%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU042+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:26:50 AM UTC 2025
% Result : Theorem 1.45s 1.62s
% Output : Proof 1.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU042+1 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 05:58:05 EDT 2025
% 0.12/0.34 % CPUTime :
% 1.45/1.62 % SZS status Theorem
% 1.45/1.62 % SZS output start Proof
% 1.45/1.62 tff(in_type, type, (
% 1.45/1.62 in: ( $i * $i ) > $o)).
% 1.45/1.62 tff(set_intersection2_type, type, (
% 1.45/1.62 set_intersection2: ( $i * $i ) > $i)).
% 1.45/1.62 tff(tptp_fun_A_16_type, type, (
% 1.45/1.62 tptp_fun_A_16: $i)).
% 1.45/1.62 tff(relation_dom_type, type, (
% 1.45/1.62 relation_dom: $i > $i)).
% 1.45/1.62 tff(tptp_fun_B_15_type, type, (
% 1.45/1.62 tptp_fun_B_15: $i)).
% 1.45/1.62 tff(tptp_fun_B_2_type, type, (
% 1.45/1.62 tptp_fun_B_2: $i > $i)).
% 1.45/1.62 tff(relation_dom_restriction_type, type, (
% 1.45/1.62 relation_dom_restriction: ( $i * $i ) > $i)).
% 1.45/1.62 tff(apply_type, type, (
% 1.45/1.62 apply: ( $i * $i ) > $i)).
% 1.45/1.62 tff(tptp_fun_C_1_type, type, (
% 1.45/1.62 tptp_fun_C_1: $i > $i)).
% 1.45/1.62 tff(function_type, type, (
% 1.45/1.62 function: $i > $o)).
% 1.45/1.62 tff(relation_type, type, (
% 1.45/1.62 relation: $i > $o)).
% 1.45/1.62 tff(one_to_one_type, type, (
% 1.45/1.62 one_to_one: $i > $o)).
% 1.45/1.62 tff(tptp_fun_D_14_type, type, (
% 1.45/1.62 tptp_fun_D_14: ( $i * $i ) > $i)).
% 1.45/1.62 tff(tptp_fun_D_0_type, type, (
% 1.45/1.62 tptp_fun_D_0: ( $i * $i * $i ) > $i)).
% 1.45/1.62 tff(1,plain,
% 1.45/1.62 ((~(one_to_one(relation_dom_restriction(B!15, A!16)) | (~(relation(B!15) & function(B!15))) | (~one_to_one(B!15)))) <=> (~(one_to_one(relation_dom_restriction(B!15, A!16)) | (~(relation(B!15) & function(B!15))) | (~one_to_one(B!15))))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(2,plain,
% 1.45/1.62 ((~![A: $i, B: $i] : (one_to_one(relation_dom_restriction(B, A)) | (~(relation(B) & function(B))) | (~one_to_one(B)))) <=> (~![A: $i, B: $i] : (one_to_one(relation_dom_restriction(B, A)) | (~(relation(B) & function(B))) | (~one_to_one(B))))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(3,plain,
% 1.45/1.62 ((~![A: $i, B: $i] : ((relation(B) & function(B)) => (one_to_one(B) => one_to_one(relation_dom_restriction(B, A))))) <=> (~![A: $i, B: $i] : (one_to_one(relation_dom_restriction(B, A)) | (~(relation(B) & function(B))) | (~one_to_one(B))))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(4,axiom,(~![A: $i, B: $i] : ((relation(B) & function(B)) => (one_to_one(B) => one_to_one(relation_dom_restriction(B, A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t84_funct_1')).
% 1.45/1.62 tff(5,plain,
% 1.45/1.62 (~![A: $i, B: $i] : (one_to_one(relation_dom_restriction(B, A)) | (~(relation(B) & function(B))) | (~one_to_one(B)))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[4, 3])).
% 1.45/1.62 tff(6,plain,
% 1.45/1.62 (~![A: $i, B: $i] : (one_to_one(relation_dom_restriction(B, A)) | (~(relation(B) & function(B))) | (~one_to_one(B)))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[5, 2])).
% 1.45/1.62 tff(7,plain,
% 1.45/1.62 (~![A: $i, B: $i] : (one_to_one(relation_dom_restriction(B, A)) | (~(relation(B) & function(B))) | (~one_to_one(B)))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[6, 2])).
% 1.45/1.62 tff(8,plain,
% 1.45/1.62 (~![A: $i, B: $i] : (one_to_one(relation_dom_restriction(B, A)) | (~(relation(B) & function(B))) | (~one_to_one(B)))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[7, 2])).
% 1.45/1.62 tff(9,plain,(
% 1.45/1.62 ~(one_to_one(relation_dom_restriction(B!15, A!16)) | (~(relation(B!15) & function(B!15))) | (~one_to_one(B!15)))),
% 1.45/1.62 inference(skolemize,[status(sab)],[8])).
% 1.45/1.62 tff(10,plain,
% 1.45/1.62 (~(one_to_one(relation_dom_restriction(B!15, A!16)) | (~(relation(B!15) & function(B!15))) | (~one_to_one(B!15)))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[9, 1])).
% 1.45/1.62 tff(11,plain,
% 1.45/1.62 (relation(B!15) & function(B!15)),
% 1.45/1.62 inference(or_elim,[status(thm)],[10])).
% 1.45/1.62 tff(12,plain,
% 1.45/1.62 (function(B!15)),
% 1.45/1.62 inference(and_elim,[status(thm)],[11])).
% 1.45/1.62 tff(13,plain,
% 1.45/1.62 (relation(B!15)),
% 1.45/1.62 inference(and_elim,[status(thm)],[11])).
% 1.45/1.62 tff(14,plain,
% 1.45/1.62 (^[A: $i, B: $i] : refl(((~relation(A)) | (~function(A)) | (~((~relation(relation_dom_restriction(A, B))) | (~function(relation_dom_restriction(A, B)))))) <=> ((~relation(A)) | (~function(A)) | (~((~relation(relation_dom_restriction(A, B))) | (~function(relation_dom_restriction(A, B)))))))),
% 1.45/1.62 inference(bind,[status(th)],[])).
% 1.45/1.62 tff(15,plain,
% 1.45/1.62 (![A: $i, B: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(relation_dom_restriction(A, B))) | (~function(relation_dom_restriction(A, B)))))) <=> ![A: $i, B: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(relation_dom_restriction(A, B))) | (~function(relation_dom_restriction(A, B))))))),
% 1.45/1.62 inference(quant_intro,[status(thm)],[14])).
% 1.45/1.62 tff(16,plain,
% 1.45/1.62 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(A) & function(A)) <=> (~((~relation(A)) | (~function(A))))), ((~(relation(A) & function(A))) <=> (~(~((~relation(A)) | (~function(A))))))), rewrite((~(~((~relation(A)) | (~function(A))))) <=> ((~relation(A)) | (~function(A)))), ((~(relation(A) & function(A))) <=> ((~relation(A)) | (~function(A))))), rewrite((relation(relation_dom_restriction(A, B)) & function(relation_dom_restriction(A, B))) <=> (~((~relation(relation_dom_restriction(A, B))) | (~function(relation_dom_restriction(A, B)))))), (((~(relation(A) & function(A))) | (relation(relation_dom_restriction(A, B)) & function(relation_dom_restriction(A, B)))) <=> (((~relation(A)) | (~function(A))) | (~((~relation(relation_dom_restriction(A, B))) | (~function(relation_dom_restriction(A, B)))))))), rewrite((((~relation(A)) | (~function(A))) | (~((~relation(relation_dom_restriction(A, B))) | (~function(relation_dom_restriction(A, B)))))) <=> ((~relation(A)) | (~function(A)) | (~((~relation(relation_dom_restriction(A, B))) | (~function(relation_dom_restriction(A, B))))))), (((~(relation(A) & function(A))) | (relation(relation_dom_restriction(A, B)) & function(relation_dom_restriction(A, B)))) <=> ((~relation(A)) | (~function(A)) | (~((~relation(relation_dom_restriction(A, B))) | (~function(relation_dom_restriction(A, B))))))))),
% 1.45/1.62 inference(bind,[status(th)],[])).
% 1.45/1.62 tff(17,plain,
% 1.45/1.62 (![A: $i, B: $i] : ((~(relation(A) & function(A))) | (relation(relation_dom_restriction(A, B)) & function(relation_dom_restriction(A, B)))) <=> ![A: $i, B: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(relation_dom_restriction(A, B))) | (~function(relation_dom_restriction(A, B))))))),
% 1.45/1.62 inference(quant_intro,[status(thm)],[16])).
% 1.45/1.62 tff(18,plain,
% 1.45/1.62 (![A: $i, B: $i] : ((~(relation(A) & function(A))) | (relation(relation_dom_restriction(A, B)) & function(relation_dom_restriction(A, B)))) <=> ![A: $i, B: $i] : ((~(relation(A) & function(A))) | (relation(relation_dom_restriction(A, B)) & function(relation_dom_restriction(A, B))))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(19,plain,
% 1.45/1.62 (^[A: $i, B: $i] : rewrite(((relation(A) & function(A)) => (relation(relation_dom_restriction(A, B)) & function(relation_dom_restriction(A, B)))) <=> ((~(relation(A) & function(A))) | (relation(relation_dom_restriction(A, B)) & function(relation_dom_restriction(A, B)))))),
% 1.45/1.62 inference(bind,[status(th)],[])).
% 1.45/1.62 tff(20,plain,
% 1.45/1.62 (![A: $i, B: $i] : ((relation(A) & function(A)) => (relation(relation_dom_restriction(A, B)) & function(relation_dom_restriction(A, B)))) <=> ![A: $i, B: $i] : ((~(relation(A) & function(A))) | (relation(relation_dom_restriction(A, B)) & function(relation_dom_restriction(A, B))))),
% 1.45/1.62 inference(quant_intro,[status(thm)],[19])).
% 1.45/1.62 tff(21,axiom,(![A: $i, B: $i] : ((relation(A) & function(A)) => (relation(relation_dom_restriction(A, B)) & function(relation_dom_restriction(A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc4_funct_1')).
% 1.45/1.62 tff(22,plain,
% 1.45/1.62 (![A: $i, B: $i] : ((~(relation(A) & function(A))) | (relation(relation_dom_restriction(A, B)) & function(relation_dom_restriction(A, B))))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[21, 20])).
% 1.45/1.62 tff(23,plain,
% 1.45/1.62 (![A: $i, B: $i] : ((~(relation(A) & function(A))) | (relation(relation_dom_restriction(A, B)) & function(relation_dom_restriction(A, B))))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[22, 18])).
% 1.45/1.62 tff(24,plain,(
% 1.45/1.62 ![A: $i, B: $i] : ((~(relation(A) & function(A))) | (relation(relation_dom_restriction(A, B)) & function(relation_dom_restriction(A, B))))),
% 1.45/1.62 inference(skolemize,[status(sab)],[23])).
% 1.45/1.62 tff(25,plain,
% 1.45/1.62 (![A: $i, B: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(relation_dom_restriction(A, B))) | (~function(relation_dom_restriction(A, B))))))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[24, 17])).
% 1.45/1.62 tff(26,plain,
% 1.45/1.62 (![A: $i, B: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(relation_dom_restriction(A, B))) | (~function(relation_dom_restriction(A, B))))))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[25, 15])).
% 1.45/1.62 tff(27,plain,
% 1.45/1.62 (((~![A: $i, B: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(relation_dom_restriction(A, B))) | (~function(relation_dom_restriction(A, B))))))) | ((~function(B!15)) | (~relation(B!15)) | (~((~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))))))) <=> ((~![A: $i, B: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(relation_dom_restriction(A, B))) | (~function(relation_dom_restriction(A, B))))))) | (~function(B!15)) | (~relation(B!15)) | (~((~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))))))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(28,plain,
% 1.45/1.62 (((~relation(B!15)) | (~function(B!15)) | (~((~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16)))))) <=> ((~function(B!15)) | (~relation(B!15)) | (~((~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))))))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(29,plain,
% 1.45/1.62 ((~((~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))))) <=> (~((~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16)))))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(30,plain,
% 1.45/1.62 (((~relation(B!15)) | (~function(B!15)) | (~((~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16)))))) <=> ((~relation(B!15)) | (~function(B!15)) | (~((~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))))))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[29])).
% 1.45/1.62 tff(31,plain,
% 1.45/1.62 (((~relation(B!15)) | (~function(B!15)) | (~((~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16)))))) <=> ((~function(B!15)) | (~relation(B!15)) | (~((~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))))))),
% 1.45/1.62 inference(transitivity,[status(thm)],[30, 28])).
% 1.45/1.62 tff(32,plain,
% 1.45/1.62 (((~![A: $i, B: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(relation_dom_restriction(A, B))) | (~function(relation_dom_restriction(A, B))))))) | ((~relation(B!15)) | (~function(B!15)) | (~((~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))))))) <=> ((~![A: $i, B: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(relation_dom_restriction(A, B))) | (~function(relation_dom_restriction(A, B))))))) | ((~function(B!15)) | (~relation(B!15)) | (~((~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16)))))))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[31])).
% 1.45/1.62 tff(33,plain,
% 1.45/1.62 (((~![A: $i, B: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(relation_dom_restriction(A, B))) | (~function(relation_dom_restriction(A, B))))))) | ((~relation(B!15)) | (~function(B!15)) | (~((~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))))))) <=> ((~![A: $i, B: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(relation_dom_restriction(A, B))) | (~function(relation_dom_restriction(A, B))))))) | (~function(B!15)) | (~relation(B!15)) | (~((~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))))))),
% 1.45/1.62 inference(transitivity,[status(thm)],[32, 27])).
% 1.45/1.62 tff(34,plain,
% 1.45/1.62 ((~![A: $i, B: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(relation_dom_restriction(A, B))) | (~function(relation_dom_restriction(A, B))))))) | ((~relation(B!15)) | (~function(B!15)) | (~((~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))))))),
% 1.45/1.62 inference(quant_inst,[status(thm)],[])).
% 1.45/1.62 tff(35,plain,
% 1.45/1.62 ((~![A: $i, B: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(relation_dom_restriction(A, B))) | (~function(relation_dom_restriction(A, B))))))) | (~function(B!15)) | (~relation(B!15)) | (~((~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16)))))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[34, 33])).
% 1.45/1.62 tff(36,plain,
% 1.45/1.62 (~((~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[35, 26, 13, 12])).
% 1.45/1.62 tff(37,plain,
% 1.45/1.62 (((~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16)))) | function(relation_dom_restriction(B!15, A!16))),
% 1.45/1.62 inference(tautology,[status(thm)],[])).
% 1.45/1.62 tff(38,plain,
% 1.45/1.62 (function(relation_dom_restriction(B!15, A!16))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[37, 36])).
% 1.45/1.62 tff(39,plain,
% 1.45/1.62 (^[A: $i, B: $i] : refl(((~relation(A)) | relation(relation_dom_restriction(A, B))) <=> ((~relation(A)) | relation(relation_dom_restriction(A, B))))),
% 1.45/1.62 inference(bind,[status(th)],[])).
% 1.45/1.62 tff(40,plain,
% 1.45/1.62 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 1.45/1.62 inference(quant_intro,[status(thm)],[39])).
% 1.45/1.62 tff(41,plain,
% 1.45/1.62 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(42,plain,
% 1.45/1.62 (^[A: $i, B: $i] : rewrite((relation(A) => relation(relation_dom_restriction(A, B))) <=> ((~relation(A)) | relation(relation_dom_restriction(A, B))))),
% 1.45/1.62 inference(bind,[status(th)],[])).
% 1.45/1.62 tff(43,plain,
% 1.45/1.62 (![A: $i, B: $i] : (relation(A) => relation(relation_dom_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 1.45/1.62 inference(quant_intro,[status(thm)],[42])).
% 1.45/1.62 tff(44,axiom,(![A: $i, B: $i] : (relation(A) => relation(relation_dom_restriction(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k7_relat_1')).
% 1.45/1.62 tff(45,plain,
% 1.45/1.62 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[44, 43])).
% 1.45/1.62 tff(46,plain,
% 1.45/1.62 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[45, 41])).
% 1.45/1.62 tff(47,plain,(
% 1.45/1.62 ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 1.45/1.62 inference(skolemize,[status(sab)],[46])).
% 1.45/1.62 tff(48,plain,
% 1.45/1.62 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[47, 40])).
% 1.45/1.62 tff(49,plain,
% 1.45/1.62 (((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | ((~relation(B!15)) | relation(relation_dom_restriction(B!15, A!16)))) <=> ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | (~relation(B!15)) | relation(relation_dom_restriction(B!15, A!16)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(50,plain,
% 1.45/1.62 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | ((~relation(B!15)) | relation(relation_dom_restriction(B!15, A!16)))),
% 1.45/1.62 inference(quant_inst,[status(thm)],[])).
% 1.45/1.62 tff(51,plain,
% 1.45/1.62 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | (~relation(B!15)) | relation(relation_dom_restriction(B!15, A!16))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[50, 49])).
% 1.45/1.62 tff(52,plain,
% 1.45/1.62 (relation(relation_dom_restriction(B!15, A!16))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[51, 48, 13])).
% 1.45/1.62 tff(53,plain,
% 1.45/1.62 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))) <=> (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))))), (((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))))) <=> ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))))))), rewrite(((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))))) <=> ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))), (((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))))) <=> ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))))))), (((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))) <=> ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))))), rewrite(((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))) <=> ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))), (((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))) <=> ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))))),
% 1.45/1.62 inference(bind,[status(th)],[])).
% 1.45/1.62 tff(54,plain,
% 1.45/1.62 (![A: $i, B: $i, C: $i, D: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))),
% 1.45/1.62 inference(quant_intro,[status(thm)],[53])).
% 1.45/1.62 tff(55,plain,
% 1.45/1.62 (^[A: $i, B: $i, C: $i, D: $i] : refl(((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))) <=> ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))))),
% 1.45/1.62 inference(bind,[status(th)],[])).
% 1.45/1.62 tff(56,plain,
% 1.45/1.62 (![A: $i, B: $i, C: $i, D: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))))))),
% 1.45/1.62 inference(quant_intro,[status(thm)],[55])).
% 1.45/1.62 tff(57,plain,
% 1.45/1.62 (![A: $i, B: $i] : ![C: $i, D: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))))))),
% 1.45/1.62 inference(pull_quant,[status(thm)],[])).
% 1.45/1.62 tff(58,plain,
% 1.45/1.62 (^[A: $i, B: $i] : trans(monotonicity(trans(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant((~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))) <=> ?[D: $i] : (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))), (((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))) <=> ((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | ?[D: $i] : (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))))), pull_quant(((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | ?[D: $i] : (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))) <=> ?[D: $i] : ((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))), (((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))) <=> ?[D: $i] : ((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))))), ((~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))) <=> (~?[D: $i] : ((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))), pull_quant((~?[D: $i] : ((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))) <=> ![D: $i] : (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))))), ((~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))) <=> ![D: $i] : (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))), (((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))))) <=> ((~(B = relation_dom_restriction(C, A))) | ![D: $i] : (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))))))), pull_quant(((~(B = relation_dom_restriction(C, A))) | ![D: $i] : (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))))) <=> ![D: $i] : ((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))), (((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))))) <=> ![D: $i] : ((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))))))), ((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) <=> (~![D: $i] : ((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))))), pull_quant((~![D: $i] : ((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) <=> ?[D: $i] : (~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))))))), ((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) <=> ?[D: $i] : (~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))))), (((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))) <=> (?[D: $i] : (~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))))), pull_quant((?[D: $i] : (~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))) <=> ?[D: $i] : ((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))), (((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))) <=> ?[D: $i] : ((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))))), ((~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))) <=> (~?[D: $i] : ((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))), pull_quant((~?[D: $i] : ((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))) <=> ![D: $i] : (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))))), ((~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))) <=> ![D: $i] : (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))), (((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))))) <=> ((~relation(C)) | (~function(C)) | ![D: $i] : (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))))))), pull_quant(((~relation(C)) | (~function(C)) | ![D: $i] : (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))))) <=> ![D: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))), (((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))))) <=> ![D: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))))), (![C: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))))) <=> ![C: $i] : ![D: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))))))), pull_quant(![C: $i] : ![D: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))))) <=> ![C: $i, D: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))), (![C: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))))) <=> ![C: $i, D: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))))))), (((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))) <=> ((~relation(B)) | (~function(B)) | ![C: $i, D: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))))), pull_quant(((~relation(B)) | (~function(B)) | ![C: $i, D: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))) <=> ![C: $i, D: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))))))), (((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))) <=> ![C: $i, D: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))))))))),
% 1.45/1.63 inference(bind,[status(th)],[])).
% 1.45/1.63 tff(59,plain,
% 1.45/1.63 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))) <=> ![A: $i, B: $i] : ![C: $i, D: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))))))),
% 1.45/1.63 inference(quant_intro,[status(thm)],[58])).
% 1.45/1.63 tff(60,plain,
% 1.45/1.63 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))))))),
% 1.45/1.63 inference(transitivity,[status(thm)],[59, 57])).
% 1.45/1.63 tff(61,plain,
% 1.45/1.63 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))))))),
% 1.45/1.63 inference(transitivity,[status(thm)],[60, 56])).
% 1.45/1.63 tff(62,plain,
% 1.45/1.63 (^[A: $i, B: $i] : rewrite(((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))))),
% 1.45/1.63 inference(bind,[status(th)],[])).
% 1.45/1.63 tff(63,plain,
% 1.45/1.63 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))))))),
% 1.45/1.63 inference(quant_intro,[status(thm)],[62])).
% 1.45/1.63 tff(64,plain,
% 1.45/1.63 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))))))),
% 1.45/1.63 inference(transitivity,[status(thm)],[63, 61])).
% 1.45/1.63 tff(65,plain,
% 1.45/1.63 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(B) & function(B)) <=> (~((~relation(B)) | (~function(B))))), ((~(relation(B) & function(B))) <=> (~(~((~relation(B)) | (~function(B))))))), rewrite((~(~((~relation(B)) | (~function(B))))) <=> ((~relation(B)) | (~function(B)))), ((~(relation(B) & function(B))) <=> ((~relation(B)) | (~function(B))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(C) & function(C)) <=> (~((~relation(C)) | (~function(C))))), ((~(relation(C) & function(C))) <=> (~(~((~relation(C)) | (~function(C))))))), rewrite((~(~((~relation(C)) | (~function(C))))) <=> ((~relation(C)) | (~function(C)))), ((~(relation(C) & function(C))) <=> ((~relation(C)) | (~function(C))))), trans(monotonicity(rewrite(((~(B = relation_dom_restriction(C, A))) | ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))) <=> ((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))), rewrite(((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))) <=> ((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))), ((((~(B = relation_dom_restriction(C, A))) | ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))) & ((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))) <=> (((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))))) & ((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))), rewrite((((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))))) & ((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))) <=> (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))))), ((((~(B = relation_dom_restriction(C, A))) | ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))) & ((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))) <=> (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))), (((~(relation(C) & function(C))) | (((~(B = relation_dom_restriction(C, A))) | ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))) & ((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))) <=> (((~relation(C)) | (~function(C))) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))))))), rewrite((((~relation(C)) | (~function(C))) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))))) <=> ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))), (((~(relation(C) & function(C))) | (((~(B = relation_dom_restriction(C, A))) | ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))) & ((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))) <=> ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))))), (![C: $i] : ((~(relation(C) & function(C))) | (((~(B = relation_dom_restriction(C, A))) | ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))) & ((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))) <=> ![C: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))))))), (((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (((~(B = relation_dom_restriction(C, A))) | ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))) & ((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))) <=> (((~relation(B)) | (~function(B))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))))), rewrite((((~relation(B)) | (~function(B))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))))))), (((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (((~(B = relation_dom_restriction(C, A))) | ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))) & ((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))))))))),
% 1.45/1.63 inference(bind,[status(th)],[])).
% 1.45/1.63 tff(66,plain,
% 1.45/1.63 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (((~(B = relation_dom_restriction(C, A))) | ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))) & ((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))))))),
% 1.45/1.63 inference(quant_intro,[status(thm)],[65])).
% 1.45/1.63 tff(67,plain,
% 1.45/1.63 (^[A: $i, B: $i] : rewrite(((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (((~(B = relation_dom_restriction(C, A))) | ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))) & ((B = relation_dom_restriction(C, A)) | ((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))))) <=> ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (((~(B = relation_dom_restriction(C, A))) | ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))) & ((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))),
% 1.45/1.63 inference(bind,[status(th)],[])).
% 1.45/1.63 tff(68,plain,
% 1.45/1.63 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (((~(B = relation_dom_restriction(C, A))) | ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))) & ((B = relation_dom_restriction(C, A)) | ((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (((~(B = relation_dom_restriction(C, A))) | ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))) & ((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))))),
% 1.45/1.63 inference(quant_intro,[status(thm)],[67])).
% 1.45/1.63 tff(69,plain,
% 1.45/1.63 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(70,plain,
% 1.45/1.63 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite(((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : (in(D, relation_dom(B)) => (apply(B, D) = apply(C, D))))) <=> ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))), (((relation(C) & function(C)) => ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : (in(D, relation_dom(B)) => (apply(B, D) = apply(C, D)))))) <=> ((relation(C) & function(C)) => ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))), rewrite(((relation(C) & function(C)) => ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))) <=> ((~(relation(C) & function(C))) | ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))))), (((relation(C) & function(C)) => ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : (in(D, relation_dom(B)) => (apply(B, D) = apply(C, D)))))) <=> ((~(relation(C) & function(C))) | ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))))))), (![C: $i] : ((relation(C) & function(C)) => ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : (in(D, relation_dom(B)) => (apply(B, D) = apply(C, D)))))) <=> ![C: $i] : ((~(relation(C) & function(C))) | ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))), (((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : (in(D, relation_dom(B)) => (apply(B, D) = apply(C, D))))))) <=> ((relation(B) & function(B)) => ![C: $i] : ((~(relation(C) & function(C))) | ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))))))), rewrite(((relation(B) & function(B)) => ![C: $i] : ((~(relation(C) & function(C))) | ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))))) <=> ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))), (((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : (in(D, relation_dom(B)) => (apply(B, D) = apply(C, D))))))) <=> ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))))),
% 1.45/1.63 inference(bind,[status(th)],[])).
% 1.45/1.63 tff(71,plain,
% 1.45/1.63 (![A: $i, B: $i] : ((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : (in(D, relation_dom(B)) => (apply(B, D) = apply(C, D))))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))),
% 1.45/1.63 inference(quant_intro,[status(thm)],[70])).
% 1.45/1.63 tff(72,axiom,(![A: $i, B: $i] : ((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : (in(D, relation_dom(B)) => (apply(B, D) = apply(C, D)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t68_funct_1')).
% 1.45/1.63 tff(73,plain,
% 1.45/1.63 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[72, 71])).
% 1.45/1.63 tff(74,plain,
% 1.45/1.63 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[73, 69])).
% 1.45/1.63 tff(75,plain,(
% 1.45/1.63 ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (((~(B = relation_dom_restriction(C, A))) | ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))) & ((B = relation_dom_restriction(C, A)) | ((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))),
% 1.45/1.63 inference(skolemize,[status(sab)],[74])).
% 1.45/1.63 tff(76,plain,
% 1.45/1.63 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (((~(B = relation_dom_restriction(C, A))) | ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))) & ((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[75, 68])).
% 1.45/1.63 tff(77,plain,
% 1.45/1.63 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))))))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[76, 66])).
% 1.45/1.63 tff(78,plain,
% 1.45/1.63 (![A: $i, B: $i, C: $i, D: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B)))))))))))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[77, 64])).
% 1.45/1.63 tff(79,plain,
% 1.45/1.63 (![A: $i, B: $i, C: $i, D: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[78, 54])).
% 1.45/1.63 tff(80,plain,
% 1.45/1.63 (((~![A: $i, B: $i, C: $i, D: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))) | ((~function(B!15)) | (~relation(B!15)) | (~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))) | (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (~((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_C_1(relation_dom_restriction(B!15, A!16)))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))) | (~function(B!15)) | (~relation(B!15)) | (~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))) | (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (~((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_C_1(relation_dom_restriction(B!15, A!16)))))))))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(81,plain,
% 1.45/1.63 (((~relation(B!15)) | (~function(B!15)) | (~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))) | (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (~((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))))))) <=> ((~function(B!15)) | (~relation(B!15)) | (~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))) | (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (~((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_C_1(relation_dom_restriction(B!15, A!16)))))))))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(82,plain,
% 1.45/1.63 ((~((~((~(relation_dom_restriction(B!15, A!16) = relation_dom_restriction(B!15, A!16))) | (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (~((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_C_1(relation_dom_restriction(B!15, A!16)))))))))) | (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (relation_dom_restriction(B!15, A!16) = relation_dom_restriction(B!15, A!16)) | (~((~in(tptp_fun_D_14(B!15, relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_D_14(B!15, relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_D_14(B!15, relation_dom_restriction(B!15, A!16)))))))))) <=> (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (~((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))))))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(83,plain,
% 1.45/1.63 (((~relation(B!15)) | (~function(B!15)) | (~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))) | (~((~((~(relation_dom_restriction(B!15, A!16) = relation_dom_restriction(B!15, A!16))) | (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (~((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_C_1(relation_dom_restriction(B!15, A!16)))))))))) | (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (relation_dom_restriction(B!15, A!16) = relation_dom_restriction(B!15, A!16)) | (~((~in(tptp_fun_D_14(B!15, relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_D_14(B!15, relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_D_14(B!15, relation_dom_restriction(B!15, A!16))))))))))) <=> ((~relation(B!15)) | (~function(B!15)) | (~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))) | (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (~((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_C_1(relation_dom_restriction(B!15, A!16)))))))))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[82])).
% 1.45/1.63 tff(84,plain,
% 1.45/1.63 (((~relation(B!15)) | (~function(B!15)) | (~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))) | (~((~((~(relation_dom_restriction(B!15, A!16) = relation_dom_restriction(B!15, A!16))) | (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (~((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_C_1(relation_dom_restriction(B!15, A!16)))))))))) | (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (relation_dom_restriction(B!15, A!16) = relation_dom_restriction(B!15, A!16)) | (~((~in(tptp_fun_D_14(B!15, relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_D_14(B!15, relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_D_14(B!15, relation_dom_restriction(B!15, A!16))))))))))) <=> ((~function(B!15)) | (~relation(B!15)) | (~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))) | (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (~((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_C_1(relation_dom_restriction(B!15, A!16)))))))))),
% 1.45/1.63 inference(transitivity,[status(thm)],[83, 81])).
% 1.45/1.63 tff(85,plain,
% 1.45/1.63 (((~![A: $i, B: $i, C: $i, D: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))) | ((~relation(B!15)) | (~function(B!15)) | (~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))) | (~((~((~(relation_dom_restriction(B!15, A!16) = relation_dom_restriction(B!15, A!16))) | (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (~((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_C_1(relation_dom_restriction(B!15, A!16)))))))))) | (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (relation_dom_restriction(B!15, A!16) = relation_dom_restriction(B!15, A!16)) | (~((~in(tptp_fun_D_14(B!15, relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_D_14(B!15, relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_D_14(B!15, relation_dom_restriction(B!15, A!16)))))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))) | ((~function(B!15)) | (~relation(B!15)) | (~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))) | (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (~((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))))))))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[84])).
% 1.45/1.63 tff(86,plain,
% 1.45/1.63 (((~![A: $i, B: $i, C: $i, D: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))) | ((~relation(B!15)) | (~function(B!15)) | (~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))) | (~((~((~(relation_dom_restriction(B!15, A!16) = relation_dom_restriction(B!15, A!16))) | (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (~((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_C_1(relation_dom_restriction(B!15, A!16)))))))))) | (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (relation_dom_restriction(B!15, A!16) = relation_dom_restriction(B!15, A!16)) | (~((~in(tptp_fun_D_14(B!15, relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_D_14(B!15, relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_D_14(B!15, relation_dom_restriction(B!15, A!16)))))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))) | (~function(B!15)) | (~relation(B!15)) | (~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))) | (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (~((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_C_1(relation_dom_restriction(B!15, A!16)))))))))),
% 1.45/1.63 inference(transitivity,[status(thm)],[85, 80])).
% 1.45/1.63 tff(87,plain,
% 1.45/1.63 ((~![A: $i, B: $i, C: $i, D: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))) | ((~relation(B!15)) | (~function(B!15)) | (~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))) | (~((~((~(relation_dom_restriction(B!15, A!16) = relation_dom_restriction(B!15, A!16))) | (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (~((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_C_1(relation_dom_restriction(B!15, A!16)))))))))) | (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (relation_dom_restriction(B!15, A!16) = relation_dom_restriction(B!15, A!16)) | (~((~in(tptp_fun_D_14(B!15, relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_D_14(B!15, relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_D_14(B!15, relation_dom_restriction(B!15, A!16)))))))))))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(88,plain,
% 1.45/1.63 ((~![A: $i, B: $i, C: $i, D: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))) | (~function(B!15)) | (~relation(B!15)) | (~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))) | (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (~((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))))))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[87, 86])).
% 1.45/1.64 tff(89,plain,
% 1.45/1.64 (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (~((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_C_1(relation_dom_restriction(B!15, A!16)))))))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[88, 79, 13, 12, 52, 38])).
% 1.45/1.64 tff(90,plain,
% 1.45/1.64 (((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (~((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))))) | (relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))),
% 1.45/1.64 inference(tautology,[status(thm)],[])).
% 1.45/1.64 tff(91,plain,
% 1.45/1.64 (relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[90, 89])).
% 1.45/1.64 tff(92,plain,
% 1.45/1.64 (set_intersection2(relation_dom(B!15), A!16) = relation_dom(relation_dom_restriction(B!15, A!16))),
% 1.45/1.64 inference(symmetry,[status(thm)],[91])).
% 1.45/1.64 tff(93,plain,
% 1.45/1.64 (in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)) <=> in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[92])).
% 1.45/1.64 tff(94,plain,
% 1.45/1.64 (in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16))) <=> in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))),
% 1.45/1.64 inference(symmetry,[status(thm)],[93])).
% 1.45/1.64 tff(95,plain,
% 1.45/1.64 (^[A: $i] : refl(((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A))))))))))) <=> ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A))))))))))))),
% 1.45/1.64 inference(bind,[status(th)],[])).
% 1.45/1.64 tff(96,plain,
% 1.45/1.64 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))))))),
% 1.45/1.64 inference(quant_intro,[status(thm)],[95])).
% 1.45/1.64 tff(97,plain,
% 1.45/1.64 (^[A: $i] : rewrite(((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A))))))))))) <=> ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A))))))))))))),
% 1.45/1.64 inference(bind,[status(th)],[])).
% 1.45/1.64 tff(98,plain,
% 1.45/1.64 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))))))),
% 1.45/1.64 inference(quant_intro,[status(thm)],[97])).
% 1.45/1.64 tff(99,plain,
% 1.45/1.64 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))))))),
% 1.45/1.64 inference(transitivity,[status(thm)],[98, 96])).
% 1.45/1.64 tff(100,plain,
% 1.45/1.64 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(A) & function(A)) <=> (~((~relation(A)) | (~function(A))))), ((~(relation(A) & function(A))) <=> (~(~((~relation(A)) | (~function(A))))))), rewrite((~(~((~relation(A)) | (~function(A))))) <=> ((~relation(A)) | (~function(A)))), ((~(relation(A) & function(A))) <=> ((~relation(A)) | (~function(A))))), 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(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))), rewrite((one_to_one(A) | (~((~(in(tptp_fun_B_2(A), relation_dom(A)) & in(tptp_fun_C_1(A), relation_dom(A)) & (apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A))))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A))))) <=> (one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(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_2(A), relation_dom(A)) & in(tptp_fun_C_1(A), relation_dom(A)) & (apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A))))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)))))) <=> (((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C))))) & (one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))))), rewrite((((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C))))) & (one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))) <=> (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(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_2(A), relation_dom(A)) & in(tptp_fun_C_1(A), relation_dom(A)) & (apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A))))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)))))) <=> (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(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_2(A), relation_dom(A)) & in(tptp_fun_C_1(A), relation_dom(A)) & (apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A))))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A))))))) <=> (((~relation(A)) | (~function(A))) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A))))))))))))), rewrite((((~relation(A)) | (~function(A))) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A))))))))))) <=> ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(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_2(A), relation_dom(A)) & in(tptp_fun_C_1(A), relation_dom(A)) & (apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A))))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A))))))) <=> ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))))))))),
% 1.45/1.64 inference(bind,[status(th)],[])).
% 1.45/1.64 tff(101,plain,
% 1.45/1.64 (![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_2(A), relation_dom(A)) & in(tptp_fun_C_1(A), relation_dom(A)) & (apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A))))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))))))),
% 1.45/1.64 inference(quant_intro,[status(thm)],[100])).
% 1.45/1.64 tff(102,plain,
% 1.45/1.64 (![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))))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(103,plain,
% 1.45/1.64 (^[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))))))),
% 1.45/1.64 inference(bind,[status(th)],[])).
% 1.45/1.64 tff(104,plain,
% 1.45/1.64 (![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))))),
% 1.45/1.64 inference(quant_intro,[status(thm)],[103])).
% 1.45/1.64 tff(105,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')).
% 1.45/1.64 tff(106,plain,
% 1.45/1.64 (![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))))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[105, 104])).
% 1.45/1.64 tff(107,plain,
% 1.45/1.64 (![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))))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[106, 102])).
% 1.45/1.64 tff(108,plain,(
% 1.45/1.64 ![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_2(A), relation_dom(A)) & in(tptp_fun_C_1(A), relation_dom(A)) & (apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A))))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)))))))),
% 1.45/1.64 inference(skolemize,[status(sab)],[107])).
% 1.45/1.64 tff(109,plain,
% 1.45/1.64 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))))))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[108, 101])).
% 1.45/1.64 tff(110,plain,
% 1.45/1.64 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))))))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[109, 99])).
% 1.45/1.64 tff(111,plain,
% 1.45/1.64 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))))))) | ((~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))) | (~((~((~one_to_one(relation_dom_restriction(B!15, A!16))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(B, relation_dom(relation_dom_restriction(B!15, A!16)))) | (~(apply(relation_dom_restriction(B!15, A!16), B) = apply(relation_dom_restriction(B!15, A!16), C)))))) | (~(one_to_one(relation_dom_restriction(B!15, A!16)) | (~((~(apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))))))) | (~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))) | (~((~((~one_to_one(relation_dom_restriction(B!15, A!16))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(B, relation_dom(relation_dom_restriction(B!15, A!16)))) | (~(apply(relation_dom_restriction(B!15, A!16), B) = apply(relation_dom_restriction(B!15, A!16), C)))))) | (~(one_to_one(relation_dom_restriction(B!15, A!16)) | (~((~(apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))))))))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(112,plain,
% 1.45/1.64 (((~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))) | (~((~((~one_to_one(relation_dom_restriction(B!15, A!16))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(B, relation_dom(relation_dom_restriction(B!15, A!16)))) | (~(apply(relation_dom_restriction(B!15, A!16), B) = apply(relation_dom_restriction(B!15, A!16), C)))))) | (~(one_to_one(relation_dom_restriction(B!15, A!16)) | (~((~(apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16)))))))))) <=> ((~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))) | (~((~((~one_to_one(relation_dom_restriction(B!15, A!16))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(B, relation_dom(relation_dom_restriction(B!15, A!16)))) | (~(apply(relation_dom_restriction(B!15, A!16), B) = apply(relation_dom_restriction(B!15, A!16), C)))))) | (~(one_to_one(relation_dom_restriction(B!15, A!16)) | (~((~(apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))))))))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(113,plain,
% 1.45/1.64 ((~((~((~one_to_one(relation_dom_restriction(B!15, A!16))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(B, relation_dom(relation_dom_restriction(B!15, A!16)))) | (~(apply(relation_dom_restriction(B!15, A!16), B) = apply(relation_dom_restriction(B!15, A!16), C)))))) | (~(one_to_one(relation_dom_restriction(B!15, A!16)) | (~((tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (~(apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))))))))) <=> (~((~((~one_to_one(relation_dom_restriction(B!15, A!16))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(B, relation_dom(relation_dom_restriction(B!15, A!16)))) | (~(apply(relation_dom_restriction(B!15, A!16), B) = apply(relation_dom_restriction(B!15, A!16), C)))))) | (~(one_to_one(relation_dom_restriction(B!15, A!16)) | (~((~(apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16)))))))))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(114,plain,
% 1.45/1.64 (((~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))) | (~((~((~one_to_one(relation_dom_restriction(B!15, A!16))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(B, relation_dom(relation_dom_restriction(B!15, A!16)))) | (~(apply(relation_dom_restriction(B!15, A!16), B) = apply(relation_dom_restriction(B!15, A!16), C)))))) | (~(one_to_one(relation_dom_restriction(B!15, A!16)) | (~((tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (~(apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16)))))))))))) <=> ((~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))) | (~((~((~one_to_one(relation_dom_restriction(B!15, A!16))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(B, relation_dom(relation_dom_restriction(B!15, A!16)))) | (~(apply(relation_dom_restriction(B!15, A!16), B) = apply(relation_dom_restriction(B!15, A!16), C)))))) | (~(one_to_one(relation_dom_restriction(B!15, A!16)) | (~((~(apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))))))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[113])).
% 1.45/1.64 tff(115,plain,
% 1.45/1.64 (((~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))) | (~((~((~one_to_one(relation_dom_restriction(B!15, A!16))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(B, relation_dom(relation_dom_restriction(B!15, A!16)))) | (~(apply(relation_dom_restriction(B!15, A!16), B) = apply(relation_dom_restriction(B!15, A!16), C)))))) | (~(one_to_one(relation_dom_restriction(B!15, A!16)) | (~((tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (~(apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16)))))))))))) <=> ((~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))) | (~((~((~one_to_one(relation_dom_restriction(B!15, A!16))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(B, relation_dom(relation_dom_restriction(B!15, A!16)))) | (~(apply(relation_dom_restriction(B!15, A!16), B) = apply(relation_dom_restriction(B!15, A!16), C)))))) | (~(one_to_one(relation_dom_restriction(B!15, A!16)) | (~((~(apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))))))))),
% 1.45/1.64 inference(transitivity,[status(thm)],[114, 112])).
% 1.45/1.64 tff(116,plain,
% 1.45/1.64 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))))))) | ((~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))) | (~((~((~one_to_one(relation_dom_restriction(B!15, A!16))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(B, relation_dom(relation_dom_restriction(B!15, A!16)))) | (~(apply(relation_dom_restriction(B!15, A!16), B) = apply(relation_dom_restriction(B!15, A!16), C)))))) | (~(one_to_one(relation_dom_restriction(B!15, A!16)) | (~((tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (~(apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))))))) | ((~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))) | (~((~((~one_to_one(relation_dom_restriction(B!15, A!16))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(B, relation_dom(relation_dom_restriction(B!15, A!16)))) | (~(apply(relation_dom_restriction(B!15, A!16), B) = apply(relation_dom_restriction(B!15, A!16), C)))))) | (~(one_to_one(relation_dom_restriction(B!15, A!16)) | (~((~(apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16)))))))))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[115])).
% 1.45/1.64 tff(117,plain,
% 1.45/1.64 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))))))) | ((~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))) | (~((~((~one_to_one(relation_dom_restriction(B!15, A!16))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(B, relation_dom(relation_dom_restriction(B!15, A!16)))) | (~(apply(relation_dom_restriction(B!15, A!16), B) = apply(relation_dom_restriction(B!15, A!16), C)))))) | (~(one_to_one(relation_dom_restriction(B!15, A!16)) | (~((tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (~(apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))))))) | (~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))) | (~((~((~one_to_one(relation_dom_restriction(B!15, A!16))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(B, relation_dom(relation_dom_restriction(B!15, A!16)))) | (~(apply(relation_dom_restriction(B!15, A!16), B) = apply(relation_dom_restriction(B!15, A!16), C)))))) | (~(one_to_one(relation_dom_restriction(B!15, A!16)) | (~((~(apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))))))))),
% 1.45/1.64 inference(transitivity,[status(thm)],[116, 111])).
% 1.45/1.64 tff(118,plain,
% 1.45/1.64 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))))))) | ((~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))) | (~((~((~one_to_one(relation_dom_restriction(B!15, A!16))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(B, relation_dom(relation_dom_restriction(B!15, A!16)))) | (~(apply(relation_dom_restriction(B!15, A!16), B) = apply(relation_dom_restriction(B!15, A!16), C)))))) | (~(one_to_one(relation_dom_restriction(B!15, A!16)) | (~((tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (~(apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))))))))))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(119,plain,
% 1.45/1.64 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))))))) | (~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))) | (~((~((~one_to_one(relation_dom_restriction(B!15, A!16))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(B, relation_dom(relation_dom_restriction(B!15, A!16)))) | (~(apply(relation_dom_restriction(B!15, A!16), B) = apply(relation_dom_restriction(B!15, A!16), C)))))) | (~(one_to_one(relation_dom_restriction(B!15, A!16)) | (~((~(apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16)))))))))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[118, 117])).
% 1.45/1.64 tff(120,plain,
% 1.45/1.64 ((~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))) | (~((~((~one_to_one(relation_dom_restriction(B!15, A!16))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(B, relation_dom(relation_dom_restriction(B!15, A!16)))) | (~(apply(relation_dom_restriction(B!15, A!16), B) = apply(relation_dom_restriction(B!15, A!16), C)))))) | (~(one_to_one(relation_dom_restriction(B!15, A!16)) | (~((~(apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16)))))))))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[119, 110])).
% 1.45/1.64 tff(121,plain,
% 1.45/1.64 (~((~((~one_to_one(relation_dom_restriction(B!15, A!16))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(B, relation_dom(relation_dom_restriction(B!15, A!16)))) | (~(apply(relation_dom_restriction(B!15, A!16), B) = apply(relation_dom_restriction(B!15, A!16), C)))))) | (~(one_to_one(relation_dom_restriction(B!15, A!16)) | (~((~(apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))))))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[120, 38, 52])).
% 1.45/1.64 tff(122,plain,
% 1.45/1.64 (((~((~one_to_one(relation_dom_restriction(B!15, A!16))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(B, relation_dom(relation_dom_restriction(B!15, A!16)))) | (~(apply(relation_dom_restriction(B!15, A!16), B) = apply(relation_dom_restriction(B!15, A!16), C)))))) | (~(one_to_one(relation_dom_restriction(B!15, A!16)) | (~((~(apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16)))))))) | (one_to_one(relation_dom_restriction(B!15, A!16)) | (~((~(apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))))),
% 1.45/1.65 inference(tautology,[status(thm)],[])).
% 1.45/1.65 tff(123,plain,
% 1.45/1.65 (one_to_one(relation_dom_restriction(B!15, A!16)) | (~((~(apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16)))))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[122, 121])).
% 1.45/1.65 tff(124,plain,
% 1.45/1.65 (~one_to_one(relation_dom_restriction(B!15, A!16))),
% 1.45/1.65 inference(or_elim,[status(thm)],[10])).
% 1.45/1.65 tff(125,plain,
% 1.45/1.65 ((~(one_to_one(relation_dom_restriction(B!15, A!16)) | (~((~(apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))))) | one_to_one(relation_dom_restriction(B!15, A!16)) | (~((~(apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16)))))),
% 1.45/1.65 inference(tautology,[status(thm)],[])).
% 1.45/1.65 tff(126,plain,
% 1.45/1.65 ((~(one_to_one(relation_dom_restriction(B!15, A!16)) | (~((~(apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))))) | (~((~(apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16)))))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[125, 124])).
% 1.45/1.65 tff(127,plain,
% 1.45/1.65 (~((~(apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[126, 123])).
% 1.45/1.65 tff(128,plain,
% 1.45/1.65 (((~(apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16)))) | in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))),
% 1.45/1.65 inference(tautology,[status(thm)],[])).
% 1.45/1.65 tff(129,plain,
% 1.45/1.65 (in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[128, 127])).
% 1.45/1.65 tff(130,plain,
% 1.45/1.65 (in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[129, 94])).
% 1.45/1.65 tff(131,plain,
% 1.45/1.65 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))))),
% 1.45/1.65 inference(bind,[status(th)],[])).
% 1.45/1.65 tff(132,plain,
% 1.45/1.65 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 1.45/1.65 inference(quant_intro,[status(thm)],[131])).
% 1.45/1.65 tff(133,plain,
% 1.45/1.65 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 1.45/1.65 inference(pull_quant,[status(thm)],[])).
% 1.45/1.65 tff(134,plain,
% 1.45/1.65 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C)))) <=> ![D: $i] : ((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))), ((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) <=> (~![D: $i] : ((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))))), pull_quant((~![D: $i] : ((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C)))))), ((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))))), (((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))) <=> (?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))), pull_quant((?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))), (((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))), ((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> (~?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))))), pull_quant((~?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))), ((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))))),
% 1.45/1.65 inference(bind,[status(th)],[])).
% 1.45/1.65 tff(135,plain,
% 1.45/1.65 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 1.45/1.65 inference(quant_intro,[status(thm)],[134])).
% 1.45/1.65 tff(136,plain,
% 1.45/1.65 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 1.45/1.65 inference(transitivity,[status(thm)],[135, 133])).
% 1.45/1.65 tff(137,plain,
% 1.45/1.65 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 1.45/1.65 inference(transitivity,[status(thm)],[136, 132])).
% 1.45/1.65 tff(138,plain,
% 1.45/1.65 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))))),
% 1.45/1.65 inference(bind,[status(th)],[])).
% 1.45/1.65 tff(139,plain,
% 1.45/1.65 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 1.45/1.65 inference(quant_intro,[status(thm)],[138])).
% 1.45/1.65 tff(140,plain,
% 1.45/1.65 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 1.45/1.65 inference(transitivity,[status(thm)],[139, 137])).
% 1.45/1.65 tff(141,plain,
% 1.45/1.65 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) <=> ((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))), rewrite(((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B))))) <=> ((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))), ((((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B)))))) <=> (((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C)))) & ((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))), rewrite((((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C)))) & ((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))), ((((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B)))))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))))),
% 1.45/1.65 inference(bind,[status(th)],[])).
% 1.45/1.65 tff(142,plain,
% 1.45/1.65 (![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 1.45/1.65 inference(quant_intro,[status(thm)],[141])).
% 1.45/1.65 tff(143,plain,
% 1.45/1.65 (![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(144,axiom,(![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_xboole_0')).
% 1.45/1.65 tff(145,plain,
% 1.45/1.65 (![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[144, 143])).
% 1.45/1.65 tff(146,plain,(
% 1.45/1.65 ![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B))))))),
% 1.45/1.65 inference(skolemize,[status(sab)],[145])).
% 1.45/1.65 tff(147,plain,
% 1.45/1.65 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[146, 142])).
% 1.45/1.65 tff(148,plain,
% 1.45/1.65 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[147, 140])).
% 1.45/1.65 tff(149,plain,
% 1.45/1.65 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))) | (~(((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))) | (~(((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(150,plain,
% 1.45/1.65 ((~(((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))) <=> (~(((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(151,plain,
% 1.45/1.65 (((((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))) | $false) <=> (((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(152,plain,
% 1.45/1.65 ((~$true) <=> $false),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(153,plain,
% 1.45/1.65 (($true | (((~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), relation_dom(B!15))) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), A!16))) <=> in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), set_intersection2(relation_dom(B!15), A!16)))) <=> $true),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(154,plain,
% 1.45/1.65 ((((~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), relation_dom(B!15))) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), A!16))) <=> in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), set_intersection2(relation_dom(B!15), A!16))) <=> (((~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), relation_dom(B!15))) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), A!16))) <=> in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), set_intersection2(relation_dom(B!15), A!16)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(155,plain,
% 1.45/1.65 ((set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16)) <=> $true),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(156,plain,
% 1.45/1.65 (((set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16)) | (((~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), relation_dom(B!15))) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), A!16))) <=> in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), set_intersection2(relation_dom(B!15), A!16)))) <=> ($true | (((~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), relation_dom(B!15))) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), A!16))) <=> in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), set_intersection2(relation_dom(B!15), A!16))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[155, 154])).
% 1.45/1.65 tff(157,plain,
% 1.45/1.65 (((set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16)) | (((~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), relation_dom(B!15))) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), A!16))) <=> in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), set_intersection2(relation_dom(B!15), A!16)))) <=> $true),
% 1.45/1.65 inference(transitivity,[status(thm)],[156, 153])).
% 1.45/1.65 tff(158,plain,
% 1.45/1.65 ((~((set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16)) | (((~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), relation_dom(B!15))) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), A!16))) <=> in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), set_intersection2(relation_dom(B!15), A!16))))) <=> (~$true)),
% 1.45/1.65 inference(monotonicity,[status(thm)],[157])).
% 1.45/1.65 tff(159,plain,
% 1.45/1.65 ((~((set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16)) | (((~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), relation_dom(B!15))) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), A!16))) <=> in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), set_intersection2(relation_dom(B!15), A!16))))) <=> $false),
% 1.45/1.65 inference(transitivity,[status(thm)],[158, 152])).
% 1.45/1.65 tff(160,plain,
% 1.45/1.65 ((~(~(((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))))) <=> (((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(161,plain,
% 1.45/1.65 (($false | (~(((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))))) <=> (~(((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(162,plain,
% 1.45/1.65 ((((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))) <=> (((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(163,plain,
% 1.45/1.65 ((~(((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))) <=> (~(((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[162])).
% 1.45/1.65 tff(164,plain,
% 1.45/1.65 ((~(((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))) <=> (~(((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))))),
% 1.45/1.65 inference(transitivity,[status(thm)],[163, 150])).
% 1.45/1.65 tff(165,plain,
% 1.45/1.65 ((~(set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16))) <=> (~$true)),
% 1.45/1.65 inference(monotonicity,[status(thm)],[155])).
% 1.45/1.65 tff(166,plain,
% 1.45/1.65 ((~(set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16))) <=> $false),
% 1.45/1.65 inference(transitivity,[status(thm)],[165, 152])).
% 1.45/1.65 tff(167,plain,
% 1.45/1.65 (((~(set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16))) | (~(((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))))) <=> ($false | (~(((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[166, 164])).
% 1.45/1.65 tff(168,plain,
% 1.45/1.65 (((~(set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16))) | (~(((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))))) <=> (~(((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))))),
% 1.45/1.65 inference(transitivity,[status(thm)],[167, 161])).
% 1.45/1.65 tff(169,plain,
% 1.45/1.65 ((~((~(set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16))) | (~(((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))))) <=> (~(~(((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[168])).
% 1.45/1.65 tff(170,plain,
% 1.45/1.65 ((~((~(set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16))) | (~(((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))))) <=> (((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))),
% 1.45/1.65 inference(transitivity,[status(thm)],[169, 160])).
% 1.45/1.65 tff(171,plain,
% 1.45/1.65 (((~((~(set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16))) | (~(((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))))) | (~((set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16)) | (((~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), relation_dom(B!15))) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), A!16))) <=> in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), set_intersection2(relation_dom(B!15), A!16)))))) <=> ((((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))) | $false)),
% 1.45/1.65 inference(monotonicity,[status(thm)],[170, 159])).
% 1.45/1.65 tff(172,plain,
% 1.45/1.65 (((~((~(set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16))) | (~(((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))))) | (~((set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16)) | (((~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), relation_dom(B!15))) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), A!16))) <=> in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), set_intersection2(relation_dom(B!15), A!16)))))) <=> (((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))),
% 1.45/1.65 inference(transitivity,[status(thm)],[171, 151])).
% 1.45/1.65 tff(173,plain,
% 1.45/1.65 ((~((~((~(set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16))) | (~(((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))))) | (~((set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16)) | (((~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), relation_dom(B!15))) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), A!16))) <=> in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), set_intersection2(relation_dom(B!15), A!16))))))) <=> (~(((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[172])).
% 1.45/1.65 tff(174,plain,
% 1.45/1.65 ((~((~((~(set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16))) | (~(((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))))) | (~((set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16)) | (((~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), relation_dom(B!15))) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), A!16))) <=> in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), set_intersection2(relation_dom(B!15), A!16))))))) <=> (~(((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))))),
% 1.45/1.65 inference(transitivity,[status(thm)],[173, 150])).
% 1.45/1.65 tff(175,plain,
% 1.45/1.65 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))) | (~((~((~(set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16))) | (~(((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))))) | (~((set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16)) | (((~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), relation_dom(B!15))) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), A!16))) <=> in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), set_intersection2(relation_dom(B!15), A!16)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))) | (~(((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[174])).
% 1.45/1.66 tff(176,plain,
% 1.45/1.66 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))) | (~((~((~(set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16))) | (~(((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))))) | (~((set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16)) | (((~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), relation_dom(B!15))) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), A!16))) <=> in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), set_intersection2(relation_dom(B!15), A!16)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))) | (~(((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))))),
% 1.45/1.66 inference(transitivity,[status(thm)],[175, 149])).
% 1.45/1.66 tff(177,plain,
% 1.45/1.66 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))) | (~((~((~(set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16))) | (~(((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))))) | (~((set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16)) | (((~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), relation_dom(B!15))) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), A!16))) <=> in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), set_intersection2(relation_dom(B!15), A!16)))))))),
% 1.45/1.66 inference(quant_inst,[status(thm)],[])).
% 1.45/1.66 tff(178,plain,
% 1.45/1.66 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))) | (~(((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[177, 176])).
% 1.45/1.66 tff(179,plain,
% 1.45/1.66 (~(((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[178, 148])).
% 1.45/1.66 tff(180,assumption,(((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))), introduced(assumption)).
% 1.45/1.66 tff(181,plain,
% 1.45/1.66 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))) | (~(((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))) | (~(((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(182,plain,
% 1.45/1.66 ((~(((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))) <=> (~(((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(183,plain,
% 1.45/1.66 (((((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))) | $false) <=> (((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(184,plain,
% 1.45/1.66 ((~(~(((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))))) <=> (((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(185,plain,
% 1.45/1.66 (($false | (~(((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))))) <=> (~(((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(186,plain,
% 1.45/1.66 ((((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))) <=> (((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(187,plain,
% 1.45/1.66 ((~(((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))) <=> (~(((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[186])).
% 1.45/1.66 tff(188,plain,
% 1.45/1.66 ((~(((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))) <=> (~(((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))))),
% 1.45/1.66 inference(transitivity,[status(thm)],[187, 182])).
% 1.45/1.66 tff(189,plain,
% 1.45/1.66 (((~(set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16))) | (~(((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))))) <=> ($false | (~(((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[166, 188])).
% 1.45/1.66 tff(190,plain,
% 1.45/1.66 (((~(set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16))) | (~(((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))))) <=> (~(((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))))),
% 1.45/1.66 inference(transitivity,[status(thm)],[189, 185])).
% 1.45/1.66 tff(191,plain,
% 1.45/1.66 ((~((~(set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16))) | (~(((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))))) <=> (~(~(((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[190])).
% 1.45/1.66 tff(192,plain,
% 1.45/1.66 ((~((~(set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16))) | (~(((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))))) <=> (((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))),
% 1.45/1.66 inference(transitivity,[status(thm)],[191, 184])).
% 1.45/1.66 tff(193,plain,
% 1.45/1.66 (((~((~(set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16))) | (~(((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))))) | (~((set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16)) | (((~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), relation_dom(B!15))) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), A!16))) <=> in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), set_intersection2(relation_dom(B!15), A!16)))))) <=> ((((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))) | $false)),
% 1.45/1.66 inference(monotonicity,[status(thm)],[192, 159])).
% 1.45/1.66 tff(194,plain,
% 1.45/1.66 (((~((~(set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16))) | (~(((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))))) | (~((set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16)) | (((~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), relation_dom(B!15))) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), A!16))) <=> in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), set_intersection2(relation_dom(B!15), A!16)))))) <=> (((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))),
% 1.45/1.66 inference(transitivity,[status(thm)],[193, 183])).
% 1.45/1.66 tff(195,plain,
% 1.45/1.66 ((~((~((~(set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16))) | (~(((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))))) | (~((set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16)) | (((~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), relation_dom(B!15))) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), A!16))) <=> in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), set_intersection2(relation_dom(B!15), A!16))))))) <=> (~(((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[194])).
% 1.45/1.66 tff(196,plain,
% 1.45/1.66 ((~((~((~(set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16))) | (~(((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))))) | (~((set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16)) | (((~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), relation_dom(B!15))) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), A!16))) <=> in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), set_intersection2(relation_dom(B!15), A!16))))))) <=> (~(((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))))),
% 1.45/1.66 inference(transitivity,[status(thm)],[195, 182])).
% 1.45/1.66 tff(197,plain,
% 1.45/1.66 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))) | (~((~((~(set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16))) | (~(((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))))) | (~((set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16)) | (((~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), relation_dom(B!15))) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), A!16))) <=> in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), set_intersection2(relation_dom(B!15), A!16)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))) | (~(((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[196])).
% 1.45/1.66 tff(198,plain,
% 1.45/1.66 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))) | (~((~((~(set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16))) | (~(((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))))) | (~((set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16)) | (((~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), relation_dom(B!15))) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), A!16))) <=> in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), set_intersection2(relation_dom(B!15), A!16)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))) | (~(((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))))),
% 1.45/1.66 inference(transitivity,[status(thm)],[197, 181])).
% 1.45/1.66 tff(199,plain,
% 1.45/1.66 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))) | (~((~((~(set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16))) | (~(((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))))) | (~((set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16)) | (((~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), relation_dom(B!15))) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), A!16))) <=> in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), set_intersection2(relation_dom(B!15), A!16)))))))),
% 1.45/1.66 inference(quant_inst,[status(thm)],[])).
% 1.45/1.66 tff(200,plain,
% 1.45/1.66 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))) | (~(((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[199, 198])).
% 1.45/1.66 tff(201,plain,
% 1.45/1.66 ($false),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[200, 148, 180])).
% 1.45/1.66 tff(202,plain,(~(((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.66 tff(203,plain,
% 1.45/1.66 (in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[92])).
% 1.45/1.66 tff(204,plain,
% 1.45/1.66 (in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16))) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))),
% 1.45/1.66 inference(symmetry,[status(thm)],[203])).
% 1.45/1.66 tff(205,plain,
% 1.45/1.66 (((~(apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16)))) | in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))),
% 1.45/1.66 inference(tautology,[status(thm)],[])).
% 1.45/1.66 tff(206,plain,
% 1.45/1.66 (in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[205, 127])).
% 1.45/1.66 tff(207,plain,
% 1.45/1.66 (in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[206, 204])).
% 1.45/1.66 tff(208,assumption,(~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))), introduced(assumption)).
% 1.45/1.66 tff(209,plain,
% 1.45/1.66 ($false),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[208, 207])).
% 1.45/1.66 tff(210,plain,(in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.66 tff(211,plain,
% 1.45/1.66 ((((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))) | (~((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16)))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))),
% 1.45/1.66 inference(tautology,[status(thm)],[])).
% 1.45/1.66 tff(212,plain,
% 1.45/1.66 ((((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))) | (~((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[211, 210])).
% 1.45/1.66 tff(213,plain,
% 1.45/1.66 (~((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16)))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[212, 202])).
% 1.45/1.66 tff(214,plain,
% 1.45/1.66 (((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))) | in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))),
% 1.45/1.66 inference(tautology,[status(thm)],[])).
% 1.45/1.66 tff(215,plain,
% 1.45/1.66 (in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[214, 213])).
% 1.45/1.66 tff(216,plain,
% 1.45/1.66 (((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (~((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))))) | ((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_C_1(relation_dom_restriction(B!15, A!16)))))),
% 1.45/1.66 inference(tautology,[status(thm)],[])).
% 1.45/1.66 tff(217,plain,
% 1.45/1.66 ((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[216, 89])).
% 1.45/1.66 tff(218,plain,
% 1.45/1.66 ((~((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_C_1(relation_dom_restriction(B!15, A!16)))))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))),
% 1.45/1.66 inference(tautology,[status(thm)],[])).
% 1.45/1.66 tff(219,plain,
% 1.45/1.66 ((~((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_C_1(relation_dom_restriction(B!15, A!16)))))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[218, 206])).
% 1.45/1.66 tff(220,plain,
% 1.45/1.66 (apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_C_1(relation_dom_restriction(B!15, A!16)))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[219, 217])).
% 1.45/1.66 tff(221,plain,
% 1.45/1.66 (((~(apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))),
% 1.45/1.66 inference(tautology,[status(thm)],[])).
% 1.45/1.66 tff(222,plain,
% 1.45/1.66 (apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16)))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[221, 127])).
% 1.45/1.66 tff(223,plain,
% 1.45/1.66 (((~![A: $i, B: $i, C: $i, D: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))) | ((~function(B!15)) | (~relation(B!15)) | (~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))) | (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (~((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16)))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))) | (~function(B!15)) | (~relation(B!15)) | (~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))) | (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (~((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16)))))))))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(224,plain,
% 1.45/1.66 (((~relation(B!15)) | (~function(B!15)) | (~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))) | (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (~((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16))))))))) <=> ((~function(B!15)) | (~relation(B!15)) | (~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))) | (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (~((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16)))))))))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(225,plain,
% 1.45/1.67 ((~((~((~(relation_dom_restriction(B!15, A!16) = relation_dom_restriction(B!15, A!16))) | (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (~((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16)))))))))) | (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (relation_dom_restriction(B!15, A!16) = relation_dom_restriction(B!15, A!16)) | (~((~in(tptp_fun_D_14(B!15, relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_D_14(B!15, relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_D_14(B!15, relation_dom_restriction(B!15, A!16)))))))))) <=> (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (~((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16))))))))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(226,plain,
% 1.45/1.67 (((~relation(B!15)) | (~function(B!15)) | (~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))) | (~((~((~(relation_dom_restriction(B!15, A!16) = relation_dom_restriction(B!15, A!16))) | (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (~((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16)))))))))) | (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (relation_dom_restriction(B!15, A!16) = relation_dom_restriction(B!15, A!16)) | (~((~in(tptp_fun_D_14(B!15, relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_D_14(B!15, relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_D_14(B!15, relation_dom_restriction(B!15, A!16))))))))))) <=> ((~relation(B!15)) | (~function(B!15)) | (~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))) | (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (~((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16)))))))))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[225])).
% 1.45/1.67 tff(227,plain,
% 1.45/1.67 (((~relation(B!15)) | (~function(B!15)) | (~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))) | (~((~((~(relation_dom_restriction(B!15, A!16) = relation_dom_restriction(B!15, A!16))) | (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (~((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16)))))))))) | (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (relation_dom_restriction(B!15, A!16) = relation_dom_restriction(B!15, A!16)) | (~((~in(tptp_fun_D_14(B!15, relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_D_14(B!15, relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_D_14(B!15, relation_dom_restriction(B!15, A!16))))))))))) <=> ((~function(B!15)) | (~relation(B!15)) | (~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))) | (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (~((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16)))))))))),
% 1.45/1.67 inference(transitivity,[status(thm)],[226, 224])).
% 1.45/1.67 tff(228,plain,
% 1.45/1.67 (((~![A: $i, B: $i, C: $i, D: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))) | ((~relation(B!15)) | (~function(B!15)) | (~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))) | (~((~((~(relation_dom_restriction(B!15, A!16) = relation_dom_restriction(B!15, A!16))) | (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (~((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16)))))))))) | (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (relation_dom_restriction(B!15, A!16) = relation_dom_restriction(B!15, A!16)) | (~((~in(tptp_fun_D_14(B!15, relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_D_14(B!15, relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_D_14(B!15, relation_dom_restriction(B!15, A!16)))))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))) | ((~function(B!15)) | (~relation(B!15)) | (~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))) | (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (~((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16))))))))))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[227])).
% 1.45/1.67 tff(229,plain,
% 1.45/1.67 (((~![A: $i, B: $i, C: $i, D: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))) | ((~relation(B!15)) | (~function(B!15)) | (~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))) | (~((~((~(relation_dom_restriction(B!15, A!16) = relation_dom_restriction(B!15, A!16))) | (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (~((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16)))))))))) | (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (relation_dom_restriction(B!15, A!16) = relation_dom_restriction(B!15, A!16)) | (~((~in(tptp_fun_D_14(B!15, relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_D_14(B!15, relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_D_14(B!15, relation_dom_restriction(B!15, A!16)))))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))) | (~function(B!15)) | (~relation(B!15)) | (~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))) | (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (~((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16)))))))))),
% 1.45/1.67 inference(transitivity,[status(thm)],[228, 223])).
% 1.45/1.67 tff(230,plain,
% 1.45/1.67 ((~![A: $i, B: $i, C: $i, D: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))) | ((~relation(B!15)) | (~function(B!15)) | (~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))) | (~((~((~(relation_dom_restriction(B!15, A!16) = relation_dom_restriction(B!15, A!16))) | (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (~((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16)))))))))) | (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (relation_dom_restriction(B!15, A!16) = relation_dom_restriction(B!15, A!16)) | (~((~in(tptp_fun_D_14(B!15, relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_D_14(B!15, relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_D_14(B!15, relation_dom_restriction(B!15, A!16)))))))))))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(231,plain,
% 1.45/1.67 ((~![A: $i, B: $i, C: $i, D: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_14(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_14(C, B)) = apply(C, tptp_fun_D_14(C, B))))))))))) | (~function(B!15)) | (~relation(B!15)) | (~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))) | (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (~((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16))))))))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[230, 229])).
% 1.45/1.67 tff(232,plain,
% 1.45/1.67 (~((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (~((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16)))))))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[231, 79, 13, 12, 52, 38])).
% 1.45/1.67 tff(233,plain,
% 1.45/1.67 (((~(relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16))) | (~((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16))))))) | ((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16)))))),
% 1.45/1.67 inference(tautology,[status(thm)],[])).
% 1.45/1.67 tff(234,plain,
% 1.45/1.67 ((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16))))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[233, 232])).
% 1.45/1.67 tff(235,plain,
% 1.45/1.67 ((~((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16)))))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16))))),
% 1.45/1.67 inference(tautology,[status(thm)],[])).
% 1.45/1.67 tff(236,plain,
% 1.45/1.67 ((~((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16)))))) | (apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16))))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[235, 129])).
% 1.45/1.67 tff(237,plain,
% 1.45/1.67 (apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16)))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[236, 234])).
% 1.45/1.67 tff(238,plain,
% 1.45/1.67 (apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16)))),
% 1.45/1.67 inference(symmetry,[status(thm)],[237])).
% 1.45/1.67 tff(239,plain,
% 1.45/1.67 (apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_C_1(relation_dom_restriction(B!15, A!16)))),
% 1.45/1.67 inference(transitivity,[status(thm)],[238, 222, 220])).
% 1.45/1.67 tff(240,plain,
% 1.45/1.67 (((~(apply(relation_dom_restriction(B!15, A!16), tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(relation_dom_restriction(B!15, A!16), tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))) | (tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16)))) | (~(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))),
% 1.45/1.67 inference(tautology,[status(thm)],[])).
% 1.45/1.67 tff(241,plain,
% 1.45/1.67 (~(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16)))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[240, 127])).
% 1.45/1.67 tff(242,plain,
% 1.45/1.67 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))))))) | ((~function(B!15)) | (~relation(B!15)) | (~((~((~one_to_one(B!15)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(B!15))) | (~in(B, relation_dom(B!15))) | (~(apply(B!15, B) = apply(B!15, C)))))) | (~(one_to_one(B!15) | (~((~(apply(B!15, tptp_fun_B_2(B!15)) = apply(B!15, tptp_fun_C_1(B!15)))) | (~in(tptp_fun_C_1(B!15), relation_dom(B!15))) | (~in(tptp_fun_B_2(B!15), relation_dom(B!15))) | (tptp_fun_B_2(B!15) = tptp_fun_C_1(B!15)))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))))))) | (~function(B!15)) | (~relation(B!15)) | (~((~((~one_to_one(B!15)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(B!15))) | (~in(B, relation_dom(B!15))) | (~(apply(B!15, B) = apply(B!15, C)))))) | (~(one_to_one(B!15) | (~((~(apply(B!15, tptp_fun_B_2(B!15)) = apply(B!15, tptp_fun_C_1(B!15)))) | (~in(tptp_fun_C_1(B!15), relation_dom(B!15))) | (~in(tptp_fun_B_2(B!15), relation_dom(B!15))) | (tptp_fun_B_2(B!15) = tptp_fun_C_1(B!15)))))))))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(243,plain,
% 1.45/1.67 (((~relation(B!15)) | (~function(B!15)) | (~((~((~one_to_one(B!15)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(B!15))) | (~in(B, relation_dom(B!15))) | (~(apply(B!15, B) = apply(B!15, C)))))) | (~(one_to_one(B!15) | (~((~(apply(B!15, tptp_fun_B_2(B!15)) = apply(B!15, tptp_fun_C_1(B!15)))) | (~in(tptp_fun_C_1(B!15), relation_dom(B!15))) | (~in(tptp_fun_B_2(B!15), relation_dom(B!15))) | (tptp_fun_B_2(B!15) = tptp_fun_C_1(B!15))))))))) <=> ((~function(B!15)) | (~relation(B!15)) | (~((~((~one_to_one(B!15)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(B!15))) | (~in(B, relation_dom(B!15))) | (~(apply(B!15, B) = apply(B!15, C)))))) | (~(one_to_one(B!15) | (~((~(apply(B!15, tptp_fun_B_2(B!15)) = apply(B!15, tptp_fun_C_1(B!15)))) | (~in(tptp_fun_C_1(B!15), relation_dom(B!15))) | (~in(tptp_fun_B_2(B!15), relation_dom(B!15))) | (tptp_fun_B_2(B!15) = tptp_fun_C_1(B!15)))))))))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(244,plain,
% 1.45/1.67 ((~((~((~one_to_one(B!15)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(B!15))) | (~in(B, relation_dom(B!15))) | (~(apply(B!15, B) = apply(B!15, C)))))) | (~(one_to_one(B!15) | (~((tptp_fun_B_2(B!15) = tptp_fun_C_1(B!15)) | (~in(tptp_fun_B_2(B!15), relation_dom(B!15))) | (~in(tptp_fun_C_1(B!15), relation_dom(B!15))) | (~(apply(B!15, tptp_fun_B_2(B!15)) = apply(B!15, tptp_fun_C_1(B!15)))))))))) <=> (~((~((~one_to_one(B!15)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(B!15))) | (~in(B, relation_dom(B!15))) | (~(apply(B!15, B) = apply(B!15, C)))))) | (~(one_to_one(B!15) | (~((~(apply(B!15, tptp_fun_B_2(B!15)) = apply(B!15, tptp_fun_C_1(B!15)))) | (~in(tptp_fun_C_1(B!15), relation_dom(B!15))) | (~in(tptp_fun_B_2(B!15), relation_dom(B!15))) | (tptp_fun_B_2(B!15) = tptp_fun_C_1(B!15))))))))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(245,plain,
% 1.45/1.67 (((~relation(B!15)) | (~function(B!15)) | (~((~((~one_to_one(B!15)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(B!15))) | (~in(B, relation_dom(B!15))) | (~(apply(B!15, B) = apply(B!15, C)))))) | (~(one_to_one(B!15) | (~((tptp_fun_B_2(B!15) = tptp_fun_C_1(B!15)) | (~in(tptp_fun_B_2(B!15), relation_dom(B!15))) | (~in(tptp_fun_C_1(B!15), relation_dom(B!15))) | (~(apply(B!15, tptp_fun_B_2(B!15)) = apply(B!15, tptp_fun_C_1(B!15))))))))))) <=> ((~relation(B!15)) | (~function(B!15)) | (~((~((~one_to_one(B!15)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(B!15))) | (~in(B, relation_dom(B!15))) | (~(apply(B!15, B) = apply(B!15, C)))))) | (~(one_to_one(B!15) | (~((~(apply(B!15, tptp_fun_B_2(B!15)) = apply(B!15, tptp_fun_C_1(B!15)))) | (~in(tptp_fun_C_1(B!15), relation_dom(B!15))) | (~in(tptp_fun_B_2(B!15), relation_dom(B!15))) | (tptp_fun_B_2(B!15) = tptp_fun_C_1(B!15)))))))))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[244])).
% 1.45/1.67 tff(246,plain,
% 1.45/1.67 (((~relation(B!15)) | (~function(B!15)) | (~((~((~one_to_one(B!15)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(B!15))) | (~in(B, relation_dom(B!15))) | (~(apply(B!15, B) = apply(B!15, C)))))) | (~(one_to_one(B!15) | (~((tptp_fun_B_2(B!15) = tptp_fun_C_1(B!15)) | (~in(tptp_fun_B_2(B!15), relation_dom(B!15))) | (~in(tptp_fun_C_1(B!15), relation_dom(B!15))) | (~(apply(B!15, tptp_fun_B_2(B!15)) = apply(B!15, tptp_fun_C_1(B!15))))))))))) <=> ((~function(B!15)) | (~relation(B!15)) | (~((~((~one_to_one(B!15)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(B!15))) | (~in(B, relation_dom(B!15))) | (~(apply(B!15, B) = apply(B!15, C)))))) | (~(one_to_one(B!15) | (~((~(apply(B!15, tptp_fun_B_2(B!15)) = apply(B!15, tptp_fun_C_1(B!15)))) | (~in(tptp_fun_C_1(B!15), relation_dom(B!15))) | (~in(tptp_fun_B_2(B!15), relation_dom(B!15))) | (tptp_fun_B_2(B!15) = tptp_fun_C_1(B!15)))))))))),
% 1.45/1.67 inference(transitivity,[status(thm)],[245, 243])).
% 1.45/1.67 tff(247,plain,
% 1.45/1.67 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))))))) | ((~relation(B!15)) | (~function(B!15)) | (~((~((~one_to_one(B!15)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(B!15))) | (~in(B, relation_dom(B!15))) | (~(apply(B!15, B) = apply(B!15, C)))))) | (~(one_to_one(B!15) | (~((tptp_fun_B_2(B!15) = tptp_fun_C_1(B!15)) | (~in(tptp_fun_B_2(B!15), relation_dom(B!15))) | (~in(tptp_fun_C_1(B!15), relation_dom(B!15))) | (~(apply(B!15, tptp_fun_B_2(B!15)) = apply(B!15, tptp_fun_C_1(B!15)))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))))))) | ((~function(B!15)) | (~relation(B!15)) | (~((~((~one_to_one(B!15)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(B!15))) | (~in(B, relation_dom(B!15))) | (~(apply(B!15, B) = apply(B!15, C)))))) | (~(one_to_one(B!15) | (~((~(apply(B!15, tptp_fun_B_2(B!15)) = apply(B!15, tptp_fun_C_1(B!15)))) | (~in(tptp_fun_C_1(B!15), relation_dom(B!15))) | (~in(tptp_fun_B_2(B!15), relation_dom(B!15))) | (tptp_fun_B_2(B!15) = tptp_fun_C_1(B!15))))))))))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[246])).
% 1.45/1.67 tff(248,plain,
% 1.45/1.67 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))))))) | ((~relation(B!15)) | (~function(B!15)) | (~((~((~one_to_one(B!15)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(B!15))) | (~in(B, relation_dom(B!15))) | (~(apply(B!15, B) = apply(B!15, C)))))) | (~(one_to_one(B!15) | (~((tptp_fun_B_2(B!15) = tptp_fun_C_1(B!15)) | (~in(tptp_fun_B_2(B!15), relation_dom(B!15))) | (~in(tptp_fun_C_1(B!15), relation_dom(B!15))) | (~(apply(B!15, tptp_fun_B_2(B!15)) = apply(B!15, tptp_fun_C_1(B!15)))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))))))) | (~function(B!15)) | (~relation(B!15)) | (~((~((~one_to_one(B!15)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(B!15))) | (~in(B, relation_dom(B!15))) | (~(apply(B!15, B) = apply(B!15, C)))))) | (~(one_to_one(B!15) | (~((~(apply(B!15, tptp_fun_B_2(B!15)) = apply(B!15, tptp_fun_C_1(B!15)))) | (~in(tptp_fun_C_1(B!15), relation_dom(B!15))) | (~in(tptp_fun_B_2(B!15), relation_dom(B!15))) | (tptp_fun_B_2(B!15) = tptp_fun_C_1(B!15)))))))))),
% 1.45/1.67 inference(transitivity,[status(thm)],[247, 242])).
% 1.45/1.67 tff(249,plain,
% 1.45/1.67 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))))))) | ((~relation(B!15)) | (~function(B!15)) | (~((~((~one_to_one(B!15)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(B!15))) | (~in(B, relation_dom(B!15))) | (~(apply(B!15, B) = apply(B!15, C)))))) | (~(one_to_one(B!15) | (~((tptp_fun_B_2(B!15) = tptp_fun_C_1(B!15)) | (~in(tptp_fun_B_2(B!15), relation_dom(B!15))) | (~in(tptp_fun_C_1(B!15), relation_dom(B!15))) | (~(apply(B!15, tptp_fun_B_2(B!15)) = apply(B!15, tptp_fun_C_1(B!15)))))))))))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(250,plain,
% 1.45/1.67 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(tptp_fun_B_2(A), relation_dom(A))) | (~in(tptp_fun_C_1(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_2(A)) = apply(A, tptp_fun_C_1(A)))))))))))) | (~function(B!15)) | (~relation(B!15)) | (~((~((~one_to_one(B!15)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(B!15))) | (~in(B, relation_dom(B!15))) | (~(apply(B!15, B) = apply(B!15, C)))))) | (~(one_to_one(B!15) | (~((~(apply(B!15, tptp_fun_B_2(B!15)) = apply(B!15, tptp_fun_C_1(B!15)))) | (~in(tptp_fun_C_1(B!15), relation_dom(B!15))) | (~in(tptp_fun_B_2(B!15), relation_dom(B!15))) | (tptp_fun_B_2(B!15) = tptp_fun_C_1(B!15))))))))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[249, 248])).
% 1.45/1.67 tff(251,plain,
% 1.45/1.67 (~((~((~one_to_one(B!15)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(B!15))) | (~in(B, relation_dom(B!15))) | (~(apply(B!15, B) = apply(B!15, C)))))) | (~(one_to_one(B!15) | (~((~(apply(B!15, tptp_fun_B_2(B!15)) = apply(B!15, tptp_fun_C_1(B!15)))) | (~in(tptp_fun_C_1(B!15), relation_dom(B!15))) | (~in(tptp_fun_B_2(B!15), relation_dom(B!15))) | (tptp_fun_B_2(B!15) = tptp_fun_C_1(B!15)))))))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[250, 110, 13, 12])).
% 1.45/1.67 tff(252,plain,
% 1.45/1.67 (((~((~one_to_one(B!15)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(B!15))) | (~in(B, relation_dom(B!15))) | (~(apply(B!15, B) = apply(B!15, C)))))) | (~(one_to_one(B!15) | (~((~(apply(B!15, tptp_fun_B_2(B!15)) = apply(B!15, tptp_fun_C_1(B!15)))) | (~in(tptp_fun_C_1(B!15), relation_dom(B!15))) | (~in(tptp_fun_B_2(B!15), relation_dom(B!15))) | (tptp_fun_B_2(B!15) = tptp_fun_C_1(B!15))))))) | ((~one_to_one(B!15)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(B!15))) | (~in(B, relation_dom(B!15))) | (~(apply(B!15, B) = apply(B!15, C)))))),
% 1.45/1.67 inference(tautology,[status(thm)],[])).
% 1.45/1.67 tff(253,plain,
% 1.45/1.67 ((~one_to_one(B!15)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(B!15))) | (~in(B, relation_dom(B!15))) | (~(apply(B!15, B) = apply(B!15, C))))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[252, 251])).
% 1.45/1.67 tff(254,plain,
% 1.45/1.67 (one_to_one(B!15)),
% 1.45/1.67 inference(or_elim,[status(thm)],[10])).
% 1.45/1.67 tff(255,plain,
% 1.45/1.67 ((~((~one_to_one(B!15)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(B!15))) | (~in(B, relation_dom(B!15))) | (~(apply(B!15, B) = apply(B!15, C)))))) | (~one_to_one(B!15)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(B!15))) | (~in(B, relation_dom(B!15))) | (~(apply(B!15, B) = apply(B!15, C))))),
% 1.45/1.67 inference(tautology,[status(thm)],[])).
% 1.45/1.67 tff(256,plain,
% 1.45/1.67 ((~((~one_to_one(B!15)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(B!15))) | (~in(B, relation_dom(B!15))) | (~(apply(B!15, B) = apply(B!15, C)))))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(B!15))) | (~in(B, relation_dom(B!15))) | (~(apply(B!15, B) = apply(B!15, C))))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[255, 254])).
% 1.45/1.67 tff(257,plain,
% 1.45/1.67 (![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(B!15))) | (~in(B, relation_dom(B!15))) | (~(apply(B!15, B) = apply(B!15, C))))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[256, 253])).
% 1.45/1.67 tff(258,plain,
% 1.45/1.67 (((~![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(B!15))) | (~in(B, relation_dom(B!15))) | (~(apply(B!15, B) = apply(B!15, C))))) | ((tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~(apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))))) <=> ((~![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(B!15))) | (~in(B, relation_dom(B!15))) | (~(apply(B!15, B) = apply(B!15, C))))) | (tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~(apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(259,plain,
% 1.45/1.68 (((tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~(apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_C_1(relation_dom_restriction(B!15, A!16)))))) <=> ((tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~(apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(260,plain,
% 1.45/1.68 (((~![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(B!15))) | (~in(B, relation_dom(B!15))) | (~(apply(B!15, B) = apply(B!15, C))))) | ((tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~(apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))))) <=> ((~![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(B!15))) | (~in(B, relation_dom(B!15))) | (~(apply(B!15, B) = apply(B!15, C))))) | ((tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~(apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_C_1(relation_dom_restriction(B!15, A!16)))))))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[259])).
% 1.45/1.68 tff(261,plain,
% 1.45/1.68 (((~![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(B!15))) | (~in(B, relation_dom(B!15))) | (~(apply(B!15, B) = apply(B!15, C))))) | ((tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~(apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))))) <=> ((~![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(B!15))) | (~in(B, relation_dom(B!15))) | (~(apply(B!15, B) = apply(B!15, C))))) | (tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~(apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))))),
% 1.45/1.68 inference(transitivity,[status(thm)],[260, 258])).
% 1.45/1.68 tff(262,plain,
% 1.45/1.68 ((~![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(B!15))) | (~in(B, relation_dom(B!15))) | (~(apply(B!15, B) = apply(B!15, C))))) | ((tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~(apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(263,plain,
% 1.45/1.68 ((~![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(B!15))) | (~in(B, relation_dom(B!15))) | (~(apply(B!15, B) = apply(B!15, C))))) | (tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~(apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_C_1(relation_dom_restriction(B!15, A!16)))))),
% 1.52/1.68 inference(modus_ponens,[status(thm)],[262, 261])).
% 1.52/1.68 tff(264,plain,
% 1.52/1.68 ((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15)))),
% 1.52/1.68 inference(unit_resolution,[status(thm)],[263, 257, 241, 239])).
% 1.52/1.68 tff(265,plain,
% 1.52/1.68 (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))),
% 1.52/1.68 inference(unit_resolution,[status(thm)],[264, 215])).
% 1.52/1.68 tff(266,plain,
% 1.52/1.68 (((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))) | in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))),
% 1.52/1.68 inference(tautology,[status(thm)],[])).
% 1.52/1.68 tff(267,plain,
% 1.52/1.68 ((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))),
% 1.52/1.68 inference(unit_resolution,[status(thm)],[266, 265])).
% 1.52/1.68 tff(268,plain,
% 1.52/1.68 ((((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))) | (~((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16)))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))),
% 1.52/1.68 inference(tautology,[status(thm)],[])).
% 1.52/1.68 tff(269,plain,
% 1.52/1.68 ((((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))) <=> in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)))),
% 1.52/1.68 inference(unit_resolution,[status(thm)],[268, 267])).
% 1.52/1.68 tff(270,plain,
% 1.52/1.68 (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))),
% 1.52/1.68 inference(unit_resolution,[status(thm)],[269, 179])).
% 1.52/1.68 tff(271,plain,
% 1.52/1.68 ($false),
% 1.52/1.68 inference(unit_resolution,[status(thm)],[270, 130])).
% 1.52/1.68 % SZS output end Proof
% 1.52/1.69 % E exiting
%------------------------------------------------------------------------------