%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU013+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:47 AM UTC 2025
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SEU013+1 : TPTP v9.0.0. Released v3.2.0.
% 0.13/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n012.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 05:56:40 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(apply_type, type, (
% 0.13/0.40 apply: ( $i * $i ) > $i)).
% 0.13/0.40 tff(tptp_fun_C_0_type, type, (
% 0.13/0.40 tptp_fun_C_0: $i > $i)).
% 0.13/0.40 tff(relation_composition_type, type, (
% 0.13/0.40 relation_composition: ( $i * $i ) > $i)).
% 0.13/0.40 tff(tptp_fun_B_12_type, type, (
% 0.13/0.40 tptp_fun_B_12: $i)).
% 0.13/0.40 tff(tptp_fun_A_11_type, type, (
% 0.13/0.40 tptp_fun_A_11: $i)).
% 0.13/0.40 tff(tptp_fun_B_1_type, type, (
% 0.13/0.40 tptp_fun_B_1: $i > $i)).
% 0.13/0.40 tff(in_type, type, (
% 0.13/0.40 in: ( $i * $i ) > $o)).
% 0.13/0.40 tff(relation_dom_type, type, (
% 0.13/0.40 relation_dom: $i > $i)).
% 0.13/0.40 tff(one_to_one_type, type, (
% 0.13/0.40 one_to_one: $i > $o)).
% 0.13/0.40 tff(relation_type, type, (
% 0.13/0.40 relation: $i > $o)).
% 0.13/0.40 tff(function_type, type, (
% 0.13/0.40 function: $i > $o)).
% 0.13/0.40 tff(1,plain,
% 0.13/0.40 (((relation(A!11) & function(A!11)) & (~(one_to_one(relation_composition(A!11, B!12)) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(A!11) & one_to_one(B!12)))))) <=> (relation(A!11) & function(A!11) & (~(one_to_one(relation_composition(A!11, B!12)) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(A!11) & one_to_one(B!12))))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(2,plain,
% 0.13/0.40 ((~(one_to_one(relation_composition(A!11, B!12)) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(A!11) & one_to_one(B!12))))) <=> (~(one_to_one(relation_composition(A!11, B!12)) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(A!11) & one_to_one(B!12)))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(3,plain,
% 0.13/0.40 (((relation(A!11) & function(A!11)) & (~(one_to_one(relation_composition(A!11, B!12)) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(A!11) & one_to_one(B!12)))))) <=> ((relation(A!11) & function(A!11)) & (~(one_to_one(relation_composition(A!11, B!12)) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(A!11) & one_to_one(B!12))))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[2])).
% 0.13/0.40 tff(4,plain,
% 0.13/0.40 (((relation(A!11) & function(A!11)) & (~(one_to_one(relation_composition(A!11, B!12)) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(A!11) & one_to_one(B!12)))))) <=> (relation(A!11) & function(A!11) & (~(one_to_one(relation_composition(A!11, B!12)) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(A!11) & one_to_one(B!12))))))),
% 0.13/0.40 inference(transitivity,[status(thm)],[3, 1])).
% 0.13/0.40 tff(5,plain,
% 0.13/0.40 ((~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(relation_composition(A, B)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & one_to_one(B)))))) <=> (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(relation_composition(A, B)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & one_to_one(B))))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(6,plain,
% 0.13/0.40 ((~![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => ((one_to_one(A) & one_to_one(B)) => one_to_one(relation_composition(A, B)))))) <=> (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(relation_composition(A, B)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & one_to_one(B))))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(7,axiom,(~![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => ((one_to_one(A) & one_to_one(B)) => one_to_one(relation_composition(A, B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t46_funct_1')).
% 0.13/0.40 tff(8,plain,
% 0.13/0.40 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(relation_composition(A, B)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & one_to_one(B)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(relation_composition(A, B)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & one_to_one(B)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(relation_composition(A, B)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & one_to_one(B)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.13/0.40 tff(11,plain,
% 0.13/0.40 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(relation_composition(A, B)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & one_to_one(B)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.13/0.40 tff(12,plain,
% 0.13/0.40 (relation(A!11) & function(A!11) & (~(one_to_one(relation_composition(A!11, B!12)) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(A!11) & one_to_one(B!12)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.13/0.40 tff(13,plain,
% 0.13/0.40 (~(one_to_one(relation_composition(A!11, B!12)) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(A!11) & one_to_one(B!12))))),
% 0.13/0.40 inference(and_elim,[status(thm)],[12])).
% 0.13/0.40 tff(14,plain,
% 0.13/0.40 (relation(B!12) & function(B!12)),
% 0.13/0.40 inference(or_elim,[status(thm)],[13])).
% 0.13/0.40 tff(15,plain,
% 0.13/0.40 (relation(B!12)),
% 0.13/0.40 inference(and_elim,[status(thm)],[14])).
% 0.13/0.40 tff(16,plain,
% 0.13/0.40 (relation(A!11)),
% 0.13/0.40 inference(and_elim,[status(thm)],[12])).
% 0.13/0.40 tff(17,plain,
% 0.13/0.40 (^[A: $i, B: $i] : refl((relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A))) <=> (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(18,plain,
% 0.13/0.40 (![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)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[17])).
% 0.13/0.40 tff(19,plain,
% 0.13/0.40 (^[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)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(20,plain,
% 0.13/0.40 (![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)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[19])).
% 0.13/0.40 tff(21,plain,
% 0.13/0.40 (![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))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(22,plain,
% 0.13/0.40 (^[A: $i, B: $i] : rewrite(((relation(A) & relation(B)) => relation(relation_composition(A, B))) <=> (relation(relation_composition(A, B)) | (~(relation(A) & relation(B)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(23,plain,
% 0.13/0.40 (![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))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[22])).
% 0.13/0.40 tff(24,axiom,(![A: $i, B: $i] : ((relation(A) & relation(B)) => relation(relation_composition(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k5_relat_1')).
% 0.13/0.40 tff(25,plain,
% 0.13/0.40 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.13/0.40 tff(26,plain,
% 0.13/0.40 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.13/0.40 tff(27,plain,(
% 0.13/0.40 ![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 0.13/0.40 inference(skolemize,[status(sab)],[26])).
% 0.13/0.40 tff(28,plain,
% 0.13/0.40 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.13/0.40 tff(29,plain,
% 0.13/0.40 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.13/0.40 tff(30,plain,
% 0.13/0.40 (((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | ((~relation(A!11)) | (~relation(B!12)) | relation(relation_composition(A!11, B!12)))) <=> ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (~relation(A!11)) | (~relation(B!12)) | relation(relation_composition(A!11, B!12)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(31,plain,
% 0.13/0.40 ((relation(relation_composition(A!11, B!12)) | (~relation(B!12)) | (~relation(A!11))) <=> ((~relation(A!11)) | (~relation(B!12)) | relation(relation_composition(A!11, B!12)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(32,plain,
% 0.13/0.40 (((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (relation(relation_composition(A!11, B!12)) | (~relation(B!12)) | (~relation(A!11)))) <=> ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | ((~relation(A!11)) | (~relation(B!12)) | relation(relation_composition(A!11, B!12))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[31])).
% 0.13/0.40 tff(33,plain,
% 0.13/0.40 (((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (relation(relation_composition(A!11, B!12)) | (~relation(B!12)) | (~relation(A!11)))) <=> ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (~relation(A!11)) | (~relation(B!12)) | relation(relation_composition(A!11, B!12)))),
% 0.13/0.40 inference(transitivity,[status(thm)],[32, 30])).
% 0.13/0.40 tff(34,plain,
% 0.13/0.40 ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (relation(relation_composition(A!11, B!12)) | (~relation(B!12)) | (~relation(A!11)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(35,plain,
% 0.13/0.40 ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (~relation(A!11)) | (~relation(B!12)) | relation(relation_composition(A!11, B!12))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.13/0.40 tff(36,plain,
% 0.13/0.40 (relation(relation_composition(A!11, B!12))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[35, 29, 16, 15])).
% 0.13/0.40 tff(37,plain,
% 0.13/0.40 (function(B!12)),
% 0.13/0.40 inference(and_elim,[status(thm)],[14])).
% 0.13/0.40 tff(38,plain,
% 0.13/0.40 (function(A!11)),
% 0.13/0.40 inference(and_elim,[status(thm)],[12])).
% 0.13/0.40 tff(39,plain,
% 0.13/0.40 (^[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)))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(40,plain,
% 0.13/0.40 (![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))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[39])).
% 0.13/0.40 tff(41,plain,
% 0.13/0.40 (^[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))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(42,plain,
% 0.13/0.41 (![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))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[41])).
% 0.13/0.41 tff(43,plain,
% 0.13/0.41 (![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))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(44,plain,
% 0.13/0.41 (^[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))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(45,plain,
% 0.13/0.41 (![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))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[44])).
% 0.13/0.41 tff(46,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/sandbox2/benchmark/theBenchmark.p','fc1_funct_1')).
% 0.13/0.41 tff(47,plain,
% 0.13/0.41 (![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.13/0.41 tff(48,plain,
% 0.13/0.41 (![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.13/0.41 tff(49,plain,(
% 0.13/0.41 ![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))),
% 0.13/0.41 inference(skolemize,[status(sab)],[48])).
% 0.13/0.41 tff(50,plain,
% 0.13/0.41 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.13/0.41 tff(51,plain,
% 0.13/0.41 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[50, 40])).
% 0.13/0.41 tff(52,plain,
% 0.13/0.41 (((~![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(A!11, B!12))) | (~relation(relation_composition(A!11, B!12))))))) <=> ((~![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(A!11, B!12))) | (~relation(relation_composition(A!11, B!12))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(53,plain,
% 0.13/0.41 (((~relation(B!12)) | (~function(B!12)) | (~relation(A!11)) | (~function(A!11)) | (~((~function(relation_composition(A!11, B!12))) | (~relation(relation_composition(A!11, B!12)))))) <=> ((~function(A!11)) | (~relation(A!11)) | (~function(B!12)) | (~relation(B!12)) | (~((~function(relation_composition(A!11, B!12))) | (~relation(relation_composition(A!11, B!12))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(54,plain,
% 0.13/0.41 ((~((~relation(relation_composition(A!11, B!12))) | (~function(relation_composition(A!11, B!12))))) <=> (~((~function(relation_composition(A!11, B!12))) | (~relation(relation_composition(A!11, B!12)))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(55,plain,
% 0.13/0.41 (((~relation(B!12)) | (~function(B!12)) | (~relation(A!11)) | (~function(A!11)) | (~((~relation(relation_composition(A!11, B!12))) | (~function(relation_composition(A!11, B!12)))))) <=> ((~relation(B!12)) | (~function(B!12)) | (~relation(A!11)) | (~function(A!11)) | (~((~function(relation_composition(A!11, B!12))) | (~relation(relation_composition(A!11, B!12))))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[54])).
% 0.13/0.41 tff(56,plain,
% 0.13/0.41 (((~relation(B!12)) | (~function(B!12)) | (~relation(A!11)) | (~function(A!11)) | (~((~relation(relation_composition(A!11, B!12))) | (~function(relation_composition(A!11, B!12)))))) <=> ((~function(A!11)) | (~relation(A!11)) | (~function(B!12)) | (~relation(B!12)) | (~((~function(relation_composition(A!11, B!12))) | (~relation(relation_composition(A!11, B!12))))))),
% 0.13/0.41 inference(transitivity,[status(thm)],[55, 53])).
% 0.13/0.41 tff(57,plain,
% 0.13/0.41 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | ((~relation(B!12)) | (~function(B!12)) | (~relation(A!11)) | (~function(A!11)) | (~((~relation(relation_composition(A!11, B!12))) | (~function(relation_composition(A!11, B!12))))))) <=> ((~![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(A!11, B!12))) | (~relation(relation_composition(A!11, B!12)))))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[56])).
% 0.13/0.41 tff(58,plain,
% 0.13/0.41 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | ((~relation(B!12)) | (~function(B!12)) | (~relation(A!11)) | (~function(A!11)) | (~((~relation(relation_composition(A!11, B!12))) | (~function(relation_composition(A!11, B!12))))))) <=> ((~![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(A!11, B!12))) | (~relation(relation_composition(A!11, B!12))))))),
% 0.13/0.41 inference(transitivity,[status(thm)],[57, 52])).
% 0.13/0.41 tff(59,plain,
% 0.13/0.41 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | ((~relation(B!12)) | (~function(B!12)) | (~relation(A!11)) | (~function(A!11)) | (~((~relation(relation_composition(A!11, B!12))) | (~function(relation_composition(A!11, B!12))))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(60,plain,
% 0.13/0.41 ((~![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(A!11, B!12))) | (~relation(relation_composition(A!11, B!12)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.13/0.41 tff(61,plain,
% 0.13/0.41 (~((~function(relation_composition(A!11, B!12))) | (~relation(relation_composition(A!11, B!12))))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[60, 51, 16, 38, 15, 37])).
% 0.13/0.41 tff(62,plain,
% 0.13/0.41 (((~function(relation_composition(A!11, B!12))) | (~relation(relation_composition(A!11, B!12)))) | function(relation_composition(A!11, B!12))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(63,plain,
% 0.13/0.41 (function(relation_composition(A!11, B!12))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.13/0.41 tff(64,plain,
% 0.13/0.41 (^[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))))))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(65,plain,
% 0.13/0.41 (![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)))))))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[64])).
% 0.13/0.41 tff(66,plain,
% 0.13/0.41 (^[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))))))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(67,plain,
% 0.13/0.41 (![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)))))))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[66])).
% 0.13/0.41 tff(68,plain,
% 0.13/0.41 (![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)))))))))))),
% 0.13/0.41 inference(transitivity,[status(thm)],[67, 65])).
% 0.13/0.41 tff(69,plain,
% 0.13/0.41 (^[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)))))))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(70,plain,
% 0.13/0.41 (![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)))))))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[69])).
% 0.13/0.41 tff(71,plain,
% 0.13/0.41 (![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))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(72,plain,
% 0.13/0.41 (^[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))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(73,plain,
% 0.13/0.41 (![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))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[72])).
% 0.13/0.41 tff(74,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/sandbox2/benchmark/theBenchmark.p','d8_funct_1')).
% 0.13/0.42 tff(75,plain,
% 0.13/0.42 (![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))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.13/0.42 tff(76,plain,
% 0.13/0.42 (![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))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.13/0.42 tff(77,plain,(
% 0.13/0.42 ![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)))))))),
% 0.13/0.42 inference(skolemize,[status(sab)],[76])).
% 0.13/0.42 tff(78,plain,
% 0.13/0.42 (![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)))))))))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[77, 70])).
% 0.13/0.42 tff(79,plain,
% 0.13/0.42 (![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)))))))))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[78, 68])).
% 0.13/0.42 tff(80,plain,
% 0.13/0.42 (((~![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)))))))))))) | ((~function(relation_composition(A!11, B!12))) | (~relation(relation_composition(A!11, B!12))) | (~((~((~one_to_one(relation_composition(A!11, B!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(A!11, B!12)))) | (~in(C, relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), B) = apply(relation_composition(A!11, B!12), C)))))) | (~(one_to_one(relation_composition(A!11, B!12)) | (~((~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, 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(relation_composition(A!11, B!12))) | (~relation(relation_composition(A!11, B!12))) | (~((~((~one_to_one(relation_composition(A!11, B!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(A!11, B!12)))) | (~in(C, relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), B) = apply(relation_composition(A!11, B!12), C)))))) | (~(one_to_one(relation_composition(A!11, B!12)) | (~((~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))))))))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(81,plain,
% 0.13/0.42 (((~relation(relation_composition(A!11, B!12))) | (~function(relation_composition(A!11, B!12))) | (~((~((~one_to_one(relation_composition(A!11, B!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(A!11, B!12)))) | (~in(C, relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), B) = apply(relation_composition(A!11, B!12), C)))))) | (~(one_to_one(relation_composition(A!11, B!12)) | (~((~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12)))))))))) <=> ((~function(relation_composition(A!11, B!12))) | (~relation(relation_composition(A!11, B!12))) | (~((~((~one_to_one(relation_composition(A!11, B!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(A!11, B!12)))) | (~in(C, relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), B) = apply(relation_composition(A!11, B!12), C)))))) | (~(one_to_one(relation_composition(A!11, B!12)) | (~((~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))))))))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(82,plain,
% 0.13/0.42 ((~((~((~one_to_one(relation_composition(A!11, B!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(A!11, B!12)))) | (~in(C, relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), B) = apply(relation_composition(A!11, B!12), C)))))) | (~(one_to_one(relation_composition(A!11, B!12)) | (~((tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))))))))))) <=> (~((~((~one_to_one(relation_composition(A!11, B!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(A!11, B!12)))) | (~in(C, relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), B) = apply(relation_composition(A!11, B!12), C)))))) | (~(one_to_one(relation_composition(A!11, B!12)) | (~((~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12)))))))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(83,plain,
% 0.13/0.42 (((~relation(relation_composition(A!11, B!12))) | (~function(relation_composition(A!11, B!12))) | (~((~((~one_to_one(relation_composition(A!11, B!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(A!11, B!12)))) | (~in(C, relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), B) = apply(relation_composition(A!11, B!12), C)))))) | (~(one_to_one(relation_composition(A!11, B!12)) | (~((tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12)))))))))))) <=> ((~relation(relation_composition(A!11, B!12))) | (~function(relation_composition(A!11, B!12))) | (~((~((~one_to_one(relation_composition(A!11, B!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(A!11, B!12)))) | (~in(C, relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), B) = apply(relation_composition(A!11, B!12), C)))))) | (~(one_to_one(relation_composition(A!11, B!12)) | (~((~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))))))))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[82])).
% 0.21/0.42 tff(84,plain,
% 0.21/0.42 (((~relation(relation_composition(A!11, B!12))) | (~function(relation_composition(A!11, B!12))) | (~((~((~one_to_one(relation_composition(A!11, B!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(A!11, B!12)))) | (~in(C, relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), B) = apply(relation_composition(A!11, B!12), C)))))) | (~(one_to_one(relation_composition(A!11, B!12)) | (~((tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12)))))))))))) <=> ((~function(relation_composition(A!11, B!12))) | (~relation(relation_composition(A!11, B!12))) | (~((~((~one_to_one(relation_composition(A!11, B!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(A!11, B!12)))) | (~in(C, relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), B) = apply(relation_composition(A!11, B!12), C)))))) | (~(one_to_one(relation_composition(A!11, B!12)) | (~((~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))))))))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[83, 81])).
% 0.21/0.42 tff(85,plain,
% 0.21/0.42 (((~![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)))))))))))) | ((~relation(relation_composition(A!11, B!12))) | (~function(relation_composition(A!11, B!12))) | (~((~((~one_to_one(relation_composition(A!11, B!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(A!11, B!12)))) | (~in(C, relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), B) = apply(relation_composition(A!11, B!12), C)))))) | (~(one_to_one(relation_composition(A!11, B!12)) | (~((tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, 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(relation_composition(A!11, B!12))) | (~relation(relation_composition(A!11, B!12))) | (~((~((~one_to_one(relation_composition(A!11, B!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(A!11, B!12)))) | (~in(C, relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), B) = apply(relation_composition(A!11, B!12), C)))))) | (~(one_to_one(relation_composition(A!11, B!12)) | (~((~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12)))))))))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[84])).
% 0.21/0.43 tff(86,plain,
% 0.21/0.43 (((~![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(relation_composition(A!11, B!12))) | (~function(relation_composition(A!11, B!12))) | (~((~((~one_to_one(relation_composition(A!11, B!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(A!11, B!12)))) | (~in(C, relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), B) = apply(relation_composition(A!11, B!12), C)))))) | (~(one_to_one(relation_composition(A!11, B!12)) | (~((tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, 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(relation_composition(A!11, B!12))) | (~relation(relation_composition(A!11, B!12))) | (~((~((~one_to_one(relation_composition(A!11, B!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(A!11, B!12)))) | (~in(C, relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), B) = apply(relation_composition(A!11, B!12), C)))))) | (~(one_to_one(relation_composition(A!11, B!12)) | (~((~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))))))))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[85, 80])).
% 0.21/0.43 tff(87,plain,
% 0.21/0.43 ((~![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(relation_composition(A!11, B!12))) | (~function(relation_composition(A!11, B!12))) | (~((~((~one_to_one(relation_composition(A!11, B!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(A!11, B!12)))) | (~in(C, relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), B) = apply(relation_composition(A!11, B!12), C)))))) | (~(one_to_one(relation_composition(A!11, B!12)) | (~((tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))))))))))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(88,plain,
% 0.21/0.43 ((~![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(relation_composition(A!11, B!12))) | (~relation(relation_composition(A!11, B!12))) | (~((~((~one_to_one(relation_composition(A!11, B!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(A!11, B!12)))) | (~in(C, relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), B) = apply(relation_composition(A!11, B!12), C)))))) | (~(one_to_one(relation_composition(A!11, B!12)) | (~((~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12)))))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.21/0.43 tff(89,plain,
% 0.21/0.43 ((~function(relation_composition(A!11, B!12))) | (~relation(relation_composition(A!11, B!12))) | (~((~((~one_to_one(relation_composition(A!11, B!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(A!11, B!12)))) | (~in(C, relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), B) = apply(relation_composition(A!11, B!12), C)))))) | (~(one_to_one(relation_composition(A!11, B!12)) | (~((~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12)))))))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[88, 79])).
% 0.21/0.43 tff(90,plain,
% 0.21/0.43 (~((~((~one_to_one(relation_composition(A!11, B!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(A!11, B!12)))) | (~in(C, relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), B) = apply(relation_composition(A!11, B!12), C)))))) | (~(one_to_one(relation_composition(A!11, B!12)) | (~((~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))))))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[89, 63, 36])).
% 0.21/0.43 tff(91,plain,
% 0.21/0.43 (((~((~one_to_one(relation_composition(A!11, B!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(A!11, B!12)))) | (~in(C, relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), B) = apply(relation_composition(A!11, B!12), C)))))) | (~(one_to_one(relation_composition(A!11, B!12)) | (~((~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12)))))))) | (one_to_one(relation_composition(A!11, B!12)) | (~((~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(92,plain,
% 0.21/0.43 (one_to_one(relation_composition(A!11, B!12)) | (~((~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12)))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.21/0.43 tff(93,plain,
% 0.21/0.43 (~one_to_one(relation_composition(A!11, B!12))),
% 0.21/0.43 inference(or_elim,[status(thm)],[13])).
% 0.21/0.43 tff(94,plain,
% 0.21/0.43 ((~(one_to_one(relation_composition(A!11, B!12)) | (~((~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))))))) | one_to_one(relation_composition(A!11, B!12)) | (~((~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12)))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(95,plain,
% 0.21/0.43 ((~(one_to_one(relation_composition(A!11, B!12)) | (~((~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))))))) | (~((~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12)))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.21/0.43 tff(96,plain,
% 0.21/0.43 (~((~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[95, 92])).
% 0.21/0.43 tff(97,plain,
% 0.21/0.43 (((~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12)))) | in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(98,plain,
% 0.21/0.43 (in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.21/0.43 tff(99,plain,
% 0.21/0.43 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))) <=> ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))), (((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))))), rewrite(((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)))), (((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(100,plain,
% 0.21/0.44 (![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[99])).
% 0.21/0.44 tff(101,plain,
% 0.21/0.44 (^[A: $i, B: $i, C: $i] : refl(((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(102,plain,
% 0.21/0.44 (![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[101])).
% 0.21/0.44 tff(103,plain,
% 0.21/0.44 (![A: $i, B: $i] : ![C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))),
% 0.21/0.44 inference(pull_quant,[status(thm)],[])).
% 0.21/0.44 tff(104,plain,
% 0.21/0.44 (^[A: $i, B: $i] : pull_quant(((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ![C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(105,plain,
% 0.21/0.44 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i] : ![C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[104])).
% 0.21/0.44 tff(106,plain,
% 0.21/0.44 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[105, 103])).
% 0.21/0.44 tff(107,plain,
% 0.21/0.44 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[106, 102])).
% 0.21/0.44 tff(108,plain,
% 0.21/0.44 (^[A: $i, B: $i] : rewrite(((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(109,plain,
% 0.21/0.44 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[108])).
% 0.21/0.44 tff(110,plain,
% 0.21/0.44 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[109, 107])).
% 0.21/0.44 tff(111,plain,
% 0.21/0.44 (^[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(C, B), A) = apply(B, apply(C, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(relation_composition(C, B))))) <=> ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | ((~relation(C)) | (~function(C))) | (~in(A, relation_dom(relation_composition(C, B))))))), rewrite(((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | ((~relation(C)) | (~function(C))) | (~in(A, relation_dom(relation_composition(C, B))))) <=> ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))), (((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(relation_composition(C, B))))) <=> ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))))), (![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(relation_composition(C, B))))) <=> ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))), (((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(relation_composition(C, B)))))) <=> (((~relation(B)) | (~function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))))), rewrite((((~relation(B)) | (~function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))), (((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(relation_composition(C, B)))))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(112,plain,
% 0.21/0.44 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(relation_composition(C, B)))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[111])).
% 0.21/0.44 tff(113,plain,
% 0.21/0.44 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(relation_composition(C, B)))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(relation_composition(C, B))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(114,plain,
% 0.21/0.44 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((in(A, relation_dom(relation_composition(C, B))) => (apply(relation_composition(C, B), A) = apply(B, apply(C, A)))) <=> ((~in(A, relation_dom(relation_composition(C, B)))) | (apply(relation_composition(C, B), A) = apply(B, apply(C, A))))), (((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) => (apply(relation_composition(C, B), A) = apply(B, apply(C, A))))) <=> ((relation(C) & function(C)) => ((~in(A, relation_dom(relation_composition(C, B)))) | (apply(relation_composition(C, B), A) = apply(B, apply(C, A))))))), rewrite(((relation(C) & function(C)) => ((~in(A, relation_dom(relation_composition(C, B)))) | (apply(relation_composition(C, B), A) = apply(B, apply(C, A))))) <=> ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(relation_composition(C, B)))))), (((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) => (apply(relation_composition(C, B), A) = apply(B, apply(C, A))))) <=> ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(relation_composition(C, B)))))))), (![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) => (apply(relation_composition(C, B), A) = apply(B, apply(C, A))))) <=> ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(relation_composition(C, B))))))), (((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) => (apply(relation_composition(C, B), A) = apply(B, apply(C, A)))))) <=> ((relation(B) & function(B)) => ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(relation_composition(C, B)))))))), rewrite(((relation(B) & function(B)) => ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(relation_composition(C, B)))))) <=> ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(relation_composition(C, B))))))), (((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) => (apply(relation_composition(C, B), A) = apply(B, apply(C, A)))))) <=> ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(relation_composition(C, B))))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(115,plain,
% 0.21/0.44 (![A: $i, B: $i] : ((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) => (apply(relation_composition(C, B), A) = apply(B, apply(C, A)))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(relation_composition(C, B))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[114])).
% 0.21/0.44 tff(116,axiom,(![A: $i, B: $i] : ((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) => (apply(relation_composition(C, B), A) = apply(B, apply(C, A))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t22_funct_1')).
% 0.21/0.44 tff(117,plain,
% 0.21/0.44 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(relation_composition(C, B))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.21/0.44 tff(118,plain,
% 0.21/0.44 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(relation_composition(C, B))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[117, 113])).
% 0.21/0.44 tff(119,plain,(
% 0.21/0.44 ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(relation_composition(C, B))))))),
% 0.21/0.44 inference(skolemize,[status(sab)],[118])).
% 0.21/0.44 tff(120,plain,
% 0.21/0.44 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[119, 112])).
% 0.21/0.44 tff(121,plain,
% 0.21/0.44 (![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[120, 110])).
% 0.21/0.44 tff(122,plain,
% 0.21/0.44 (![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[121, 100])).
% 0.21/0.44 tff(123,plain,
% 0.21/0.44 (((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)))) | ((~function(A!11)) | (~relation(A!11)) | (~function(B!12)) | (~relation(B!12)) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))))))) <=> ((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)))) | (~function(A!11)) | (~relation(A!11)) | (~function(B!12)) | (~relation(B!12)) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(124,plain,
% 0.21/0.44 (((apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12))) <=> ((~function(A!11)) | (~relation(A!11)) | (~function(B!12)) | (~relation(B!12)) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(125,plain,
% 0.21/0.44 (((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)))) | ((apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)))) <=> ((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)))) | ((~function(A!11)) | (~relation(A!11)) | (~function(B!12)) | (~relation(B!12)) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12)))))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[124])).
% 0.21/0.44 tff(126,plain,
% 0.21/0.44 (((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)))) | ((apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)))) <=> ((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)))) | (~function(A!11)) | (~relation(A!11)) | (~function(B!12)) | (~relation(B!12)) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[125, 123])).
% 0.21/0.44 tff(127,plain,
% 0.21/0.44 ((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)))) | ((apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(128,plain,
% 0.21/0.45 ((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)))) | (~function(A!11)) | (~relation(A!11)) | (~function(B!12)) | (~relation(B!12)) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12)))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.21/0.45 tff(129,plain,
% 0.21/0.45 (apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[128, 122, 16, 38, 15, 37, 98])).
% 0.21/0.45 tff(130,plain,
% 0.21/0.45 (((~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12)))) | (apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(131,plain,
% 0.21/0.45 (apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[130, 96])).
% 0.21/0.45 tff(132,plain,
% 0.21/0.45 (((~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12)))) | in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(133,plain,
% 0.21/0.45 (in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[132, 96])).
% 0.21/0.45 tff(134,plain,
% 0.21/0.45 (((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)))) | ((~function(A!11)) | (~relation(A!11)) | (~function(B!12)) | (~relation(B!12)) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))))))) <=> ((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)))) | (~function(A!11)) | (~relation(A!11)) | (~function(B!12)) | (~relation(B!12)) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(135,plain,
% 0.21/0.45 (((apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12))) <=> ((~function(A!11)) | (~relation(A!11)) | (~function(B!12)) | (~relation(B!12)) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(136,plain,
% 0.21/0.45 (((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)))) | ((apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)))) <=> ((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)))) | ((~function(A!11)) | (~relation(A!11)) | (~function(B!12)) | (~relation(B!12)) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12)))))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[135])).
% 0.21/0.45 tff(137,plain,
% 0.21/0.45 (((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)))) | ((apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)))) <=> ((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)))) | (~function(A!11)) | (~relation(A!11)) | (~function(B!12)) | (~relation(B!12)) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[136, 134])).
% 0.21/0.45 tff(138,plain,
% 0.21/0.45 ((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)))) | ((apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(139,plain,
% 0.21/0.45 ((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)))) | (~function(A!11)) | (~relation(A!11)) | (~function(B!12)) | (~relation(B!12)) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12)))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.21/0.45 tff(140,plain,
% 0.21/0.45 (apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[139, 122, 16, 38, 15, 37, 133])).
% 0.21/0.45 tff(141,plain,
% 0.21/0.45 (apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12)))) = apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12)))),
% 0.21/0.45 inference(symmetry,[status(thm)],[140])).
% 0.21/0.45 tff(142,plain,
% 0.21/0.45 (apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12)))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[141, 131, 129])).
% 0.21/0.45 tff(143,plain,
% 0.21/0.45 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))) <=> (((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))), ((~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))) <=> (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))), rewrite((~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))) <=> (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))), ((~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))) <=> (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))), (((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))) <=> ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))))), rewrite(((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))) <=> ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))), (((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))) <=> ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))))), (((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) <=> ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))))), rewrite(((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) <=> ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))), (((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) <=> ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(144,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[143])).
% 0.21/0.45 tff(145,plain,
% 0.21/0.45 (^[A: $i, B: $i, C: $i] : refl(((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) <=> ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(146,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[145])).
% 0.21/0.45 tff(147,plain,
% 0.21/0.45 (![A: $i, B: $i] : ![C: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))))),
% 0.21/0.45 inference(pull_quant,[status(thm)],[])).
% 0.21/0.45 tff(148,plain,
% 0.21/0.45 (^[A: $i, B: $i] : pull_quant(((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) <=> ![C: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(149,plain,
% 0.21/0.45 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) <=> ![A: $i, B: $i] : ![C: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[148])).
% 0.21/0.45 tff(150,plain,
% 0.21/0.45 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[149, 147])).
% 0.21/0.45 tff(151,plain,
% 0.21/0.45 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[150, 146])).
% 0.21/0.45 tff(152,plain,
% 0.21/0.45 (^[A: $i, B: $i] : rewrite(((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(153,plain,
% 0.21/0.45 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[152])).
% 0.21/0.45 tff(154,plain,
% 0.21/0.45 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[153, 151])).
% 0.21/0.45 tff(155,plain,
% 0.21/0.45 (^[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))))), trans(trans(monotonicity(rewrite((in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))), ((in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B)))) <=> (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))))), rewrite((in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))) <=> (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))), ((in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B)))) <=> (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))), rewrite((~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))) <=> (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))), ((in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B)))) <=> (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))), (((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))) <=> (((~relation(C)) | (~function(C))) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))))), rewrite((((~relation(C)) | (~function(C))) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))) <=> ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))), (((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))) <=> ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))))), (![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))) <=> ![C: $i] : ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))))), (((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B)))))) <=> (((~relation(B)) | (~function(B))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))))), rewrite((((~relation(B)) | (~function(B))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))))), (((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B)))))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(156,plain,
% 0.21/0.46 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B)))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[155])).
% 0.21/0.46 tff(157,plain,
% 0.21/0.46 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B)))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(158,plain,
% 0.21/0.46 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite(((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))) <=> ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))))), (![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))) <=> ![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))))), (((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B)))))) <=> ((relation(B) & function(B)) => ![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B)))))))), rewrite(((relation(B) & function(B)) => ![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B)))))) <=> ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))))), (((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B)))))) <=> ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(159,plain,
% 0.21/0.46 (![A: $i, B: $i] : ((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B)))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[158])).
% 0.21/0.46 tff(160,axiom,(![A: $i, B: $i] : ((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t21_funct_1')).
% 0.21/0.46 tff(161,plain,
% 0.21/0.46 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.21/0.46 tff(162,plain,
% 0.21/0.46 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[161, 157])).
% 0.21/0.46 tff(163,plain,(
% 0.21/0.46 ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))))),
% 0.21/0.46 inference(skolemize,[status(sab)],[162])).
% 0.21/0.46 tff(164,plain,
% 0.21/0.46 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[163, 156])).
% 0.21/0.46 tff(165,plain,
% 0.21/0.46 (![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[164, 154])).
% 0.21/0.46 tff(166,plain,
% 0.21/0.46 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[165, 144])).
% 0.21/0.46 tff(167,plain,
% 0.21/0.46 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) | ((~function(A!11)) | (~relation(A!11)) | (~function(B!12)) | (~relation(B!12)) | (~(((~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12)))) <=> in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) | (~function(A!11)) | (~relation(A!11)) | (~function(B!12)) | (~relation(B!12)) | (~(((~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12)))) <=> in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12))))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(168,plain,
% 0.21/0.46 (((~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~(((~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12)))) <=> in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))))) <=> ((~function(A!11)) | (~relation(A!11)) | (~function(B!12)) | (~relation(B!12)) | (~(((~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12)))) <=> in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12))))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(169,plain,
% 0.21/0.46 ((~(((~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12)))) <=> in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12))))) <=> (~(((~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12)))) <=> in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(170,plain,
% 0.21/0.46 (((~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~(((~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12)))) <=> in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))))) <=> ((~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~(((~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12)))) <=> in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12))))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[169])).
% 0.21/0.46 tff(171,plain,
% 0.21/0.46 (((~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~(((~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12)))) <=> in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))))) <=> ((~function(A!11)) | (~relation(A!11)) | (~function(B!12)) | (~relation(B!12)) | (~(((~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12)))) <=> in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12))))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[170, 168])).
% 0.21/0.46 tff(172,plain,
% 0.21/0.46 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) | ((~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~(((~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12)))) <=> in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) | ((~function(A!11)) | (~relation(A!11)) | (~function(B!12)) | (~relation(B!12)) | (~(((~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12)))) <=> in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[171])).
% 0.21/0.46 tff(173,plain,
% 0.21/0.46 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) | ((~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~(((~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12)))) <=> in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) | (~function(A!11)) | (~relation(A!11)) | (~function(B!12)) | (~relation(B!12)) | (~(((~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12)))) <=> in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12))))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[172, 167])).
% 0.21/0.46 tff(174,plain,
% 0.21/0.46 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) | ((~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~(((~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12)))) <=> in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12))))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(175,plain,
% 0.21/0.46 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) | (~function(A!11)) | (~relation(A!11)) | (~function(B!12)) | (~relation(B!12)) | (~(((~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12)))) <=> in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.21/0.47 tff(176,plain,
% 0.21/0.47 (~(((~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12)))) <=> in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[175, 166, 16, 38, 15, 37])).
% 0.21/0.47 tff(177,plain,
% 0.21/0.47 ((((~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12)))) <=> in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~((~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12))))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12))))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(178,plain,
% 0.21/0.47 ((((~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12)))) <=> in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~((~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12)))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[177, 98])).
% 0.21/0.47 tff(179,plain,
% 0.21/0.47 (~((~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[178, 176])).
% 0.21/0.47 tff(180,plain,
% 0.21/0.47 (((~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12)))) | in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(181,plain,
% 0.21/0.47 (in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[180, 179])).
% 0.21/0.47 tff(182,plain,
% 0.21/0.47 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) | ((~function(A!11)) | (~relation(A!11)) | (~function(B!12)) | (~relation(B!12)) | (~(((~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12)))) <=> in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) | (~function(A!11)) | (~relation(A!11)) | (~function(B!12)) | (~relation(B!12)) | (~(((~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12)))) <=> in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(183,plain,
% 0.21/0.47 (((~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~(((~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12)))) <=> in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))))) <=> ((~function(A!11)) | (~relation(A!11)) | (~function(B!12)) | (~relation(B!12)) | (~(((~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12)))) <=> in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(184,plain,
% 0.21/0.47 ((~(((~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12)))) <=> in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12))))) <=> (~(((~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12)))) <=> in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(185,plain,
% 0.21/0.47 (((~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~(((~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12)))) <=> in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))))) <=> ((~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~(((~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12)))) <=> in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12))))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[184])).
% 0.21/0.47 tff(186,plain,
% 0.21/0.47 (((~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~(((~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12)))) <=> in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))))) <=> ((~function(A!11)) | (~relation(A!11)) | (~function(B!12)) | (~relation(B!12)) | (~(((~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12)))) <=> in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12))))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[185, 183])).
% 0.21/0.47 tff(187,plain,
% 0.21/0.47 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) | ((~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~(((~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12)))) <=> in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) | ((~function(A!11)) | (~relation(A!11)) | (~function(B!12)) | (~relation(B!12)) | (~(((~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12)))) <=> in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[186])).
% 0.21/0.47 tff(188,plain,
% 0.21/0.47 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) | ((~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~(((~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12)))) <=> in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) | (~function(A!11)) | (~relation(A!11)) | (~function(B!12)) | (~relation(B!12)) | (~(((~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12)))) <=> in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12))))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[187, 182])).
% 0.21/0.47 tff(189,plain,
% 0.21/0.47 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) | ((~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~(((~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12)))) <=> in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12))))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(190,plain,
% 0.21/0.47 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) | (~function(A!11)) | (~relation(A!11)) | (~function(B!12)) | (~relation(B!12)) | (~(((~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12)))) <=> in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.21/0.47 tff(191,plain,
% 0.21/0.47 (~(((~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12)))) <=> in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[190, 166, 16, 38, 15, 37])).
% 0.21/0.47 tff(192,plain,
% 0.21/0.47 ((((~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12)))) <=> in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~((~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12))))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12))))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(193,plain,
% 0.21/0.47 ((((~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12)))) <=> in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~((~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12)))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[192, 133])).
% 0.21/0.47 tff(194,plain,
% 0.21/0.47 (~((~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[193, 191])).
% 0.21/0.47 tff(195,plain,
% 0.21/0.47 (((~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12)))) | in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(196,plain,
% 0.21/0.47 (in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[195, 194])).
% 0.21/0.47 tff(197,plain,
% 0.21/0.47 (((~![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(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)))))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(198,plain,
% 0.21/0.47 (((~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)))))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(199,plain,
% 0.21/0.47 ((~((~((~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))))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(200,plain,
% 0.21/0.47 (((~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)))))))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[199])).
% 0.21/0.47 tff(201,plain,
% 0.21/0.47 (((~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)))))))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[200, 198])).
% 0.21/0.47 tff(202,plain,
% 0.21/0.47 (((~![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(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))))))))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[201])).
% 0.21/0.47 tff(203,plain,
% 0.21/0.47 (((~![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(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)))))))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[202, 197])).
% 0.21/0.48 tff(204,plain,
% 0.21/0.48 ((~![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)))))))))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(205,plain,
% 0.21/0.48 ((~![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))))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.21/0.48 tff(206,plain,
% 0.21/0.48 (~((~((~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)))))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[205, 79, 15, 37])).
% 0.21/0.48 tff(207,plain,
% 0.21/0.48 (((~((~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)) | ![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)))))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(208,plain,
% 0.21/0.48 ((~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))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[207, 206])).
% 0.21/0.48 tff(209,plain,
% 0.21/0.48 (one_to_one(A!11) & one_to_one(B!12)),
% 0.21/0.48 inference(or_elim,[status(thm)],[13])).
% 0.21/0.48 tff(210,plain,
% 0.21/0.48 (one_to_one(B!12)),
% 0.21/0.48 inference(and_elim,[status(thm)],[209])).
% 0.21/0.48 tff(211,plain,
% 0.21/0.48 ((~((~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)) | ![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))))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(212,plain,
% 0.21/0.48 ((~((~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)))))) | ![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))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[211, 210])).
% 0.21/0.48 tff(213,plain,
% 0.21/0.48 (![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))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[212, 208])).
% 0.21/0.48 tff(214,plain,
% 0.21/0.48 (((~![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))))) | ((~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12))) | (apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12)))) | (~(apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12)))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, 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))))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12))) | (apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12)))) | (~(apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12)))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12)))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(215,plain,
% 0.21/0.48 (((apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12)))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12))) | (~(apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12)))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))))))) <=> ((~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12))) | (apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12)))) | (~(apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12)))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12)))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(216,plain,
% 0.21/0.48 (((~![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))))) | ((apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12)))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12))) | (~(apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12)))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, 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))))) | ((~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12))) | (apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12)))) | (~(apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12)))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))))))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[215])).
% 0.21/0.48 tff(217,plain,
% 0.21/0.48 (((~![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))))) | ((apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12)))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12))) | (~(apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12)))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, 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))))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12))) | (apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12)))) | (~(apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12)))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12)))))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[216, 214])).
% 0.21/0.48 tff(218,plain,
% 0.21/0.48 ((~![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))))) | ((apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12)))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12))) | (~(apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12)))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12)))))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(219,plain,
% 0.21/0.48 ((~![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))))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12))) | (apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12)))) | (~(apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12)))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.21/0.48 tff(220,plain,
% 0.21/0.48 (apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[219, 213, 196, 181, 142])).
% 0.21/0.48 tff(221,plain,
% 0.21/0.48 (((~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12)))) | in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(222,plain,
% 0.21/0.48 (in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[221, 179])).
% 0.21/0.48 tff(223,plain,
% 0.21/0.48 (((~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12)))) | in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(224,plain,
% 0.21/0.48 (in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[223, 194])).
% 0.21/0.48 tff(225,plain,
% 0.21/0.48 (((~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12)))) | (~(tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(226,plain,
% 0.21/0.48 (~(tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[225, 96])).
% 0.21/0.48 tff(227,plain,
% 0.21/0.48 (((~![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(A!11)) | (~relation(A!11)) | (~((~((~one_to_one(A!11)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C)))))) | (~(one_to_one(A!11) | (~((~(apply(A!11, tptp_fun_B_1(A!11)) = apply(A!11, tptp_fun_C_0(A!11)))) | (~in(tptp_fun_C_0(A!11), relation_dom(A!11))) | (~in(tptp_fun_B_1(A!11), relation_dom(A!11))) | (tptp_fun_B_1(A!11) = tptp_fun_C_0(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(A!11)) | (~relation(A!11)) | (~((~((~one_to_one(A!11)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C)))))) | (~(one_to_one(A!11) | (~((~(apply(A!11, tptp_fun_B_1(A!11)) = apply(A!11, tptp_fun_C_0(A!11)))) | (~in(tptp_fun_C_0(A!11), relation_dom(A!11))) | (~in(tptp_fun_B_1(A!11), relation_dom(A!11))) | (tptp_fun_B_1(A!11) = tptp_fun_C_0(A!11)))))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(228,plain,
% 0.21/0.48 (((~relation(A!11)) | (~function(A!11)) | (~((~((~one_to_one(A!11)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C)))))) | (~(one_to_one(A!11) | (~((~(apply(A!11, tptp_fun_B_1(A!11)) = apply(A!11, tptp_fun_C_0(A!11)))) | (~in(tptp_fun_C_0(A!11), relation_dom(A!11))) | (~in(tptp_fun_B_1(A!11), relation_dom(A!11))) | (tptp_fun_B_1(A!11) = tptp_fun_C_0(A!11))))))))) <=> ((~function(A!11)) | (~relation(A!11)) | (~((~((~one_to_one(A!11)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C)))))) | (~(one_to_one(A!11) | (~((~(apply(A!11, tptp_fun_B_1(A!11)) = apply(A!11, tptp_fun_C_0(A!11)))) | (~in(tptp_fun_C_0(A!11), relation_dom(A!11))) | (~in(tptp_fun_B_1(A!11), relation_dom(A!11))) | (tptp_fun_B_1(A!11) = tptp_fun_C_0(A!11)))))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(229,plain,
% 0.21/0.48 ((~((~((~one_to_one(A!11)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C)))))) | (~(one_to_one(A!11) | (~((tptp_fun_B_1(A!11) = tptp_fun_C_0(A!11)) | (~in(tptp_fun_B_1(A!11), relation_dom(A!11))) | (~in(tptp_fun_C_0(A!11), relation_dom(A!11))) | (~(apply(A!11, tptp_fun_B_1(A!11)) = apply(A!11, tptp_fun_C_0(A!11)))))))))) <=> (~((~((~one_to_one(A!11)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C)))))) | (~(one_to_one(A!11) | (~((~(apply(A!11, tptp_fun_B_1(A!11)) = apply(A!11, tptp_fun_C_0(A!11)))) | (~in(tptp_fun_C_0(A!11), relation_dom(A!11))) | (~in(tptp_fun_B_1(A!11), relation_dom(A!11))) | (tptp_fun_B_1(A!11) = tptp_fun_C_0(A!11))))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(230,plain,
% 0.21/0.48 (((~relation(A!11)) | (~function(A!11)) | (~((~((~one_to_one(A!11)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C)))))) | (~(one_to_one(A!11) | (~((tptp_fun_B_1(A!11) = tptp_fun_C_0(A!11)) | (~in(tptp_fun_B_1(A!11), relation_dom(A!11))) | (~in(tptp_fun_C_0(A!11), relation_dom(A!11))) | (~(apply(A!11, tptp_fun_B_1(A!11)) = apply(A!11, tptp_fun_C_0(A!11))))))))))) <=> ((~relation(A!11)) | (~function(A!11)) | (~((~((~one_to_one(A!11)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C)))))) | (~(one_to_one(A!11) | (~((~(apply(A!11, tptp_fun_B_1(A!11)) = apply(A!11, tptp_fun_C_0(A!11)))) | (~in(tptp_fun_C_0(A!11), relation_dom(A!11))) | (~in(tptp_fun_B_1(A!11), relation_dom(A!11))) | (tptp_fun_B_1(A!11) = tptp_fun_C_0(A!11)))))))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[229])).
% 0.21/0.48 tff(231,plain,
% 0.21/0.48 (((~relation(A!11)) | (~function(A!11)) | (~((~((~one_to_one(A!11)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C)))))) | (~(one_to_one(A!11) | (~((tptp_fun_B_1(A!11) = tptp_fun_C_0(A!11)) | (~in(tptp_fun_B_1(A!11), relation_dom(A!11))) | (~in(tptp_fun_C_0(A!11), relation_dom(A!11))) | (~(apply(A!11, tptp_fun_B_1(A!11)) = apply(A!11, tptp_fun_C_0(A!11))))))))))) <=> ((~function(A!11)) | (~relation(A!11)) | (~((~((~one_to_one(A!11)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C)))))) | (~(one_to_one(A!11) | (~((~(apply(A!11, tptp_fun_B_1(A!11)) = apply(A!11, tptp_fun_C_0(A!11)))) | (~in(tptp_fun_C_0(A!11), relation_dom(A!11))) | (~in(tptp_fun_B_1(A!11), relation_dom(A!11))) | (tptp_fun_B_1(A!11) = tptp_fun_C_0(A!11)))))))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[230, 228])).
% 0.21/0.48 tff(232,plain,
% 0.21/0.48 (((~![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(A!11)) | (~function(A!11)) | (~((~((~one_to_one(A!11)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C)))))) | (~(one_to_one(A!11) | (~((tptp_fun_B_1(A!11) = tptp_fun_C_0(A!11)) | (~in(tptp_fun_B_1(A!11), relation_dom(A!11))) | (~in(tptp_fun_C_0(A!11), relation_dom(A!11))) | (~(apply(A!11, tptp_fun_B_1(A!11)) = apply(A!11, tptp_fun_C_0(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(A!11)) | (~relation(A!11)) | (~((~((~one_to_one(A!11)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C)))))) | (~(one_to_one(A!11) | (~((~(apply(A!11, tptp_fun_B_1(A!11)) = apply(A!11, tptp_fun_C_0(A!11)))) | (~in(tptp_fun_C_0(A!11), relation_dom(A!11))) | (~in(tptp_fun_B_1(A!11), relation_dom(A!11))) | (tptp_fun_B_1(A!11) = tptp_fun_C_0(A!11))))))))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[231])).
% 0.21/0.49 tff(233,plain,
% 0.21/0.49 (((~![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(A!11)) | (~function(A!11)) | (~((~((~one_to_one(A!11)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C)))))) | (~(one_to_one(A!11) | (~((tptp_fun_B_1(A!11) = tptp_fun_C_0(A!11)) | (~in(tptp_fun_B_1(A!11), relation_dom(A!11))) | (~in(tptp_fun_C_0(A!11), relation_dom(A!11))) | (~(apply(A!11, tptp_fun_B_1(A!11)) = apply(A!11, tptp_fun_C_0(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(A!11)) | (~relation(A!11)) | (~((~((~one_to_one(A!11)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C)))))) | (~(one_to_one(A!11) | (~((~(apply(A!11, tptp_fun_B_1(A!11)) = apply(A!11, tptp_fun_C_0(A!11)))) | (~in(tptp_fun_C_0(A!11), relation_dom(A!11))) | (~in(tptp_fun_B_1(A!11), relation_dom(A!11))) | (tptp_fun_B_1(A!11) = tptp_fun_C_0(A!11)))))))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[232, 227])).
% 0.21/0.49 tff(234,plain,
% 0.21/0.49 ((~![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(A!11)) | (~function(A!11)) | (~((~((~one_to_one(A!11)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C)))))) | (~(one_to_one(A!11) | (~((tptp_fun_B_1(A!11) = tptp_fun_C_0(A!11)) | (~in(tptp_fun_B_1(A!11), relation_dom(A!11))) | (~in(tptp_fun_C_0(A!11), relation_dom(A!11))) | (~(apply(A!11, tptp_fun_B_1(A!11)) = apply(A!11, tptp_fun_C_0(A!11)))))))))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(235,plain,
% 0.21/0.49 ((~![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(A!11)) | (~relation(A!11)) | (~((~((~one_to_one(A!11)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C)))))) | (~(one_to_one(A!11) | (~((~(apply(A!11, tptp_fun_B_1(A!11)) = apply(A!11, tptp_fun_C_0(A!11)))) | (~in(tptp_fun_C_0(A!11), relation_dom(A!11))) | (~in(tptp_fun_B_1(A!11), relation_dom(A!11))) | (tptp_fun_B_1(A!11) = tptp_fun_C_0(A!11))))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.21/0.49 tff(236,plain,
% 0.21/0.49 (~((~((~one_to_one(A!11)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C)))))) | (~(one_to_one(A!11) | (~((~(apply(A!11, tptp_fun_B_1(A!11)) = apply(A!11, tptp_fun_C_0(A!11)))) | (~in(tptp_fun_C_0(A!11), relation_dom(A!11))) | (~in(tptp_fun_B_1(A!11), relation_dom(A!11))) | (tptp_fun_B_1(A!11) = tptp_fun_C_0(A!11)))))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[235, 79, 16, 38])).
% 0.21/0.49 tff(237,plain,
% 0.21/0.49 (((~((~one_to_one(A!11)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C)))))) | (~(one_to_one(A!11) | (~((~(apply(A!11, tptp_fun_B_1(A!11)) = apply(A!11, tptp_fun_C_0(A!11)))) | (~in(tptp_fun_C_0(A!11), relation_dom(A!11))) | (~in(tptp_fun_B_1(A!11), relation_dom(A!11))) | (tptp_fun_B_1(A!11) = tptp_fun_C_0(A!11))))))) | ((~one_to_one(A!11)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C)))))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(238,plain,
% 0.21/0.49 ((~one_to_one(A!11)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[237, 236])).
% 0.21/0.49 tff(239,plain,
% 0.21/0.49 (one_to_one(A!11)),
% 0.21/0.49 inference(and_elim,[status(thm)],[209])).
% 0.21/0.49 tff(240,plain,
% 0.21/0.49 ((~((~one_to_one(A!11)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C)))))) | (~one_to_one(A!11)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C))))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(241,plain,
% 0.21/0.49 ((~((~one_to_one(A!11)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C)))))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[240, 239])).
% 0.21/0.49 tff(242,plain,
% 0.21/0.49 (![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[241, 238])).
% 0.21/0.49 tff(243,plain,
% 0.21/0.49 (((~![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C))))) | ((tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))))))) <=> ((~![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C))))) | (tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(244,plain,
% 0.21/0.49 ((~![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C))))) | ((tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(245,plain,
% 0.21/0.49 ((~![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C))))) | (tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12)))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[244, 243])).
% 0.21/0.49 tff(246,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[245, 242, 226, 224, 222, 220])).
% 0.21/0.49 % SZS output end Proof
% 0.21/0.49 % E exiting
%------------------------------------------------------------------------------