%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU220+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:27:17 AM UTC 2025
% Result : Theorem 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU220+1 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 06:22:26 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.43 % SZS status Theorem
% 0.20/0.43 % SZS output start Proof
% 0.20/0.43 tff(apply_type, type, (
% 0.20/0.43 apply: ( $i * $i ) > $i)).
% 0.20/0.43 tff(tptp_fun_A_12_type, type, (
% 0.20/0.43 tptp_fun_A_12: $i)).
% 0.20/0.43 tff(function_inverse_type, type, (
% 0.20/0.43 function_inverse: $i > $i)).
% 0.20/0.43 tff(tptp_fun_B_11_type, type, (
% 0.20/0.43 tptp_fun_B_11: $i)).
% 0.20/0.43 tff(relation_composition_type, type, (
% 0.20/0.43 relation_composition: ( $i * $i ) > $i)).
% 0.20/0.43 tff(in_type, type, (
% 0.20/0.43 in: ( $i * $i ) > $o)).
% 0.20/0.43 tff(relation_dom_type, type, (
% 0.20/0.43 relation_dom: $i > $i)).
% 0.20/0.43 tff(relation_rng_type, type, (
% 0.20/0.43 relation_rng: $i > $i)).
% 0.20/0.43 tff(one_to_one_type, type, (
% 0.20/0.43 one_to_one: $i > $o)).
% 0.20/0.43 tff(function_type, type, (
% 0.20/0.43 function: $i > $o)).
% 0.20/0.43 tff(relation_type, type, (
% 0.20/0.43 relation: $i > $o)).
% 0.20/0.43 tff(tptp_fun_C_10_type, type, (
% 0.20/0.43 tptp_fun_C_10: ( $i * $i ) > $i)).
% 0.20/0.43 tff(tptp_fun_D_9_type, type, (
% 0.20/0.43 tptp_fun_D_9: ( $i * $i ) > $i)).
% 0.20/0.43 tff(1,plain,
% 0.20/0.43 ((~(((A!12 = apply(B!11, apply(function_inverse(B!11), A!12))) & (A!12 = apply(relation_composition(function_inverse(B!11), B!11), A!12))) | (~(relation(B!11) & function(B!11))) | (~(one_to_one(B!11) & in(A!12, relation_rng(B!11)))))) <=> (~(((A!12 = apply(B!11, apply(function_inverse(B!11), A!12))) & (A!12 = apply(relation_composition(function_inverse(B!11), B!11), A!12))) | (~(relation(B!11) & function(B!11))) | (~(one_to_one(B!11) & in(A!12, relation_rng(B!11))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(2,plain,
% 0.20/0.43 ((~![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))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(3,plain,
% 0.20/0.43 ((~![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))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 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/sandbox2/benchmark/theBenchmark.p','t57_funct_1')).
% 0.20/0.43 tff(5,plain,
% 0.20/0.43 (~![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)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.43 tff(6,plain,
% 0.20/0.43 (~![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)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.20/0.43 tff(7,plain,
% 0.20/0.43 (~![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)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.43 tff(8,plain,
% 0.20/0.43 (~![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)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.20/0.43 tff(9,plain,(
% 0.20/0.43 ~(((A!12 = apply(B!11, apply(function_inverse(B!11), A!12))) & (A!12 = apply(relation_composition(function_inverse(B!11), B!11), A!12))) | (~(relation(B!11) & function(B!11))) | (~(one_to_one(B!11) & in(A!12, relation_rng(B!11)))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[8])).
% 0.20/0.43 tff(10,plain,
% 0.20/0.43 (~(((A!12 = apply(B!11, apply(function_inverse(B!11), A!12))) & (A!12 = apply(relation_composition(function_inverse(B!11), B!11), A!12))) | (~(relation(B!11) & function(B!11))) | (~(one_to_one(B!11) & in(A!12, relation_rng(B!11)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.20/0.43 tff(11,plain,
% 0.20/0.43 (one_to_one(B!11) & in(A!12, relation_rng(B!11))),
% 0.20/0.43 inference(or_elim,[status(thm)],[10])).
% 0.20/0.43 tff(12,plain,
% 0.20/0.43 (one_to_one(B!11)),
% 0.20/0.43 inference(and_elim,[status(thm)],[11])).
% 0.20/0.43 tff(13,plain,
% 0.20/0.43 (relation(B!11) & function(B!11)),
% 0.20/0.43 inference(or_elim,[status(thm)],[10])).
% 0.20/0.43 tff(14,plain,
% 0.20/0.43 (function(B!11)),
% 0.20/0.43 inference(and_elim,[status(thm)],[13])).
% 0.20/0.43 tff(15,plain,
% 0.20/0.43 (relation(B!11)),
% 0.20/0.43 inference(and_elim,[status(thm)],[13])).
% 0.20/0.43 tff(16,plain,
% 0.20/0.43 (^[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))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(17,plain,
% 0.20/0.43 (![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)))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[16])).
% 0.20/0.43 tff(18,plain,
% 0.20/0.43 (^[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)))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(19,plain,
% 0.20/0.43 (![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)))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[18])).
% 0.20/0.43 tff(20,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(21,plain,
% 0.20/0.43 (^[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)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(22,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[21])).
% 0.20/0.43 tff(23,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/sandbox2/benchmark/theBenchmark.p','t55_funct_1')).
% 0.20/0.43 tff(24,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.43 tff(25,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.20/0.43 tff(26,plain,(
% 0.20/0.43 ![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)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[25])).
% 0.20/0.43 tff(27,plain,
% 0.20/0.43 (![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)))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.20/0.43 tff(28,plain,
% 0.20/0.43 (![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)))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.20/0.43 tff(29,plain,
% 0.20/0.43 (((~![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!11)) | (~relation(B!11)) | (~function(B!11)) | (~((~(relation_rng(B!11) = relation_dom(function_inverse(B!11)))) | (~(relation_dom(B!11) = relation_rng(function_inverse(B!11)))))))) <=> ((~![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!11)) | (~relation(B!11)) | (~function(B!11)) | (~((~(relation_rng(B!11) = relation_dom(function_inverse(B!11)))) | (~(relation_dom(B!11) = relation_rng(function_inverse(B!11)))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(30,plain,
% 0.20/0.43 ((~![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!11)) | (~relation(B!11)) | (~function(B!11)) | (~((~(relation_rng(B!11) = relation_dom(function_inverse(B!11)))) | (~(relation_dom(B!11) = relation_rng(function_inverse(B!11)))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(31,plain,
% 0.20/0.43 ((~![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!11)) | (~relation(B!11)) | (~function(B!11)) | (~((~(relation_rng(B!11) = relation_dom(function_inverse(B!11)))) | (~(relation_dom(B!11) = relation_rng(function_inverse(B!11))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.20/0.43 tff(32,plain,
% 0.20/0.43 (~((~(relation_rng(B!11) = relation_dom(function_inverse(B!11)))) | (~(relation_dom(B!11) = relation_rng(function_inverse(B!11)))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[31, 28, 15, 14, 12])).
% 0.20/0.43 tff(33,plain,
% 0.20/0.43 (((~(relation_rng(B!11) = relation_dom(function_inverse(B!11)))) | (~(relation_dom(B!11) = relation_rng(function_inverse(B!11))))) | (relation_rng(B!11) = relation_dom(function_inverse(B!11)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(34,plain,
% 0.20/0.43 (relation_rng(B!11) = relation_dom(function_inverse(B!11))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.20/0.43 tff(35,plain,
% 0.20/0.43 (relation_dom(function_inverse(B!11)) = relation_rng(B!11)),
% 0.20/0.43 inference(symmetry,[status(thm)],[34])).
% 0.20/0.43 tff(36,plain,
% 0.20/0.43 (in(A!12, relation_dom(function_inverse(B!11))) <=> in(A!12, relation_rng(B!11))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[35])).
% 0.20/0.43 tff(37,plain,
% 0.20/0.43 (in(A!12, relation_rng(B!11)) <=> in(A!12, relation_dom(function_inverse(B!11)))),
% 0.20/0.43 inference(symmetry,[status(thm)],[36])).
% 0.20/0.43 tff(38,plain,
% 0.20/0.43 (in(A!12, relation_rng(B!11))),
% 0.20/0.43 inference(and_elim,[status(thm)],[11])).
% 0.20/0.43 tff(39,plain,
% 0.20/0.43 (in(A!12, relation_dom(function_inverse(B!11)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.20/0.43 tff(40,plain,
% 0.20/0.43 (^[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)))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(41,plain,
% 0.20/0.43 (![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))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[40])).
% 0.20/0.43 tff(42,plain,
% 0.20/0.43 (^[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))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(43,plain,
% 0.20/0.44 (![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))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[42])).
% 0.20/0.44 tff(44,plain,
% 0.20/0.44 (![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))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(45,plain,
% 0.20/0.44 (^[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)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(46,plain,
% 0.20/0.44 (![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))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[45])).
% 0.20/0.44 tff(47,axiom,(![A: $i] : ((relation(A) & function(A)) => (relation(function_inverse(A)) & function(function_inverse(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k2_funct_1')).
% 0.20/0.44 tff(48,plain,
% 0.20/0.44 (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.20/0.44 tff(49,plain,
% 0.20/0.44 (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.20/0.44 tff(50,plain,(
% 0.20/0.44 ![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 0.20/0.44 inference(skolemize,[status(sab)],[49])).
% 0.20/0.44 tff(51,plain,
% 0.20/0.44 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.20/0.44 tff(52,plain,
% 0.20/0.44 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[51, 41])).
% 0.20/0.44 tff(53,plain,
% 0.20/0.44 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | ((~relation(B!11)) | (~function(B!11)) | (~((~function(function_inverse(B!11))) | (~relation(function_inverse(B!11))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | (~relation(B!11)) | (~function(B!11)) | (~((~function(function_inverse(B!11))) | (~relation(function_inverse(B!11))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(54,plain,
% 0.20/0.44 (((~relation(B!11)) | (~function(B!11)) | (~((~function(function_inverse(B!11))) | (~relation(function_inverse(B!11)))))) <=> ((~relation(B!11)) | (~function(B!11)) | (~((~function(function_inverse(B!11))) | (~relation(function_inverse(B!11))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(55,plain,
% 0.20/0.44 ((~((~relation(function_inverse(B!11))) | (~function(function_inverse(B!11))))) <=> (~((~function(function_inverse(B!11))) | (~relation(function_inverse(B!11)))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(56,plain,
% 0.20/0.44 (((~relation(B!11)) | (~function(B!11)) | (~((~relation(function_inverse(B!11))) | (~function(function_inverse(B!11)))))) <=> ((~relation(B!11)) | (~function(B!11)) | (~((~function(function_inverse(B!11))) | (~relation(function_inverse(B!11))))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[55])).
% 0.20/0.44 tff(57,plain,
% 0.20/0.44 (((~relation(B!11)) | (~function(B!11)) | (~((~relation(function_inverse(B!11))) | (~function(function_inverse(B!11)))))) <=> ((~relation(B!11)) | (~function(B!11)) | (~((~function(function_inverse(B!11))) | (~relation(function_inverse(B!11))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[56, 54])).
% 0.20/0.44 tff(58,plain,
% 0.20/0.44 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | ((~relation(B!11)) | (~function(B!11)) | (~((~relation(function_inverse(B!11))) | (~function(function_inverse(B!11))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | ((~relation(B!11)) | (~function(B!11)) | (~((~function(function_inverse(B!11))) | (~relation(function_inverse(B!11)))))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[57])).
% 0.20/0.44 tff(59,plain,
% 0.20/0.44 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | ((~relation(B!11)) | (~function(B!11)) | (~((~relation(function_inverse(B!11))) | (~function(function_inverse(B!11))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | (~relation(B!11)) | (~function(B!11)) | (~((~function(function_inverse(B!11))) | (~relation(function_inverse(B!11))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[58, 53])).
% 0.20/0.44 tff(60,plain,
% 0.20/0.44 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | ((~relation(B!11)) | (~function(B!11)) | (~((~relation(function_inverse(B!11))) | (~function(function_inverse(B!11))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(61,plain,
% 0.20/0.44 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | (~relation(B!11)) | (~function(B!11)) | (~((~function(function_inverse(B!11))) | (~relation(function_inverse(B!11)))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.20/0.44 tff(62,plain,
% 0.20/0.44 (~((~function(function_inverse(B!11))) | (~relation(function_inverse(B!11))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[61, 52, 15, 14])).
% 0.20/0.44 tff(63,plain,
% 0.20/0.44 (((~function(function_inverse(B!11))) | (~relation(function_inverse(B!11)))) | function(function_inverse(B!11))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(64,plain,
% 0.20/0.44 (function(function_inverse(B!11))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.20/0.44 tff(65,plain,
% 0.20/0.44 (((~function(function_inverse(B!11))) | (~relation(function_inverse(B!11)))) | relation(function_inverse(B!11))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(66,plain,
% 0.20/0.44 (relation(function_inverse(B!11))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[65, 62])).
% 0.20/0.44 tff(67,plain,
% 0.20/0.44 (^[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)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(68,plain,
% 0.20/0.44 (![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))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[67])).
% 0.20/0.44 tff(69,plain,
% 0.20/0.44 (^[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)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(70,plain,
% 0.20/0.44 (![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))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[69])).
% 0.20/0.44 tff(71,plain,
% 0.20/0.44 (![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))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[70, 68])).
% 0.20/0.44 tff(72,plain,
% 0.20/0.44 (^[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))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(73,plain,
% 0.20/0.44 (![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))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[72])).
% 0.20/0.44 tff(74,plain,
% 0.20/0.44 (![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)))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(75,plain,
% 0.20/0.44 (^[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)))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(76,plain,
% 0.20/0.44 (![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)))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[75])).
% 0.20/0.44 tff(77,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/sandbox2/benchmark/theBenchmark.p','t23_funct_1')).
% 0.20/0.44 tff(78,plain,
% 0.20/0.44 (![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)))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.20/0.44 tff(79,plain,
% 0.20/0.44 (![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)))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.20/0.44 tff(80,plain,(
% 0.20/0.44 ![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)))))),
% 0.20/0.44 inference(skolemize,[status(sab)],[79])).
% 0.20/0.44 tff(81,plain,
% 0.20/0.44 (![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))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.20/0.44 tff(82,plain,
% 0.20/0.44 (![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))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[81, 71])).
% 0.20/0.44 tff(83,plain,
% 0.20/0.44 (((~![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))))) | ((~function(function_inverse(B!11))) | (~relation(function_inverse(B!11))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(function_inverse(B!11), C), A!12) = apply(C, apply(function_inverse(B!11), A!12))) | (~in(A!12, relation_dom(function_inverse(B!11))))))) <=> ((~![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))))) | (~function(function_inverse(B!11))) | (~relation(function_inverse(B!11))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(function_inverse(B!11), C), A!12) = apply(C, apply(function_inverse(B!11), A!12))) | (~in(A!12, relation_dom(function_inverse(B!11))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(84,plain,
% 0.20/0.44 (((~relation(function_inverse(B!11))) | (~function(function_inverse(B!11))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(function_inverse(B!11), C), A!12) = apply(C, apply(function_inverse(B!11), A!12))) | (~in(A!12, relation_dom(function_inverse(B!11)))))) <=> ((~function(function_inverse(B!11))) | (~relation(function_inverse(B!11))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(function_inverse(B!11), C), A!12) = apply(C, apply(function_inverse(B!11), A!12))) | (~in(A!12, relation_dom(function_inverse(B!11))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(85,plain,
% 0.20/0.44 (^[C: $i] : rewrite(((apply(relation_composition(function_inverse(B!11), C), A!12) = apply(C, apply(function_inverse(B!11), A!12))) | (~in(A!12, relation_dom(function_inverse(B!11)))) | (~relation(C)) | (~function(C))) <=> ((~relation(C)) | (~function(C)) | (apply(relation_composition(function_inverse(B!11), C), A!12) = apply(C, apply(function_inverse(B!11), A!12))) | (~in(A!12, relation_dom(function_inverse(B!11))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(86,plain,
% 0.20/0.44 (![C: $i] : ((apply(relation_composition(function_inverse(B!11), C), A!12) = apply(C, apply(function_inverse(B!11), A!12))) | (~in(A!12, relation_dom(function_inverse(B!11)))) | (~relation(C)) | (~function(C))) <=> ![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(function_inverse(B!11), C), A!12) = apply(C, apply(function_inverse(B!11), A!12))) | (~in(A!12, relation_dom(function_inverse(B!11)))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[85])).
% 0.20/0.44 tff(87,plain,
% 0.20/0.44 (((~relation(function_inverse(B!11))) | (~function(function_inverse(B!11))) | ![C: $i] : ((apply(relation_composition(function_inverse(B!11), C), A!12) = apply(C, apply(function_inverse(B!11), A!12))) | (~in(A!12, relation_dom(function_inverse(B!11)))) | (~relation(C)) | (~function(C)))) <=> ((~relation(function_inverse(B!11))) | (~function(function_inverse(B!11))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(function_inverse(B!11), C), A!12) = apply(C, apply(function_inverse(B!11), A!12))) | (~in(A!12, relation_dom(function_inverse(B!11))))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[86])).
% 0.20/0.45 tff(88,plain,
% 0.20/0.45 (((~relation(function_inverse(B!11))) | (~function(function_inverse(B!11))) | ![C: $i] : ((apply(relation_composition(function_inverse(B!11), C), A!12) = apply(C, apply(function_inverse(B!11), A!12))) | (~in(A!12, relation_dom(function_inverse(B!11)))) | (~relation(C)) | (~function(C)))) <=> ((~function(function_inverse(B!11))) | (~relation(function_inverse(B!11))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(function_inverse(B!11), C), A!12) = apply(C, apply(function_inverse(B!11), A!12))) | (~in(A!12, relation_dom(function_inverse(B!11))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[87, 84])).
% 0.20/0.45 tff(89,plain,
% 0.20/0.45 (((~![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!11))) | (~function(function_inverse(B!11))) | ![C: $i] : ((apply(relation_composition(function_inverse(B!11), C), A!12) = apply(C, apply(function_inverse(B!11), A!12))) | (~in(A!12, relation_dom(function_inverse(B!11)))) | (~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))))) | ((~function(function_inverse(B!11))) | (~relation(function_inverse(B!11))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(function_inverse(B!11), C), A!12) = apply(C, apply(function_inverse(B!11), A!12))) | (~in(A!12, relation_dom(function_inverse(B!11)))))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[88])).
% 0.20/0.45 tff(90,plain,
% 0.20/0.45 (((~![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!11))) | (~function(function_inverse(B!11))) | ![C: $i] : ((apply(relation_composition(function_inverse(B!11), C), A!12) = apply(C, apply(function_inverse(B!11), A!12))) | (~in(A!12, relation_dom(function_inverse(B!11)))) | (~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))))) | (~function(function_inverse(B!11))) | (~relation(function_inverse(B!11))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(function_inverse(B!11), C), A!12) = apply(C, apply(function_inverse(B!11), A!12))) | (~in(A!12, relation_dom(function_inverse(B!11))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[89, 83])).
% 0.20/0.45 tff(91,plain,
% 0.20/0.45 ((~![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!11))) | (~function(function_inverse(B!11))) | ![C: $i] : ((apply(relation_composition(function_inverse(B!11), C), A!12) = apply(C, apply(function_inverse(B!11), A!12))) | (~in(A!12, relation_dom(function_inverse(B!11)))) | (~relation(C)) | (~function(C))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(92,plain,
% 0.20/0.45 ((~![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))))) | (~function(function_inverse(B!11))) | (~relation(function_inverse(B!11))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(function_inverse(B!11), C), A!12) = apply(C, apply(function_inverse(B!11), A!12))) | (~in(A!12, relation_dom(function_inverse(B!11)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.20/0.45 tff(93,plain,
% 0.20/0.45 ((~function(function_inverse(B!11))) | (~relation(function_inverse(B!11))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(function_inverse(B!11), C), A!12) = apply(C, apply(function_inverse(B!11), A!12))) | (~in(A!12, relation_dom(function_inverse(B!11)))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[92, 82])).
% 0.20/0.45 tff(94,plain,
% 0.20/0.45 (![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(function_inverse(B!11), C), A!12) = apply(C, apply(function_inverse(B!11), A!12))) | (~in(A!12, relation_dom(function_inverse(B!11)))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[93, 66, 64])).
% 0.20/0.45 tff(95,plain,
% 0.20/0.45 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(function_inverse(B!11), C), A!12) = apply(C, apply(function_inverse(B!11), A!12))) | (~in(A!12, relation_dom(function_inverse(B!11)))))) | ((~relation(B!11)) | (~function(B!11)) | (~in(A!12, relation_dom(function_inverse(B!11)))) | (apply(relation_composition(function_inverse(B!11), B!11), A!12) = apply(B!11, apply(function_inverse(B!11), A!12))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(function_inverse(B!11), C), A!12) = apply(C, apply(function_inverse(B!11), A!12))) | (~in(A!12, relation_dom(function_inverse(B!11)))))) | (~relation(B!11)) | (~function(B!11)) | (~in(A!12, relation_dom(function_inverse(B!11)))) | (apply(relation_composition(function_inverse(B!11), B!11), A!12) = apply(B!11, apply(function_inverse(B!11), A!12))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(96,plain,
% 0.20/0.45 (((~relation(B!11)) | (~function(B!11)) | (apply(relation_composition(function_inverse(B!11), B!11), A!12) = apply(B!11, apply(function_inverse(B!11), A!12))) | (~in(A!12, relation_dom(function_inverse(B!11))))) <=> ((~relation(B!11)) | (~function(B!11)) | (~in(A!12, relation_dom(function_inverse(B!11)))) | (apply(relation_composition(function_inverse(B!11), B!11), A!12) = apply(B!11, apply(function_inverse(B!11), A!12))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(97,plain,
% 0.20/0.45 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(function_inverse(B!11), C), A!12) = apply(C, apply(function_inverse(B!11), A!12))) | (~in(A!12, relation_dom(function_inverse(B!11)))))) | ((~relation(B!11)) | (~function(B!11)) | (apply(relation_composition(function_inverse(B!11), B!11), A!12) = apply(B!11, apply(function_inverse(B!11), A!12))) | (~in(A!12, relation_dom(function_inverse(B!11)))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(function_inverse(B!11), C), A!12) = apply(C, apply(function_inverse(B!11), A!12))) | (~in(A!12, relation_dom(function_inverse(B!11)))))) | ((~relation(B!11)) | (~function(B!11)) | (~in(A!12, relation_dom(function_inverse(B!11)))) | (apply(relation_composition(function_inverse(B!11), B!11), A!12) = apply(B!11, apply(function_inverse(B!11), A!12)))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[96])).
% 0.20/0.45 tff(98,plain,
% 0.20/0.45 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(function_inverse(B!11), C), A!12) = apply(C, apply(function_inverse(B!11), A!12))) | (~in(A!12, relation_dom(function_inverse(B!11)))))) | ((~relation(B!11)) | (~function(B!11)) | (apply(relation_composition(function_inverse(B!11), B!11), A!12) = apply(B!11, apply(function_inverse(B!11), A!12))) | (~in(A!12, relation_dom(function_inverse(B!11)))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(function_inverse(B!11), C), A!12) = apply(C, apply(function_inverse(B!11), A!12))) | (~in(A!12, relation_dom(function_inverse(B!11)))))) | (~relation(B!11)) | (~function(B!11)) | (~in(A!12, relation_dom(function_inverse(B!11)))) | (apply(relation_composition(function_inverse(B!11), B!11), A!12) = apply(B!11, apply(function_inverse(B!11), A!12))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[97, 95])).
% 0.20/0.45 tff(99,plain,
% 0.20/0.45 ((~![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(function_inverse(B!11), C), A!12) = apply(C, apply(function_inverse(B!11), A!12))) | (~in(A!12, relation_dom(function_inverse(B!11)))))) | ((~relation(B!11)) | (~function(B!11)) | (apply(relation_composition(function_inverse(B!11), B!11), A!12) = apply(B!11, apply(function_inverse(B!11), A!12))) | (~in(A!12, relation_dom(function_inverse(B!11)))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(100,plain,
% 0.20/0.45 ((~![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(function_inverse(B!11), C), A!12) = apply(C, apply(function_inverse(B!11), A!12))) | (~in(A!12, relation_dom(function_inverse(B!11)))))) | (~relation(B!11)) | (~function(B!11)) | (~in(A!12, relation_dom(function_inverse(B!11)))) | (apply(relation_composition(function_inverse(B!11), B!11), A!12) = apply(B!11, apply(function_inverse(B!11), A!12)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.20/0.45 tff(101,plain,
% 0.20/0.45 ((~in(A!12, relation_dom(function_inverse(B!11)))) | (apply(relation_composition(function_inverse(B!11), B!11), A!12) = apply(B!11, apply(function_inverse(B!11), A!12)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[100, 15, 14, 94])).
% 0.20/0.45 tff(102,plain,
% 0.20/0.45 (apply(relation_composition(function_inverse(B!11), B!11), A!12) = apply(B!11, apply(function_inverse(B!11), A!12))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[101, 39])).
% 0.20/0.45 tff(103,plain,
% 0.20/0.45 ((A!12 = apply(relation_composition(function_inverse(B!11), B!11), A!12)) <=> (A!12 = apply(B!11, apply(function_inverse(B!11), A!12)))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[102])).
% 0.20/0.45 tff(104,plain,
% 0.20/0.45 ((~(A!12 = apply(relation_composition(function_inverse(B!11), B!11), A!12))) <=> (~(A!12 = apply(B!11, apply(function_inverse(B!11), A!12))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[103])).
% 0.20/0.45 tff(105,plain,
% 0.20/0.45 (^[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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))))) <=> (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))))))))) <=> ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(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))))))))))))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(106,plain,
% 0.20/0.45 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))) | (~((~((~in(C, relation_rng(A))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))))) | (~((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(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))))))))))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[105])).
% 0.20/0.46 tff(107,plain,
% 0.20/0.46 (^[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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(108,plain,
% 0.20/0.46 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[107])).
% 0.20/0.46 tff(109,plain,
% 0.20/0.46 (^[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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(110,plain,
% 0.20/0.46 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[109])).
% 0.20/0.46 tff(111,plain,
% 0.20/0.46 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = function_inverse(A))) | (~((~(relation_dom(B) = relation_rng(A))) | (~![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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))))))))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[110, 108])).
% 0.20/0.46 tff(112,plain,
% 0.20/0.46 (^[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_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) <=> (~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))))), ((~(in(tptp_fun_C_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))) <=> (~(~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))))))), rewrite((~(~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))))) <=> ((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))), ((~(in(tptp_fun_C_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))) <=> ((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))))), rewrite((in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))) <=> (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))))), (((~(in(tptp_fun_C_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))) | (in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) <=> (((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))))))), rewrite((((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))))) <=> ((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))), (((~(in(tptp_fun_C_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))) | (in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) <=> ((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))))))), trans(monotonicity(trans(monotonicity(rewrite((in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))) <=> (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))))), ((~(in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) <=> (~(~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))))))), rewrite((~(~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))))) <=> ((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))), ((~(in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) <=> ((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))))), rewrite((in(tptp_fun_C_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) <=> (~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))))), (((~(in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) | (in(tptp_fun_C_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))) <=> (((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) | (~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))))))), rewrite((((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) | (~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))))) <=> ((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))), (((~(in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) | (in(tptp_fun_C_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))) <=> ((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))))), ((((~(in(tptp_fun_C_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))) | (in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) & ((~(in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) | (in(tptp_fun_C_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) <=> (((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))))) & ((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))), rewrite((((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))))) & ((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))) <=> (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))))))), ((((~(in(tptp_fun_C_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))) | (in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) & ((~(in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) | (in(tptp_fun_C_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) <=> (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))))), ((~(((~(in(tptp_fun_C_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))) | (in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) & ((~(in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) | (in(tptp_fun_C_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))))) <=> (~(~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))))))))), rewrite((~(~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))))))) <=> ((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))), ((~(((~(in(tptp_fun_C_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))) | (in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) & ((~(in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) | (in(tptp_fun_C_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))))) <=> ((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))))))), (((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))) | (in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) & ((~(in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) | (in(tptp_fun_C_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))))) <=> ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | ((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))))), rewrite(((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | ((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) <=> ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))), (((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~(((~(in(tptp_fun_C_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))) | (in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) & ((~(in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) | (in(tptp_fun_C_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))))) <=> ((B = function_inverse(A)) | (~(relation_dom(B) = relation_rng(A))) | (~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(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_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))) | (in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) & ((~(in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) | (in(tptp_fun_C_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(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_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))) | (in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) & ((~(in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) | (in(tptp_fun_C_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(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_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))) | (in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) & ((~(in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) | (in(tptp_fun_C_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(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_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))) | (in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) & ((~(in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) | (in(tptp_fun_C_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(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_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))) | (in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) & ((~(in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) | (in(tptp_fun_C_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(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_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))) | (in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) & ((~(in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) | (in(tptp_fun_C_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(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_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))) | (in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) & ((~(in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) | (in(tptp_fun_C_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))))))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(113,plain,
% 0.20/0.47 (![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_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))) | (in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) & ((~(in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) | (in(tptp_fun_C_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[112])).
% 0.20/0.47 tff(114,plain,
% 0.20/0.47 (^[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_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))) | (in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) & ((~(in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) | (in(tptp_fun_C_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(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_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))) | (in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) & ((~(in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) | (in(tptp_fun_C_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(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_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))) | (in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) & ((~(in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) | (in(tptp_fun_C_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(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_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))) | (in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) & ((~(in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) | (in(tptp_fun_C_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(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_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))) | (in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) & ((~(in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) | (in(tptp_fun_C_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(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_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))) | (in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) & ((~(in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) | (in(tptp_fun_C_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(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_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))) | (in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) & ((~(in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) | (in(tptp_fun_C_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(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_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))) | (in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) & ((~(in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) | (in(tptp_fun_C_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(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_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))) | (in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) & ((~(in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) | (in(tptp_fun_C_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(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_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))) | (in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) & ((~(in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) | (in(tptp_fun_C_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(115,plain,
% 0.20/0.47 (![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_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))) | (in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) & ((~(in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) | (in(tptp_fun_C_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(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_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))) | (in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) & ((~(in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) | (in(tptp_fun_C_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[114])).
% 0.20/0.47 tff(116,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(117,plain,
% 0.20/0.47 (^[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)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(118,plain,
% 0.20/0.48 (![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)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[117])).
% 0.20/0.48 tff(119,axiom,(![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => ![B: $i] : ((relation(B) & function(B)) => ((B = function_inverse(A)) <=> ((relation_dom(B) = relation_rng(A)) & ![C: $i, D: $i] : (((in(C, relation_rng(A)) & (D = apply(B, C))) => (in(D, relation_dom(A)) & (C = apply(A, D)))) & ((in(D, relation_dom(A)) & (C = apply(A, D))) => (in(C, relation_rng(A)) & (D = apply(B, C))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t54_funct_1')).
% 0.20/0.48 tff(120,plain,
% 0.20/0.48 (![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)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.20/0.48 tff(121,plain,
% 0.20/0.48 (![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)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[120, 116])).
% 0.20/0.48 tff(122,plain,(
% 0.20/0.48 ![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_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))) | (in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) & ((~(in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) | (in(tptp_fun_C_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))))))))) | (~one_to_one(A)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[121])).
% 0.20/0.48 tff(123,plain,
% 0.20/0.48 (![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_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A))))) | (in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) & ((~(in(tptp_fun_D_9(B, A), relation_dom(A)) & (tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))) | (in(tptp_fun_C_10(B, A), relation_rng(A)) & (tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[122, 115])).
% 0.20/0.48 tff(124,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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[123, 113])).
% 0.20/0.48 tff(125,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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A))))))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[124, 111])).
% 0.20/0.48 tff(126,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))) | (~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(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(modus_ponens,[status(thm)],[125, 106])).
% 0.20/0.48 tff(127,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))) | (~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(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!11)) | (~relation(B!11)) | (~function(B!11)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!11))) | (B = function_inverse(B!11)) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))))))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))))))))) | (~((~(B = function_inverse(B!11))) | (~((~(relation_dom(B) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11))))))))))))))))))) <=> ((~![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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(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!11)) | (~relation(B!11)) | (~function(B!11)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!11))) | (B = function_inverse(B!11)) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))))))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))))))))) | (~((~(B = function_inverse(B!11))) | (~((~(relation_dom(B) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11))))))))))))))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(128,plain,
% 0.20/0.48 (((~one_to_one(B!11)) | (~relation(B!11)) | (~function(B!11)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!11))) | (B = function_inverse(B!11)) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))))))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))))))))) | (~((~(B = function_inverse(B!11))) | (~((~(relation_dom(B) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11)))))))))))))))))) <=> ((~one_to_one(B!11)) | (~relation(B!11)) | (~function(B!11)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!11))) | (B = function_inverse(B!11)) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))))))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))))))))) | (~((~(B = function_inverse(B!11))) | (~((~(relation_dom(B) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11))))))))))))))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(129,plain,
% 0.20/0.48 (^[B: $i] : trans(monotonicity(rewrite((~((~((B = function_inverse(B!11)) | (~(relation_dom(B) = relation_rng(B!11))) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))))))) | (~((~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))))) | (~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))))))) | (~((~(B = function_inverse(B!11))) | (~((~(relation_dom(B) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!11))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))))) | (~((~((~in(C, relation_rng(B!11))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D)))))))))))))) <=> (~((~((~(relation_dom(B) = relation_rng(B!11))) | (B = function_inverse(B!11)) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))))))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))))))))) | (~((~(B = function_inverse(B!11))) | (~((~(relation_dom(B) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11))))))))))))))))), (((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!11)) | (~(relation_dom(B) = relation_rng(B!11))) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))))))) | (~((~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))))) | (~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))))))) | (~((~(B = function_inverse(B!11))) | (~((~(relation_dom(B) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!11))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))))) | (~((~((~in(C, relation_rng(B!11))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))))))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!11))) | (B = function_inverse(B!11)) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))))))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))))))))) | (~((~(B = function_inverse(B!11))) | (~((~(relation_dom(B) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11))))))))))))))))))), rewrite(((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!11))) | (B = function_inverse(B!11)) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))))))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))))))))) | (~((~(B = function_inverse(B!11))) | (~((~(relation_dom(B) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11))))))))))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!11))) | (B = function_inverse(B!11)) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))))))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))))))))) | (~((~(B = function_inverse(B!11))) | (~((~(relation_dom(B) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11)))))))))))))))))), (((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!11)) | (~(relation_dom(B) = relation_rng(B!11))) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))))))) | (~((~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))))) | (~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))))))) | (~((~(B = function_inverse(B!11))) | (~((~(relation_dom(B) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!11))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))))) | (~((~((~in(C, relation_rng(B!11))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))))))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!11))) | (B = function_inverse(B!11)) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))))))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))))))))) | (~((~(B = function_inverse(B!11))) | (~((~(relation_dom(B) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11)))))))))))))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(130,plain,
% 0.20/0.49 (![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!11)) | (~(relation_dom(B) = relation_rng(B!11))) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))))))) | (~((~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))))) | (~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))))))) | (~((~(B = function_inverse(B!11))) | (~((~(relation_dom(B) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!11))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))))) | (~((~((~in(C, relation_rng(B!11))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))))))))))))) <=> ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!11))) | (B = function_inverse(B!11)) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))))))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))))))))) | (~((~(B = function_inverse(B!11))) | (~((~(relation_dom(B) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11)))))))))))))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[129])).
% 0.20/0.49 tff(131,plain,
% 0.20/0.49 (((~one_to_one(B!11)) | (~relation(B!11)) | (~function(B!11)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!11)) | (~(relation_dom(B) = relation_rng(B!11))) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))))))) | (~((~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))))) | (~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))))))) | (~((~(B = function_inverse(B!11))) | (~((~(relation_dom(B) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!11))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))))) | (~((~((~in(C, relation_rng(B!11))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D)))))))))))))))) <=> ((~one_to_one(B!11)) | (~relation(B!11)) | (~function(B!11)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!11))) | (B = function_inverse(B!11)) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))))))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))))))))) | (~((~(B = function_inverse(B!11))) | (~((~(relation_dom(B) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11))))))))))))))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[130])).
% 0.20/0.49 tff(132,plain,
% 0.20/0.49 (((~one_to_one(B!11)) | (~relation(B!11)) | (~function(B!11)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!11)) | (~(relation_dom(B) = relation_rng(B!11))) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))))))) | (~((~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))))) | (~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))))))) | (~((~(B = function_inverse(B!11))) | (~((~(relation_dom(B) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!11))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))))) | (~((~((~in(C, relation_rng(B!11))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D)))))))))))))))) <=> ((~one_to_one(B!11)) | (~relation(B!11)) | (~function(B!11)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!11))) | (B = function_inverse(B!11)) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))))))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))))))))) | (~((~(B = function_inverse(B!11))) | (~((~(relation_dom(B) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11))))))))))))))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[131, 128])).
% 0.20/0.49 tff(133,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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(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!11)) | (~relation(B!11)) | (~function(B!11)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!11)) | (~(relation_dom(B) = relation_rng(B!11))) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))))))) | (~((~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))))) | (~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))))))) | (~((~(B = function_inverse(B!11))) | (~((~(relation_dom(B) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!11))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))))) | (~((~((~in(C, relation_rng(B!11))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(B!11))) | (~(C = apply(B!11, 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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(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!11)) | (~relation(B!11)) | (~function(B!11)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!11))) | (B = function_inverse(B!11)) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))))))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))))))))) | (~((~(B = function_inverse(B!11))) | (~((~(relation_dom(B) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11)))))))))))))))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[132])).
% 0.20/0.49 tff(134,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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(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!11)) | (~relation(B!11)) | (~function(B!11)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!11)) | (~(relation_dom(B) = relation_rng(B!11))) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))))))) | (~((~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))))) | (~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))))))) | (~((~(B = function_inverse(B!11))) | (~((~(relation_dom(B) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!11))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))))) | (~((~((~in(C, relation_rng(B!11))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(B!11))) | (~(C = apply(B!11, 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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(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!11)) | (~relation(B!11)) | (~function(B!11)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!11))) | (B = function_inverse(B!11)) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))))))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))))))))) | (~((~(B = function_inverse(B!11))) | (~((~(relation_dom(B) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11))))))))))))))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[133, 127])).
% 0.20/0.49 tff(135,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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(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!11)) | (~relation(B!11)) | (~function(B!11)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = function_inverse(B!11)) | (~(relation_dom(B) = relation_rng(B!11))) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))))))) | (~((~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))))) | (~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))))))) | (~((~(B = function_inverse(B!11))) | (~((~(relation_dom(B) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!11))) | (~(D = apply(B, C))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))))) | (~((~((~in(C, relation_rng(B!11))) | (~(D = apply(B, C))))) | (~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))))))))))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(136,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_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))) | (~((~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(B, A)))))))) | (~((~((~in(tptp_fun_C_10(B, A), relation_rng(A))) | (~(tptp_fun_D_9(B, A) = apply(B, tptp_fun_C_10(B, A)))))) | (~in(tptp_fun_D_9(B, A), relation_dom(A))) | (~(tptp_fun_C_10(B, A) = apply(A, tptp_fun_D_9(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!11)) | (~relation(B!11)) | (~function(B!11)) | ![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!11))) | (B = function_inverse(B!11)) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))))))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))))))))) | (~((~(B = function_inverse(B!11))) | (~((~(relation_dom(B) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11)))))))))))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.20/0.49 tff(137,plain,
% 0.20/0.49 (![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!11))) | (B = function_inverse(B!11)) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))))))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))))))))) | (~((~(B = function_inverse(B!11))) | (~((~(relation_dom(B) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11)))))))))))))))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[136, 126, 15, 14, 12])).
% 0.20/0.49 tff(138,plain,
% 0.20/0.49 (((~![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!11))) | (B = function_inverse(B!11)) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))))))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))))))))) | (~((~(B = function_inverse(B!11))) | (~((~(relation_dom(B) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11)))))))))))))))))) | ((~function(function_inverse(B!11))) | (~relation(function_inverse(B!11))) | (~((~(relation_dom(function_inverse(B!11)) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))) | (~(D = apply(function_inverse(B!11), C))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~in(C, relation_rng(B!11))) | (~(D = apply(function_inverse(B!11), C)))))))))))))) <=> ((~![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!11))) | (B = function_inverse(B!11)) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))))))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))))))))) | (~((~(B = function_inverse(B!11))) | (~((~(relation_dom(B) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11)))))))))))))))))) | (~function(function_inverse(B!11))) | (~relation(function_inverse(B!11))) | (~((~(relation_dom(function_inverse(B!11)) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))) | (~(D = apply(function_inverse(B!11), C))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~in(C, relation_rng(B!11))) | (~(D = apply(function_inverse(B!11), C)))))))))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(139,plain,
% 0.20/0.50 (((~relation(function_inverse(B!11))) | (~function(function_inverse(B!11))) | (~((~(relation_dom(function_inverse(B!11)) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))) | (~(D = apply(function_inverse(B!11), C))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~in(C, relation_rng(B!11))) | (~(D = apply(function_inverse(B!11), C))))))))))))) <=> ((~function(function_inverse(B!11))) | (~relation(function_inverse(B!11))) | (~((~(relation_dom(function_inverse(B!11)) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))) | (~(D = apply(function_inverse(B!11), C))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~in(C, relation_rng(B!11))) | (~(D = apply(function_inverse(B!11), C)))))))))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(140,plain,
% 0.20/0.50 ((~((~((~(relation_dom(function_inverse(B!11)) = relation_rng(B!11))) | (function_inverse(B!11) = function_inverse(B!11)) | (~((~in(tptp_fun_C_10(function_inverse(B!11), B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(function_inverse(B!11), B!11) = apply(function_inverse(B!11), tptp_fun_C_10(function_inverse(B!11), B!11)))) | (~((~in(tptp_fun_D_9(function_inverse(B!11), B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(function_inverse(B!11), B!11) = apply(B!11, tptp_fun_D_9(function_inverse(B!11), B!11)))))))) | (~((~in(tptp_fun_D_9(function_inverse(B!11), B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(function_inverse(B!11), B!11) = apply(B!11, tptp_fun_D_9(function_inverse(B!11), B!11)))) | (~((~in(tptp_fun_C_10(function_inverse(B!11), B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(function_inverse(B!11), B!11) = apply(function_inverse(B!11), tptp_fun_C_10(function_inverse(B!11), B!11)))))))))) | (~((~(function_inverse(B!11) = function_inverse(B!11))) | (~((~(relation_dom(function_inverse(B!11)) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~(D = apply(function_inverse(B!11), C))) | (~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~(D = apply(function_inverse(B!11), C))) | (~in(C, relation_rng(B!11)))))))))))))))) <=> (~((~(relation_dom(function_inverse(B!11)) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))) | (~(D = apply(function_inverse(B!11), C))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~in(C, relation_rng(B!11))) | (~(D = apply(function_inverse(B!11), C))))))))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(141,plain,
% 0.20/0.50 (((~relation(function_inverse(B!11))) | (~function(function_inverse(B!11))) | (~((~((~(relation_dom(function_inverse(B!11)) = relation_rng(B!11))) | (function_inverse(B!11) = function_inverse(B!11)) | (~((~in(tptp_fun_C_10(function_inverse(B!11), B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(function_inverse(B!11), B!11) = apply(function_inverse(B!11), tptp_fun_C_10(function_inverse(B!11), B!11)))) | (~((~in(tptp_fun_D_9(function_inverse(B!11), B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(function_inverse(B!11), B!11) = apply(B!11, tptp_fun_D_9(function_inverse(B!11), B!11)))))))) | (~((~in(tptp_fun_D_9(function_inverse(B!11), B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(function_inverse(B!11), B!11) = apply(B!11, tptp_fun_D_9(function_inverse(B!11), B!11)))) | (~((~in(tptp_fun_C_10(function_inverse(B!11), B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(function_inverse(B!11), B!11) = apply(function_inverse(B!11), tptp_fun_C_10(function_inverse(B!11), B!11)))))))))) | (~((~(function_inverse(B!11) = function_inverse(B!11))) | (~((~(relation_dom(function_inverse(B!11)) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~(D = apply(function_inverse(B!11), C))) | (~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~(D = apply(function_inverse(B!11), C))) | (~in(C, relation_rng(B!11))))))))))))))))) <=> ((~relation(function_inverse(B!11))) | (~function(function_inverse(B!11))) | (~((~(relation_dom(function_inverse(B!11)) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))) | (~(D = apply(function_inverse(B!11), C))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~in(C, relation_rng(B!11))) | (~(D = apply(function_inverse(B!11), C)))))))))))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[140])).
% 0.20/0.50 tff(142,plain,
% 0.20/0.50 (((~relation(function_inverse(B!11))) | (~function(function_inverse(B!11))) | (~((~((~(relation_dom(function_inverse(B!11)) = relation_rng(B!11))) | (function_inverse(B!11) = function_inverse(B!11)) | (~((~in(tptp_fun_C_10(function_inverse(B!11), B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(function_inverse(B!11), B!11) = apply(function_inverse(B!11), tptp_fun_C_10(function_inverse(B!11), B!11)))) | (~((~in(tptp_fun_D_9(function_inverse(B!11), B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(function_inverse(B!11), B!11) = apply(B!11, tptp_fun_D_9(function_inverse(B!11), B!11)))))))) | (~((~in(tptp_fun_D_9(function_inverse(B!11), B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(function_inverse(B!11), B!11) = apply(B!11, tptp_fun_D_9(function_inverse(B!11), B!11)))) | (~((~in(tptp_fun_C_10(function_inverse(B!11), B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(function_inverse(B!11), B!11) = apply(function_inverse(B!11), tptp_fun_C_10(function_inverse(B!11), B!11)))))))))) | (~((~(function_inverse(B!11) = function_inverse(B!11))) | (~((~(relation_dom(function_inverse(B!11)) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~(D = apply(function_inverse(B!11), C))) | (~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~(D = apply(function_inverse(B!11), C))) | (~in(C, relation_rng(B!11))))))))))))))))) <=> ((~function(function_inverse(B!11))) | (~relation(function_inverse(B!11))) | (~((~(relation_dom(function_inverse(B!11)) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))) | (~(D = apply(function_inverse(B!11), C))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~in(C, relation_rng(B!11))) | (~(D = apply(function_inverse(B!11), C)))))))))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[141, 139])).
% 0.20/0.50 tff(143,plain,
% 0.20/0.50 (((~![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!11))) | (B = function_inverse(B!11)) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))))))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))))))))) | (~((~(B = function_inverse(B!11))) | (~((~(relation_dom(B) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11)))))))))))))))))) | ((~relation(function_inverse(B!11))) | (~function(function_inverse(B!11))) | (~((~((~(relation_dom(function_inverse(B!11)) = relation_rng(B!11))) | (function_inverse(B!11) = function_inverse(B!11)) | (~((~in(tptp_fun_C_10(function_inverse(B!11), B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(function_inverse(B!11), B!11) = apply(function_inverse(B!11), tptp_fun_C_10(function_inverse(B!11), B!11)))) | (~((~in(tptp_fun_D_9(function_inverse(B!11), B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(function_inverse(B!11), B!11) = apply(B!11, tptp_fun_D_9(function_inverse(B!11), B!11)))))))) | (~((~in(tptp_fun_D_9(function_inverse(B!11), B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(function_inverse(B!11), B!11) = apply(B!11, tptp_fun_D_9(function_inverse(B!11), B!11)))) | (~((~in(tptp_fun_C_10(function_inverse(B!11), B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(function_inverse(B!11), B!11) = apply(function_inverse(B!11), tptp_fun_C_10(function_inverse(B!11), B!11)))))))))) | (~((~(function_inverse(B!11) = function_inverse(B!11))) | (~((~(relation_dom(function_inverse(B!11)) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~(D = apply(function_inverse(B!11), C))) | (~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~(D = apply(function_inverse(B!11), C))) | (~in(C, relation_rng(B!11)))))))))))))))))) <=> ((~![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!11))) | (B = function_inverse(B!11)) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))))))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))))))))) | (~((~(B = function_inverse(B!11))) | (~((~(relation_dom(B) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11)))))))))))))))))) | ((~function(function_inverse(B!11))) | (~relation(function_inverse(B!11))) | (~((~(relation_dom(function_inverse(B!11)) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))) | (~(D = apply(function_inverse(B!11), C))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~in(C, relation_rng(B!11))) | (~(D = apply(function_inverse(B!11), C))))))))))))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[142])).
% 0.20/0.50 tff(144,plain,
% 0.20/0.50 (((~![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!11))) | (B = function_inverse(B!11)) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))))))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))))))))) | (~((~(B = function_inverse(B!11))) | (~((~(relation_dom(B) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11)))))))))))))))))) | ((~relation(function_inverse(B!11))) | (~function(function_inverse(B!11))) | (~((~((~(relation_dom(function_inverse(B!11)) = relation_rng(B!11))) | (function_inverse(B!11) = function_inverse(B!11)) | (~((~in(tptp_fun_C_10(function_inverse(B!11), B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(function_inverse(B!11), B!11) = apply(function_inverse(B!11), tptp_fun_C_10(function_inverse(B!11), B!11)))) | (~((~in(tptp_fun_D_9(function_inverse(B!11), B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(function_inverse(B!11), B!11) = apply(B!11, tptp_fun_D_9(function_inverse(B!11), B!11)))))))) | (~((~in(tptp_fun_D_9(function_inverse(B!11), B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(function_inverse(B!11), B!11) = apply(B!11, tptp_fun_D_9(function_inverse(B!11), B!11)))) | (~((~in(tptp_fun_C_10(function_inverse(B!11), B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(function_inverse(B!11), B!11) = apply(function_inverse(B!11), tptp_fun_C_10(function_inverse(B!11), B!11)))))))))) | (~((~(function_inverse(B!11) = function_inverse(B!11))) | (~((~(relation_dom(function_inverse(B!11)) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~(D = apply(function_inverse(B!11), C))) | (~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~(D = apply(function_inverse(B!11), C))) | (~in(C, relation_rng(B!11)))))))))))))))))) <=> ((~![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!11))) | (B = function_inverse(B!11)) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))))))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))))))))) | (~((~(B = function_inverse(B!11))) | (~((~(relation_dom(B) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11)))))))))))))))))) | (~function(function_inverse(B!11))) | (~relation(function_inverse(B!11))) | (~((~(relation_dom(function_inverse(B!11)) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))) | (~(D = apply(function_inverse(B!11), C))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~in(C, relation_rng(B!11))) | (~(D = apply(function_inverse(B!11), C)))))))))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[143, 138])).
% 0.20/0.50 tff(145,plain,
% 0.20/0.50 ((~![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!11))) | (B = function_inverse(B!11)) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))))))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))))))))) | (~((~(B = function_inverse(B!11))) | (~((~(relation_dom(B) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11)))))))))))))))))) | ((~relation(function_inverse(B!11))) | (~function(function_inverse(B!11))) | (~((~((~(relation_dom(function_inverse(B!11)) = relation_rng(B!11))) | (function_inverse(B!11) = function_inverse(B!11)) | (~((~in(tptp_fun_C_10(function_inverse(B!11), B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(function_inverse(B!11), B!11) = apply(function_inverse(B!11), tptp_fun_C_10(function_inverse(B!11), B!11)))) | (~((~in(tptp_fun_D_9(function_inverse(B!11), B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(function_inverse(B!11), B!11) = apply(B!11, tptp_fun_D_9(function_inverse(B!11), B!11)))))))) | (~((~in(tptp_fun_D_9(function_inverse(B!11), B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(function_inverse(B!11), B!11) = apply(B!11, tptp_fun_D_9(function_inverse(B!11), B!11)))) | (~((~in(tptp_fun_C_10(function_inverse(B!11), B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(function_inverse(B!11), B!11) = apply(function_inverse(B!11), tptp_fun_C_10(function_inverse(B!11), B!11)))))))))) | (~((~(function_inverse(B!11) = function_inverse(B!11))) | (~((~(relation_dom(function_inverse(B!11)) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~(D = apply(function_inverse(B!11), C))) | (~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~(D = apply(function_inverse(B!11), C))) | (~in(C, relation_rng(B!11)))))))))))))))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(146,plain,
% 0.20/0.50 ((~![B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(relation_dom(B) = relation_rng(B!11))) | (B = function_inverse(B!11)) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))))))) | (~((~in(tptp_fun_D_9(B, B!11), relation_dom(B!11))) | (~(tptp_fun_C_10(B, B!11) = apply(B!11, tptp_fun_D_9(B, B!11)))) | (~((~in(tptp_fun_C_10(B, B!11), relation_rng(B!11))) | (~(tptp_fun_D_9(B, B!11) = apply(B, tptp_fun_C_10(B, B!11)))))))))) | (~((~(B = function_inverse(B!11))) | (~((~(relation_dom(B) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~(D = apply(B, C))) | (~in(C, relation_rng(B!11)))))))))))))))))) | (~function(function_inverse(B!11))) | (~relation(function_inverse(B!11))) | (~((~(relation_dom(function_inverse(B!11)) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))) | (~(D = apply(function_inverse(B!11), C))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~in(C, relation_rng(B!11))) | (~(D = apply(function_inverse(B!11), C))))))))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.20/0.50 tff(147,plain,
% 0.20/0.50 ((~function(function_inverse(B!11))) | (~relation(function_inverse(B!11))) | (~((~(relation_dom(function_inverse(B!11)) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))) | (~(D = apply(function_inverse(B!11), C))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~in(C, relation_rng(B!11))) | (~(D = apply(function_inverse(B!11), C))))))))))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[146, 137])).
% 0.20/0.50 tff(148,plain,
% 0.20/0.50 (~((~(relation_dom(function_inverse(B!11)) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))) | (~(D = apply(function_inverse(B!11), C))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~in(C, relation_rng(B!11))) | (~(D = apply(function_inverse(B!11), C)))))))))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[147, 66, 64])).
% 0.20/0.50 tff(149,plain,
% 0.20/0.50 (((~(relation_dom(function_inverse(B!11)) = relation_rng(B!11))) | (~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))) | (~(D = apply(function_inverse(B!11), C))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~in(C, relation_rng(B!11))) | (~(D = apply(function_inverse(B!11), C))))))))))) | ![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))) | (~(D = apply(function_inverse(B!11), C))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~in(C, relation_rng(B!11))) | (~(D = apply(function_inverse(B!11), C)))))))))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(150,plain,
% 0.20/0.50 (![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))) | (~(D = apply(function_inverse(B!11), C))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~in(C, relation_rng(B!11))) | (~(D = apply(function_inverse(B!11), C)))))))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.20/0.50 tff(151,plain,
% 0.20/0.50 (((~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))) | (~(D = apply(function_inverse(B!11), C))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~in(C, relation_rng(B!11))) | (~(D = apply(function_inverse(B!11), C)))))))))) | (~((~((~in(apply(function_inverse(B!11), A!12), relation_dom(B!11))) | (~(A!12 = apply(B!11, apply(function_inverse(B!11), A!12)))) | in(A!12, relation_rng(B!11)))) | (~((~in(A!12, relation_rng(B!11))) | (~((~in(apply(function_inverse(B!11), A!12), relation_dom(B!11))) | (~(A!12 = apply(B!11, apply(function_inverse(B!11), A!12))))))))))) <=> ((~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))) | (~(D = apply(function_inverse(B!11), C))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~in(C, relation_rng(B!11))) | (~(D = apply(function_inverse(B!11), C)))))))))) | (~((~((~in(apply(function_inverse(B!11), A!12), relation_dom(B!11))) | (~(A!12 = apply(B!11, apply(function_inverse(B!11), A!12)))) | in(A!12, relation_rng(B!11)))) | (~((~in(A!12, relation_rng(B!11))) | (~((~in(apply(function_inverse(B!11), A!12), relation_dom(B!11))) | (~(A!12 = apply(B!11, apply(function_inverse(B!11), A!12)))))))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(152,plain,
% 0.20/0.50 ((~((~((~in(A!12, relation_rng(B!11))) | (~((~in(apply(function_inverse(B!11), A!12), relation_dom(B!11))) | (~(A!12 = apply(B!11, apply(function_inverse(B!11), A!12)))))) | (~(apply(function_inverse(B!11), A!12) = apply(function_inverse(B!11), A!12))))) | (~((~in(apply(function_inverse(B!11), A!12), relation_dom(B!11))) | (~(A!12 = apply(B!11, apply(function_inverse(B!11), A!12)))) | (~((~in(A!12, relation_rng(B!11))) | (~(apply(function_inverse(B!11), A!12) = apply(function_inverse(B!11), A!12))))))))) <=> (~((~((~in(apply(function_inverse(B!11), A!12), relation_dom(B!11))) | (~(A!12 = apply(B!11, apply(function_inverse(B!11), A!12)))) | in(A!12, relation_rng(B!11)))) | (~((~in(A!12, relation_rng(B!11))) | (~((~in(apply(function_inverse(B!11), A!12), relation_dom(B!11))) | (~(A!12 = apply(B!11, apply(function_inverse(B!11), A!12))))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(153,plain,
% 0.20/0.51 (((~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))) | (~(D = apply(function_inverse(B!11), C))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~in(C, relation_rng(B!11))) | (~(D = apply(function_inverse(B!11), C)))))))))) | (~((~((~in(A!12, relation_rng(B!11))) | (~((~in(apply(function_inverse(B!11), A!12), relation_dom(B!11))) | (~(A!12 = apply(B!11, apply(function_inverse(B!11), A!12)))))) | (~(apply(function_inverse(B!11), A!12) = apply(function_inverse(B!11), A!12))))) | (~((~in(apply(function_inverse(B!11), A!12), relation_dom(B!11))) | (~(A!12 = apply(B!11, apply(function_inverse(B!11), A!12)))) | (~((~in(A!12, relation_rng(B!11))) | (~(apply(function_inverse(B!11), A!12) = apply(function_inverse(B!11), A!12)))))))))) <=> ((~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))) | (~(D = apply(function_inverse(B!11), C))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~in(C, relation_rng(B!11))) | (~(D = apply(function_inverse(B!11), C)))))))))) | (~((~((~in(apply(function_inverse(B!11), A!12), relation_dom(B!11))) | (~(A!12 = apply(B!11, apply(function_inverse(B!11), A!12)))) | in(A!12, relation_rng(B!11)))) | (~((~in(A!12, relation_rng(B!11))) | (~((~in(apply(function_inverse(B!11), A!12), relation_dom(B!11))) | (~(A!12 = apply(B!11, apply(function_inverse(B!11), A!12)))))))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[152])).
% 0.20/0.51 tff(154,plain,
% 0.20/0.51 (((~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))) | (~(D = apply(function_inverse(B!11), C))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~in(C, relation_rng(B!11))) | (~(D = apply(function_inverse(B!11), C)))))))))) | (~((~((~in(A!12, relation_rng(B!11))) | (~((~in(apply(function_inverse(B!11), A!12), relation_dom(B!11))) | (~(A!12 = apply(B!11, apply(function_inverse(B!11), A!12)))))) | (~(apply(function_inverse(B!11), A!12) = apply(function_inverse(B!11), A!12))))) | (~((~in(apply(function_inverse(B!11), A!12), relation_dom(B!11))) | (~(A!12 = apply(B!11, apply(function_inverse(B!11), A!12)))) | (~((~in(A!12, relation_rng(B!11))) | (~(apply(function_inverse(B!11), A!12) = apply(function_inverse(B!11), A!12)))))))))) <=> ((~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))) | (~(D = apply(function_inverse(B!11), C))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~in(C, relation_rng(B!11))) | (~(D = apply(function_inverse(B!11), C)))))))))) | (~((~((~in(apply(function_inverse(B!11), A!12), relation_dom(B!11))) | (~(A!12 = apply(B!11, apply(function_inverse(B!11), A!12)))) | in(A!12, relation_rng(B!11)))) | (~((~in(A!12, relation_rng(B!11))) | (~((~in(apply(function_inverse(B!11), A!12), relation_dom(B!11))) | (~(A!12 = apply(B!11, apply(function_inverse(B!11), A!12)))))))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[153, 151])).
% 0.20/0.51 tff(155,plain,
% 0.20/0.51 ((~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))) | (~(D = apply(function_inverse(B!11), C))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~in(C, relation_rng(B!11))) | (~(D = apply(function_inverse(B!11), C)))))))))) | (~((~((~in(A!12, relation_rng(B!11))) | (~((~in(apply(function_inverse(B!11), A!12), relation_dom(B!11))) | (~(A!12 = apply(B!11, apply(function_inverse(B!11), A!12)))))) | (~(apply(function_inverse(B!11), A!12) = apply(function_inverse(B!11), A!12))))) | (~((~in(apply(function_inverse(B!11), A!12), relation_dom(B!11))) | (~(A!12 = apply(B!11, apply(function_inverse(B!11), A!12)))) | (~((~in(A!12, relation_rng(B!11))) | (~(apply(function_inverse(B!11), A!12) = apply(function_inverse(B!11), A!12)))))))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(156,plain,
% 0.20/0.51 ((~![C: $i, D: $i] : (~((~((~in(C, relation_rng(B!11))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))))) | (~(D = apply(function_inverse(B!11), C))))) | (~((~in(D, relation_dom(B!11))) | (~(C = apply(B!11, D))) | (~((~in(C, relation_rng(B!11))) | (~(D = apply(function_inverse(B!11), C)))))))))) | (~((~((~in(apply(function_inverse(B!11), A!12), relation_dom(B!11))) | (~(A!12 = apply(B!11, apply(function_inverse(B!11), A!12)))) | in(A!12, relation_rng(B!11)))) | (~((~in(A!12, relation_rng(B!11))) | (~((~in(apply(function_inverse(B!11), A!12), relation_dom(B!11))) | (~(A!12 = apply(B!11, apply(function_inverse(B!11), A!12))))))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.20/0.51 tff(157,plain,
% 0.20/0.51 (~((~((~in(apply(function_inverse(B!11), A!12), relation_dom(B!11))) | (~(A!12 = apply(B!11, apply(function_inverse(B!11), A!12)))) | in(A!12, relation_rng(B!11)))) | (~((~in(A!12, relation_rng(B!11))) | (~((~in(apply(function_inverse(B!11), A!12), relation_dom(B!11))) | (~(A!12 = apply(B!11, apply(function_inverse(B!11), A!12)))))))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[156, 150])).
% 0.20/0.51 tff(158,plain,
% 0.20/0.51 (((~((~in(apply(function_inverse(B!11), A!12), relation_dom(B!11))) | (~(A!12 = apply(B!11, apply(function_inverse(B!11), A!12)))) | in(A!12, relation_rng(B!11)))) | (~((~in(A!12, relation_rng(B!11))) | (~((~in(apply(function_inverse(B!11), A!12), relation_dom(B!11))) | (~(A!12 = apply(B!11, apply(function_inverse(B!11), A!12))))))))) | ((~in(A!12, relation_rng(B!11))) | (~((~in(apply(function_inverse(B!11), A!12), relation_dom(B!11))) | (~(A!12 = apply(B!11, apply(function_inverse(B!11), A!12)))))))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(159,plain,
% 0.20/0.51 ((~in(A!12, relation_rng(B!11))) | (~((~in(apply(function_inverse(B!11), A!12), relation_dom(B!11))) | (~(A!12 = apply(B!11, apply(function_inverse(B!11), A!12))))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[158, 157])).
% 0.20/0.51 tff(160,plain,
% 0.20/0.51 ((~((~in(A!12, relation_rng(B!11))) | (~((~in(apply(function_inverse(B!11), A!12), relation_dom(B!11))) | (~(A!12 = apply(B!11, apply(function_inverse(B!11), A!12)))))))) | (~in(A!12, relation_rng(B!11))) | (~((~in(apply(function_inverse(B!11), A!12), relation_dom(B!11))) | (~(A!12 = apply(B!11, apply(function_inverse(B!11), A!12))))))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(161,plain,
% 0.20/0.51 ((~((~in(A!12, relation_rng(B!11))) | (~((~in(apply(function_inverse(B!11), A!12), relation_dom(B!11))) | (~(A!12 = apply(B!11, apply(function_inverse(B!11), A!12)))))))) | (~((~in(apply(function_inverse(B!11), A!12), relation_dom(B!11))) | (~(A!12 = apply(B!11, apply(function_inverse(B!11), A!12))))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[160, 38])).
% 0.20/0.51 tff(162,plain,
% 0.20/0.51 (~((~in(apply(function_inverse(B!11), A!12), relation_dom(B!11))) | (~(A!12 = apply(B!11, apply(function_inverse(B!11), A!12)))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[161, 159])).
% 0.20/0.51 tff(163,plain,
% 0.20/0.51 (((~in(apply(function_inverse(B!11), A!12), relation_dom(B!11))) | (~(A!12 = apply(B!11, apply(function_inverse(B!11), A!12))))) | (A!12 = apply(B!11, apply(function_inverse(B!11), A!12)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(164,plain,
% 0.20/0.51 (A!12 = apply(B!11, apply(function_inverse(B!11), A!12))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[163, 162])).
% 0.20/0.51 tff(165,plain,
% 0.20/0.51 ((~(~((~(A!12 = apply(B!11, apply(function_inverse(B!11), A!12)))) | (~(A!12 = apply(relation_composition(function_inverse(B!11), B!11), A!12)))))) <=> ((~(A!12 = apply(B!11, apply(function_inverse(B!11), A!12)))) | (~(A!12 = apply(relation_composition(function_inverse(B!11), B!11), A!12))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(166,plain,
% 0.20/0.51 (((A!12 = apply(B!11, apply(function_inverse(B!11), A!12))) & (A!12 = apply(relation_composition(function_inverse(B!11), B!11), A!12))) <=> (~((~(A!12 = apply(B!11, apply(function_inverse(B!11), A!12)))) | (~(A!12 = apply(relation_composition(function_inverse(B!11), B!11), A!12)))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(167,plain,
% 0.20/0.51 ((~((A!12 = apply(B!11, apply(function_inverse(B!11), A!12))) & (A!12 = apply(relation_composition(function_inverse(B!11), B!11), A!12)))) <=> (~(~((~(A!12 = apply(B!11, apply(function_inverse(B!11), A!12)))) | (~(A!12 = apply(relation_composition(function_inverse(B!11), B!11), A!12))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[166])).
% 0.20/0.51 tff(168,plain,
% 0.20/0.51 ((~((A!12 = apply(B!11, apply(function_inverse(B!11), A!12))) & (A!12 = apply(relation_composition(function_inverse(B!11), B!11), A!12)))) <=> ((~(A!12 = apply(B!11, apply(function_inverse(B!11), A!12)))) | (~(A!12 = apply(relation_composition(function_inverse(B!11), B!11), A!12))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[167, 165])).
% 0.20/0.51 tff(169,plain,
% 0.20/0.51 (~((A!12 = apply(B!11, apply(function_inverse(B!11), A!12))) & (A!12 = apply(relation_composition(function_inverse(B!11), B!11), A!12)))),
% 0.20/0.51 inference(or_elim,[status(thm)],[10])).
% 0.20/0.51 tff(170,plain,
% 0.20/0.51 ((~(A!12 = apply(B!11, apply(function_inverse(B!11), A!12)))) | (~(A!12 = apply(relation_composition(function_inverse(B!11), B!11), A!12)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.20/0.51 tff(171,plain,
% 0.20/0.51 (~(A!12 = apply(relation_composition(function_inverse(B!11), B!11), A!12))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[170, 164])).
% 0.20/0.51 tff(172,plain,
% 0.20/0.51 (~(A!12 = apply(B!11, apply(function_inverse(B!11), A!12)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[171, 104])).
% 0.20/0.51 tff(173,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[164, 172])).
% 0.20/0.51 % SZS output end Proof
% 0.20/0.51 % E exiting
%------------------------------------------------------------------------------