%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU014+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:47 AM UTC 2025
% Result : Theorem 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU014+1 : TPTP v9.0.0. Released v3.2.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 05:57:24 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 tff(in_type, type, (
% 0.20/0.41 in: ( $i * $i ) > $o)).
% 0.20/0.41 tff(relation_dom_type, type, (
% 0.20/0.41 relation_dom: $i > $i)).
% 0.20/0.41 tff(relation_composition_type, type, (
% 0.20/0.41 relation_composition: ( $i * $i ) > $i)).
% 0.20/0.41 tff(tptp_fun_A_11_type, type, (
% 0.20/0.41 tptp_fun_A_11: $i)).
% 0.20/0.41 tff(tptp_fun_B_12_type, type, (
% 0.20/0.41 tptp_fun_B_12: $i)).
% 0.20/0.41 tff(tptp_fun_C_0_type, type, (
% 0.20/0.41 tptp_fun_C_0: $i > $i)).
% 0.20/0.41 tff(subset_type, type, (
% 0.20/0.41 subset: ( $i * $i ) > $o)).
% 0.20/0.41 tff(relation_rng_type, type, (
% 0.20/0.41 relation_rng: $i > $i)).
% 0.20/0.41 tff(relation_type, type, (
% 0.20/0.41 relation: $i > $o)).
% 0.20/0.41 tff(function_type, type, (
% 0.20/0.41 function: $i > $o)).
% 0.20/0.41 tff(one_to_one_type, type, (
% 0.20/0.41 one_to_one: $i > $o)).
% 0.20/0.41 tff(tptp_fun_B_1_type, type, (
% 0.20/0.41 tptp_fun_B_1: $i > $i)).
% 0.20/0.41 tff(apply_type, type, (
% 0.20/0.41 apply: ( $i * $i ) > $i)).
% 0.20/0.41 tff(1,plain,
% 0.20/0.41 (((relation(A!11) & function(A!11)) & (~(one_to_one(B!12) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(relation_composition(B!12, A!11)) & subset(relation_rng(B!12), relation_dom(A!11))))))) <=> (relation(A!11) & function(A!11) & (~(one_to_one(B!12) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(relation_composition(B!12, A!11)) & subset(relation_rng(B!12), relation_dom(A!11)))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(2,plain,
% 0.20/0.41 ((~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))))))) <=> (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A)))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(3,plain,
% 0.20/0.41 ((~![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => ((one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))) => one_to_one(B))))) <=> (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A)))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(4,axiom,(~![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => ((one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))) => one_to_one(B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t47_funct_1')).
% 0.20/0.41 tff(5,plain,
% 0.20/0.41 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.41 tff(6,plain,
% 0.20/0.41 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.20/0.41 tff(7,plain,
% 0.20/0.41 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.41 tff(8,plain,
% 0.20/0.41 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.20/0.41 tff(9,plain,
% 0.20/0.41 (relation(A!11) & function(A!11) & (~(one_to_one(B!12) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(relation_composition(B!12, A!11)) & subset(relation_rng(B!12), relation_dom(A!11))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.20/0.41 tff(10,plain,
% 0.20/0.41 (~(one_to_one(B!12) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(relation_composition(B!12, A!11)) & subset(relation_rng(B!12), relation_dom(A!11)))))),
% 0.20/0.41 inference(and_elim,[status(thm)],[9])).
% 0.20/0.41 tff(11,plain,
% 0.20/0.41 (relation(B!12) & function(B!12)),
% 0.20/0.41 inference(or_elim,[status(thm)],[10])).
% 0.20/0.41 tff(12,plain,
% 0.20/0.41 (relation(B!12)),
% 0.20/0.41 inference(and_elim,[status(thm)],[11])).
% 0.20/0.41 tff(13,plain,
% 0.20/0.41 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))) <=> ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(14,plain,
% 0.20/0.41 (![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.41 tff(15,plain,
% 0.20/0.41 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))) <=> ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(16,plain,
% 0.20/0.41 (![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.41 tff(17,plain,
% 0.20/0.41 (![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[16, 14])).
% 0.20/0.41 tff(18,plain,
% 0.20/0.41 (![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(19,plain,
% 0.20/0.41 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((subset(relation_rng(A), relation_dom(B)) => (relation_dom(relation_composition(A, B)) = relation_dom(A))) <=> ((~subset(relation_rng(A), relation_dom(B))) | (relation_dom(relation_composition(A, B)) = relation_dom(A)))), ((relation(B) => (subset(relation_rng(A), relation_dom(B)) => (relation_dom(relation_composition(A, B)) = relation_dom(A)))) <=> (relation(B) => ((~subset(relation_rng(A), relation_dom(B))) | (relation_dom(relation_composition(A, B)) = relation_dom(A)))))), rewrite((relation(B) => ((~subset(relation_rng(A), relation_dom(B))) | (relation_dom(relation_composition(A, B)) = relation_dom(A)))) <=> ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))), ((relation(B) => (subset(relation_rng(A), relation_dom(B)) => (relation_dom(relation_composition(A, B)) = relation_dom(A)))) <=> ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))))), (![B: $i] : (relation(B) => (subset(relation_rng(A), relation_dom(B)) => (relation_dom(relation_composition(A, B)) = relation_dom(A)))) <=> ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))), ((relation(A) => ![B: $i] : (relation(B) => (subset(relation_rng(A), relation_dom(B)) => (relation_dom(relation_composition(A, B)) = relation_dom(A))))) <=> (relation(A) => ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))))), rewrite((relation(A) => ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))) <=> ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))), ((relation(A) => ![B: $i] : (relation(B) => (subset(relation_rng(A), relation_dom(B)) => (relation_dom(relation_composition(A, B)) = relation_dom(A))))) <=> ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(20,plain,
% 0.20/0.42 (![A: $i] : (relation(A) => ![B: $i] : (relation(B) => (subset(relation_rng(A), relation_dom(B)) => (relation_dom(relation_composition(A, B)) = relation_dom(A))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[19])).
% 0.20/0.42 tff(21,axiom,(![A: $i] : (relation(A) => ![B: $i] : (relation(B) => (subset(relation_rng(A), relation_dom(B)) => (relation_dom(relation_composition(A, B)) = relation_dom(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t46_relat_1')).
% 0.20/0.42 tff(22,plain,
% 0.20/0.42 (![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.20/0.42 tff(23,plain,
% 0.20/0.42 (![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.20/0.42 tff(24,plain,(
% 0.20/0.42 ![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[23])).
% 0.20/0.42 tff(25,plain,
% 0.20/0.42 (![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.20/0.42 tff(26,plain,
% 0.20/0.42 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))) | ((~relation(B!12)) | ![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(B!12, B)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(B)))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))) | (~relation(B!12)) | ![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(B!12, B)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(B)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(27,plain,
% 0.20/0.42 (((~relation(B!12)) | ![B: $i] : ((relation_dom(relation_composition(B!12, B)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(B))) | (~relation(B)))) <=> ((~relation(B!12)) | ![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(B!12, B)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(B)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(28,plain,
% 0.20/0.42 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))) | ((~relation(B!12)) | ![B: $i] : ((relation_dom(relation_composition(B!12, B)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(B))) | (~relation(B))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))) | ((~relation(B!12)) | ![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(B!12, B)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(B))))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[27])).
% 0.20/0.42 tff(29,plain,
% 0.20/0.42 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))) | ((~relation(B!12)) | ![B: $i] : ((relation_dom(relation_composition(B!12, B)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(B))) | (~relation(B))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))) | (~relation(B!12)) | ![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(B!12, B)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(B)))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[28, 26])).
% 0.20/0.42 tff(30,plain,
% 0.20/0.42 ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))) | ((~relation(B!12)) | ![B: $i] : ((relation_dom(relation_composition(B!12, B)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(B))) | (~relation(B))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(31,plain,
% 0.20/0.42 ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))) | (~relation(B!12)) | ![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(B!12, B)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(B))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.20/0.42 tff(32,plain,
% 0.20/0.42 (![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(B!12, B)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(B))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[31, 25, 12])).
% 0.20/0.42 tff(33,plain,
% 0.20/0.42 (one_to_one(relation_composition(B!12, A!11)) & subset(relation_rng(B!12), relation_dom(A!11))),
% 0.20/0.42 inference(or_elim,[status(thm)],[10])).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 (subset(relation_rng(B!12), relation_dom(A!11))),
% 0.20/0.42 inference(and_elim,[status(thm)],[33])).
% 0.20/0.42 tff(35,plain,
% 0.20/0.42 (relation(A!11)),
% 0.20/0.42 inference(and_elim,[status(thm)],[9])).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 (((~![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(B!12, B)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(B))))) | ((~relation(A!11)) | (~subset(relation_rng(B!12), relation_dom(A!11))) | (relation_dom(relation_composition(B!12, A!11)) = relation_dom(B!12)))) <=> ((~![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(B!12, B)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(B))))) | (~relation(A!11)) | (~subset(relation_rng(B!12), relation_dom(A!11))) | (relation_dom(relation_composition(B!12, A!11)) = relation_dom(B!12)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(37,plain,
% 0.20/0.42 (((~relation(A!11)) | (relation_dom(relation_composition(B!12, A!11)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(A!11)))) <=> ((~relation(A!11)) | (~subset(relation_rng(B!12), relation_dom(A!11))) | (relation_dom(relation_composition(B!12, A!11)) = relation_dom(B!12)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(38,plain,
% 0.20/0.42 (((~![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(B!12, B)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(B))))) | ((~relation(A!11)) | (relation_dom(relation_composition(B!12, A!11)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(A!11))))) <=> ((~![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(B!12, B)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(B))))) | ((~relation(A!11)) | (~subset(relation_rng(B!12), relation_dom(A!11))) | (relation_dom(relation_composition(B!12, A!11)) = relation_dom(B!12))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[37])).
% 0.20/0.42 tff(39,plain,
% 0.20/0.42 (((~![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(B!12, B)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(B))))) | ((~relation(A!11)) | (relation_dom(relation_composition(B!12, A!11)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(A!11))))) <=> ((~![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(B!12, B)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(B))))) | (~relation(A!11)) | (~subset(relation_rng(B!12), relation_dom(A!11))) | (relation_dom(relation_composition(B!12, A!11)) = relation_dom(B!12)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[38, 36])).
% 0.20/0.42 tff(40,plain,
% 0.20/0.42 ((~![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(B!12, B)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(B))))) | ((~relation(A!11)) | (relation_dom(relation_composition(B!12, A!11)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(A!11))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(41,plain,
% 0.20/0.42 ((~![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(B!12, B)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(B))))) | (~relation(A!11)) | (~subset(relation_rng(B!12), relation_dom(A!11))) | (relation_dom(relation_composition(B!12, A!11)) = relation_dom(B!12))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 (relation_dom(relation_composition(B!12, A!11)) = relation_dom(B!12)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[41, 35, 34, 32])).
% 0.20/0.42 tff(43,plain,
% 0.20/0.42 (in(tptp_fun_C_0(B!12), relation_dom(relation_composition(B!12, A!11))) <=> in(tptp_fun_C_0(B!12), relation_dom(B!12))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[42])).
% 0.20/0.42 tff(44,plain,
% 0.20/0.42 (in(tptp_fun_C_0(B!12), relation_dom(B!12)) <=> in(tptp_fun_C_0(B!12), relation_dom(relation_composition(B!12, A!11)))),
% 0.20/0.42 inference(symmetry,[status(thm)],[43])).
% 0.20/0.42 tff(45,plain,
% 0.20/0.42 (function(B!12)),
% 0.20/0.42 inference(and_elim,[status(thm)],[11])).
% 0.20/0.42 tff(46,plain,
% 0.20/0.42 (^[A: $i] : refl(((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))))))))) <=> ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(47,plain,
% 0.20/0.42 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[46])).
% 0.20/0.42 tff(48,plain,
% 0.20/0.42 (^[A: $i] : rewrite(((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))))))))) <=> ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(49,plain,
% 0.20/0.42 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[48])).
% 0.20/0.42 tff(50,plain,
% 0.20/0.42 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[49, 47])).
% 0.20/0.42 tff(51,plain,
% 0.20/0.42 (^[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))))), trans(monotonicity(rewrite(((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) <=> ((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))), rewrite((one_to_one(A) | (~((~(in(tptp_fun_B_1(A), relation_dom(A)) & in(tptp_fun_C_0(A), relation_dom(A)) & (apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))) | (tptp_fun_B_1(A) = tptp_fun_C_0(A))))) <=> (one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))), ((((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) & (one_to_one(A) | (~((~(in(tptp_fun_B_1(A), relation_dom(A)) & in(tptp_fun_C_0(A), relation_dom(A)) & (apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))) | (tptp_fun_B_1(A) = tptp_fun_C_0(A)))))) <=> (((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C))))) & (one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))), rewrite((((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C))))) & (one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))) <=> (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))))))))), ((((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) & (one_to_one(A) | (~((~(in(tptp_fun_B_1(A), relation_dom(A)) & in(tptp_fun_C_0(A), relation_dom(A)) & (apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))) | (tptp_fun_B_1(A) = tptp_fun_C_0(A)))))) <=> (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))), (((~(relation(A) & function(A))) | (((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) & (one_to_one(A) | (~((~(in(tptp_fun_B_1(A), relation_dom(A)) & in(tptp_fun_C_0(A), relation_dom(A)) & (apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))) | (tptp_fun_B_1(A) = tptp_fun_C_0(A))))))) <=> (((~relation(A)) | (~function(A))) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))))))))))), rewrite((((~relation(A)) | (~function(A))) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))))))))) <=> ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))), (((~(relation(A) & function(A))) | (((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) & (one_to_one(A) | (~((~(in(tptp_fun_B_1(A), relation_dom(A)) & in(tptp_fun_C_0(A), relation_dom(A)) & (apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))) | (tptp_fun_B_1(A) = tptp_fun_C_0(A))))))) <=> ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(52,plain,
% 0.20/0.42 (![A: $i] : ((~(relation(A) & function(A))) | (((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) & (one_to_one(A) | (~((~(in(tptp_fun_B_1(A), relation_dom(A)) & in(tptp_fun_C_0(A), relation_dom(A)) & (apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))) | (tptp_fun_B_1(A) = tptp_fun_C_0(A))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[51])).
% 0.20/0.42 tff(53,plain,
% 0.20/0.42 (![A: $i] : ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C)))) <=> ![A: $i] : ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(54,plain,
% 0.20/0.42 (^[A: $i] : trans(monotonicity(rewrite((one_to_one(A) <=> ![B: $i, C: $i] : (((in(B, relation_dom(A)) & in(C, relation_dom(A))) & (apply(A, B) = apply(A, C))) => (B = C))) <=> (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C)))), (((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : (((in(B, relation_dom(A)) & in(C, relation_dom(A))) & (apply(A, B) = apply(A, C))) => (B = C)))) <=> ((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C)))))), rewrite(((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C)))) <=> ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))), (((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : (((in(B, relation_dom(A)) & in(C, relation_dom(A))) & (apply(A, B) = apply(A, C))) => (B = C)))) <=> ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(55,plain,
% 0.20/0.42 (![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : (((in(B, relation_dom(A)) & in(C, relation_dom(A))) & (apply(A, B) = apply(A, C))) => (B = C)))) <=> ![A: $i] : ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[54])).
% 0.20/0.42 tff(56,axiom,(![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : (((in(B, relation_dom(A)) & in(C, relation_dom(A))) & (apply(A, B) = apply(A, C))) => (B = C))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d8_funct_1')).
% 0.20/0.42 tff(57,plain,
% 0.20/0.42 (![A: $i] : ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.20/0.42 tff(58,plain,
% 0.20/0.42 (![A: $i] : ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.20/0.42 tff(59,plain,(
% 0.20/0.42 ![A: $i] : ((~(relation(A) & function(A))) | (((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) & (one_to_one(A) | (~((~(in(tptp_fun_B_1(A), relation_dom(A)) & in(tptp_fun_C_0(A), relation_dom(A)) & (apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))) | (tptp_fun_B_1(A) = tptp_fun_C_0(A)))))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[58])).
% 0.20/0.42 tff(60,plain,
% 0.20/0.42 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.20/0.43 tff(61,plain,
% 0.20/0.43 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[60, 50])).
% 0.20/0.43 tff(62,plain,
% 0.20/0.43 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))) | ((~function(B!12)) | (~relation(B!12)) | (~((~((~one_to_one(B!12)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(B!12))) | (~in(C, relation_dom(B!12))) | (~(apply(B!12, B) = apply(B!12, C)))))) | (~(one_to_one(B!12) | (~((~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12)))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))) | (~function(B!12)) | (~relation(B!12)) | (~((~((~one_to_one(B!12)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(B!12))) | (~in(C, relation_dom(B!12))) | (~(apply(B!12, B) = apply(B!12, C)))))) | (~(one_to_one(B!12) | (~((~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12)))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)))))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(63,plain,
% 0.20/0.43 (((~relation(B!12)) | (~function(B!12)) | (~((~((~one_to_one(B!12)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(B!12))) | (~in(C, relation_dom(B!12))) | (~(apply(B!12, B) = apply(B!12, C)))))) | (~(one_to_one(B!12) | (~((~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12)))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12))))))))) <=> ((~function(B!12)) | (~relation(B!12)) | (~((~((~one_to_one(B!12)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(B!12))) | (~in(C, relation_dom(B!12))) | (~(apply(B!12, B) = apply(B!12, C)))))) | (~(one_to_one(B!12) | (~((~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12)))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)))))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(64,plain,
% 0.20/0.43 ((~((~((~one_to_one(B!12)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(B!12))) | (~in(C, relation_dom(B!12))) | (~(apply(B!12, B) = apply(B!12, C)))))) | (~(one_to_one(B!12) | (~((tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12)))))))))) <=> (~((~((~one_to_one(B!12)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(B!12))) | (~in(C, relation_dom(B!12))) | (~(apply(B!12, B) = apply(B!12, C)))))) | (~(one_to_one(B!12) | (~((~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12)))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12))))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(65,plain,
% 0.20/0.43 (((~relation(B!12)) | (~function(B!12)) | (~((~((~one_to_one(B!12)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(B!12))) | (~in(C, relation_dom(B!12))) | (~(apply(B!12, B) = apply(B!12, C)))))) | (~(one_to_one(B!12) | (~((tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12))))))))))) <=> ((~relation(B!12)) | (~function(B!12)) | (~((~((~one_to_one(B!12)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(B!12))) | (~in(C, relation_dom(B!12))) | (~(apply(B!12, B) = apply(B!12, C)))))) | (~(one_to_one(B!12) | (~((~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12)))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)))))))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[64])).
% 0.20/0.43 tff(66,plain,
% 0.20/0.43 (((~relation(B!12)) | (~function(B!12)) | (~((~((~one_to_one(B!12)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(B!12))) | (~in(C, relation_dom(B!12))) | (~(apply(B!12, B) = apply(B!12, C)))))) | (~(one_to_one(B!12) | (~((tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12))))))))))) <=> ((~function(B!12)) | (~relation(B!12)) | (~((~((~one_to_one(B!12)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(B!12))) | (~in(C, relation_dom(B!12))) | (~(apply(B!12, B) = apply(B!12, C)))))) | (~(one_to_one(B!12) | (~((~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12)))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)))))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[65, 63])).
% 0.20/0.43 tff(67,plain,
% 0.20/0.43 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))) | ((~relation(B!12)) | (~function(B!12)) | (~((~((~one_to_one(B!12)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(B!12))) | (~in(C, relation_dom(B!12))) | (~(apply(B!12, B) = apply(B!12, C)))))) | (~(one_to_one(B!12) | (~((tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12)))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))) | ((~function(B!12)) | (~relation(B!12)) | (~((~((~one_to_one(B!12)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(B!12))) | (~in(C, relation_dom(B!12))) | (~(apply(B!12, B) = apply(B!12, C)))))) | (~(one_to_one(B!12) | (~((~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12)))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12))))))))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[66])).
% 0.20/0.43 tff(68,plain,
% 0.20/0.43 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))) | ((~relation(B!12)) | (~function(B!12)) | (~((~((~one_to_one(B!12)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(B!12))) | (~in(C, relation_dom(B!12))) | (~(apply(B!12, B) = apply(B!12, C)))))) | (~(one_to_one(B!12) | (~((tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12)))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))) | (~function(B!12)) | (~relation(B!12)) | (~((~((~one_to_one(B!12)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(B!12))) | (~in(C, relation_dom(B!12))) | (~(apply(B!12, B) = apply(B!12, C)))))) | (~(one_to_one(B!12) | (~((~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12)))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)))))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[67, 62])).
% 0.20/0.43 tff(69,plain,
% 0.20/0.43 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))) | ((~relation(B!12)) | (~function(B!12)) | (~((~((~one_to_one(B!12)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(B!12))) | (~in(C, relation_dom(B!12))) | (~(apply(B!12, B) = apply(B!12, C)))))) | (~(one_to_one(B!12) | (~((tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12)))))))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(70,plain,
% 0.20/0.43 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))) | (~function(B!12)) | (~relation(B!12)) | (~((~((~one_to_one(B!12)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(B!12))) | (~in(C, relation_dom(B!12))) | (~(apply(B!12, B) = apply(B!12, C)))))) | (~(one_to_one(B!12) | (~((~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12)))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.20/0.43 tff(71,plain,
% 0.20/0.43 (~((~((~one_to_one(B!12)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(B!12))) | (~in(C, relation_dom(B!12))) | (~(apply(B!12, B) = apply(B!12, C)))))) | (~(one_to_one(B!12) | (~((~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12)))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[70, 61, 12, 45])).
% 0.20/0.43 tff(72,plain,
% 0.20/0.44 (((~((~one_to_one(B!12)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(B!12))) | (~in(C, relation_dom(B!12))) | (~(apply(B!12, B) = apply(B!12, C)))))) | (~(one_to_one(B!12) | (~((~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12)))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12))))))) | (one_to_one(B!12) | (~((~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12)))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(73,plain,
% 0.20/0.44 (one_to_one(B!12) | (~((~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12)))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.20/0.44 tff(74,plain,
% 0.20/0.44 (~one_to_one(B!12)),
% 0.20/0.44 inference(or_elim,[status(thm)],[10])).
% 0.20/0.44 tff(75,plain,
% 0.20/0.44 ((~(one_to_one(B!12) | (~((~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12)))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)))))) | one_to_one(B!12) | (~((~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12)))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(76,plain,
% 0.20/0.44 ((~(one_to_one(B!12) | (~((~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12)))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)))))) | (~((~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12)))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.20/0.44 tff(77,plain,
% 0.20/0.44 (~((~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12)))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[76, 73])).
% 0.20/0.44 tff(78,plain,
% 0.20/0.44 (((~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12)))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12))) | in(tptp_fun_C_0(B!12), relation_dom(B!12))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(79,plain,
% 0.20/0.44 (in(tptp_fun_C_0(B!12), relation_dom(B!12))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.20/0.44 tff(80,plain,
% 0.20/0.44 (in(tptp_fun_C_0(B!12), relation_dom(relation_composition(B!12, A!11)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[79, 44])).
% 0.20/0.44 tff(81,plain,
% 0.20/0.44 (in(tptp_fun_B_1(B!12), relation_dom(relation_composition(B!12, A!11))) <=> in(tptp_fun_B_1(B!12), relation_dom(B!12))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[42])).
% 0.20/0.44 tff(82,plain,
% 0.20/0.44 (in(tptp_fun_B_1(B!12), relation_dom(B!12)) <=> in(tptp_fun_B_1(B!12), relation_dom(relation_composition(B!12, A!11)))),
% 0.20/0.44 inference(symmetry,[status(thm)],[81])).
% 0.20/0.44 tff(83,plain,
% 0.20/0.44 (((~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12)))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12))) | in(tptp_fun_B_1(B!12), relation_dom(B!12))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(84,plain,
% 0.20/0.44 (in(tptp_fun_B_1(B!12), relation_dom(B!12))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[83, 77])).
% 0.20/0.44 tff(85,plain,
% 0.20/0.44 (in(tptp_fun_B_1(B!12), relation_dom(relation_composition(B!12, A!11)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[84, 82])).
% 0.20/0.44 tff(86,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(87,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)],[86])).
% 0.20/0.44 tff(88,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(89,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)],[88])).
% 0.20/0.44 tff(90,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)],[89, 87])).
% 0.20/0.44 tff(91,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(92,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)],[91])).
% 0.20/0.44 tff(93,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(94,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(95,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)],[94])).
% 0.20/0.44 tff(96,axiom,(![A: $i, B: $i] : ((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t23_funct_1')).
% 0.20/0.44 tff(97,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)],[96, 95])).
% 0.20/0.44 tff(98,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)],[97, 93])).
% 0.20/0.44 tff(99,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)],[98])).
% 0.20/0.44 tff(100,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)],[99, 92])).
% 0.20/0.44 tff(101,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)],[100, 90])).
% 0.20/0.44 tff(102,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(B!12)) | (~relation(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12))))))) <=> ((~![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(B!12)) | (~relation(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(103,plain,
% 0.20/0.44 (((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12)))))) <=> ((~function(B!12)) | (~relation(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(104,plain,
% 0.20/0.44 (^[C: $i] : rewrite(((apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12)))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~relation(C)) | (~function(C))) <=> ((~relation(C)) | (~function(C)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(105,plain,
% 0.20/0.44 (![C: $i] : ((apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12)))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~relation(C)) | (~function(C))) <=> ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12)))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[104])).
% 0.20/0.44 tff(106,plain,
% 0.20/0.44 (((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12)))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12))))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[105])).
% 0.20/0.44 tff(107,plain,
% 0.20/0.44 (((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12)))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~relation(C)) | (~function(C)))) <=> ((~function(B!12)) | (~relation(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[106, 103])).
% 0.20/0.44 tff(108,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))))) | ((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12)))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~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(B!12)) | (~relation(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12)))))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[107])).
% 0.20/0.44 tff(109,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))))) | ((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12)))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~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(B!12)) | (~relation(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[108, 102])).
% 0.20/0.44 tff(110,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))))) | ((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12)))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~relation(C)) | (~function(C))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(111,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(B!12)) | (~relation(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.20/0.45 tff(112,plain,
% 0.20/0.45 (![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12)))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[111, 101, 12, 45])).
% 0.20/0.45 tff(113,plain,
% 0.20/0.45 (function(A!11)),
% 0.20/0.45 inference(and_elim,[status(thm)],[9])).
% 0.20/0.45 tff(114,plain,
% 0.20/0.45 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12)))))) | ((~function(A!11)) | (~relation(A!11)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, A!11), tptp_fun_C_0(B!12)) = apply(A!11, apply(B!12, tptp_fun_C_0(B!12)))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12)))))) | (~function(A!11)) | (~relation(A!11)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, A!11), tptp_fun_C_0(B!12)) = apply(A!11, apply(B!12, tptp_fun_C_0(B!12)))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(115,plain,
% 0.20/0.45 (((~relation(A!11)) | (~function(A!11)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, A!11), tptp_fun_C_0(B!12)) = apply(A!11, apply(B!12, tptp_fun_C_0(B!12))))) <=> ((~function(A!11)) | (~relation(A!11)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, A!11), tptp_fun_C_0(B!12)) = apply(A!11, apply(B!12, tptp_fun_C_0(B!12)))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(116,plain,
% 0.20/0.45 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12)))))) | ((~relation(A!11)) | (~function(A!11)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, A!11), tptp_fun_C_0(B!12)) = apply(A!11, apply(B!12, tptp_fun_C_0(B!12)))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12)))))) | ((~function(A!11)) | (~relation(A!11)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, A!11), tptp_fun_C_0(B!12)) = apply(A!11, apply(B!12, tptp_fun_C_0(B!12))))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[115])).
% 0.20/0.45 tff(117,plain,
% 0.20/0.45 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12)))))) | ((~relation(A!11)) | (~function(A!11)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, A!11), tptp_fun_C_0(B!12)) = apply(A!11, apply(B!12, tptp_fun_C_0(B!12)))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12)))))) | (~function(A!11)) | (~relation(A!11)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, A!11), tptp_fun_C_0(B!12)) = apply(A!11, apply(B!12, tptp_fun_C_0(B!12)))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[116, 114])).
% 0.20/0.45 tff(118,plain,
% 0.20/0.45 ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12)))))) | ((~relation(A!11)) | (~function(A!11)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, A!11), tptp_fun_C_0(B!12)) = apply(A!11, apply(B!12, tptp_fun_C_0(B!12)))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(119,plain,
% 0.20/0.45 ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12)))))) | (~function(A!11)) | (~relation(A!11)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, A!11), tptp_fun_C_0(B!12)) = apply(A!11, apply(B!12, tptp_fun_C_0(B!12))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.20/0.45 tff(120,plain,
% 0.20/0.45 (apply(relation_composition(B!12, A!11), tptp_fun_C_0(B!12)) = apply(A!11, apply(B!12, tptp_fun_C_0(B!12)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[119, 35, 113, 79, 112])).
% 0.20/0.45 tff(121,plain,
% 0.20/0.45 (apply(A!11, apply(B!12, tptp_fun_C_0(B!12))) = apply(relation_composition(B!12, A!11), tptp_fun_C_0(B!12))),
% 0.20/0.45 inference(symmetry,[status(thm)],[120])).
% 0.20/0.45 tff(122,plain,
% 0.20/0.45 (((~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12)))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12))) | (apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(123,plain,
% 0.20/0.45 (apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[122, 77])).
% 0.20/0.45 tff(124,plain,
% 0.20/0.45 (apply(B!12, tptp_fun_C_0(B!12)) = apply(B!12, tptp_fun_B_1(B!12))),
% 0.20/0.45 inference(symmetry,[status(thm)],[123])).
% 0.20/0.45 tff(125,plain,
% 0.20/0.45 (apply(A!11, apply(B!12, tptp_fun_C_0(B!12))) = apply(A!11, apply(B!12, tptp_fun_B_1(B!12)))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[124])).
% 0.20/0.45 tff(126,plain,
% 0.20/0.45 (apply(A!11, apply(B!12, tptp_fun_B_1(B!12))) = apply(A!11, apply(B!12, tptp_fun_C_0(B!12)))),
% 0.20/0.45 inference(symmetry,[status(thm)],[125])).
% 0.20/0.45 tff(127,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(B!12)) | (~relation(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12))))))) <=> ((~![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(B!12)) | (~relation(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(128,plain,
% 0.20/0.45 (((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12)))))) <=> ((~function(B!12)) | (~relation(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(129,plain,
% 0.20/0.45 (^[C: $i] : rewrite(((apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12)))) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (~relation(C)) | (~function(C))) <=> ((~relation(C)) | (~function(C)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(130,plain,
% 0.20/0.45 (![C: $i] : ((apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12)))) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (~relation(C)) | (~function(C))) <=> ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12)))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[129])).
% 0.20/0.45 tff(131,plain,
% 0.20/0.45 (((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12)))) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12))))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[130])).
% 0.20/0.45 tff(132,plain,
% 0.20/0.45 (((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12)))) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (~relation(C)) | (~function(C)))) <=> ((~function(B!12)) | (~relation(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[131, 128])).
% 0.20/0.45 tff(133,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(B!12)) | (~function(B!12)) | ![C: $i] : ((apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12)))) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (~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(B!12)) | (~relation(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12)))))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[132])).
% 0.20/0.45 tff(134,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(B!12)) | (~function(B!12)) | ![C: $i] : ((apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12)))) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (~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(B!12)) | (~relation(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[133, 127])).
% 0.20/0.45 tff(135,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(B!12)) | (~function(B!12)) | ![C: $i] : ((apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12)))) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (~relation(C)) | (~function(C))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(136,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(B!12)) | (~relation(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.20/0.45 tff(137,plain,
% 0.20/0.45 (![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12)))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[136, 101, 12, 45])).
% 0.20/0.45 tff(138,plain,
% 0.20/0.45 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12)))))) | ((~function(A!11)) | (~relation(A!11)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, A!11), tptp_fun_B_1(B!12)) = apply(A!11, apply(B!12, tptp_fun_B_1(B!12)))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12)))))) | (~function(A!11)) | (~relation(A!11)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, A!11), tptp_fun_B_1(B!12)) = apply(A!11, apply(B!12, tptp_fun_B_1(B!12)))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(139,plain,
% 0.20/0.45 (((~relation(A!11)) | (~function(A!11)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, A!11), tptp_fun_B_1(B!12)) = apply(A!11, apply(B!12, tptp_fun_B_1(B!12))))) <=> ((~function(A!11)) | (~relation(A!11)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, A!11), tptp_fun_B_1(B!12)) = apply(A!11, apply(B!12, tptp_fun_B_1(B!12)))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(140,plain,
% 0.20/0.45 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12)))))) | ((~relation(A!11)) | (~function(A!11)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, A!11), tptp_fun_B_1(B!12)) = apply(A!11, apply(B!12, tptp_fun_B_1(B!12)))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12)))))) | ((~function(A!11)) | (~relation(A!11)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, A!11), tptp_fun_B_1(B!12)) = apply(A!11, apply(B!12, tptp_fun_B_1(B!12))))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[139])).
% 0.20/0.45 tff(141,plain,
% 0.20/0.45 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12)))))) | ((~relation(A!11)) | (~function(A!11)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, A!11), tptp_fun_B_1(B!12)) = apply(A!11, apply(B!12, tptp_fun_B_1(B!12)))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12)))))) | (~function(A!11)) | (~relation(A!11)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, A!11), tptp_fun_B_1(B!12)) = apply(A!11, apply(B!12, tptp_fun_B_1(B!12)))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[140, 138])).
% 0.20/0.45 tff(142,plain,
% 0.20/0.45 ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12)))))) | ((~relation(A!11)) | (~function(A!11)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, A!11), tptp_fun_B_1(B!12)) = apply(A!11, apply(B!12, tptp_fun_B_1(B!12)))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(143,plain,
% 0.20/0.46 ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12)))))) | (~function(A!11)) | (~relation(A!11)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, A!11), tptp_fun_B_1(B!12)) = apply(A!11, apply(B!12, tptp_fun_B_1(B!12))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.20/0.46 tff(144,plain,
% 0.20/0.46 (apply(relation_composition(B!12, A!11), tptp_fun_B_1(B!12)) = apply(A!11, apply(B!12, tptp_fun_B_1(B!12)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[143, 35, 113, 84, 137])).
% 0.20/0.46 tff(145,plain,
% 0.20/0.46 (apply(relation_composition(B!12, A!11), tptp_fun_B_1(B!12)) = apply(relation_composition(B!12, A!11), tptp_fun_C_0(B!12))),
% 0.20/0.46 inference(transitivity,[status(thm)],[144, 126, 121])).
% 0.20/0.46 tff(146,plain,
% 0.20/0.46 (^[A: $i, B: $i] : refl((relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A))) <=> (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(147,plain,
% 0.20/0.46 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A))) <=> ![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[146])).
% 0.20/0.46 tff(148,plain,
% 0.20/0.46 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(A) & relation(B)) <=> (~((~relation(B)) | (~relation(A))))), ((~(relation(A) & relation(B))) <=> (~(~((~relation(B)) | (~relation(A))))))), rewrite((~(~((~relation(B)) | (~relation(A))))) <=> ((~relation(B)) | (~relation(A)))), ((~(relation(A) & relation(B))) <=> ((~relation(B)) | (~relation(A))))), ((relation(relation_composition(A, B)) | (~(relation(A) & relation(B)))) <=> (relation(relation_composition(A, B)) | ((~relation(B)) | (~relation(A)))))), rewrite((relation(relation_composition(A, B)) | ((~relation(B)) | (~relation(A)))) <=> (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))), ((relation(relation_composition(A, B)) | (~(relation(A) & relation(B)))) <=> (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(149,plain,
% 0.20/0.46 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B)))) <=> ![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[148])).
% 0.20/0.46 tff(150,plain,
% 0.20/0.46 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B)))) <=> ![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(151,plain,
% 0.20/0.46 (^[A: $i, B: $i] : rewrite(((relation(A) & relation(B)) => relation(relation_composition(A, B))) <=> (relation(relation_composition(A, B)) | (~(relation(A) & relation(B)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(152,plain,
% 0.20/0.46 (![A: $i, B: $i] : ((relation(A) & relation(B)) => relation(relation_composition(A, B))) <=> ![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[151])).
% 0.20/0.46 tff(153,axiom,(![A: $i, B: $i] : ((relation(A) & relation(B)) => relation(relation_composition(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k5_relat_1')).
% 0.20/0.46 tff(154,plain,
% 0.20/0.46 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.20/0.46 tff(155,plain,
% 0.20/0.46 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[154, 150])).
% 0.20/0.46 tff(156,plain,(
% 0.20/0.46 ![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 0.20/0.46 inference(skolemize,[status(sab)],[155])).
% 0.20/0.46 tff(157,plain,
% 0.20/0.46 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[156, 149])).
% 0.20/0.46 tff(158,plain,
% 0.20/0.46 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[157, 147])).
% 0.20/0.46 tff(159,plain,
% 0.20/0.46 (((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | ((~relation(A!11)) | (~relation(B!12)) | relation(relation_composition(B!12, A!11)))) <=> ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (~relation(A!11)) | (~relation(B!12)) | relation(relation_composition(B!12, A!11)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(160,plain,
% 0.20/0.46 ((relation(relation_composition(B!12, A!11)) | (~relation(A!11)) | (~relation(B!12))) <=> ((~relation(A!11)) | (~relation(B!12)) | relation(relation_composition(B!12, A!11)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(161,plain,
% 0.20/0.46 (((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (relation(relation_composition(B!12, A!11)) | (~relation(A!11)) | (~relation(B!12)))) <=> ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | ((~relation(A!11)) | (~relation(B!12)) | relation(relation_composition(B!12, A!11))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[160])).
% 0.20/0.46 tff(162,plain,
% 0.20/0.46 (((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (relation(relation_composition(B!12, A!11)) | (~relation(A!11)) | (~relation(B!12)))) <=> ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (~relation(A!11)) | (~relation(B!12)) | relation(relation_composition(B!12, A!11)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[161, 159])).
% 0.20/0.46 tff(163,plain,
% 0.20/0.46 ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (relation(relation_composition(B!12, A!11)) | (~relation(A!11)) | (~relation(B!12)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(164,plain,
% 0.20/0.46 ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (~relation(A!11)) | (~relation(B!12)) | relation(relation_composition(B!12, A!11))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.20/0.46 tff(165,plain,
% 0.20/0.46 (relation(relation_composition(B!12, A!11))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[164, 158, 35, 12])).
% 0.20/0.46 tff(166,plain,
% 0.20/0.46 (^[A: $i, B: $i] : refl(((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B)))))) <=> ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B)))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(167,plain,
% 0.20/0.46 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B)))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[166])).
% 0.20/0.46 tff(168,plain,
% 0.20/0.46 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(A) & function(A) & relation(B) & function(B)) <=> (~((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A))))), ((~(relation(A) & function(A) & relation(B) & function(B))) <=> (~(~((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A))))))), rewrite((~(~((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A))))) <=> ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)))), ((~(relation(A) & function(A) & relation(B) & function(B))) <=> ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A))))), rewrite((relation(relation_composition(A, B)) & function(relation_composition(A, B))) <=> (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B)))))), (((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> (((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A))) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B)))))))), rewrite((((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A))) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B)))))) <=> ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))), (((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(169,plain,
% 0.20/0.46 (![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[168])).
% 0.20/0.46 tff(170,plain,
% 0.20/0.46 (![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> ![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(171,plain,
% 0.20/0.46 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((relation(A) & function(A)) & relation(B)) <=> (relation(A) & function(A) & relation(B))), ((((relation(A) & function(A)) & relation(B)) & function(B)) <=> ((relation(A) & function(A) & relation(B)) & function(B)))), rewrite(((relation(A) & function(A) & relation(B)) & function(B)) <=> (relation(A) & function(A) & relation(B) & function(B))), ((((relation(A) & function(A)) & relation(B)) & function(B)) <=> (relation(A) & function(A) & relation(B) & function(B)))), (((((relation(A) & function(A)) & relation(B)) & function(B)) => (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> ((relation(A) & function(A) & relation(B) & function(B)) => (relation(relation_composition(A, B)) & function(relation_composition(A, B)))))), rewrite(((relation(A) & function(A) & relation(B) & function(B)) => (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))), (((((relation(A) & function(A)) & relation(B)) & function(B)) => (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(172,plain,
% 0.20/0.46 (![A: $i, B: $i] : ((((relation(A) & function(A)) & relation(B)) & function(B)) => (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> ![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[171])).
% 0.20/0.46 tff(173,axiom,(![A: $i, B: $i] : ((((relation(A) & function(A)) & relation(B)) & function(B)) => (relation(relation_composition(A, B)) & function(relation_composition(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_funct_1')).
% 0.20/0.46 tff(174,plain,
% 0.20/0.46 (![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.20/0.46 tff(175,plain,
% 0.20/0.46 (![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[174, 170])).
% 0.20/0.46 tff(176,plain,(
% 0.20/0.46 ![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))),
% 0.20/0.46 inference(skolemize,[status(sab)],[175])).
% 0.20/0.46 tff(177,plain,
% 0.20/0.46 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[176, 169])).
% 0.20/0.46 tff(178,plain,
% 0.20/0.46 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[177, 167])).
% 0.20/0.46 tff(179,plain,
% 0.20/0.46 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | ((~function(A!11)) | (~relation(A!11)) | (~function(B!12)) | (~relation(B!12)) | (~((~function(relation_composition(B!12, A!11))) | (~relation(relation_composition(B!12, A!11))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | (~function(A!11)) | (~relation(A!11)) | (~function(B!12)) | (~relation(B!12)) | (~((~function(relation_composition(B!12, A!11))) | (~relation(relation_composition(B!12, A!11))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(180,plain,
% 0.20/0.46 (((~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~((~function(relation_composition(B!12, A!11))) | (~relation(relation_composition(B!12, A!11)))))) <=> ((~function(A!11)) | (~relation(A!11)) | (~function(B!12)) | (~relation(B!12)) | (~((~function(relation_composition(B!12, A!11))) | (~relation(relation_composition(B!12, A!11))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(181,plain,
% 0.20/0.46 ((~((~relation(relation_composition(B!12, A!11))) | (~function(relation_composition(B!12, A!11))))) <=> (~((~function(relation_composition(B!12, A!11))) | (~relation(relation_composition(B!12, A!11)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(182,plain,
% 0.20/0.46 (((~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~((~relation(relation_composition(B!12, A!11))) | (~function(relation_composition(B!12, A!11)))))) <=> ((~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~((~function(relation_composition(B!12, A!11))) | (~relation(relation_composition(B!12, A!11))))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[181])).
% 0.20/0.46 tff(183,plain,
% 0.20/0.46 (((~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~((~relation(relation_composition(B!12, A!11))) | (~function(relation_composition(B!12, A!11)))))) <=> ((~function(A!11)) | (~relation(A!11)) | (~function(B!12)) | (~relation(B!12)) | (~((~function(relation_composition(B!12, A!11))) | (~relation(relation_composition(B!12, A!11))))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[182, 180])).
% 0.20/0.46 tff(184,plain,
% 0.20/0.46 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | ((~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~((~relation(relation_composition(B!12, A!11))) | (~function(relation_composition(B!12, A!11))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | ((~function(A!11)) | (~relation(A!11)) | (~function(B!12)) | (~relation(B!12)) | (~((~function(relation_composition(B!12, A!11))) | (~relation(relation_composition(B!12, A!11)))))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[183])).
% 0.20/0.46 tff(185,plain,
% 0.20/0.46 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | ((~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~((~relation(relation_composition(B!12, A!11))) | (~function(relation_composition(B!12, A!11))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | (~function(A!11)) | (~relation(A!11)) | (~function(B!12)) | (~relation(B!12)) | (~((~function(relation_composition(B!12, A!11))) | (~relation(relation_composition(B!12, A!11))))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[184, 179])).
% 0.20/0.46 tff(186,plain,
% 0.20/0.46 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | ((~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~((~relation(relation_composition(B!12, A!11))) | (~function(relation_composition(B!12, A!11))))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(187,plain,
% 0.20/0.46 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | (~function(A!11)) | (~relation(A!11)) | (~function(B!12)) | (~relation(B!12)) | (~((~function(relation_composition(B!12, A!11))) | (~relation(relation_composition(B!12, A!11)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.20/0.46 tff(188,plain,
% 0.20/0.46 (~((~function(relation_composition(B!12, A!11))) | (~relation(relation_composition(B!12, A!11))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[187, 178, 35, 113, 12, 45])).
% 0.20/0.46 tff(189,plain,
% 0.20/0.46 (((~function(relation_composition(B!12, A!11))) | (~relation(relation_composition(B!12, A!11)))) | function(relation_composition(B!12, A!11))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(190,plain,
% 0.20/0.46 (function(relation_composition(B!12, A!11))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[189, 188])).
% 0.20/0.46 tff(191,plain,
% 0.20/0.46 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))) | ((~function(relation_composition(B!12, A!11))) | (~relation(relation_composition(B!12, A!11))) | (~((~((~one_to_one(relation_composition(B!12, A!11))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C)))))) | (~(one_to_one(relation_composition(B!12, A!11)) | (~((~(apply(relation_composition(B!12, A!11), tptp_fun_B_1(relation_composition(B!12, A!11))) = apply(relation_composition(B!12, A!11), tptp_fun_C_0(relation_composition(B!12, A!11))))) | (~in(tptp_fun_C_0(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_B_1(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (tptp_fun_B_1(relation_composition(B!12, A!11)) = tptp_fun_C_0(relation_composition(B!12, A!11))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))) | (~function(relation_composition(B!12, A!11))) | (~relation(relation_composition(B!12, A!11))) | (~((~((~one_to_one(relation_composition(B!12, A!11))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C)))))) | (~(one_to_one(relation_composition(B!12, A!11)) | (~((~(apply(relation_composition(B!12, A!11), tptp_fun_B_1(relation_composition(B!12, A!11))) = apply(relation_composition(B!12, A!11), tptp_fun_C_0(relation_composition(B!12, A!11))))) | (~in(tptp_fun_C_0(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_B_1(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (tptp_fun_B_1(relation_composition(B!12, A!11)) = tptp_fun_C_0(relation_composition(B!12, A!11))))))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(192,plain,
% 0.20/0.47 (((~relation(relation_composition(B!12, A!11))) | (~function(relation_composition(B!12, A!11))) | (~((~((~one_to_one(relation_composition(B!12, A!11))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C)))))) | (~(one_to_one(relation_composition(B!12, A!11)) | (~((~(apply(relation_composition(B!12, A!11), tptp_fun_B_1(relation_composition(B!12, A!11))) = apply(relation_composition(B!12, A!11), tptp_fun_C_0(relation_composition(B!12, A!11))))) | (~in(tptp_fun_C_0(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_B_1(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (tptp_fun_B_1(relation_composition(B!12, A!11)) = tptp_fun_C_0(relation_composition(B!12, A!11)))))))))) <=> ((~function(relation_composition(B!12, A!11))) | (~relation(relation_composition(B!12, A!11))) | (~((~((~one_to_one(relation_composition(B!12, A!11))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C)))))) | (~(one_to_one(relation_composition(B!12, A!11)) | (~((~(apply(relation_composition(B!12, A!11), tptp_fun_B_1(relation_composition(B!12, A!11))) = apply(relation_composition(B!12, A!11), tptp_fun_C_0(relation_composition(B!12, A!11))))) | (~in(tptp_fun_C_0(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_B_1(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (tptp_fun_B_1(relation_composition(B!12, A!11)) = tptp_fun_C_0(relation_composition(B!12, A!11))))))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(193,plain,
% 0.20/0.47 ((~((~((~one_to_one(relation_composition(B!12, A!11))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C)))))) | (~(one_to_one(relation_composition(B!12, A!11)) | (~((tptp_fun_B_1(relation_composition(B!12, A!11)) = tptp_fun_C_0(relation_composition(B!12, A!11))) | (~in(tptp_fun_B_1(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_C_0(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), tptp_fun_B_1(relation_composition(B!12, A!11))) = apply(relation_composition(B!12, A!11), tptp_fun_C_0(relation_composition(B!12, A!11))))))))))) <=> (~((~((~one_to_one(relation_composition(B!12, A!11))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C)))))) | (~(one_to_one(relation_composition(B!12, A!11)) | (~((~(apply(relation_composition(B!12, A!11), tptp_fun_B_1(relation_composition(B!12, A!11))) = apply(relation_composition(B!12, A!11), tptp_fun_C_0(relation_composition(B!12, A!11))))) | (~in(tptp_fun_C_0(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_B_1(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (tptp_fun_B_1(relation_composition(B!12, A!11)) = tptp_fun_C_0(relation_composition(B!12, A!11)))))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(194,plain,
% 0.20/0.47 (((~relation(relation_composition(B!12, A!11))) | (~function(relation_composition(B!12, A!11))) | (~((~((~one_to_one(relation_composition(B!12, A!11))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C)))))) | (~(one_to_one(relation_composition(B!12, A!11)) | (~((tptp_fun_B_1(relation_composition(B!12, A!11)) = tptp_fun_C_0(relation_composition(B!12, A!11))) | (~in(tptp_fun_B_1(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_C_0(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), tptp_fun_B_1(relation_composition(B!12, A!11))) = apply(relation_composition(B!12, A!11), tptp_fun_C_0(relation_composition(B!12, A!11)))))))))))) <=> ((~relation(relation_composition(B!12, A!11))) | (~function(relation_composition(B!12, A!11))) | (~((~((~one_to_one(relation_composition(B!12, A!11))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C)))))) | (~(one_to_one(relation_composition(B!12, A!11)) | (~((~(apply(relation_composition(B!12, A!11), tptp_fun_B_1(relation_composition(B!12, A!11))) = apply(relation_composition(B!12, A!11), tptp_fun_C_0(relation_composition(B!12, A!11))))) | (~in(tptp_fun_C_0(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_B_1(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (tptp_fun_B_1(relation_composition(B!12, A!11)) = tptp_fun_C_0(relation_composition(B!12, A!11))))))))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[193])).
% 0.20/0.47 tff(195,plain,
% 0.20/0.47 (((~relation(relation_composition(B!12, A!11))) | (~function(relation_composition(B!12, A!11))) | (~((~((~one_to_one(relation_composition(B!12, A!11))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C)))))) | (~(one_to_one(relation_composition(B!12, A!11)) | (~((tptp_fun_B_1(relation_composition(B!12, A!11)) = tptp_fun_C_0(relation_composition(B!12, A!11))) | (~in(tptp_fun_B_1(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_C_0(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), tptp_fun_B_1(relation_composition(B!12, A!11))) = apply(relation_composition(B!12, A!11), tptp_fun_C_0(relation_composition(B!12, A!11)))))))))))) <=> ((~function(relation_composition(B!12, A!11))) | (~relation(relation_composition(B!12, A!11))) | (~((~((~one_to_one(relation_composition(B!12, A!11))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C)))))) | (~(one_to_one(relation_composition(B!12, A!11)) | (~((~(apply(relation_composition(B!12, A!11), tptp_fun_B_1(relation_composition(B!12, A!11))) = apply(relation_composition(B!12, A!11), tptp_fun_C_0(relation_composition(B!12, A!11))))) | (~in(tptp_fun_C_0(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_B_1(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (tptp_fun_B_1(relation_composition(B!12, A!11)) = tptp_fun_C_0(relation_composition(B!12, A!11))))))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[194, 192])).
% 0.20/0.47 tff(196,plain,
% 0.20/0.47 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))) | ((~relation(relation_composition(B!12, A!11))) | (~function(relation_composition(B!12, A!11))) | (~((~((~one_to_one(relation_composition(B!12, A!11))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C)))))) | (~(one_to_one(relation_composition(B!12, A!11)) | (~((tptp_fun_B_1(relation_composition(B!12, A!11)) = tptp_fun_C_0(relation_composition(B!12, A!11))) | (~in(tptp_fun_B_1(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_C_0(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), tptp_fun_B_1(relation_composition(B!12, A!11))) = apply(relation_composition(B!12, A!11), tptp_fun_C_0(relation_composition(B!12, A!11))))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))) | ((~function(relation_composition(B!12, A!11))) | (~relation(relation_composition(B!12, A!11))) | (~((~((~one_to_one(relation_composition(B!12, A!11))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C)))))) | (~(one_to_one(relation_composition(B!12, A!11)) | (~((~(apply(relation_composition(B!12, A!11), tptp_fun_B_1(relation_composition(B!12, A!11))) = apply(relation_composition(B!12, A!11), tptp_fun_C_0(relation_composition(B!12, A!11))))) | (~in(tptp_fun_C_0(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_B_1(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (tptp_fun_B_1(relation_composition(B!12, A!11)) = tptp_fun_C_0(relation_composition(B!12, A!11)))))))))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[195])).
% 0.20/0.47 tff(197,plain,
% 0.20/0.47 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))) | ((~relation(relation_composition(B!12, A!11))) | (~function(relation_composition(B!12, A!11))) | (~((~((~one_to_one(relation_composition(B!12, A!11))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C)))))) | (~(one_to_one(relation_composition(B!12, A!11)) | (~((tptp_fun_B_1(relation_composition(B!12, A!11)) = tptp_fun_C_0(relation_composition(B!12, A!11))) | (~in(tptp_fun_B_1(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_C_0(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), tptp_fun_B_1(relation_composition(B!12, A!11))) = apply(relation_composition(B!12, A!11), tptp_fun_C_0(relation_composition(B!12, A!11))))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))) | (~function(relation_composition(B!12, A!11))) | (~relation(relation_composition(B!12, A!11))) | (~((~((~one_to_one(relation_composition(B!12, A!11))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C)))))) | (~(one_to_one(relation_composition(B!12, A!11)) | (~((~(apply(relation_composition(B!12, A!11), tptp_fun_B_1(relation_composition(B!12, A!11))) = apply(relation_composition(B!12, A!11), tptp_fun_C_0(relation_composition(B!12, A!11))))) | (~in(tptp_fun_C_0(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_B_1(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (tptp_fun_B_1(relation_composition(B!12, A!11)) = tptp_fun_C_0(relation_composition(B!12, A!11))))))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[196, 191])).
% 0.20/0.47 tff(198,plain,
% 0.20/0.47 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))) | ((~relation(relation_composition(B!12, A!11))) | (~function(relation_composition(B!12, A!11))) | (~((~((~one_to_one(relation_composition(B!12, A!11))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C)))))) | (~(one_to_one(relation_composition(B!12, A!11)) | (~((tptp_fun_B_1(relation_composition(B!12, A!11)) = tptp_fun_C_0(relation_composition(B!12, A!11))) | (~in(tptp_fun_B_1(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_C_0(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), tptp_fun_B_1(relation_composition(B!12, A!11))) = apply(relation_composition(B!12, A!11), tptp_fun_C_0(relation_composition(B!12, A!11))))))))))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(199,plain,
% 0.20/0.47 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))) | (~function(relation_composition(B!12, A!11))) | (~relation(relation_composition(B!12, A!11))) | (~((~((~one_to_one(relation_composition(B!12, A!11))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C)))))) | (~(one_to_one(relation_composition(B!12, A!11)) | (~((~(apply(relation_composition(B!12, A!11), tptp_fun_B_1(relation_composition(B!12, A!11))) = apply(relation_composition(B!12, A!11), tptp_fun_C_0(relation_composition(B!12, A!11))))) | (~in(tptp_fun_C_0(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_B_1(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (tptp_fun_B_1(relation_composition(B!12, A!11)) = tptp_fun_C_0(relation_composition(B!12, A!11)))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.20/0.47 tff(200,plain,
% 0.20/0.47 ((~function(relation_composition(B!12, A!11))) | (~relation(relation_composition(B!12, A!11))) | (~((~((~one_to_one(relation_composition(B!12, A!11))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C)))))) | (~(one_to_one(relation_composition(B!12, A!11)) | (~((~(apply(relation_composition(B!12, A!11), tptp_fun_B_1(relation_composition(B!12, A!11))) = apply(relation_composition(B!12, A!11), tptp_fun_C_0(relation_composition(B!12, A!11))))) | (~in(tptp_fun_C_0(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_B_1(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (tptp_fun_B_1(relation_composition(B!12, A!11)) = tptp_fun_C_0(relation_composition(B!12, A!11)))))))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[199, 61])).
% 0.20/0.47 tff(201,plain,
% 0.20/0.47 (~((~((~one_to_one(relation_composition(B!12, A!11))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C)))))) | (~(one_to_one(relation_composition(B!12, A!11)) | (~((~(apply(relation_composition(B!12, A!11), tptp_fun_B_1(relation_composition(B!12, A!11))) = apply(relation_composition(B!12, A!11), tptp_fun_C_0(relation_composition(B!12, A!11))))) | (~in(tptp_fun_C_0(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_B_1(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (tptp_fun_B_1(relation_composition(B!12, A!11)) = tptp_fun_C_0(relation_composition(B!12, A!11))))))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[200, 190, 165])).
% 0.20/0.47 tff(202,plain,
% 0.20/0.47 (((~((~one_to_one(relation_composition(B!12, A!11))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C)))))) | (~(one_to_one(relation_composition(B!12, A!11)) | (~((~(apply(relation_composition(B!12, A!11), tptp_fun_B_1(relation_composition(B!12, A!11))) = apply(relation_composition(B!12, A!11), tptp_fun_C_0(relation_composition(B!12, A!11))))) | (~in(tptp_fun_C_0(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_B_1(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (tptp_fun_B_1(relation_composition(B!12, A!11)) = tptp_fun_C_0(relation_composition(B!12, A!11)))))))) | ((~one_to_one(relation_composition(B!12, A!11))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C)))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(203,plain,
% 0.20/0.47 ((~one_to_one(relation_composition(B!12, A!11))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[202, 201])).
% 0.20/0.47 tff(204,plain,
% 0.20/0.47 (one_to_one(relation_composition(B!12, A!11))),
% 0.20/0.47 inference(and_elim,[status(thm)],[33])).
% 0.20/0.47 tff(205,plain,
% 0.20/0.47 ((~((~one_to_one(relation_composition(B!12, A!11))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C)))))) | (~one_to_one(relation_composition(B!12, A!11))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(206,plain,
% 0.20/0.47 ((~((~one_to_one(relation_composition(B!12, A!11))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C)))))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[205, 204])).
% 0.20/0.47 tff(207,plain,
% 0.20/0.47 (![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[206, 203])).
% 0.20/0.47 tff(208,plain,
% 0.20/0.47 (((~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12)))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12))) | (~(tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(209,plain,
% 0.20/0.47 (~(tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[208, 77])).
% 0.20/0.47 tff(210,plain,
% 0.20/0.47 (((~![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C))))) | ((tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)) | (~in(tptp_fun_C_0(B!12), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_B_1(B!12), relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), tptp_fun_B_1(B!12)) = apply(relation_composition(B!12, A!11), tptp_fun_C_0(B!12)))))) <=> ((~![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C))))) | (tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)) | (~in(tptp_fun_C_0(B!12), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_B_1(B!12), relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), tptp_fun_B_1(B!12)) = apply(relation_composition(B!12, A!11), tptp_fun_C_0(B!12)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(211,plain,
% 0.20/0.47 (((tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)) | (~in(tptp_fun_B_1(B!12), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_C_0(B!12), relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), tptp_fun_B_1(B!12)) = apply(relation_composition(B!12, A!11), tptp_fun_C_0(B!12))))) <=> ((tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)) | (~in(tptp_fun_C_0(B!12), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_B_1(B!12), relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), tptp_fun_B_1(B!12)) = apply(relation_composition(B!12, A!11), tptp_fun_C_0(B!12)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(212,plain,
% 0.20/0.48 (((~![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C))))) | ((tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)) | (~in(tptp_fun_B_1(B!12), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_C_0(B!12), relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), tptp_fun_B_1(B!12)) = apply(relation_composition(B!12, A!11), tptp_fun_C_0(B!12)))))) <=> ((~![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C))))) | ((tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)) | (~in(tptp_fun_C_0(B!12), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_B_1(B!12), relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), tptp_fun_B_1(B!12)) = apply(relation_composition(B!12, A!11), tptp_fun_C_0(B!12))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[211])).
% 0.20/0.48 tff(213,plain,
% 0.20/0.48 (((~![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C))))) | ((tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)) | (~in(tptp_fun_B_1(B!12), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_C_0(B!12), relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), tptp_fun_B_1(B!12)) = apply(relation_composition(B!12, A!11), tptp_fun_C_0(B!12)))))) <=> ((~![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C))))) | (tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)) | (~in(tptp_fun_C_0(B!12), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_B_1(B!12), relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), tptp_fun_B_1(B!12)) = apply(relation_composition(B!12, A!11), tptp_fun_C_0(B!12)))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[212, 210])).
% 0.20/0.48 tff(214,plain,
% 0.20/0.48 ((~![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C))))) | ((tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)) | (~in(tptp_fun_B_1(B!12), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_C_0(B!12), relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), tptp_fun_B_1(B!12)) = apply(relation_composition(B!12, A!11), tptp_fun_C_0(B!12)))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(215,plain,
% 0.20/0.48 ((~![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C))))) | (tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)) | (~in(tptp_fun_C_0(B!12), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_B_1(B!12), relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), tptp_fun_B_1(B!12)) = apply(relation_composition(B!12, A!11), tptp_fun_C_0(B!12))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.20/0.48 tff(216,plain,
% 0.20/0.48 ((~in(tptp_fun_C_0(B!12), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_B_1(B!12), relation_dom(relation_composition(B!12, A!11))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[215, 209, 207, 145])).
% 0.20/0.48 tff(217,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[216, 85, 80])).
% 0.20/0.48 % SZS output end Proof
% 0.20/0.48 % E exiting
%------------------------------------------------------------------------------