 3.72/2.64      inference(bind,[status(th)],[])).
% 3.72/2.64  tff(91,plain,
% 3.72/2.64      (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))))))) <=> ![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))))))),
% 3.72/2.64      inference(quant_intro,[status(thm)],[90])).
% 3.72/2.64  tff(92,plain,
% 3.72/2.64      (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))))))) <=> ![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))))))),
% 3.72/2.64      inference(transitivity,[status(thm)],[91, 89])).
% 3.72/2.64  tff(93,plain,
% 3.72/2.64      (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(A) & function(A)) <=> (~((~relation(A)) | (~function(A))))), ((~(relation(A) & function(A))) <=> (~(~((~relation(A)) | (~function(A))))))), rewrite((~(~((~relation(A)) | (~function(A))))) <=> ((~relation(A)) | (~function(A)))), ((~(relation(A) & function(A))) <=> ((~relation(A)) | (~function(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(B) & function(B)) <=> (~((~relation(B)) | (~function(B))))), ((~(relation(B) & function(B))) <=> (~(~((~relation(B)) | (~function(B))))))), rewrite((~(~((~relation(B)) | (~function(B))))) <=> ((~relation(B)) | (~function(B)))), ((~(relation(B) & function(B))) <=> ((~relation(B)) | (~function(B))))), trans(monotonicity(rewrite(((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) <=> ((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))), trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) <=> (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))))), ((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) <=> (~(~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))))))), rewrite((~(~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))))) <=> ((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))), ((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) <=> ((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))))), rewrite((in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))) <=> (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))), (((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) <=> (((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))), rewrite((((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))) <=> ((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))), (((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) <=> ((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))), trans(monotonicity(trans(monotonicity(rewrite((in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))) <=> (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))), ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) <=> (~(~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))), rewrite((~(~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))) <=> ((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))), ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) <=> ((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))), rewrite((in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) <=> (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))))), (((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) <=> (((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))))))), rewrite((((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))))) <=> ((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))), (((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) <=> ((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))), ((((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) <=> (((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))) & ((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))), rewrite((((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))) & ((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))) <=> (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))), ((((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) <=> (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))))), ((~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))))) <=> (~(~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))))), rewrite((~(~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))) <=> ((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))), ((~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))))) <=> ((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))), (((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))))) <=> ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | ((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))))), rewrite(((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | ((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) <=> ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))), (((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))))) <=> ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))), ((((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))))))) <=> (((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))))) & ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))))), rewrite((((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))))) & ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) <=> (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))))), ((((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))))))) <=> (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))))))), (((~(relation(B) & function(B))) | (((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))))))) <=> (((~relation(B)) | (~function(B))) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))))))), rewrite((((~relation(B)) | (~function(B))) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))))))), (((~(relation(B) & function(B))) | (((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))))))))), (![B: $i] : ((~(relation(B) & function(B))) | (((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))))))) <=> ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))))))), (((~(relation(A) & function(A))) | (~one_to_one(A)) | ![B: $i] : ((~(relation(B) & function(B))) | (((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))))))))) <=> (((~relation(A)) | (~function(A))) | (~one_to_one(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))))))))), rewrite((((~relation(A)) | (~function(A))) | (~one_to_one(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))))))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))))))), (((~(relation(A) & function(A))) | (~one_to_one(A)) | ![B: $i] : ((~(relation(B) & function(B))) | (((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))))))))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))))))))),
% 3.72/2.65      inference(bind,[status(th)],[])).
% 3.72/2.65  tff(94,plain,
% 3.72/2.65      (![A: $i] : ((~(relation(A) & function(A))) | (~one_to_one(A)) | ![B: $i] : ((~(relation(B) & function(B))) | (((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))))))))) <=> ![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))))))),
% 3.72/2.65      inference(quant_intro,[status(thm)],[93])).
% 3.72/2.65  tff(95,plain,
% 3.72/2.65      (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite(((~(relation(B) & function(B))) | (((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | ((~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))))))))) <=> ((~(relation(B) & function(B))) | (((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))))))))), (![B: $i] : ((~(relation(B) & function(B))) | (((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | ((~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))))))))) <=> ![B: $i] : ((~(relation(B) & function(B))) | (((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))))))))), (((~(relation(A) & function(A))) | ![B: $i] : ((~(relation(B) & function(B))) | (((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | ((~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))))))))) | (~one_to_one(A))) <=> ((~(relation(A) & function(A))) | ![B: $i] : ((~(relation(B) & function(B))) | (((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))))))) | (~one_to_one(A))))), rewrite(((~(relation(A) & function(A))) | ![B: $i] : ((~(relation(B) & function(B))) | (((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))))))) | (~one_to_one(A))) <=> ((~(relation(A) & function(A))) | (~one_to_one(A)) | ![B: $i] : ((~(relation(B) & function(B))) | (((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))))))))), (((~(relation(A) & function(A))) | ![B: $i] : ((~(relation(B) & function(B))) | (((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | ((~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))))))))) | (~one_to_one(A))) <=> ((~(relation(A) & function(A))) | (~one_to_one(A)) | ![B: $i] : ((~(relation(B) & function(B))) | (((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))))))))))),
% 3.72/2.65      inference(bind,[status(th)],[])).
% 3.72/2.65  tff(96,plain,
% 3.72/2.65      (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((~(relation(B) & function(B))) | (((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | ((~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))))))))) | (~one_to_one(A))) <=> ![A: $i] : ((~(relation(A) & function(A))) | (~one_to_one(A)) | ![B: $i] : ((~(relation(B) & function(B))) | (((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))))))))),
% 3.72/2.65      inference(quant_intro,[status(thm)],[95])).
% 3.72/2.65  tff(97,plain,
% 3.72/2.65      (![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)))),
% 3.72/2.65      inference(rewrite,[status(thm)],[])).
% 3.72/2.65  tff(98,plain,
% 3.72/2.65      (^[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)))))),
% 3.72/2.65      inference(bind,[status(th)],[])).
% 3.72/2.65  tff(99,plain,
% 3.72/2.65      (![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)))),
% 3.72/2.65      inference(quant_intro,[status(thm)],[98])).
% 3.72/2.65  tff(100,axiom,(![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => ![B: $i] : ((relation(B) & function(B)) => ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((in(C, relation_rng(A)) & (D = apply(B, C))) => (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((in(D, relation_dom(A)) & (C = apply(A, D))) => (in(C, relation_rng(A)) & (D = apply(B, C))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t54_funct_1')).
% 3.72/2.65  tff(101,plain,
% 3.72/2.65      (![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)))),
% 3.72/2.65      inference(modus_ponens,[status(thm)],[100, 99])).
% 3.72/2.65  tff(102,plain,
% 3.72/2.65      (![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)))),
% 3.72/2.65      inference(modus_ponens,[status(thm)],[101, 97])).
% 3.72/2.65  tff(103,plain,(
% 3.72/2.65      ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((~(relation(B) & function(B))) | (((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | ((~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))))))))) | (~one_to_one(A)))),
% 3.72/2.65      inference(skolemize,[status(sab)],[102])).
% 3.72/2.65  tff(104,plain,
% 3.72/2.65      (![A: $i] : ((~(relation(A) & function(A))) | (~one_to_one(A)) | ![B: $i] : ((~(relation(B) & function(B))) | (((~(B = function_inverse(A))) | ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))) & ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A))))) | (in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) & ((~(in(tptp_fun_D_11(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))) | (in(tptp_fun_C_12(B, A), relation_rng(A)) & (tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))))))))),
% 3.72/2.65      inference(modus_ponens,[status(thm)],[103, 96])).
% 3.72/2.65  tff(105,plain,
% 3.72/2.65      (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))))))),
% 3.72/2.65      inference(modus_ponens,[status(thm)],[104, 94])).
% 3.72/2.65  tff(106,plain,
% 3.72/2.65      (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A))))))))))))),
% 3.72/2.65      inference(modus_ponens,[status(thm)],[105, 92])).
% 3.72/2.65  tff(107,plain,
% 3.72/2.65      (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))))))))))),
% 3.72/2.65      inference(modus_ponens,[status(thm)],[106, 87])).
% 3.72/2.65  tff(108,plain,
% 3.72/2.65      (((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))))))))))) | ((~relation(B!13)) | (~function(B!13)) | (~one_to_one(B!13)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!13)) | (~(relation_dom(B) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))))))))))))))))))) <=> ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))))))))))) | (~relation(B!13)) | (~function(B!13)) | (~one_to_one(B!13)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!13)) | (~(relation_dom(B) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))))))))))))))))))),
% 3.72/2.65      inference(rewrite,[status(thm)],[])).
% 3.72/2.65  tff(109,plain,
% 3.72/2.65      (((~one_to_one(B!13)) | (~relation(B!13)) | (~function(B!13)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!13)) | (~(relation_dom(B) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13)))))))))))))))))) <=> ((~relation(B!13)) | (~function(B!13)) | (~one_to_one(B!13)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!13)) | (~(relation_dom(B) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))))))))))))))))))),
% 3.72/2.65      inference(rewrite,[status(thm)],[])).
% 3.72/2.65  tff(110,plain,
% 3.72/2.65      (^[B: $i] : trans(monotonicity(rewrite((~((~((B = function_inverse(B!13)) | (~(relation_dom(B) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))) | (~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~((~in(C, relation_rng(B!13))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D)))))))))))))) <=> (~((~((B = function_inverse(B!13)) | (~(relation_dom(B) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))))))))))))))))), (((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!13)) | (~(relation_dom(B) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))) | (~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~((~in(C, relation_rng(B!13))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!13)) | (~(relation_dom(B) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))))))))))))))))))), rewrite(((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!13)) | (~(relation_dom(B) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))))))))))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!13)) | (~(relation_dom(B) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13)))))))))))))))))), (((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!13)) | (~(relation_dom(B) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))) | (~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~((~in(C, relation_rng(B!13))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!13)) | (~(relation_dom(B) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13)))))))))))))))))))),
% 3.72/2.65      inference(bind,[status(th)],[])).
% 3.72/2.65  tff(111,plain,
% 3.72/2.65      (![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!13)) | (~(relation_dom(B) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))) | (~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~((~in(C, relation_rng(B!13))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))))))))))) <=> ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!13)) | (~(relation_dom(B) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13)))))))))))))))))),
% 3.72/2.65      inference(quant_intro,[status(thm)],[110])).
% 3.72/2.65  tff(112,plain,
% 3.72/2.65      (((~one_to_one(B!13)) | (~relation(B!13)) | (~function(B!13)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!13)) | (~(relation_dom(B) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))) | (~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~((~in(C, relation_rng(B!13))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D)))))))))))))))) <=> ((~one_to_one(B!13)) | (~relation(B!13)) | (~function(B!13)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!13)) | (~(relation_dom(B) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))))))))))))))))))),
% 3.72/2.66      inference(monotonicity,[status(thm)],[111])).
% 3.72/2.66  tff(113,plain,
% 3.72/2.66      (((~one_to_one(B!13)) | (~relation(B!13)) | (~function(B!13)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!13)) | (~(relation_dom(B) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))) | (~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~((~in(C, relation_rng(B!13))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D)))))))))))))))) <=> ((~relation(B!13)) | (~function(B!13)) | (~one_to_one(B!13)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!13)) | (~(relation_dom(B) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))))))))))))))))))),
% 3.72/2.66      inference(transitivity,[status(thm)],[112, 109])).
% 3.72/2.66  tff(114,plain,
% 3.72/2.66      (((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))))))))))) | ((~one_to_one(B!13)) | (~relation(B!13)) | (~function(B!13)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!13)) | (~(relation_dom(B) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))) | (~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~((~in(C, relation_rng(B!13))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))))))))))))) <=> ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))))))))))) | ((~relation(B!13)) | (~function(B!13)) | (~one_to_one(B!13)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!13)) | (~(relation_dom(B) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13)))))))))))))))))))),
% 3.72/2.66      inference(monotonicity,[status(thm)],[113])).
% 3.72/2.66  tff(115,plain,
% 3.72/2.66      (((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))))))))))) | ((~one_to_one(B!13)) | (~relation(B!13)) | (~function(B!13)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!13)) | (~(relation_dom(B) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))) | (~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~((~in(C, relation_rng(B!13))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))))))))))))) <=> ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))))))))))) | (~relation(B!13)) | (~function(B!13)) | (~one_to_one(B!13)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!13)) | (~(relation_dom(B) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))))))))))))))))))),
% 3.72/2.66      inference(transitivity,[status(thm)],[114, 108])).
% 3.72/2.66  tff(116,plain,
% 3.72/2.66      ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))))))))))) | ((~one_to_one(B!13)) | (~relation(B!13)) | (~function(B!13)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!13)) | (~(relation_dom(B) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))) | (~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~((~in(C, relation_rng(B!13))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))))))))))))),
% 3.72/2.66      inference(quant_inst,[status(thm)],[])).
% 3.72/2.66  tff(117,plain,
% 3.72/2.66      ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))) | (~((~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~((~in(tptp_fun_C_12(B, A), relation_rng(A))) | (~(tptp_fun_D_11(B, A) = apply(B, tptp_fun_C_12(B, A)))))) | (~in(tptp_fun_D_11(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_11(B, A)))))))) | (~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))))))))))) | (~relation(B!13)) | (~function(B!13)) | (~one_to_one(B!13)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!13)) | (~(relation_dom(B) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13)))))))))))))))))),
% 3.72/2.66      inference(modus_ponens,[status(thm)],[116, 115])).
% 3.72/2.66  tff(118,plain,
% 3.72/2.66      (![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!13)) | (~(relation_dom(B) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13)))))))))))))))))),
% 3.72/2.66      inference(unit_resolution,[status(thm)],[117, 107, 16, 15, 85])).
% 3.72/2.66  tff(119,plain,
% 3.72/2.66      (((~![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!13)) | (~(relation_dom(B) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13)))))))))))))))))) | ((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (~((~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C)))))))))))))) <=> ((~![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!13)) | (~(relation_dom(B) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13)))))))))))))))))) | (~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (~((~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C)))))))))))))),
% 3.72/2.66      inference(rewrite,[status(thm)],[])).
% 3.72/2.66  tff(120,plain,
% 3.72/2.66      (((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (~((~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C))))))))))))) <=> ((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (~((~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C)))))))))))))),
% 3.72/2.66      inference(rewrite,[status(thm)],[])).
% 3.72/2.66  tff(121,plain,
% 3.72/2.66      ((~((~((function_inverse(B!13) = function_inverse(B!13)) | (~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(function_inverse(B!13), B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(function_inverse(B!13), B!13) = apply(function_inverse(B!13), tptp_fun_C_12(function_inverse(B!13), B!13)))) | (~((~in(tptp_fun_D_11(function_inverse(B!13), B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(function_inverse(B!13), B!13) = apply(B!13, tptp_fun_D_11(function_inverse(B!13), B!13)))))))) | (~((~in(tptp_fun_D_11(function_inverse(B!13), B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(function_inverse(B!13), B!13) = apply(B!13, tptp_fun_D_11(function_inverse(B!13), B!13)))) | (~((~in(tptp_fun_C_12(function_inverse(B!13), B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(function_inverse(B!13), B!13) = apply(function_inverse(B!13), tptp_fun_C_12(function_inverse(B!13), B!13)))))))))) | (~((~(function_inverse(B!13) = function_inverse(B!13))) | (~((~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(function_inverse(B!13), C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(function_inverse(B!13), C))) | (~in(C, relation_rng(B!13)))))))))))))))) <=> (~((~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C))))))))))))),
% 3.72/2.66      inference(rewrite,[status(thm)],[])).
% 3.72/2.66  tff(122,plain,
% 3.72/2.66      (((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (~((~((function_inverse(B!13) = function_inverse(B!13)) | (~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(function_inverse(B!13), B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(function_inverse(B!13), B!13) = apply(function_inverse(B!13), tptp_fun_C_12(function_inverse(B!13), B!13)))) | (~((~in(tptp_fun_D_11(function_inverse(B!13), B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(function_inverse(B!13), B!13) = apply(B!13, tptp_fun_D_11(function_inverse(B!13), B!13)))))))) | (~((~in(tptp_fun_D_11(function_inverse(B!13), B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(function_inverse(B!13), B!13) = apply(B!13, tptp_fun_D_11(function_inverse(B!13), B!13)))) | (~((~in(tptp_fun_C_12(function_inverse(B!13), B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(function_inverse(B!13), B!13) = apply(function_inverse(B!13), tptp_fun_C_12(function_inverse(B!13), B!13)))))))))) | (~((~(function_inverse(B!13) = function_inverse(B!13))) | (~((~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(function_inverse(B!13), C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(function_inverse(B!13), C))) | (~in(C, relation_rng(B!13))))))))))))))))) <=> ((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (~((~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C)))))))))))))),
% 3.72/2.66      inference(monotonicity,[status(thm)],[121])).
% 3.72/2.66  tff(123,plain,
% 3.72/2.66      (((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (~((~((function_inverse(B!13) = function_inverse(B!13)) | (~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(function_inverse(B!13), B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(function_inverse(B!13), B!13) = apply(function_inverse(B!13), tptp_fun_C_12(function_inverse(B!13), B!13)))) | (~((~in(tptp_fun_D_11(function_inverse(B!13), B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(function_inverse(B!13), B!13) = apply(B!13, tptp_fun_D_11(function_inverse(B!13), B!13)))))))) | (~((~in(tptp_fun_D_11(function_inverse(B!13), B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(function_inverse(B!13), B!13) = apply(B!13, tptp_fun_D_11(function_inverse(B!13), B!13)))) | (~((~in(tptp_fun_C_12(function_inverse(B!13), B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(function_inverse(B!13), B!13) = apply(function_inverse(B!13), tptp_fun_C_12(function_inverse(B!13), B!13)))))))))) | (~((~(function_inverse(B!13) = function_inverse(B!13))) | (~((~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(function_inverse(B!13), C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(function_inverse(B!13), C))) | (~in(C, relation_rng(B!13))))))))))))))))) <=> ((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (~((~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C)))))))))))))),
% 3.72/2.66      inference(transitivity,[status(thm)],[122, 120])).
% 3.72/2.66  tff(124,plain,
% 3.72/2.66      (((~![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!13)) | (~(relation_dom(B) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13)))))))))))))))))) | ((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (~((~((function_inverse(B!13) = function_inverse(B!13)) | (~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(function_inverse(B!13), B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(function_inverse(B!13), B!13) = apply(function_inverse(B!13), tptp_fun_C_12(function_inverse(B!13), B!13)))) | (~((~in(tptp_fun_D_11(function_inverse(B!13), B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(function_inverse(B!13), B!13) = apply(B!13, tptp_fun_D_11(function_inverse(B!13), B!13)))))))) | (~((~in(tptp_fun_D_11(function_inverse(B!13), B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(function_inverse(B!13), B!13) = apply(B!13, tptp_fun_D_11(function_inverse(B!13), B!13)))) | (~((~in(tptp_fun_C_12(function_inverse(B!13), B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(function_inverse(B!13), B!13) = apply(function_inverse(B!13), tptp_fun_C_12(function_inverse(B!13), B!13)))))))))) | (~((~(function_inverse(B!13) = function_inverse(B!13))) | (~((~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(function_inverse(B!13), C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(function_inverse(B!13), C))) | (~in(C, relation_rng(B!13)))))))))))))))))) <=> ((~![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!13)) | (~(relation_dom(B) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13)))))))))))))))))) | ((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (~((~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C))))))))))))))),
% 3.72/2.66      inference(monotonicity,[status(thm)],[123])).
% 3.72/2.66  tff(125,plain,
% 3.72/2.66      (((~![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!13)) | (~(relation_dom(B) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13)))))))))))))))))) | ((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (~((~((function_inverse(B!13) = function_inverse(B!13)) | (~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(function_inverse(B!13), B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(function_inverse(B!13), B!13) = apply(function_inverse(B!13), tptp_fun_C_12(function_inverse(B!13), B!13)))) | (~((~in(tptp_fun_D_11(function_inverse(B!13), B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(function_inverse(B!13), B!13) = apply(B!13, tptp_fun_D_11(function_inverse(B!13), B!13)))))))) | (~((~in(tptp_fun_D_11(function_inverse(B!13), B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(function_inverse(B!13), B!13) = apply(B!13, tptp_fun_D_11(function_inverse(B!13), B!13)))) | (~((~in(tptp_fun_C_12(function_inverse(B!13), B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(function_inverse(B!13), B!13) = apply(function_inverse(B!13), tptp_fun_C_12(function_inverse(B!13), B!13)))))))))) | (~((~(function_inverse(B!13) = function_inverse(B!13))) | (~((~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(function_inverse(B!13), C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(function_inverse(B!13), C))) | (~in(C, relation_rng(B!13)))))))))))))))))) <=> ((~![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!13)) | (~(relation_dom(B) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13)))))))))))))))))) | (~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (~((~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C)))))))))))))),
% 3.72/2.67      inference(transitivity,[status(thm)],[124, 119])).
% 3.72/2.67  tff(126,plain,
% 3.72/2.67      ((~![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!13)) | (~(relation_dom(B) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13)))))))))))))))))) | ((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (~((~((function_inverse(B!13) = function_inverse(B!13)) | (~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(function_inverse(B!13), B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(function_inverse(B!13), B!13) = apply(function_inverse(B!13), tptp_fun_C_12(function_inverse(B!13), B!13)))) | (~((~in(tptp_fun_D_11(function_inverse(B!13), B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(function_inverse(B!13), B!13) = apply(B!13, tptp_fun_D_11(function_inverse(B!13), B!13)))))))) | (~((~in(tptp_fun_D_11(function_inverse(B!13), B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(function_inverse(B!13), B!13) = apply(B!13, tptp_fun_D_11(function_inverse(B!13), B!13)))) | (~((~in(tptp_fun_C_12(function_inverse(B!13), B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(function_inverse(B!13), B!13) = apply(function_inverse(B!13), tptp_fun_C_12(function_inverse(B!13), B!13)))))))))) | (~((~(function_inverse(B!13) = function_inverse(B!13))) | (~((~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(function_inverse(B!13), C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(function_inverse(B!13), C))) | (~in(C, relation_rng(B!13)))))))))))))))))),
% 3.81/2.67      inference(quant_inst,[status(thm)],[])).
% 3.81/2.67  tff(127,plain,
% 3.81/2.67      ((~![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!13)) | (~(relation_dom(B) = relation_rng(B!13))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))))))) | (~((~in(tptp_fun_D_11(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_12(B, B!13) = apply(B!13, tptp_fun_D_11(B, B!13)))) | (~((~in(tptp_fun_C_12(B, B!13), relation_rng(B!13))) | (~(tptp_fun_D_11(B, B!13) = apply(B, tptp_fun_C_12(B, B!13)))))))))) | (~((~(B = function_inverse(B!13))) | (~((~(relation_dom(B) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!13)))))))))))))))))) | (~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | (~((~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C))))))))))))),
% 3.81/2.67      inference(modus_ponens,[status(thm)],[126, 125])).
% 3.81/2.67  tff(128,plain,
% 3.81/2.67      (~((~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C)))))))))))),
% 3.81/2.67      inference(unit_resolution,[status(thm)],[127, 118, 35, 37])).
% 3.81/2.67  tff(129,plain,
% 3.81/2.67      (((~(relation_dom(function_inverse(B!13)) = relation_rng(B!13))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C))))))))))) | ![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C)))))))))),
% 3.81/2.67      inference(tautology,[status(thm)],[])).
% 3.81/2.67  tff(130,plain,
% 3.81/2.67      (![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C)))))))))),
% 3.81/2.67      inference(unit_resolution,[status(thm)],[129, 128])).
% 3.81/2.67  tff(131,plain,
% 3.81/2.67      (((~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C)))))))))) | (~((~(in(A!14, relation_dom(B!13)) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))) | (~in(apply(B!13, A!14), relation_rng(B!13))))) | (~((~in(A!14, relation_dom(B!13))) | (~((~in(apply(B!13, A!14), relation_rng(B!13))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14))))))))))) <=> ((~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C)))))))))) | (~((~(in(A!14, relation_dom(B!13)) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))) | (~in(apply(B!13, A!14), relation_rng(B!13))))) | (~((~in(A!14, relation_dom(B!13))) | (~((~in(apply(B!13, A!14), relation_rng(B!13))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))))))))))),
% 3.81/2.67      inference(rewrite,[status(thm)],[])).
% 3.81/2.67  tff(132,plain,
% 3.81/2.67      ((~((~((~in(apply(B!13, A!14), relation_rng(B!13))) | (~((~in(A!14, relation_dom(B!13))) | (~(apply(B!13, A!14) = apply(B!13, A!14))))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))))) | (~((~in(A!14, relation_dom(B!13))) | (~(apply(B!13, A!14) = apply(B!13, A!14))) | (~((~in(apply(B!13, A!14), relation_rng(B!13))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))))))))) <=> (~((~(in(A!14, relation_dom(B!13)) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))) | (~in(apply(B!13, A!14), relation_rng(B!13))))) | (~((~in(A!14, relation_dom(B!13))) | (~((~in(apply(B!13, A!14), relation_rng(B!13))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14))))))))))),
% 3.81/2.67      inference(rewrite,[status(thm)],[])).
% 3.81/2.67  tff(133,plain,
% 3.81/2.67      (((~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C)))))))))) | (~((~((~in(apply(B!13, A!14), relation_rng(B!13))) | (~((~in(A!14, relation_dom(B!13))) | (~(apply(B!13, A!14) = apply(B!13, A!14))))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))))) | (~((~in(A!14, relation_dom(B!13))) | (~(apply(B!13, A!14) = apply(B!13, A!14))) | (~((~in(apply(B!13, A!14), relation_rng(B!13))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14))))))))))) <=> ((~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C)))))))))) | (~((~(in(A!14, relation_dom(B!13)) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))) | (~in(apply(B!13, A!14), relation_rng(B!13))))) | (~((~in(A!14, relation_dom(B!13))) | (~((~in(apply(B!13, A!14), relation_rng(B!13))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))))))))))),
% 3.81/2.67      inference(monotonicity,[status(thm)],[132])).
% 3.81/2.67  tff(134,plain,
% 3.81/2.67      (((~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C)))))))))) | (~((~((~in(apply(B!13, A!14), relation_rng(B!13))) | (~((~in(A!14, relation_dom(B!13))) | (~(apply(B!13, A!14) = apply(B!13, A!14))))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))))) | (~((~in(A!14, relation_dom(B!13))) | (~(apply(B!13, A!14) = apply(B!13, A!14))) | (~((~in(apply(B!13, A!14), relation_rng(B!13))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14))))))))))) <=> ((~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C)))))))))) | (~((~(in(A!14, relation_dom(B!13)) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))) | (~in(apply(B!13, A!14), relation_rng(B!13))))) | (~((~in(A!14, relation_dom(B!13))) | (~((~in(apply(B!13, A!14), relation_rng(B!13))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))))))))))),
% 3.81/2.67      inference(transitivity,[status(thm)],[133, 131])).
% 3.81/2.67  tff(135,plain,
% 3.81/2.67      ((~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C)))))))))) | (~((~((~in(apply(B!13, A!14), relation_rng(B!13))) | (~((~in(A!14, relation_dom(B!13))) | (~(apply(B!13, A!14) = apply(B!13, A!14))))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))))) | (~((~in(A!14, relation_dom(B!13))) | (~(apply(B!13, A!14) = apply(B!13, A!14))) | (~((~in(apply(B!13, A!14), relation_rng(B!13))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14))))))))))),
% 3.81/2.67      inference(quant_inst,[status(thm)],[])).
% 3.81/2.67  tff(136,plain,
% 3.81/2.67      ((~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!13))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~(D = apply(function_inverse(B!13), C))))) | (~((~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))) | (~((~in(C, relation_rng(B!13))) | (~(D = apply(function_inverse(B!13), C)))))))))) | (~((~(in(A!14, relation_dom(B!13)) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))) | (~in(apply(B!13, A!14), relation_rng(B!13))))) | (~((~in(A!14, relation_dom(B!13))) | (~((~in(apply(B!13, A!14), relation_rng(B!13))) | (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14))))))))))),
% 3.81/2.67      inference(modus_ponens,[status(thm)],[135, 134])).
% 3.81/2.67  tff(137,plain,
% 3.81/2.67      ($false),
% 3.81/2.67      inference(unit_resolution,[status(thm)],[136, 130, 84])).
% 3.81/2.67  tff(138,plain,(A!14 = apply(relation_composition(B!13, function_inverse(B!13)), A!14)), inference(lemma,lemma(discharge,[]))).
% 3.81/2.67  tff(139,plain,
% 3.81/2.67      (A!14 = apply(function_inverse(B!13), apply(B!13, A!14))),
% 3.81/2.67      inference(transitivity,[status(thm)],[138, 74])).
% 3.81/2.67  tff(140,plain,
% 3.81/2.67      ((~(~((~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))) | (~(A!14 = apply(relation_composition(B!13, function_inverse(B!13)), A!14)))))) <=> ((~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))) | (~(A!14 = apply(relation_composition(B!13, function_inverse(B!13)), A!14))))),
% 3.81/2.67      inference(rewrite,[status(thm)],[])).
% 3.81/2.67  tff(141,plain,
% 3.81/2.67      (((A!14 = apply(function_inverse(B!13), apply(B!13, A!14))) & (A!14 = apply(relation_composition(B!13, function_inverse(B!13)), A!14))) <=> (~((~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))) | (~(A!14 = apply(relation_composition(B!13, function_inverse(B!13)), A!14)))))),
% 3.81/2.67      inference(rewrite,[status(thm)],[])).
% 3.81/2.67  tff(142,plain,
% 3.81/2.67      ((~((A!14 = apply(function_inverse(B!13), apply(B!13, A!14))) & (A!14 = apply(relation_composition(B!13, function_inverse(B!13)), A!14)))) <=> (~(~((~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))) | (~(A!14 = apply(relation_composition(B!13, function_inverse(B!13)), A!14))))))),
% 3.81/2.67      inference(monotonicity,[status(thm)],[141])).
% 3.81/2.67  tff(143,plain,
% 3.81/2.67      ((~((A!14 = apply(function_inverse(B!13), apply(B!13, A!14))) & (A!14 = apply(relation_composition(B!13, function_inverse(B!13)), A!14)))) <=> ((~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))) | (~(A!14 = apply(relation_composition(B!13, function_inverse(B!13)), A!14))))),
% 3.81/2.67      inference(transitivity,[status(thm)],[142, 140])).
% 3.81/2.67  tff(144,plain,
% 3.81/2.67      (~((A!14 = apply(function_inverse(B!13), apply(B!13, A!14))) & (A!14 = apply(relation_composition(B!13, function_inverse(B!13)), A!14)))),
% 3.81/2.67      inference(or_elim,[status(thm)],[13])).
% 3.81/2.67  tff(145,plain,
% 3.81/2.67      ((~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))) | (~(A!14 = apply(relation_composition(B!13, function_inverse(B!13)), A!14)))),
% 3.81/2.68      inference(modus_ponens,[status(thm)],[144, 143])).
% 3.81/2.68  tff(146,plain,
% 3.81/2.68      (~(A!14 = apply(function_inverse(B!13), apply(B!13, A!14)))),
% 3.81/2.68      inference(unit_resolution,[status(thm)],[145, 138])).
% 3.81/2.68  tff(147,plain,
% 3.81/2.68      ($false),
% 3.81/2.68      inference(unit_resolution,[status(thm)],[146, 139])).
% 3.81/2.68  % SZS output end Proof
%------------------------------------------------------------------------------