TSTP Solution File: SEU220+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU220+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 07:28:16 EDT 2022
% Result : Theorem 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU220+3 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 10:34:18 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.46 % SZS status Theorem
% 0.20/0.46 % SZS output start Proof
% 0.20/0.46 tff(apply_type, type, (
% 0.20/0.46 apply: ( $i * $i ) > $i)).
% 0.20/0.46 tff(tptp_fun_A_14_type, type, (
% 0.20/0.46 tptp_fun_A_14: $i)).
% 0.20/0.46 tff(function_inverse_type, type, (
% 0.20/0.46 function_inverse: $i > $i)).
% 0.20/0.46 tff(tptp_fun_B_13_type, type, (
% 0.20/0.46 tptp_fun_B_13: $i)).
% 0.20/0.46 tff(relation_composition_type, type, (
% 0.20/0.46 relation_composition: ( $i * $i ) > $i)).
% 0.20/0.46 tff(in_type, type, (
% 0.20/0.46 in: ( $i * $i ) > $o)).
% 0.20/0.46 tff(relation_dom_type, type, (
% 0.20/0.46 relation_dom: $i > $i)).
% 0.20/0.46 tff(relation_rng_type, type, (
% 0.20/0.46 relation_rng: $i > $i)).
% 0.20/0.46 tff(one_to_one_type, type, (
% 0.20/0.46 one_to_one: $i > $o)).
% 0.20/0.46 tff(function_type, type, (
% 0.20/0.46 function: $i > $o)).
% 0.20/0.46 tff(relation_type, type, (
% 0.20/0.46 relation: $i > $o)).
% 0.20/0.46 tff(tptp_fun_C_12_type, type, (
% 0.20/0.46 tptp_fun_C_12: ( $i * $i ) > $i)).
% 0.20/0.46 tff(tptp_fun_D_11_type, type, (
% 0.20/0.46 tptp_fun_D_11: ( $i * $i ) > $i)).
% 0.20/0.46 tff(1,plain,
% 0.20/0.46 ((~(((A!14 = apply(B!13, apply(function_inverse(B!13), A!14))) & (A!14 = apply(relation_composition(function_inverse(B!13), B!13), A!14))) | (~(relation(B!13) & function(B!13))) | (~(one_to_one(B!13) & in(A!14, relation_rng(B!13)))))) <=> (~(((A!14 = apply(B!13, apply(function_inverse(B!13), A!14))) & (A!14 = apply(relation_composition(function_inverse(B!13), B!13), A!14))) | (~(relation(B!13) & function(B!13))) | (~(one_to_one(B!13) & in(A!14, relation_rng(B!13))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(2,plain,
% 0.20/0.46 ((~![A: $i, B: $i] : (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B)))))) <=> (~![A: $i, B: $i] : (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(3,plain,
% 0.20/0.46 ((~![A: $i, B: $i] : ((relation(B) & function(B)) => ((one_to_one(B) & in(A, relation_rng(B))) => ((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A)))))) <=> (~![A: $i, B: $i] : (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(4,axiom,(~![A: $i, B: $i] : ((relation(B) & function(B)) => ((one_to_one(B) & in(A, relation_rng(B))) => ((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t57_funct_1')).
% 0.20/0.46 tff(5,plain,
% 0.20/0.46 (~![A: $i, B: $i] : (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.46 tff(6,plain,
% 0.20/0.46 (~![A: $i, B: $i] : (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.20/0.46 tff(7,plain,
% 0.20/0.46 (~![A: $i, B: $i] : (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.46 tff(8,plain,
% 0.20/0.46 (~![A: $i, B: $i] : (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.20/0.46 tff(9,plain,
% 0.20/0.46 (~![A: $i, B: $i] : (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.20/0.46 tff(10,plain,
% 0.20/0.46 (~![A: $i, B: $i] : (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.20/0.46 tff(11,plain,
% 0.20/0.46 (~![A: $i, B: $i] : (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.20/0.46 tff(12,plain,(
% 0.20/0.46 ~(((A!14 = apply(B!13, apply(function_inverse(B!13), A!14))) & (A!14 = apply(relation_composition(function_inverse(B!13), B!13), A!14))) | (~(relation(B!13) & function(B!13))) | (~(one_to_one(B!13) & in(A!14, relation_rng(B!13)))))),
% 0.20/0.46 inference(skolemize,[status(sab)],[11])).
% 0.20/0.46 tff(13,plain,
% 0.20/0.46 (~(((A!14 = apply(B!13, apply(function_inverse(B!13), A!14))) & (A!14 = apply(relation_composition(function_inverse(B!13), B!13), A!14))) | (~(relation(B!13) & function(B!13))) | (~(one_to_one(B!13) & in(A!14, relation_rng(B!13)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[12, 1])).
% 0.20/0.46 tff(14,plain,
% 0.20/0.46 (one_to_one(B!13) & in(A!14, relation_rng(B!13))),
% 0.20/0.46 inference(or_elim,[status(thm)],[13])).
% 0.20/0.46 tff(15,plain,
% 0.20/0.46 (one_to_one(B!13)),
% 0.20/0.46 inference(and_elim,[status(thm)],[14])).
% 0.20/0.46 tff(16,plain,
% 0.20/0.46 (relation(B!13) & function(B!13)),
% 0.20/0.46 inference(or_elim,[status(thm)],[13])).
% 0.20/0.46 tff(17,plain,
% 0.20/0.46 (function(B!13)),
% 0.20/0.46 inference(and_elim,[status(thm)],[16])).
% 0.20/0.46 tff(18,plain,
% 0.20/0.46 (relation(B!13)),
% 0.20/0.46 inference(and_elim,[status(thm)],[16])).
% 0.20/0.46 tff(19,plain,
% 0.20/0.46 (^[A: $i] : refl(((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A))))))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(20,plain,
% 0.20/0.46 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A))))))) <=> ![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[19])).
% 0.20/0.46 tff(21,plain,
% 0.20/0.46 (^[A: $i] : trans(monotonicity(rewrite(((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) <=> (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A))))))), 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))))), ((((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ((~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))) | ((~relation(A)) | (~function(A))) | (~one_to_one(A))))), rewrite(((~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))) | ((~relation(A)) | (~function(A))) | (~one_to_one(A))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))), ((((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(22,plain,
% 0.20/0.46 (![A: $i] : (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[21])).
% 0.20/0.46 tff(23,plain,
% 0.20/0.46 (![A: $i] : (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ![A: $i] : (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(24,plain,
% 0.20/0.46 (^[A: $i] : trans(monotonicity(rewrite((one_to_one(A) => ((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A))))) <=> ((~one_to_one(A)) | ((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))))), (((relation(A) & function(A)) => (one_to_one(A) => ((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))))) <=> ((relation(A) & function(A)) => ((~one_to_one(A)) | ((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))))))), rewrite(((relation(A) & function(A)) => ((~one_to_one(A)) | ((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))))) <=> (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))), (((relation(A) & function(A)) => (one_to_one(A) => ((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))))) <=> (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(25,plain,
% 0.20/0.46 (![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => ((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))))) <=> ![A: $i] : (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.46 tff(26,axiom,(![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => ((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t55_funct_1')).
% 0.20/0.46 tff(27,plain,
% 0.20/0.46 (![A: $i] : (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.46 tff(28,plain,
% 0.20/0.46 (![A: $i] : (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.20/0.46 tff(29,plain,(
% 0.20/0.46 ![A: $i] : (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[28])).
% 0.20/0.46 tff(30,plain,
% 0.20/0.46 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.20/0.46 tff(31,plain,
% 0.20/0.46 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[30, 20])).
% 0.20/0.47 tff(32,plain,
% 0.20/0.47 (((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))) | ((~one_to_one(B!13)) | (~relation(B!13)) | (~function(B!13)) | (~((~(relation_rng(B!13) = relation_dom(function_inverse(B!13)))) | (~(relation_dom(B!13) = relation_rng(function_inverse(B!13)))))))) <=> ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))) | (~one_to_one(B!13)) | (~relation(B!13)) | (~function(B!13)) | (~((~(relation_rng(B!13) = relation_dom(function_inverse(B!13)))) | (~(relation_dom(B!13) = relation_rng(function_inverse(B!13)))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(33,plain,
% 0.20/0.47 ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))) | ((~one_to_one(B!13)) | (~relation(B!13)) | (~function(B!13)) | (~((~(relation_rng(B!13) = relation_dom(function_inverse(B!13)))) | (~(relation_dom(B!13) = relation_rng(function_inverse(B!13)))))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(34,plain,
% 0.20/0.47 ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))) | (~one_to_one(B!13)) | (~relation(B!13)) | (~function(B!13)) | (~((~(relation_rng(B!13) = relation_dom(function_inverse(B!13)))) | (~(relation_dom(B!13) = relation_rng(function_inverse(B!13))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.20/0.47 tff(35,plain,
% 0.20/0.47 (~((~(relation_rng(B!13) = relation_dom(function_inverse(B!13)))) | (~(relation_dom(B!13) = relation_rng(function_inverse(B!13)))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[34, 31, 18, 17, 15])).
% 0.20/0.47 tff(36,plain,
% 0.20/0.47 (((~(relation_rng(B!13) = relation_dom(function_inverse(B!13)))) | (~(relation_dom(B!13) = relation_rng(function_inverse(B!13))))) | (relation_rng(B!13) = relation_dom(function_inverse(B!13)))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(37,plain,
% 0.20/0.47 (relation_rng(B!13) = relation_dom(function_inverse(B!13))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.20/0.47 tff(38,plain,
% 0.20/0.47 (relation_dom(function_inverse(B!13)) = relation_rng(B!13)),
% 0.20/0.47 inference(symmetry,[status(thm)],[37])).
% 0.20/0.47 tff(39,plain,
% 0.20/0.47 (in(A!14, relation_dom(function_inverse(B!13))) <=> in(A!14, relation_rng(B!13))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[38])).
% 0.20/0.47 tff(40,plain,
% 0.20/0.47 (in(A!14, relation_rng(B!13)) <=> in(A!14, relation_dom(function_inverse(B!13)))),
% 0.20/0.47 inference(symmetry,[status(thm)],[39])).
% 0.20/0.47 tff(41,plain,
% 0.20/0.47 (in(A!14, relation_rng(B!13))),
% 0.20/0.47 inference(and_elim,[status(thm)],[14])).
% 0.20/0.47 tff(42,plain,
% 0.20/0.47 (in(A!14, relation_dom(function_inverse(B!13)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.20/0.47 tff(43,plain,
% 0.20/0.47 (^[A: $i] : refl(((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A)))))) <=> ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A)))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(44,plain,
% 0.20/0.47 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A)))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[43])).
% 0.20/0.47 tff(45,plain,
% 0.20/0.47 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(A) & function(A)) <=> (~((~relation(A)) | (~function(A))))), ((~(relation(A) & function(A))) <=> (~(~((~relation(A)) | (~function(A))))))), rewrite((~(~((~relation(A)) | (~function(A))))) <=> ((~relation(A)) | (~function(A)))), ((~(relation(A) & function(A))) <=> ((~relation(A)) | (~function(A))))), rewrite((relation(function_inverse(A)) & function(function_inverse(A))) <=> (~((~relation(function_inverse(A))) | (~function(function_inverse(A)))))), (((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A)))) <=> (((~relation(A)) | (~function(A))) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A)))))))), rewrite((((~relation(A)) | (~function(A))) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A)))))) <=> ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))), (((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A)))) <=> ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(46,plain,
% 0.20/0.47 (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A)))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[45])).
% 0.20/0.47 tff(47,plain,
% 0.20/0.47 (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A)))) <=> ![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(48,plain,
% 0.20/0.47 (^[A: $i] : rewrite(((relation(A) & function(A)) => (relation(function_inverse(A)) & function(function_inverse(A)))) <=> ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(49,plain,
% 0.20/0.47 (![A: $i] : ((relation(A) & function(A)) => (relation(function_inverse(A)) & function(function_inverse(A)))) <=> ![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[48])).
% 0.20/0.47 tff(50,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')).
% 0.20/0.47 tff(51,plain,
% 0.20/0.47 (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.20/0.47 tff(52,plain,
% 0.20/0.47 (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.20/0.47 tff(53,plain,(
% 0.20/0.47 ![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 0.20/0.47 inference(skolemize,[status(sab)],[52])).
% 0.20/0.47 tff(54,plain,
% 0.20/0.47 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.20/0.47 tff(55,plain,
% 0.20/0.47 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[54, 44])).
% 0.20/0.47 tff(56,plain,
% 0.20/0.47 (((~![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))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(57,plain,
% 0.20/0.47 ((~![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))))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(58,plain,
% 0.20/0.47 ((~![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)))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.20/0.47 tff(59,plain,
% 0.20/0.47 (~((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[58, 55, 18, 17])).
% 0.20/0.47 tff(60,plain,
% 0.20/0.47 (((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13)))) | relation(function_inverse(B!13))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(61,plain,
% 0.20/0.47 (relation(function_inverse(B!13))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.20/0.47 tff(62,plain,
% 0.20/0.47 (((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13)))) | function(function_inverse(B!13))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(63,plain,
% 0.20/0.47 (function(function_inverse(B!13))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[62, 59])).
% 0.20/0.47 tff(64,plain,
% 0.20/0.47 (^[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)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(65,plain,
% 0.20/0.47 (![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))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[64])).
% 0.20/0.47 tff(66,plain,
% 0.20/0.47 (^[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)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(67,plain,
% 0.20/0.47 (![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))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[66])).
% 0.20/0.47 tff(68,plain,
% 0.20/0.47 (![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))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[67, 65])).
% 0.20/0.47 tff(69,plain,
% 0.20/0.47 (^[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))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(70,plain,
% 0.20/0.47 (![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))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[69])).
% 0.20/0.47 tff(71,plain,
% 0.20/0.47 (![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)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(72,plain,
% 0.20/0.47 (^[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)))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(73,plain,
% 0.20/0.47 (![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)))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[72])).
% 0.20/0.47 tff(74,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')).
% 0.20/0.47 tff(75,plain,
% 0.20/0.47 (![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)))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.20/0.47 tff(76,plain,
% 0.20/0.47 (![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)))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.20/0.47 tff(77,plain,(
% 0.20/0.47 ![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)))))),
% 0.20/0.47 inference(skolemize,[status(sab)],[76])).
% 0.20/0.47 tff(78,plain,
% 0.20/0.47 (![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))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[77, 70])).
% 0.20/0.47 tff(79,plain,
% 0.20/0.47 (![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))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[78, 68])).
% 0.20/0.47 tff(80,plain,
% 0.20/0.47 (((~![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(function_inverse(B!13))) | (~function(function_inverse(B!13))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(function_inverse(B!13), C), A!14) = apply(C, apply(function_inverse(B!13), A!14))) | (~in(A!14, relation_dom(function_inverse(B!13))))))) <=> ((~![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(function_inverse(B!13))) | (~function(function_inverse(B!13))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(function_inverse(B!13), C), A!14) = apply(C, apply(function_inverse(B!13), A!14))) | (~in(A!14, relation_dom(function_inverse(B!13))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(81,plain,
% 0.20/0.47 (((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(function_inverse(B!13), C), A!14) = apply(C, apply(function_inverse(B!13), A!14))) | (~in(A!14, relation_dom(function_inverse(B!13)))))) <=> ((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(function_inverse(B!13), C), A!14) = apply(C, apply(function_inverse(B!13), A!14))) | (~in(A!14, relation_dom(function_inverse(B!13))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(82,plain,
% 0.20/0.47 (^[C: $i] : rewrite(((apply(relation_composition(function_inverse(B!13), C), A!14) = apply(C, apply(function_inverse(B!13), A!14))) | (~in(A!14, relation_dom(function_inverse(B!13)))) | (~relation(C)) | (~function(C))) <=> ((~relation(C)) | (~function(C)) | (apply(relation_composition(function_inverse(B!13), C), A!14) = apply(C, apply(function_inverse(B!13), A!14))) | (~in(A!14, relation_dom(function_inverse(B!13))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(83,plain,
% 0.20/0.47 (![C: $i] : ((apply(relation_composition(function_inverse(B!13), C), A!14) = apply(C, apply(function_inverse(B!13), A!14))) | (~in(A!14, relation_dom(function_inverse(B!13)))) | (~relation(C)) | (~function(C))) <=> ![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(function_inverse(B!13), C), A!14) = apply(C, apply(function_inverse(B!13), A!14))) | (~in(A!14, relation_dom(function_inverse(B!13)))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[82])).
% 0.20/0.47 tff(84,plain,
% 0.20/0.47 (((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | ![C: $i] : ((apply(relation_composition(function_inverse(B!13), C), A!14) = apply(C, apply(function_inverse(B!13), A!14))) | (~in(A!14, relation_dom(function_inverse(B!13)))) | (~relation(C)) | (~function(C)))) <=> ((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(function_inverse(B!13), C), A!14) = apply(C, apply(function_inverse(B!13), A!14))) | (~in(A!14, relation_dom(function_inverse(B!13))))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[83])).
% 0.20/0.47 tff(85,plain,
% 0.20/0.47 (((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | ![C: $i] : ((apply(relation_composition(function_inverse(B!13), C), A!14) = apply(C, apply(function_inverse(B!13), A!14))) | (~in(A!14, relation_dom(function_inverse(B!13)))) | (~relation(C)) | (~function(C)))) <=> ((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(function_inverse(B!13), C), A!14) = apply(C, apply(function_inverse(B!13), A!14))) | (~in(A!14, relation_dom(function_inverse(B!13))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[84, 81])).
% 0.20/0.47 tff(86,plain,
% 0.20/0.47 (((~![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(function_inverse(B!13))) | (~function(function_inverse(B!13))) | ![C: $i] : ((apply(relation_composition(function_inverse(B!13), C), A!14) = apply(C, apply(function_inverse(B!13), A!14))) | (~in(A!14, relation_dom(function_inverse(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(function_inverse(B!13))) | (~function(function_inverse(B!13))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(function_inverse(B!13), C), A!14) = apply(C, apply(function_inverse(B!13), A!14))) | (~in(A!14, relation_dom(function_inverse(B!13)))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[85])).
% 0.20/0.48 tff(87,plain,
% 0.20/0.48 (((~![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(function_inverse(B!13))) | (~function(function_inverse(B!13))) | ![C: $i] : ((apply(relation_composition(function_inverse(B!13), C), A!14) = apply(C, apply(function_inverse(B!13), A!14))) | (~in(A!14, relation_dom(function_inverse(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(function_inverse(B!13))) | (~function(function_inverse(B!13))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(function_inverse(B!13), C), A!14) = apply(C, apply(function_inverse(B!13), A!14))) | (~in(A!14, relation_dom(function_inverse(B!13))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[86, 80])).
% 0.20/0.48 tff(88,plain,
% 0.20/0.48 ((~![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(function_inverse(B!13))) | (~function(function_inverse(B!13))) | ![C: $i] : ((apply(relation_composition(function_inverse(B!13), C), A!14) = apply(C, apply(function_inverse(B!13), A!14))) | (~in(A!14, relation_dom(function_inverse(B!13)))) | (~relation(C)) | (~function(C))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(89,plain,
% 0.20/0.48 ((~![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(function_inverse(B!13))) | (~function(function_inverse(B!13))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(function_inverse(B!13), C), A!14) = apply(C, apply(function_inverse(B!13), A!14))) | (~in(A!14, relation_dom(function_inverse(B!13)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.20/0.48 tff(90,plain,
% 0.20/0.48 ((~relation(function_inverse(B!13))) | (~function(function_inverse(B!13))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(function_inverse(B!13), C), A!14) = apply(C, apply(function_inverse(B!13), A!14))) | (~in(A!14, relation_dom(function_inverse(B!13)))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[89, 79])).
% 0.20/0.48 tff(91,plain,
% 0.20/0.48 (![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(function_inverse(B!13), C), A!14) = apply(C, apply(function_inverse(B!13), A!14))) | (~in(A!14, relation_dom(function_inverse(B!13)))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[90, 63, 61])).
% 0.20/0.48 tff(92,plain,
% 0.20/0.48 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(function_inverse(B!13), C), A!14) = apply(C, apply(function_inverse(B!13), A!14))) | (~in(A!14, relation_dom(function_inverse(B!13)))))) | ((~relation(B!13)) | (~function(B!13)) | (~in(A!14, relation_dom(function_inverse(B!13)))) | (apply(relation_composition(function_inverse(B!13), B!13), A!14) = apply(B!13, apply(function_inverse(B!13), A!14))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(function_inverse(B!13), C), A!14) = apply(C, apply(function_inverse(B!13), A!14))) | (~in(A!14, relation_dom(function_inverse(B!13)))))) | (~relation(B!13)) | (~function(B!13)) | (~in(A!14, relation_dom(function_inverse(B!13)))) | (apply(relation_composition(function_inverse(B!13), B!13), A!14) = apply(B!13, apply(function_inverse(B!13), A!14))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(93,plain,
% 0.20/0.48 (((~relation(B!13)) | (~function(B!13)) | (apply(relation_composition(function_inverse(B!13), B!13), A!14) = apply(B!13, apply(function_inverse(B!13), A!14))) | (~in(A!14, relation_dom(function_inverse(B!13))))) <=> ((~relation(B!13)) | (~function(B!13)) | (~in(A!14, relation_dom(function_inverse(B!13)))) | (apply(relation_composition(function_inverse(B!13), B!13), A!14) = apply(B!13, apply(function_inverse(B!13), A!14))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(94,plain,
% 0.20/0.48 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(function_inverse(B!13), C), A!14) = apply(C, apply(function_inverse(B!13), A!14))) | (~in(A!14, relation_dom(function_inverse(B!13)))))) | ((~relation(B!13)) | (~function(B!13)) | (apply(relation_composition(function_inverse(B!13), B!13), A!14) = apply(B!13, apply(function_inverse(B!13), A!14))) | (~in(A!14, relation_dom(function_inverse(B!13)))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(function_inverse(B!13), C), A!14) = apply(C, apply(function_inverse(B!13), A!14))) | (~in(A!14, relation_dom(function_inverse(B!13)))))) | ((~relation(B!13)) | (~function(B!13)) | (~in(A!14, relation_dom(function_inverse(B!13)))) | (apply(relation_composition(function_inverse(B!13), B!13), A!14) = apply(B!13, apply(function_inverse(B!13), A!14)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[93])).
% 0.20/0.48 tff(95,plain,
% 0.20/0.48 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(function_inverse(B!13), C), A!14) = apply(C, apply(function_inverse(B!13), A!14))) | (~in(A!14, relation_dom(function_inverse(B!13)))))) | ((~relation(B!13)) | (~function(B!13)) | (apply(relation_composition(function_inverse(B!13), B!13), A!14) = apply(B!13, apply(function_inverse(B!13), A!14))) | (~in(A!14, relation_dom(function_inverse(B!13)))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(function_inverse(B!13), C), A!14) = apply(C, apply(function_inverse(B!13), A!14))) | (~in(A!14, relation_dom(function_inverse(B!13)))))) | (~relation(B!13)) | (~function(B!13)) | (~in(A!14, relation_dom(function_inverse(B!13)))) | (apply(relation_composition(function_inverse(B!13), B!13), A!14) = apply(B!13, apply(function_inverse(B!13), A!14))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[94, 92])).
% 0.20/0.48 tff(96,plain,
% 0.20/0.48 ((~![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(function_inverse(B!13), C), A!14) = apply(C, apply(function_inverse(B!13), A!14))) | (~in(A!14, relation_dom(function_inverse(B!13)))))) | ((~relation(B!13)) | (~function(B!13)) | (apply(relation_composition(function_inverse(B!13), B!13), A!14) = apply(B!13, apply(function_inverse(B!13), A!14))) | (~in(A!14, relation_dom(function_inverse(B!13)))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(97,plain,
% 0.20/0.48 ((~![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(function_inverse(B!13), C), A!14) = apply(C, apply(function_inverse(B!13), A!14))) | (~in(A!14, relation_dom(function_inverse(B!13)))))) | (~relation(B!13)) | (~function(B!13)) | (~in(A!14, relation_dom(function_inverse(B!13)))) | (apply(relation_composition(function_inverse(B!13), B!13), A!14) = apply(B!13, apply(function_inverse(B!13), A!14)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.20/0.48 tff(98,plain,
% 0.20/0.48 ((~in(A!14, relation_dom(function_inverse(B!13)))) | (apply(relation_composition(function_inverse(B!13), B!13), A!14) = apply(B!13, apply(function_inverse(B!13), A!14)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[97, 18, 17, 91])).
% 0.20/0.48 tff(99,plain,
% 0.20/0.48 (apply(relation_composition(function_inverse(B!13), B!13), A!14) = apply(B!13, apply(function_inverse(B!13), A!14))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[98, 42])).
% 0.20/0.48 tff(100,plain,
% 0.20/0.48 ((A!14 = apply(relation_composition(function_inverse(B!13), B!13), A!14)) <=> (A!14 = apply(B!13, apply(function_inverse(B!13), A!14)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[99])).
% 0.20/0.48 tff(101,plain,
% 0.20/0.48 ((~(A!14 = apply(relation_composition(function_inverse(B!13), B!13), A!14))) <=> (~(A!14 = apply(B!13, apply(function_inverse(B!13), A!14))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[100])).
% 0.20/0.48 tff(102,plain,
% 0.20/0.48 (^[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))))))))))))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(103,plain,
% 0.20/0.48 (![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))))))))))))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[102])).
% 0.20/0.48 tff(104,plain,
% 0.20/0.48 (^[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)))))))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(105,plain,
% 0.20/0.48 (![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))))))))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[104])).
% 0.20/0.48 tff(106,plain,
% 0.20/0.48 (^[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)))))))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(107,plain,
% 0.20/0.48 (![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))))))))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[106])).
% 0.20/0.48 tff(108,plain,
% 0.20/0.48 (![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))))))))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[107, 105])).
% 0.20/0.48 tff(109,plain,
% 0.20/0.48 (^[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))))))))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(110,plain,
% 0.20/0.49 (![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))))))))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[109])).
% 0.20/0.49 tff(111,plain,
% 0.20/0.49 (^[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)))))))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(112,plain,
% 0.20/0.49 (![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)))))))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[111])).
% 0.20/0.49 tff(113,plain,
% 0.20/0.49 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((~(relation(B) & function(B))) | ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C)))))))) | (~one_to_one(A))) <=> ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((~(relation(B) & function(B))) | ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C)))))))) | (~one_to_one(A)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(114,plain,
% 0.20/0.49 (^[A: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite(((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((in(C, relation_rng(A)) & (D = apply(B, C))) => (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((in(D, relation_dom(A)) & (C = apply(A, D))) => (in(C, relation_rng(A)) & (D = apply(B, C))))))) <=> ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C)))))))), (((relation(B) & function(B)) => ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((in(C, relation_rng(A)) & (D = apply(B, C))) => (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((in(D, relation_dom(A)) & (C = apply(A, D))) => (in(C, relation_rng(A)) & (D = apply(B, C)))))))) <=> ((relation(B) & function(B)) => ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C)))))))))), rewrite(((relation(B) & function(B)) => ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C)))))))) <=> ((~(relation(B) & function(B))) | ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))))), (((relation(B) & function(B)) => ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((in(C, relation_rng(A)) & (D = apply(B, C))) => (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((in(D, relation_dom(A)) & (C = apply(A, D))) => (in(C, relation_rng(A)) & (D = apply(B, C)))))))) <=> ((~(relation(B) & function(B))) | ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))))))), (![B: $i] : ((relation(B) & function(B)) => ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((in(C, relation_rng(A)) & (D = apply(B, C))) => (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((in(D, relation_dom(A)) & (C = apply(A, D))) => (in(C, relation_rng(A)) & (D = apply(B, C)))))))) <=> ![B: $i] : ((~(relation(B) & function(B))) | ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C)))))))))), ((one_to_one(A) => ![B: $i] : ((relation(B) & function(B)) => ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((in(C, relation_rng(A)) & (D = apply(B, C))) => (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((in(D, relation_dom(A)) & (C = apply(A, D))) => (in(C, relation_rng(A)) & (D = apply(B, C))))))))) <=> (one_to_one(A) => ![B: $i] : ((~(relation(B) & function(B))) | ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))))))), rewrite((one_to_one(A) => ![B: $i] : ((~(relation(B) & function(B))) | ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))))) <=> ((~one_to_one(A)) | ![B: $i] : ((~(relation(B) & function(B))) | ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C)))))))))), ((one_to_one(A) => ![B: $i] : ((relation(B) & function(B)) => ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((in(C, relation_rng(A)) & (D = apply(B, C))) => (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((in(D, relation_dom(A)) & (C = apply(A, D))) => (in(C, relation_rng(A)) & (D = apply(B, C))))))))) <=> ((~one_to_one(A)) | ![B: $i] : ((~(relation(B) & function(B))) | ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C))))))))))), (((relation(A) & function(A)) => (one_to_one(A) => ![B: $i] : ((relation(B) & function(B)) => ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((in(C, relation_rng(A)) & (D = apply(B, C))) => (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((in(D, relation_dom(A)) & (C = apply(A, D))) => (in(C, relation_rng(A)) & (D = apply(B, C)))))))))) <=> ((relation(A) & function(A)) => ((~one_to_one(A)) | ![B: $i] : ((~(relation(B) & function(B))) | ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C)))))))))))), rewrite(((relation(A) & function(A)) => ((~one_to_one(A)) | ![B: $i] : ((~(relation(B) & function(B))) | ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C)))))))))) <=> ((~(relation(A) & function(A))) | ![B: $i] : ((~(relation(B) & function(B))) | ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C)))))))) | (~one_to_one(A)))), (((relation(A) & function(A)) => (one_to_one(A) => ![B: $i] : ((relation(B) & function(B)) => ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((in(C, relation_rng(A)) & (D = apply(B, C))) => (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((in(D, relation_dom(A)) & (C = apply(A, D))) => (in(C, relation_rng(A)) & (D = apply(B, C)))))))))) <=> ((~(relation(A) & function(A))) | ![B: $i] : ((~(relation(B) & function(B))) | ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C)))))))) | (~one_to_one(A)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(115,plain,
% 0.20/0.49 (![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => ![B: $i] : ((relation(B) & function(B)) => ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((in(C, relation_rng(A)) & (D = apply(B, C))) => (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((in(D, relation_dom(A)) & (C = apply(A, D))) => (in(C, relation_rng(A)) & (D = apply(B, C)))))))))) <=> ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((~(relation(B) & function(B))) | ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C)))))))) | (~one_to_one(A)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[114])).
% 0.20/0.49 tff(116,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')).
% 0.20/0.49 tff(117,plain,
% 0.20/0.49 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((~(relation(B) & function(B))) | ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C)))))))) | (~one_to_one(A)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.20/0.49 tff(118,plain,
% 0.20/0.49 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((~(relation(B) & function(B))) | ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((~(in(C, relation_rng(A)) & (D = apply(B, C)))) | (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((~(in(D, relation_dom(A)) & (C = apply(A, D)))) | (in(C, relation_rng(A)) & (D = apply(B, C)))))))) | (~one_to_one(A)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[117, 113])).
% 0.20/0.49 tff(119,plain,(
% 0.20/0.49 ![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)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[118])).
% 0.20/0.49 tff(120,plain,
% 0.20/0.49 (![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)))))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[119, 112])).
% 0.20/0.49 tff(121,plain,
% 0.20/0.49 (![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))))))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[120, 110])).
% 0.20/0.49 tff(122,plain,
% 0.20/0.49 (![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))))))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[121, 108])).
% 0.20/0.49 tff(123,plain,
% 0.20/0.49 (![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))))))))))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[122, 103])).
% 0.20/0.49 tff(124,plain,
% 0.20/0.49 (((~![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_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))))))))))))))))) | (~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))))))))))))))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(125,plain,
% 0.20/0.49 (((~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)))))))))))))))))) <=> ((~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))))))))))))))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(126,plain,
% 0.20/0.49 (^[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)))))))))))))))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(127,plain,
% 0.20/0.50 (![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)))))))))))))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[126])).
% 0.20/0.50 tff(128,plain,
% 0.20/0.50 (((~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))))))))))))))))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[127])).
% 0.20/0.50 tff(129,plain,
% 0.20/0.50 (((~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))))))))))))))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[128, 125])).
% 0.20/0.50 tff(130,plain,
% 0.20/0.50 (((~![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))))))))))))))))) | ((~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)))))))))))))))))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[129])).
% 0.20/0.50 tff(131,plain,
% 0.20/0.50 (((~![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))))))))))))))))) | (~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))))))))))))))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[130, 124])).
% 0.20/0.50 tff(132,plain,
% 0.20/0.50 ((~![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))))))))))))))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(133,plain,
% 0.20/0.50 ((~![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_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)))))))))))))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.20/0.51 tff(134,plain,
% 0.20/0.51 (![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)))))))))))))))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[133, 123, 18, 17, 15])).
% 0.20/0.51 tff(135,plain,
% 0.20/0.51 (((~![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)))))))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(136,plain,
% 0.20/0.51 (((~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)))))))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(137,plain,
% 0.20/0.51 ((~((~((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))))))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(138,plain,
% 0.20/0.51 (((~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)))))))))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[137])).
% 0.20/0.51 tff(139,plain,
% 0.20/0.51 (((~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)))))))))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[138, 136])).
% 0.20/0.51 tff(140,plain,
% 0.20/0.51 (((~![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))))))))))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[139])).
% 0.20/0.51 tff(141,plain,
% 0.20/0.51 (((~![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)))))))))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[140, 135])).
% 0.20/0.51 tff(142,plain,
% 0.20/0.51 ((~![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)))))))))))))))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(143,plain,
% 0.20/0.51 ((~![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))))))))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.20/0.51 tff(144,plain,
% 0.20/0.51 ((~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))))))))))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[143, 134])).
% 0.20/0.52 tff(145,plain,
% 0.20/0.52 (~((~(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)))))))))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[144, 63, 61])).
% 0.20/0.52 tff(146,plain,
% 0.20/0.52 (((~(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)))))))))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(147,plain,
% 0.20/0.52 (![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)))))))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.20/0.52 tff(148,plain,
% 0.20/0.52 (((~![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(function_inverse(B!13), A!14), relation_dom(B!13))) | (~(A!14 = apply(B!13, apply(function_inverse(B!13), A!14)))) | in(A!14, relation_rng(B!13)))) | (~((~in(A!14, relation_rng(B!13))) | (~((~in(apply(function_inverse(B!13), A!14), relation_dom(B!13))) | (~(A!14 = apply(B!13, apply(function_inverse(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(apply(function_inverse(B!13), A!14), relation_dom(B!13))) | (~(A!14 = apply(B!13, apply(function_inverse(B!13), A!14)))) | in(A!14, relation_rng(B!13)))) | (~((~in(A!14, relation_rng(B!13))) | (~((~in(apply(function_inverse(B!13), A!14), relation_dom(B!13))) | (~(A!14 = apply(B!13, apply(function_inverse(B!13), A!14)))))))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(149,plain,
% 0.20/0.52 ((~((~((~in(A!14, relation_rng(B!13))) | (~((~in(apply(function_inverse(B!13), A!14), relation_dom(B!13))) | (~(A!14 = apply(B!13, apply(function_inverse(B!13), A!14)))))) | (~(apply(function_inverse(B!13), A!14) = apply(function_inverse(B!13), A!14))))) | (~((~in(apply(function_inverse(B!13), A!14), relation_dom(B!13))) | (~(A!14 = apply(B!13, apply(function_inverse(B!13), A!14)))) | (~((~in(A!14, relation_rng(B!13))) | (~(apply(function_inverse(B!13), A!14) = apply(function_inverse(B!13), A!14))))))))) <=> (~((~((~in(apply(function_inverse(B!13), A!14), relation_dom(B!13))) | (~(A!14 = apply(B!13, apply(function_inverse(B!13), A!14)))) | in(A!14, relation_rng(B!13)))) | (~((~in(A!14, relation_rng(B!13))) | (~((~in(apply(function_inverse(B!13), A!14), relation_dom(B!13))) | (~(A!14 = apply(B!13, apply(function_inverse(B!13), A!14))))))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(150,plain,
% 0.20/0.52 (((~![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_rng(B!13))) | (~((~in(apply(function_inverse(B!13), A!14), relation_dom(B!13))) | (~(A!14 = apply(B!13, apply(function_inverse(B!13), A!14)))))) | (~(apply(function_inverse(B!13), A!14) = apply(function_inverse(B!13), A!14))))) | (~((~in(apply(function_inverse(B!13), A!14), relation_dom(B!13))) | (~(A!14 = apply(B!13, apply(function_inverse(B!13), A!14)))) | (~((~in(A!14, relation_rng(B!13))) | (~(apply(function_inverse(B!13), A!14) = apply(function_inverse(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(apply(function_inverse(B!13), A!14), relation_dom(B!13))) | (~(A!14 = apply(B!13, apply(function_inverse(B!13), A!14)))) | in(A!14, relation_rng(B!13)))) | (~((~in(A!14, relation_rng(B!13))) | (~((~in(apply(function_inverse(B!13), A!14), relation_dom(B!13))) | (~(A!14 = apply(B!13, apply(function_inverse(B!13), A!14)))))))))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[149])).
% 0.20/0.52 tff(151,plain,
% 0.20/0.52 (((~![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_rng(B!13))) | (~((~in(apply(function_inverse(B!13), A!14), relation_dom(B!13))) | (~(A!14 = apply(B!13, apply(function_inverse(B!13), A!14)))))) | (~(apply(function_inverse(B!13), A!14) = apply(function_inverse(B!13), A!14))))) | (~((~in(apply(function_inverse(B!13), A!14), relation_dom(B!13))) | (~(A!14 = apply(B!13, apply(function_inverse(B!13), A!14)))) | (~((~in(A!14, relation_rng(B!13))) | (~(apply(function_inverse(B!13), A!14) = apply(function_inverse(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(apply(function_inverse(B!13), A!14), relation_dom(B!13))) | (~(A!14 = apply(B!13, apply(function_inverse(B!13), A!14)))) | in(A!14, relation_rng(B!13)))) | (~((~in(A!14, relation_rng(B!13))) | (~((~in(apply(function_inverse(B!13), A!14), relation_dom(B!13))) | (~(A!14 = apply(B!13, apply(function_inverse(B!13), A!14)))))))))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[150, 148])).
% 0.20/0.52 tff(152,plain,
% 0.20/0.52 ((~![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_rng(B!13))) | (~((~in(apply(function_inverse(B!13), A!14), relation_dom(B!13))) | (~(A!14 = apply(B!13, apply(function_inverse(B!13), A!14)))))) | (~(apply(function_inverse(B!13), A!14) = apply(function_inverse(B!13), A!14))))) | (~((~in(apply(function_inverse(B!13), A!14), relation_dom(B!13))) | (~(A!14 = apply(B!13, apply(function_inverse(B!13), A!14)))) | (~((~in(A!14, relation_rng(B!13))) | (~(apply(function_inverse(B!13), A!14) = apply(function_inverse(B!13), A!14)))))))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(153,plain,
% 0.20/0.52 ((~![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(function_inverse(B!13), A!14), relation_dom(B!13))) | (~(A!14 = apply(B!13, apply(function_inverse(B!13), A!14)))) | in(A!14, relation_rng(B!13)))) | (~((~in(A!14, relation_rng(B!13))) | (~((~in(apply(function_inverse(B!13), A!14), relation_dom(B!13))) | (~(A!14 = apply(B!13, apply(function_inverse(B!13), A!14))))))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.20/0.52 tff(154,plain,
% 0.20/0.52 (~((~((~in(apply(function_inverse(B!13), A!14), relation_dom(B!13))) | (~(A!14 = apply(B!13, apply(function_inverse(B!13), A!14)))) | in(A!14, relation_rng(B!13)))) | (~((~in(A!14, relation_rng(B!13))) | (~((~in(apply(function_inverse(B!13), A!14), relation_dom(B!13))) | (~(A!14 = apply(B!13, apply(function_inverse(B!13), A!14)))))))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[153, 147])).
% 0.20/0.52 tff(155,plain,
% 0.20/0.52 (((~((~in(apply(function_inverse(B!13), A!14), relation_dom(B!13))) | (~(A!14 = apply(B!13, apply(function_inverse(B!13), A!14)))) | in(A!14, relation_rng(B!13)))) | (~((~in(A!14, relation_rng(B!13))) | (~((~in(apply(function_inverse(B!13), A!14), relation_dom(B!13))) | (~(A!14 = apply(B!13, apply(function_inverse(B!13), A!14))))))))) | ((~in(A!14, relation_rng(B!13))) | (~((~in(apply(function_inverse(B!13), A!14), relation_dom(B!13))) | (~(A!14 = apply(B!13, apply(function_inverse(B!13), A!14)))))))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(156,plain,
% 0.20/0.52 ((~in(A!14, relation_rng(B!13))) | (~((~in(apply(function_inverse(B!13), A!14), relation_dom(B!13))) | (~(A!14 = apply(B!13, apply(function_inverse(B!13), A!14))))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[155, 154])).
% 0.20/0.52 tff(157,plain,
% 0.20/0.52 ((~((~in(A!14, relation_rng(B!13))) | (~((~in(apply(function_inverse(B!13), A!14), relation_dom(B!13))) | (~(A!14 = apply(B!13, apply(function_inverse(B!13), A!14)))))))) | (~in(A!14, relation_rng(B!13))) | (~((~in(apply(function_inverse(B!13), A!14), relation_dom(B!13))) | (~(A!14 = apply(B!13, apply(function_inverse(B!13), A!14))))))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(158,plain,
% 0.20/0.52 ((~((~in(A!14, relation_rng(B!13))) | (~((~in(apply(function_inverse(B!13), A!14), relation_dom(B!13))) | (~(A!14 = apply(B!13, apply(function_inverse(B!13), A!14)))))))) | (~((~in(apply(function_inverse(B!13), A!14), relation_dom(B!13))) | (~(A!14 = apply(B!13, apply(function_inverse(B!13), A!14))))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[157, 41])).
% 0.20/0.52 tff(159,plain,
% 0.20/0.52 (~((~in(apply(function_inverse(B!13), A!14), relation_dom(B!13))) | (~(A!14 = apply(B!13, apply(function_inverse(B!13), A!14)))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[158, 156])).
% 0.20/0.52 tff(160,plain,
% 0.20/0.52 (((~in(apply(function_inverse(B!13), A!14), relation_dom(B!13))) | (~(A!14 = apply(B!13, apply(function_inverse(B!13), A!14))))) | (A!14 = apply(B!13, apply(function_inverse(B!13), A!14)))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(161,plain,
% 0.20/0.52 (A!14 = apply(B!13, apply(function_inverse(B!13), A!14))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[160, 159])).
% 0.20/0.52 tff(162,plain,
% 0.20/0.52 ((~(~((~(A!14 = apply(B!13, apply(function_inverse(B!13), A!14)))) | (~(A!14 = apply(relation_composition(function_inverse(B!13), B!13), A!14)))))) <=> ((~(A!14 = apply(B!13, apply(function_inverse(B!13), A!14)))) | (~(A!14 = apply(relation_composition(function_inverse(B!13), B!13), A!14))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(163,plain,
% 0.20/0.52 (((A!14 = apply(B!13, apply(function_inverse(B!13), A!14))) & (A!14 = apply(relation_composition(function_inverse(B!13), B!13), A!14))) <=> (~((~(A!14 = apply(B!13, apply(function_inverse(B!13), A!14)))) | (~(A!14 = apply(relation_composition(function_inverse(B!13), B!13), A!14)))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(164,plain,
% 0.20/0.52 ((~((A!14 = apply(B!13, apply(function_inverse(B!13), A!14))) & (A!14 = apply(relation_composition(function_inverse(B!13), B!13), A!14)))) <=> (~(~((~(A!14 = apply(B!13, apply(function_inverse(B!13), A!14)))) | (~(A!14 = apply(relation_composition(function_inverse(B!13), B!13), A!14))))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[163])).
% 0.20/0.52 tff(165,plain,
% 0.20/0.52 ((~((A!14 = apply(B!13, apply(function_inverse(B!13), A!14))) & (A!14 = apply(relation_composition(function_inverse(B!13), B!13), A!14)))) <=> ((~(A!14 = apply(B!13, apply(function_inverse(B!13), A!14)))) | (~(A!14 = apply(relation_composition(function_inverse(B!13), B!13), A!14))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[164, 162])).
% 0.20/0.52 tff(166,plain,
% 0.20/0.52 (~((A!14 = apply(B!13, apply(function_inverse(B!13), A!14))) & (A!14 = apply(relation_composition(function_inverse(B!13), B!13), A!14)))),
% 0.20/0.52 inference(or_elim,[status(thm)],[13])).
% 0.20/0.52 tff(167,plain,
% 0.20/0.52 ((~(A!14 = apply(B!13, apply(function_inverse(B!13), A!14)))) | (~(A!14 = apply(relation_composition(function_inverse(B!13), B!13), A!14)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.20/0.52 tff(168,plain,
% 0.20/0.52 (~(A!14 = apply(relation_composition(function_inverse(B!13), B!13), A!14))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[167, 161])).
% 0.20/0.52 tff(169,plain,
% 0.20/0.52 (~(A!14 = apply(B!13, apply(function_inverse(B!13), A!14)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[168, 101])).
% 0.20/0.52 tff(170,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[161, 169])).
% 0.20/0.52 % SZS output end Proof
%------------------------------------------------------------------------------