TSTP Solution File: SEU042+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU042+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 07:27:22 EDT 2022
% Result : Theorem 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU042+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 09:06:39 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.42 % SZS status Theorem
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 tff(tptp_fun_B_2_type, type, (
% 0.20/0.42 tptp_fun_B_2: $i > $i)).
% 0.20/0.42 tff(relation_dom_restriction_type, type, (
% 0.20/0.42 relation_dom_restriction: ( $i * $i ) > $i)).
% 0.20/0.42 tff(tptp_fun_A_16_type, type, (
% 0.20/0.42 tptp_fun_A_16: $i)).
% 0.20/0.42 tff(tptp_fun_B_15_type, type, (
% 0.20/0.42 tptp_fun_B_15: $i)).
% 0.20/0.42 tff(tptp_fun_C_1_type, type, (
% 0.20/0.42 tptp_fun_C_1: $i > $i)).
% 0.20/0.42 tff(apply_type, type, (
% 0.20/0.42 apply: ( $i * $i ) > $i)).
% 0.20/0.42 tff(in_type, type, (
% 0.20/0.42 in: ( $i * $i ) > $o)).
% 0.20/0.42 tff(relation_dom_type, type, (
% 0.20/0.42 relation_dom: $i > $i)).
% 0.20/0.42 tff(one_to_one_type, type, (
% 0.20/0.42 one_to_one: $i > $o)).
% 0.20/0.42 tff(relation_type, type, (
% 0.20/0.42 relation: $i > $o)).
% 0.20/0.42 tff(function_type, type, (
% 0.20/0.42 function: $i > $o)).
% 0.20/0.42 tff(set_intersection2_type, type, (
% 0.20/0.42 set_intersection2: ( $i * $i ) > $i)).
% 0.20/0.42 tff(tptp_fun_D_0_type, type, (
% 0.20/0.42 tptp_fun_D_0: ( $i * $i * $i ) > $i)).
% 0.20/0.42 tff(tptp_fun_D_14_type, type, (
% 0.20/0.42 tptp_fun_D_14: ( $i * $i ) > $i)).
% 0.20/0.42 tff(1,plain,
% 0.20/0.42 ((tptp_fun_C_1(relation_dom_restriction(B!15, A!16)) = tptp_fun_B_2(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)))),
% 0.20/0.42 inference(commutativity,[status(thm)],[])).
% 0.20/0.42 tff(2,plain,
% 0.20/0.42 ((tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(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)))),
% 0.20/0.42 inference(symmetry,[status(thm)],[1])).
% 0.20/0.42 tff(3,plain,
% 0.20/0.42 ((~(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(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))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[2])).
% 0.20/0.42 tff(4,plain,
% 0.20/0.42 ((~(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))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(5,plain,
% 0.20/0.42 ((~![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))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(6,plain,
% 0.20/0.42 ((~![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))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(7,axiom,(~![A: $i, B: $i] : ((relation(B) & function(B)) => (one_to_one(B) => one_to_one(relation_dom_restriction(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t84_funct_1')).
% 0.20/0.42 tff(8,plain,
% 0.20/0.42 (~![A: $i, B: $i] : (one_to_one(relation_dom_restriction(B, A)) | (~(relation(B) & function(B))) | (~one_to_one(B)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.20/0.42 tff(9,plain,
% 0.20/0.42 (~![A: $i, B: $i] : (one_to_one(relation_dom_restriction(B, A)) | (~(relation(B) & function(B))) | (~one_to_one(B)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.20/0.42 tff(10,plain,
% 0.20/0.42 (~![A: $i, B: $i] : (one_to_one(relation_dom_restriction(B, A)) | (~(relation(B) & function(B))) | (~one_to_one(B)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.20/0.42 tff(11,plain,
% 0.20/0.42 (~![A: $i, B: $i] : (one_to_one(relation_dom_restriction(B, A)) | (~(relation(B) & function(B))) | (~one_to_one(B)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.20/0.42 tff(12,plain,
% 0.20/0.42 (~![A: $i, B: $i] : (one_to_one(relation_dom_restriction(B, A)) | (~(relation(B) & function(B))) | (~one_to_one(B)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[11, 5])).
% 0.20/0.42 tff(13,plain,
% 0.20/0.42 (~![A: $i, B: $i] : (one_to_one(relation_dom_restriction(B, A)) | (~(relation(B) & function(B))) | (~one_to_one(B)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.20/0.42 tff(14,plain,
% 0.20/0.42 (~![A: $i, B: $i] : (one_to_one(relation_dom_restriction(B, A)) | (~(relation(B) & function(B))) | (~one_to_one(B)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[13, 5])).
% 0.20/0.42 tff(15,plain,(
% 0.20/0.42 ~(one_to_one(relation_dom_restriction(B!15, A!16)) | (~(relation(B!15) & function(B!15))) | (~one_to_one(B!15)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[14])).
% 0.20/0.42 tff(16,plain,
% 0.20/0.42 (~(one_to_one(relation_dom_restriction(B!15, A!16)) | (~(relation(B!15) & function(B!15))) | (~one_to_one(B!15)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[15, 4])).
% 0.20/0.42 tff(17,plain,
% 0.20/0.42 (relation(B!15) & function(B!15)),
% 0.20/0.42 inference(or_elim,[status(thm)],[16])).
% 0.20/0.42 tff(18,plain,
% 0.20/0.42 (relation(B!15)),
% 0.20/0.42 inference(and_elim,[status(thm)],[17])).
% 0.20/0.42 tff(19,plain,
% 0.20/0.42 (^[A: $i, B: $i] : refl(((~relation(A)) | relation(relation_dom_restriction(A, B))) <=> ((~relation(A)) | relation(relation_dom_restriction(A, B))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(20,plain,
% 0.20/0.42 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[19])).
% 0.20/0.42 tff(21,plain,
% 0.20/0.42 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(22,plain,
% 0.20/0.42 (^[A: $i, B: $i] : rewrite((relation(A) => relation(relation_dom_restriction(A, B))) <=> ((~relation(A)) | relation(relation_dom_restriction(A, B))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(23,plain,
% 0.20/0.42 (![A: $i, B: $i] : (relation(A) => relation(relation_dom_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[22])).
% 0.20/0.42 tff(24,axiom,(![A: $i, B: $i] : (relation(A) => relation(relation_dom_restriction(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k7_relat_1')).
% 0.20/0.42 tff(25,plain,
% 0.20/0.42 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.42 tff(26,plain,
% 0.20/0.42 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.20/0.42 tff(27,plain,(
% 0.20/0.42 ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[26])).
% 0.20/0.42 tff(28,plain,
% 0.20/0.42 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.20/0.42 tff(29,plain,
% 0.20/0.42 (((~![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)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(30,plain,
% 0.20/0.42 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | ((~relation(B!15)) | relation(relation_dom_restriction(B!15, A!16)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(31,plain,
% 0.20/0.42 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | (~relation(B!15)) | relation(relation_dom_restriction(B!15, A!16))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.20/0.42 tff(32,plain,
% 0.20/0.42 (relation(relation_dom_restriction(B!15, A!16))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[31, 28, 18])).
% 0.20/0.42 tff(33,plain,
% 0.20/0.42 (function(B!15)),
% 0.20/0.42 inference(and_elim,[status(thm)],[17])).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 (^[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)))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(35,plain,
% 0.20/0.42 (![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))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[34])).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 (^[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))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(37,plain,
% 0.20/0.42 (![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))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[36])).
% 0.20/0.42 tff(38,plain,
% 0.20/0.42 (![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))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(39,plain,
% 0.20/0.42 (^[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)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(40,plain,
% 0.20/0.42 (![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))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[39])).
% 0.20/0.42 tff(41,axiom,(![A: $i, B: $i] : ((relation(A) & function(A)) => (relation(relation_dom_restriction(A, B)) & function(relation_dom_restriction(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc4_funct_1')).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 (![A: $i, B: $i] : ((~(relation(A) & function(A))) | (relation(relation_dom_restriction(A, B)) & function(relation_dom_restriction(A, B))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.20/0.42 tff(43,plain,
% 0.20/0.42 (![A: $i, B: $i] : ((~(relation(A) & function(A))) | (relation(relation_dom_restriction(A, B)) & function(relation_dom_restriction(A, B))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.20/0.42 tff(44,plain,(
% 0.20/0.42 ![A: $i, B: $i] : ((~(relation(A) & function(A))) | (relation(relation_dom_restriction(A, B)) & function(relation_dom_restriction(A, B))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[43])).
% 0.20/0.42 tff(45,plain,
% 0.20/0.42 (![A: $i, B: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(relation_dom_restriction(A, B))) | (~function(relation_dom_restriction(A, B))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.20/0.42 tff(46,plain,
% 0.20/0.42 (![A: $i, B: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(relation_dom_restriction(A, B))) | (~function(relation_dom_restriction(A, B))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[45, 35])).
% 0.20/0.42 tff(47,plain,
% 0.20/0.42 (((~![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))))))) | (~relation(B!15)) | (~function(B!15)) | (~((~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(48,plain,
% 0.20/0.42 ((~![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))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(49,plain,
% 0.20/0.42 ((~![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)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.20/0.42 tff(50,plain,
% 0.20/0.42 (~((~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[49, 46, 18, 33])).
% 0.20/0.42 tff(51,plain,
% 0.20/0.42 (((~relation(relation_dom_restriction(B!15, A!16))) | (~function(relation_dom_restriction(B!15, A!16)))) | function(relation_dom_restriction(B!15, A!16))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(52,plain,
% 0.20/0.42 (function(relation_dom_restriction(B!15, A!16))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.20/0.42 tff(53,plain,
% 0.20/0.42 (^[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))))))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(54,plain,
% 0.20/0.42 (![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)))))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[53])).
% 0.20/0.42 tff(55,plain,
% 0.20/0.42 (^[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))))))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(56,plain,
% 0.20/0.42 (![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)))))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[55])).
% 0.20/0.42 tff(57,plain,
% 0.20/0.42 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((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)))))))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[56, 54])).
% 0.20/0.42 tff(58,plain,
% 0.20/0.42 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(A) & function(A)) <=> (~((~relation(A)) | (~function(A))))), ((~(relation(A) & function(A))) <=> (~(~((~relation(A)) | (~function(A))))))), rewrite((~(~((~relation(A)) | (~function(A))))) <=> ((~relation(A)) | (~function(A)))), ((~(relation(A) & function(A))) <=> ((~relation(A)) | (~function(A))))), trans(monotonicity(rewrite(((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) <=> ((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(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)))))))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(59,plain,
% 0.20/0.43 (![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)))))))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[58])).
% 0.20/0.43 tff(60,plain,
% 0.20/0.43 (![A: $i] : ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C)))) <=> ![A: $i] : ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(61,plain,
% 0.20/0.43 (^[A: $i] : trans(monotonicity(rewrite((one_to_one(A) <=> ![B: $i, C: $i] : (((in(B, relation_dom(A)) & in(C, relation_dom(A))) & (apply(A, B) = apply(A, C))) => (B = C))) <=> (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C)))), (((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : (((in(B, relation_dom(A)) & in(C, relation_dom(A))) & (apply(A, B) = apply(A, C))) => (B = C)))) <=> ((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C)))))), rewrite(((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C)))) <=> ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))), (((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : (((in(B, relation_dom(A)) & in(C, relation_dom(A))) & (apply(A, B) = apply(A, C))) => (B = C)))) <=> ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(62,plain,
% 0.20/0.43 (![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : (((in(B, relation_dom(A)) & in(C, relation_dom(A))) & (apply(A, B) = apply(A, C))) => (B = C)))) <=> ![A: $i] : ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[61])).
% 0.20/0.43 tff(63,axiom,(![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : (((in(B, relation_dom(A)) & in(C, relation_dom(A))) & (apply(A, B) = apply(A, C))) => (B = C))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d8_funct_1')).
% 0.20/0.43 tff(64,plain,
% 0.20/0.43 (![A: $i] : ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.20/0.43 tff(65,plain,
% 0.20/0.43 (![A: $i] : ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.20/0.43 tff(66,plain,(
% 0.20/0.43 ![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)))))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[65])).
% 0.20/0.43 tff(67,plain,
% 0.20/0.43 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(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)))))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.20/0.43 tff(68,plain,
% 0.20/0.43 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(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)))))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[67, 57])).
% 0.20/0.43 tff(69,plain,
% 0.20/0.43 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(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)) | (~((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))))))))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(70,plain,
% 0.20/0.43 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(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))))))))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(71,plain,
% 0.20/0.43 ((~![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)))))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.20/0.43 tff(72,plain,
% 0.20/0.43 ((~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)))))))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[71, 68])).
% 0.20/0.43 tff(73,plain,
% 0.20/0.43 (~((~((~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))))))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[72, 52, 32])).
% 0.20/0.43 tff(74,plain,
% 0.20/0.43 (((~((~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)) | (~((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))))))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(75,plain,
% 0.20/0.44 (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)))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.20/0.44 tff(76,plain,
% 0.20/0.44 (~one_to_one(relation_dom_restriction(B!15, A!16))),
% 0.20/0.44 inference(or_elim,[status(thm)],[16])).
% 0.20/0.44 tff(77,plain,
% 0.20/0.44 ((~(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)) | (~((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)))))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(78,plain,
% 0.20/0.44 ((~(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))))))))) | (~((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)))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.20/0.44 tff(79,plain,
% 0.20/0.44 (~((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))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[78, 75])).
% 0.20/0.44 tff(80,plain,
% 0.20/0.44 (((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)))))) | (~(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(81,plain,
% 0.20/0.44 (~(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)) = tptp_fun_C_1(relation_dom_restriction(B!15, A!16)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.20/0.44 tff(82,plain,
% 0.20/0.44 (~(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)) = tptp_fun_B_2(relation_dom_restriction(B!15, A!16)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[81, 3])).
% 0.20/0.44 tff(83,plain,
% 0.20/0.44 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_intersection2(A, B))) | (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))) | (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)))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(84,plain,
% 0.20/0.44 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (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, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (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))))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[83])).
% 0.20/0.44 tff(85,plain,
% 0.20/0.44 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (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, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (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))))))))),
% 0.20/0.44 inference(pull_quant,[status(thm)],[])).
% 0.20/0.44 tff(86,plain,
% 0.20/0.44 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B)))))) <=> ![D: $i] : ((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))), ((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) <=> (~![D: $i] : ((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))))), pull_quant((~![D: $i] : ((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) <=> ?[D: $i] : (~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B)))))))), ((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) <=> ?[D: $i] : (~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))))), (((~((~(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))))))) <=> (?[D: $i] : (~((~(C = set_intersection2(A, B))) | (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))))))))), pull_quant((?[D: $i] : (~((~(C = set_intersection2(A, B))) | (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))))))) <=> ?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (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, 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))))))) <=> ?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (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, 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)))))))) <=> (~?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (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)))))))))), pull_quant((~?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (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)))))))) <=> ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (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, 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)))))))) <=> ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (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))))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(87,plain,
% 0.20/0.44 (![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] : ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (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))))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[86])).
% 0.20/0.44 tff(88,plain,
% 0.20/0.44 (![A: $i, B: $i, 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, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (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))))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[87, 85])).
% 0.20/0.44 tff(89,plain,
% 0.20/0.44 (![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, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (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))))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[88, 84])).
% 0.20/0.44 tff(90,plain,
% 0.20/0.44 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(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, 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)))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(91,plain,
% 0.20/0.44 (![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, 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))))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[90])).
% 0.20/0.44 tff(92,plain,
% 0.20/0.44 (![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, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (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))))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[91, 89])).
% 0.20/0.44 tff(93,plain,
% 0.20/0.44 (^[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, C) <=> (~((~in(D, A)) | (~in(D, B))))))), 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), 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, 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, 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)))))))), rewrite((((~(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, 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, 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, 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))))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(94,plain,
% 0.20/0.44 (![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, 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))))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[93])).
% 0.20/0.44 tff(95,plain,
% 0.20/0.44 (^[A: $i, B: $i, C: $i] : rewrite((((~(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, 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))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(96,plain,
% 0.20/0.44 (![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, 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)))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[95])).
% 0.20/0.44 tff(97,plain,
% 0.20/0.44 (![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))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(98,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/sandbox/benchmark/theBenchmark.p','d3_xboole_0')).
% 0.20/0.44 tff(99,plain,
% 0.20/0.44 (![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.20/0.44 tff(100,plain,(
% 0.20/0.44 ![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))))))),
% 0.20/0.44 inference(skolemize,[status(sab)],[99])).
% 0.20/0.44 tff(101,plain,
% 0.20/0.44 (![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)))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.20/0.44 tff(102,plain,
% 0.20/0.44 (![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))))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[101, 94])).
% 0.20/0.44 tff(103,plain,
% 0.20/0.44 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (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))))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[102, 92])).
% 0.20/0.44 tff(104,plain,
% 0.20/0.44 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (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))))))))) | ((~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))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (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))))))))) | ((~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)))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(105,plain,
% 0.20/0.44 ((~(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))) <=> ((~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))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(106,plain,
% 0.20/0.44 (((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)))) | $false) <=> (in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)) <=> ((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(107,plain,
% 0.20/0.45 ((~$true) <=> $false),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(108,plain,
% 0.20/0.45 (($true | (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))))) <=> $true),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(109,plain,
% 0.20/0.45 ((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)) <=> ((~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))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(110,plain,
% 0.20/0.45 ((set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16)) <=> $true),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(111,plain,
% 0.20/0.45 (((set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16)) | (in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), set_intersection2(relation_dom(B!15), A!16)) <=> ((~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), relation_dom(B!15))) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), A!16))))) <=> ($true | (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)))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[110, 109])).
% 0.20/0.45 tff(112,plain,
% 0.20/0.45 (((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)), 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))))) <=> $true),
% 0.20/0.45 inference(transitivity,[status(thm)],[111, 108])).
% 0.20/0.45 tff(113,plain,
% 0.20/0.45 ((~((set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16)) | (in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), set_intersection2(relation_dom(B!15), A!16)) <=> ((~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), relation_dom(B!15))) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(B!15), A!16), A!16, relation_dom(B!15)), A!16)))))) <=> (~$true)),
% 0.20/0.45 inference(monotonicity,[status(thm)],[112])).
% 0.20/0.45 tff(114,plain,
% 0.20/0.45 ((~((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)), 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)))))) <=> $false),
% 0.20/0.45 inference(transitivity,[status(thm)],[113, 107])).
% 0.20/0.45 tff(115,plain,
% 0.20/0.45 ((~(in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)) <=> (~((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16)))))) <=> (in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)) <=> ((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(116,plain,
% 0.20/0.45 (($false | (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)) <=> (~((~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)))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(117,plain,
% 0.20/0.45 ((~((~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))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(118,plain,
% 0.20/0.45 ((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)) <=> (~((~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)))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[117])).
% 0.20/0.45 tff(119,plain,
% 0.20/0.45 ((~(set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16))) <=> (~$true)),
% 0.20/0.45 inference(monotonicity,[status(thm)],[110])).
% 0.20/0.45 tff(120,plain,
% 0.20/0.45 ((~(set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16))) <=> $false),
% 0.20/0.45 inference(transitivity,[status(thm)],[119, 107])).
% 0.20/0.45 tff(121,plain,
% 0.20/0.45 (((~(set_intersection2(relation_dom(B!15), A!16) = set_intersection2(relation_dom(B!15), A!16))) | (in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)) <=> (~((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), A!16)))))) <=> ($false | (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))))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[120, 118])).
% 0.20/0.45 tff(122,plain,
% 0.20/0.45 (((~(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)), 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)))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[121, 116])).
% 0.20/0.45 tff(123,plain,
% 0.20/0.45 ((~((~(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)), 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))))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[122])).
% 0.20/0.45 tff(124,plain,
% 0.20/0.45 ((~((~(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)), 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))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[123, 115])).
% 0.20/0.45 tff(125,plain,
% 0.20/0.45 (((~((~(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)), 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))))))) | (~((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)), 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_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)))) | $false)),
% 0.20/0.45 inference(monotonicity,[status(thm)],[124, 114])).
% 0.20/0.45 tff(126,plain,
% 0.20/0.45 (((~((~(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)), 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))))))) | (~((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)), 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_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))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[125, 106])).
% 0.20/0.45 tff(127,plain,
% 0.20/0.45 ((~((~((~(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)), 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))))))) | (~((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)), 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_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)))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[126])).
% 0.20/0.45 tff(128,plain,
% 0.20/0.45 ((~((~((~(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)), 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))))))) | (~((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)), 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_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))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[127, 105])).
% 0.20/0.45 tff(129,plain,
% 0.20/0.45 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (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))))))))) | (~((~((~(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)), 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))))))) | (~((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)), 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))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (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))))))))) | ((~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)))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[128])).
% 0.20/0.45 tff(130,plain,
% 0.20/0.45 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (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))))))))) | (~((~((~(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)), 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))))))) | (~((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)), 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))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (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))))))))) | ((~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)))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[129, 104])).
% 0.20/0.45 tff(131,plain,
% 0.20/0.45 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (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))))))))) | (~((~((~(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)), 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))))))) | (~((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)), 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))))))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(132,plain,
% 0.20/0.45 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (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))))))))) | ((~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))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.20/0.45 tff(133,plain,
% 0.20/0.45 ((~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)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[132, 103])).
% 0.20/0.45 tff(134,plain,
% 0.20/0.45 (^[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))))))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(135,plain,
% 0.20/0.46 (![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))))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[134])).
% 0.20/0.46 tff(136,plain,
% 0.20/0.46 (^[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))))))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(137,plain,
% 0.20/0.46 (![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)))))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[136])).
% 0.20/0.46 tff(138,plain,
% 0.20/0.46 (![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)))))))))))),
% 0.20/0.46 inference(pull_quant,[status(thm)],[])).
% 0.20/0.46 tff(139,plain,
% 0.20/0.46 (^[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)))))))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(140,plain,
% 0.20/0.46 (![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)))))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[139])).
% 0.20/0.46 tff(141,plain,
% 0.20/0.46 (![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)))))))))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[140, 138])).
% 0.20/0.46 tff(142,plain,
% 0.20/0.46 (![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)))))))))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[141, 137])).
% 0.20/0.46 tff(143,plain,
% 0.20/0.46 (^[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))))))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(144,plain,
% 0.20/0.46 (![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)))))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[143])).
% 0.20/0.46 tff(145,plain,
% 0.20/0.46 (![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)))))))))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[144, 142])).
% 0.20/0.46 tff(146,plain,
% 0.20/0.46 (^[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)))))))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(147,plain,
% 0.20/0.46 (![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)))))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[146])).
% 0.20/0.46 tff(148,plain,
% 0.20/0.46 (^[A: $i, B: $i] : 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))))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(149,plain,
% 0.20/0.46 (![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)))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[148])).
% 0.20/0.46 tff(150,plain,
% 0.20/0.46 (![A: $i, B: $i] : ((~(relation(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)))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(151,plain,
% 0.20/0.46 (^[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)))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(152,plain,
% 0.20/0.46 (![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)))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[151])).
% 0.20/0.46 tff(153,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/sandbox/benchmark/theBenchmark.p','t68_funct_1')).
% 0.20/0.46 tff(154,plain,
% 0.20/0.46 (![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)))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.20/0.46 tff(155,plain,
% 0.20/0.46 (![A: $i, B: $i] : ((~(relation(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)))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[154, 150])).
% 0.20/0.46 tff(156,plain,(
% 0.20/0.46 ![A: $i, B: $i] : ((~(relation(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))))))))))),
% 0.20/0.46 inference(skolemize,[status(sab)],[155])).
% 0.20/0.46 tff(157,plain,
% 0.20/0.46 (![A: $i, B: $i] : ((~(relation(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)))))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[156, 149])).
% 0.20/0.46 tff(158,plain,
% 0.20/0.46 (![A: $i, B: $i] : ((~relation(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)))))))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[157, 147])).
% 0.20/0.46 tff(159,plain,
% 0.20/0.46 (![A: $i, B: $i, 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)))))))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[158, 145])).
% 0.20/0.46 tff(160,plain,
% 0.20/0.46 (![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))))))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[159, 135])).
% 0.20/0.46 tff(161,plain,
% 0.20/0.46 (((~![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(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))))))))))) | (~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)))))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(162,plain,
% 0.20/0.47 (((~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))))))))) <=> ((~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)))))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(163,plain,
% 0.20/0.47 ((~((~((~(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))))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(164,plain,
% 0.20/0.47 (((~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)))))))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[163])).
% 0.20/0.47 tff(165,plain,
% 0.20/0.47 (((~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)))))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[164, 162])).
% 0.20/0.47 tff(166,plain,
% 0.20/0.47 (((~![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))))))))))) | ((~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))))))))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[165])).
% 0.20/0.47 tff(167,plain,
% 0.20/0.47 (((~![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))))))))))) | (~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)))))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[166, 161])).
% 0.20/0.47 tff(168,plain,
% 0.20/0.47 ((~![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)))))))))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(169,plain,
% 0.20/0.47 ((~![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(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))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.20/0.47 tff(170,plain,
% 0.20/0.47 (~((~(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)))))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[169, 160, 18, 33, 32, 52])).
% 0.20/0.47 tff(171,plain,
% 0.20/0.47 (((~(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))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(172,plain,
% 0.20/0.47 (relation_dom(relation_dom_restriction(B!15, A!16)) = set_intersection2(relation_dom(B!15), A!16)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[171, 170])).
% 0.20/0.47 tff(173,plain,
% 0.20/0.47 (set_intersection2(relation_dom(B!15), A!16) = relation_dom(relation_dom_restriction(B!15, A!16))),
% 0.20/0.47 inference(symmetry,[status(thm)],[172])).
% 0.20/0.47 tff(174,plain,
% 0.20/0.47 (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)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[173])).
% 0.20/0.47 tff(175,plain,
% 0.20/0.47 (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))),
% 0.20/0.47 inference(symmetry,[status(thm)],[174])).
% 0.20/0.47 tff(176,plain,
% 0.20/0.47 (((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)))))) | in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(177,plain,
% 0.20/0.47 (in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[176, 79])).
% 0.20/0.47 tff(178,plain,
% 0.20/0.47 (in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[177, 175])).
% 0.20/0.47 tff(179,plain,
% 0.20/0.47 ((~((~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))) | (~((~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))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(180,plain,
% 0.20/0.47 (~((~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)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[179, 178, 133])).
% 0.20/0.47 tff(181,plain,
% 0.20/0.47 (((~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))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(182,plain,
% 0.20/0.47 (in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[181, 180])).
% 0.20/0.47 tff(183,plain,
% 0.20/0.47 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (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))))))))) | ((~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))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (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))))))))) | ((~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)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(184,plain,
% 0.20/0.47 ((~(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))) <=> ((~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))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(185,plain,
% 0.20/0.47 (((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)))) | $false) <=> (in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)) <=> ((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(186,plain,
% 0.20/0.47 ((~(in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)) <=> (~((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16)))))) <=> (in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16)) <=> ((~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(187,plain,
% 0.20/0.47 (($false | (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)) <=> (~((~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)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(188,plain,
% 0.20/0.47 ((~((~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))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), A!16))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(189,plain,
% 0.20/0.48 ((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)) <=> (~((~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)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[188])).
% 0.20/0.48 tff(190,plain,
% 0.20/0.48 (((~(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)), 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)))))) <=> ($false | (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))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[120, 189])).
% 0.20/0.48 tff(191,plain,
% 0.20/0.48 (((~(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)), 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)))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[190, 187])).
% 0.20/0.48 tff(192,plain,
% 0.20/0.48 ((~((~(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)), 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))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[191])).
% 0.20/0.48 tff(193,plain,
% 0.20/0.48 ((~((~(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)), 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))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[192, 186])).
% 0.20/0.48 tff(194,plain,
% 0.20/0.48 (((~((~(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)), 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))))))) | (~((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)), 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_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)))) | $false)),
% 0.20/0.48 inference(monotonicity,[status(thm)],[193, 114])).
% 0.20/0.48 tff(195,plain,
% 0.20/0.48 (((~((~(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)), 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))))))) | (~((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)), 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_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))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[194, 185])).
% 0.20/0.48 tff(196,plain,
% 0.20/0.48 ((~((~((~(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)), 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))))))) | (~((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)), 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_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)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[195])).
% 0.20/0.48 tff(197,plain,
% 0.20/0.48 ((~((~((~(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)), 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))))))) | (~((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)), 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_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))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[196, 184])).
% 0.20/0.48 tff(198,plain,
% 0.20/0.48 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (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))))))))) | (~((~((~(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)), 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))))))) | (~((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)), 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))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (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))))))))) | ((~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)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[197])).
% 0.20/0.48 tff(199,plain,
% 0.20/0.48 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (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))))))))) | (~((~((~(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)), 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))))))) | (~((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)), 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))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (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))))))))) | ((~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)))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[198, 183])).
% 0.20/0.48 tff(200,plain,
% 0.20/0.48 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (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))))))))) | (~((~((~(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)), 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))))))) | (~((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)), 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))))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(201,plain,
% 0.20/0.48 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (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))))))))) | ((~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))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.20/0.48 tff(202,plain,
% 0.20/0.48 ((~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)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[201, 103])).
% 0.20/0.48 tff(203,plain,
% 0.20/0.48 (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)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[173])).
% 0.20/0.48 tff(204,plain,
% 0.20/0.48 (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))),
% 0.20/0.48 inference(symmetry,[status(thm)],[203])).
% 0.20/0.48 tff(205,plain,
% 0.20/0.48 (((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)))))) | in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(206,plain,
% 0.20/0.48 (in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(relation_dom_restriction(B!15, A!16)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[205, 79])).
% 0.20/0.48 tff(207,plain,
% 0.20/0.48 (in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), set_intersection2(relation_dom(B!15), A!16))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[206, 204])).
% 0.20/0.48 tff(208,plain,
% 0.20/0.48 ((~((~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))) | (~((~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))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(209,plain,
% 0.20/0.48 (~((~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)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[208, 207, 202])).
% 0.20/0.48 tff(210,plain,
% 0.20/0.48 (((~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))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(211,plain,
% 0.20/0.48 (in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[210, 209])).
% 0.20/0.48 tff(212,plain,
% 0.20/0.48 (((~![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(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))))))))))) | (~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)))))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(213,plain,
% 0.20/0.48 (((~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))))))))) <=> ((~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)))))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(214,plain,
% 0.20/0.48 ((~((~((~(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))))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(215,plain,
% 0.20/0.48 (((~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)))))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[214])).
% 0.20/0.49 tff(216,plain,
% 0.20/0.49 (((~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)))))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[215, 213])).
% 0.20/0.49 tff(217,plain,
% 0.20/0.49 (((~![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))))))))))) | ((~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))))))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[216])).
% 0.20/0.49 tff(218,plain,
% 0.20/0.49 (((~![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))))))))))) | (~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)))))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[217, 212])).
% 0.20/0.49 tff(219,plain,
% 0.20/0.49 ((~![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)))))))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(220,plain,
% 0.20/0.49 ((~![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(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))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.20/0.49 tff(221,plain,
% 0.20/0.49 (~((~(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)))))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[220, 160, 18, 33, 32, 52])).
% 0.20/0.49 tff(222,plain,
% 0.20/0.49 (((~(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)))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(223,plain,
% 0.20/0.49 ((~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))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[222, 221])).
% 0.20/0.49 tff(224,plain,
% 0.20/0.49 ((~((~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))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(225,plain,
% 0.20/0.49 ((~((~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))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[224, 177])).
% 0.20/0.49 tff(226,plain,
% 0.20/0.49 (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)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[225, 223])).
% 0.20/0.49 tff(227,plain,
% 0.20/0.49 (((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)))))) | (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))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(228,plain,
% 0.20/0.49 (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)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[227, 79])).
% 0.20/0.49 tff(229,plain,
% 0.20/0.49 (apply(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)))),
% 0.20/0.49 inference(symmetry,[status(thm)],[228])).
% 0.20/0.49 tff(230,plain,
% 0.20/0.49 (((~(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)))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(231,plain,
% 0.20/0.49 ((~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))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[230, 170])).
% 0.20/0.49 tff(232,plain,
% 0.20/0.49 ((~((~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))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(233,plain,
% 0.20/0.49 ((~((~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))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[232, 206])).
% 0.20/0.49 tff(234,plain,
% 0.20/0.49 (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)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[233, 231])).
% 0.20/0.49 tff(235,plain,
% 0.20/0.49 (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)))),
% 0.20/0.49 inference(symmetry,[status(thm)],[234])).
% 0.20/0.49 tff(236,plain,
% 0.20/0.49 (apply(B!15, tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[235, 229, 226])).
% 0.20/0.49 tff(237,plain,
% 0.20/0.49 (((~![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)))))))))))) | (~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)))))))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(238,plain,
% 0.20/0.49 ((~![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)))))))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(239,plain,
% 0.20/0.49 ((~![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))))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.20/0.49 tff(240,plain,
% 0.20/0.49 (~((~((~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)))))))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[239, 68, 18, 33])).
% 0.20/0.49 tff(241,plain,
% 0.20/0.49 (((~((~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)))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(242,plain,
% 0.20/0.49 ((~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))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[241, 240])).
% 0.20/0.49 tff(243,plain,
% 0.20/0.49 (one_to_one(B!15)),
% 0.20/0.49 inference(or_elim,[status(thm)],[16])).
% 0.20/0.49 tff(244,plain,
% 0.20/0.49 ((~((~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))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(245,plain,
% 0.20/0.49 ((~((~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))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[244, 243])).
% 0.20/0.49 tff(246,plain,
% 0.20/0.49 (![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))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[245, 242])).
% 0.20/0.49 tff(247,plain,
% 0.20/0.49 (((~![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))))) | ((~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))) | (tptp_fun_C_1(relation_dom_restriction(B!15, A!16)) = 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))) = apply(B!15, tptp_fun_B_2(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))))) | (~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))) | (tptp_fun_C_1(relation_dom_restriction(B!15, A!16)) = 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))) = apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(248,plain,
% 0.20/0.49 (((tptp_fun_C_1(relation_dom_restriction(B!15, A!16)) = 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(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~(apply(B!15, tptp_fun_C_1(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(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (tptp_fun_C_1(relation_dom_restriction(B!15, A!16)) = 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))) = apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(249,plain,
% 0.20/0.49 (((~![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_C_1(relation_dom_restriction(B!15, A!16)) = 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(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~(apply(B!15, tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_B_2(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))))) | ((~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))) | (tptp_fun_C_1(relation_dom_restriction(B!15, A!16)) = 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))) = apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16)))))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[248])).
% 0.20/0.50 tff(250,plain,
% 0.20/0.50 (((~![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_C_1(relation_dom_restriction(B!15, A!16)) = 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(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~(apply(B!15, tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_B_2(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))))) | (~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))) | (tptp_fun_C_1(relation_dom_restriction(B!15, A!16)) = 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))) = apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[249, 247])).
% 0.20/0.50 tff(251,plain,
% 0.20/0.50 ((~![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_C_1(relation_dom_restriction(B!15, A!16)) = 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(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~(apply(B!15, tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16))))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(252,plain,
% 0.20/0.50 ((~![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(B!15))) | (~in(B, relation_dom(B!15))) | (~(apply(B!15, B) = apply(B!15, C))))) | (~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (tptp_fun_C_1(relation_dom_restriction(B!15, A!16)) = tptp_fun_B_2(relation_dom_restriction(B!15, A!16))) | (~(apply(B!15, tptp_fun_C_1(relation_dom_restriction(B!15, A!16))) = apply(B!15, tptp_fun_B_2(relation_dom_restriction(B!15, A!16)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.20/0.50 tff(253,plain,
% 0.20/0.50 ((~in(tptp_fun_B_2(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (~in(tptp_fun_C_1(relation_dom_restriction(B!15, A!16)), relation_dom(B!15))) | (tptp_fun_C_1(relation_dom_restriction(B!15, A!16)) = tptp_fun_B_2(relation_dom_restriction(B!15, A!16)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[252, 246, 236])).
% 0.20/0.50 tff(254,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[253, 211, 182, 82])).
% 0.20/0.50 % SZS output end Proof
%------------------------------------------------------------------------------