TSTP Solution File: SEU245+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU245+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 07:28:28 EDT 2022
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU245+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 11:22:10 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(in_type, type, (
% 0.12/0.39 in: ( $i * $i ) > $o)).
% 0.12/0.39 tff(set_intersection2_type, type, (
% 0.12/0.39 set_intersection2: ( $i * $i ) > $i)).
% 0.12/0.39 tff(cartesian_product2_type, type, (
% 0.12/0.39 cartesian_product2: ( $i * $i ) > $i)).
% 0.12/0.39 tff(tptp_fun_B_7_type, type, (
% 0.12/0.39 tptp_fun_B_7: $i)).
% 0.12/0.39 tff(tptp_fun_C_6_type, type, (
% 0.12/0.39 tptp_fun_C_6: $i)).
% 0.12/0.39 tff(tptp_fun_A_8_type, type, (
% 0.12/0.39 tptp_fun_A_8: $i)).
% 0.12/0.39 tff(relation_restriction_type, type, (
% 0.12/0.39 relation_restriction: ( $i * $i ) > $i)).
% 0.12/0.39 tff(relation_type, type, (
% 0.12/0.39 relation: $i > $o)).
% 0.12/0.39 tff(tptp_fun_D_9_type, type, (
% 0.12/0.39 tptp_fun_D_9: ( $i * $i * $i ) > $i)).
% 0.12/0.39 tff(1,plain,
% 0.12/0.39 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))) <=> (~![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 ((~![A: $i, B: $i, C: $i] : (relation(C) => (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))) <=> (~![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(3,axiom,(~![A: $i, B: $i, C: $i] : (relation(C) => (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t16_wellord1')).
% 0.12/0.39 tff(4,plain,
% 0.12/0.39 (~![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.12/0.39 tff(5,plain,
% 0.12/0.39 (~![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.12/0.39 tff(6,plain,
% 0.12/0.39 (~![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.12/0.39 tff(7,plain,
% 0.12/0.39 (~![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 (~![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 (~![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 (~![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.12/0.39 tff(11,plain,(
% 0.12/0.39 ~((~relation(C!6)) | (in(A!8, relation_restriction(C!6, B!7)) <=> (in(A!8, C!6) & in(A!8, cartesian_product2(B!7, B!7)))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[10])).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 (relation(C!6)),
% 0.12/0.39 inference(or_elim,[status(thm)],[11])).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B)))) <=> ((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 (![A: $i] : ((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[13])).
% 0.12/0.39 tff(15,plain,
% 0.12/0.39 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B)))) <=> ((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 (![A: $i] : ((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[15])).
% 0.12/0.39 tff(17,plain,
% 0.12/0.39 (![A: $i] : ((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[16, 14])).
% 0.12/0.39 tff(18,plain,
% 0.12/0.39 (![A: $i] : ((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 (^[A: $i] : rewrite((relation(A) => ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B)))) <=> ((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 (![A: $i] : (relation(A) => ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[19])).
% 0.12/0.39 tff(21,axiom,(![A: $i] : (relation(A) => ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d6_wellord1')).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 (![A: $i] : ((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.12/0.39 tff(23,plain,
% 0.12/0.39 (![A: $i] : ((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.12/0.39 tff(24,plain,(
% 0.12/0.39 ![A: $i] : ((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[23])).
% 0.12/0.39 tff(25,plain,
% 0.12/0.39 (![A: $i] : ((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.12/0.39 tff(26,plain,
% 0.12/0.39 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B))))) | ((~relation(C!6)) | ![B: $i] : (relation_restriction(C!6, B) = set_intersection2(C!6, cartesian_product2(B, B))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B))))) | (~relation(C!6)) | ![B: $i] : (relation_restriction(C!6, B) = set_intersection2(C!6, cartesian_product2(B, B))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B))))) | ((~relation(C!6)) | ![B: $i] : (relation_restriction(C!6, B) = set_intersection2(C!6, cartesian_product2(B, B))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(28,plain,
% 0.12/0.39 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B))))) | (~relation(C!6)) | ![B: $i] : (relation_restriction(C!6, B) = set_intersection2(C!6, cartesian_product2(B, B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.12/0.39 tff(29,plain,
% 0.12/0.39 (![B: $i] : (relation_restriction(C!6, B) = set_intersection2(C!6, cartesian_product2(B, B)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[28, 25, 12])).
% 0.12/0.39 tff(30,plain,
% 0.12/0.39 ((~![B: $i] : (relation_restriction(C!6, B) = set_intersection2(C!6, cartesian_product2(B, B)))) | (relation_restriction(C!6, B!7) = set_intersection2(C!6, cartesian_product2(B!7, B!7)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(31,plain,
% 0.12/0.40 (relation_restriction(C!6, B!7) = set_intersection2(C!6, cartesian_product2(B!7, B!7))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.12/0.40 tff(32,plain,
% 0.12/0.40 (set_intersection2(C!6, cartesian_product2(B!7, B!7)) = relation_restriction(C!6, B!7)),
% 0.12/0.40 inference(symmetry,[status(thm)],[31])).
% 0.12/0.40 tff(33,plain,
% 0.12/0.40 (in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))) <=> in(A!8, relation_restriction(C!6, B!7))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[32])).
% 0.12/0.40 tff(34,plain,
% 0.12/0.40 (in(A!8, relation_restriction(C!6, B!7)) <=> in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7)))),
% 0.12/0.40 inference(symmetry,[status(thm)],[33])).
% 0.12/0.40 tff(35,plain,
% 0.12/0.40 ((~in(A!8, relation_restriction(C!6, B!7))) <=> (~in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[34])).
% 0.12/0.40 tff(36,assumption,(~((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7))))), introduced(assumption)).
% 0.12/0.40 tff(37,plain,
% 0.12/0.40 ((~(in(A!8, relation_restriction(C!6, B!7)) <=> (~((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7))))))) <=> (in(A!8, relation_restriction(C!6, B!7)) <=> ((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(38,plain,
% 0.12/0.40 ((in(A!8, relation_restriction(C!6, B!7)) <=> (in(A!8, C!6) & in(A!8, cartesian_product2(B!7, B!7)))) <=> (in(A!8, relation_restriction(C!6, B!7)) <=> (~((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7))))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(39,plain,
% 0.12/0.40 ((~(in(A!8, relation_restriction(C!6, B!7)) <=> (in(A!8, C!6) & in(A!8, cartesian_product2(B!7, B!7))))) <=> (~(in(A!8, relation_restriction(C!6, B!7)) <=> (~((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[38])).
% 0.12/0.40 tff(40,plain,
% 0.12/0.40 ((~(in(A!8, relation_restriction(C!6, B!7)) <=> (in(A!8, C!6) & in(A!8, cartesian_product2(B!7, B!7))))) <=> (in(A!8, relation_restriction(C!6, B!7)) <=> ((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[39, 37])).
% 0.12/0.40 tff(41,plain,
% 0.12/0.40 (~(in(A!8, relation_restriction(C!6, B!7)) <=> (in(A!8, C!6) & in(A!8, cartesian_product2(B!7, B!7))))),
% 0.12/0.40 inference(or_elim,[status(thm)],[11])).
% 0.12/0.40 tff(42,plain,
% 0.12/0.40 (in(A!8, relation_restriction(C!6, B!7)) <=> ((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.12/0.40 tff(43,plain,
% 0.12/0.40 ((~in(A!8, relation_restriction(C!6, B!7))) | ((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))) | (~(in(A!8, relation_restriction(C!6, B!7)) <=> ((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7))))))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(44,plain,
% 0.12/0.40 ((~in(A!8, relation_restriction(C!6, B!7))) | ((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.12/0.40 tff(45,plain,
% 0.12/0.40 (~in(A!8, relation_restriction(C!6, B!7))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[44, 36])).
% 0.12/0.40 tff(46,plain,
% 0.12/0.40 (~in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[45, 35])).
% 0.12/0.40 tff(47,plain,
% 0.12/0.40 (^[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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B)))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(48,plain,
% 0.12/0.40 (![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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[47])).
% 0.12/0.40 tff(49,plain,
% 0.12/0.40 (![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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))))))))),
% 0.12/0.40 inference(pull_quant,[status(thm)],[])).
% 0.12/0.40 tff(50,plain,
% 0.12/0.40 (^[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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(51,plain,
% 0.12/0.40 (![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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[50])).
% 0.12/0.40 tff(52,plain,
% 0.12/0.40 (![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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))))))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[51, 49])).
% 0.12/0.40 tff(53,plain,
% 0.12/0.40 (![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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))))))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[52, 48])).
% 0.12/0.40 tff(54,plain,
% 0.12/0.40 (^[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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B)))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(55,plain,
% 0.12/0.40 (![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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[54])).
% 0.12/0.40 tff(56,plain,
% 0.12/0.40 (![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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))))))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[55, 53])).
% 0.12/0.40 tff(57,plain,
% 0.12/0.40 (^[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_9(C, B, A), C)) <=> (in(tptp_fun_D_9(C, B, A), A) & in(tptp_fun_D_9(C, B, A), B)))) <=> ((C = set_intersection2(A, B)) | (in(tptp_fun_D_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(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_9(C, B, A), C)) <=> (in(tptp_fun_D_9(C, B, A), A) & in(tptp_fun_D_9(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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(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_9(C, B, A), C)) <=> (in(tptp_fun_D_9(C, B, A), A) & in(tptp_fun_D_9(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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(58,plain,
% 0.12/0.40 (![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_9(C, B, A), C)) <=> (in(tptp_fun_D_9(C, B, A), A) & in(tptp_fun_D_9(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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[57])).
% 0.12/0.40 tff(59,plain,
% 0.12/0.40 (^[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_9(C, B, A), C) <=> (in(tptp_fun_D_9(C, B, A), A) & in(tptp_fun_D_9(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_9(C, B, A), C)) <=> (in(tptp_fun_D_9(C, B, A), A) & in(tptp_fun_D_9(C, B, A), B))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(60,plain,
% 0.12/0.40 (![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_9(C, B, A), C) <=> (in(tptp_fun_D_9(C, B, A), A) & in(tptp_fun_D_9(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_9(C, B, A), C)) <=> (in(tptp_fun_D_9(C, B, A), A) & in(tptp_fun_D_9(C, B, A), B)))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[59])).
% 0.12/0.40 tff(61,plain,
% 0.12/0.40 (![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))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(62,axiom,(![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_xboole_0')).
% 0.12/0.41 tff(63,plain,
% 0.12/0.41 (![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.12/0.41 tff(64,plain,(
% 0.12/0.41 ![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_9(C, B, A), C) <=> (in(tptp_fun_D_9(C, B, A), A) & in(tptp_fun_D_9(C, B, A), B))))))),
% 0.12/0.41 inference(skolemize,[status(sab)],[63])).
% 0.12/0.41 tff(65,plain,
% 0.12/0.41 (![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_9(C, B, A), C)) <=> (in(tptp_fun_D_9(C, B, A), A) & in(tptp_fun_D_9(C, B, A), B)))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.12/0.41 tff(66,plain,
% 0.12/0.41 (![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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))))))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.12/0.41 tff(67,plain,
% 0.12/0.41 (![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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))))))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[66, 56])).
% 0.12/0.41 tff(68,plain,
% 0.12/0.41 (((~![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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))))))))) | ((~in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7)))) <=> ((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))))) <=> ((~![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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))))))))) | ((~in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7)))) <=> ((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7))))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(69,plain,
% 0.12/0.41 ((~(in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))) <=> ((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))))) <=> ((~in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7)))) <=> ((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(70,plain,
% 0.12/0.41 (((in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))) <=> ((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7))))) | $false) <=> (in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))) <=> ((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(71,plain,
% 0.12/0.41 ((~$true) <=> $false),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(72,plain,
% 0.12/0.41 (($true | (in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7), C!6), set_intersection2(C!6, cartesian_product2(B!7, B!7))) <=> ((~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7), C!6), C!6)) | (~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7), C!6), cartesian_product2(B!7, B!7)))))) <=> $true),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(73,plain,
% 0.12/0.41 ((set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(C!6, cartesian_product2(B!7, B!7))) <=> $true),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(74,plain,
% 0.19/0.41 (((set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(C!6, cartesian_product2(B!7, B!7))) | (in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7), C!6), set_intersection2(C!6, cartesian_product2(B!7, B!7))) <=> ((~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7), C!6), C!6)) | (~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7), C!6), cartesian_product2(B!7, B!7)))))) <=> ($true | (in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7), C!6), set_intersection2(C!6, cartesian_product2(B!7, B!7))) <=> ((~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7), C!6), C!6)) | (~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7), C!6), cartesian_product2(B!7, B!7))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[73])).
% 0.19/0.41 tff(75,plain,
% 0.19/0.41 (((set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(C!6, cartesian_product2(B!7, B!7))) | (in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7), C!6), set_intersection2(C!6, cartesian_product2(B!7, B!7))) <=> ((~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7), C!6), C!6)) | (~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7), C!6), cartesian_product2(B!7, B!7)))))) <=> $true),
% 0.19/0.41 inference(transitivity,[status(thm)],[74, 72])).
% 0.19/0.41 tff(76,plain,
% 0.19/0.41 ((~((set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(C!6, cartesian_product2(B!7, B!7))) | (in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7), C!6), set_intersection2(C!6, cartesian_product2(B!7, B!7))) <=> ((~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7), C!6), C!6)) | (~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7), C!6), cartesian_product2(B!7, B!7))))))) <=> (~$true)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[75])).
% 0.19/0.41 tff(77,plain,
% 0.19/0.41 ((~((set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(C!6, cartesian_product2(B!7, B!7))) | (in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7), C!6), set_intersection2(C!6, cartesian_product2(B!7, B!7))) <=> ((~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7), C!6), C!6)) | (~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7), C!6), cartesian_product2(B!7, B!7))))))) <=> $false),
% 0.19/0.41 inference(transitivity,[status(thm)],[76, 71])).
% 0.19/0.41 tff(78,plain,
% 0.19/0.41 ((~(in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))) <=> (~((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7))))))) <=> (in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))) <=> ((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(79,plain,
% 0.19/0.41 (($false | (in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))) <=> (~((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7))))))) <=> (in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))) <=> (~((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(80,plain,
% 0.19/0.41 ((~(set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(C!6, cartesian_product2(B!7, B!7)))) <=> (~$true)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[73])).
% 0.19/0.41 tff(81,plain,
% 0.19/0.41 ((~(set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(C!6, cartesian_product2(B!7, B!7)))) <=> $false),
% 0.19/0.41 inference(transitivity,[status(thm)],[80, 71])).
% 0.19/0.41 tff(82,plain,
% 0.19/0.41 (((~(set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(C!6, cartesian_product2(B!7, B!7)))) | (in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))) <=> (~((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7))))))) <=> ($false | (in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))) <=> (~((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[81])).
% 0.19/0.41 tff(83,plain,
% 0.19/0.41 (((~(set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(C!6, cartesian_product2(B!7, B!7)))) | (in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))) <=> (~((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7))))))) <=> (in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))) <=> (~((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[82, 79])).
% 0.19/0.41 tff(84,plain,
% 0.19/0.41 ((~((~(set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(C!6, cartesian_product2(B!7, B!7)))) | (in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))) <=> (~((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))))))) <=> (~(in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))) <=> (~((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[83])).
% 0.19/0.41 tff(85,plain,
% 0.19/0.41 ((~((~(set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(C!6, cartesian_product2(B!7, B!7)))) | (in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))) <=> (~((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))))))) <=> (in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))) <=> ((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[84, 78])).
% 0.19/0.41 tff(86,plain,
% 0.19/0.41 (((~((~(set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(C!6, cartesian_product2(B!7, B!7)))) | (in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))) <=> (~((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))))))) | (~((set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(C!6, cartesian_product2(B!7, B!7))) | (in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7), C!6), set_intersection2(C!6, cartesian_product2(B!7, B!7))) <=> ((~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7), C!6), C!6)) | (~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7), C!6), cartesian_product2(B!7, B!7)))))))) <=> ((in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))) <=> ((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7))))) | $false)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[85, 77])).
% 0.19/0.41 tff(87,plain,
% 0.19/0.41 (((~((~(set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(C!6, cartesian_product2(B!7, B!7)))) | (in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))) <=> (~((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))))))) | (~((set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(C!6, cartesian_product2(B!7, B!7))) | (in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7), C!6), set_intersection2(C!6, cartesian_product2(B!7, B!7))) <=> ((~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7), C!6), C!6)) | (~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7), C!6), cartesian_product2(B!7, B!7)))))))) <=> (in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))) <=> ((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[86, 70])).
% 0.19/0.41 tff(88,plain,
% 0.19/0.41 ((~((~((~(set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(C!6, cartesian_product2(B!7, B!7)))) | (in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))) <=> (~((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))))))) | (~((set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(C!6, cartesian_product2(B!7, B!7))) | (in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7), C!6), set_intersection2(C!6, cartesian_product2(B!7, B!7))) <=> ((~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7), C!6), C!6)) | (~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7), C!6), cartesian_product2(B!7, B!7))))))))) <=> (~(in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))) <=> ((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7))))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[87])).
% 0.19/0.42 tff(89,plain,
% 0.19/0.42 ((~((~((~(set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(C!6, cartesian_product2(B!7, B!7)))) | (in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))) <=> (~((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))))))) | (~((set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(C!6, cartesian_product2(B!7, B!7))) | (in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7), C!6), set_intersection2(C!6, cartesian_product2(B!7, B!7))) <=> ((~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7), C!6), C!6)) | (~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7), C!6), cartesian_product2(B!7, B!7))))))))) <=> ((~in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7)))) <=> ((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[88, 69])).
% 0.19/0.42 tff(90,plain,
% 0.19/0.42 (((~![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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))))))))) | (~((~((~(set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(C!6, cartesian_product2(B!7, B!7)))) | (in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))) <=> (~((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))))))) | (~((set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(C!6, cartesian_product2(B!7, B!7))) | (in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7), C!6), set_intersection2(C!6, cartesian_product2(B!7, B!7))) <=> ((~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7), C!6), C!6)) | (~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7), C!6), cartesian_product2(B!7, B!7)))))))))) <=> ((~![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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))))))))) | ((~in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7)))) <=> ((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7))))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[89])).
% 0.19/0.42 tff(91,plain,
% 0.19/0.42 (((~![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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))))))))) | (~((~((~(set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(C!6, cartesian_product2(B!7, B!7)))) | (in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))) <=> (~((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))))))) | (~((set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(C!6, cartesian_product2(B!7, B!7))) | (in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7), C!6), set_intersection2(C!6, cartesian_product2(B!7, B!7))) <=> ((~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7), C!6), C!6)) | (~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7), C!6), cartesian_product2(B!7, B!7)))))))))) <=> ((~![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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))))))))) | ((~in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7)))) <=> ((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[90, 68])).
% 0.19/0.42 tff(92,plain,
% 0.19/0.42 ((~![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_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))))))))) | (~((~((~(set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(C!6, cartesian_product2(B!7, B!7)))) | (in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))) <=> (~((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))))))) | (~((set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(C!6, cartesian_product2(B!7, B!7))) | (in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7), C!6), set_intersection2(C!6, cartesian_product2(B!7, B!7))) <=> ((~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7), C!6), C!6)) | (~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7), C!6), cartesian_product2(B!7, B!7)))))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(93,plain,
% 0.19/0.42 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_9(C, B, A), C) <=> ((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))))))))) | ((~in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7)))) <=> ((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.19/0.42 tff(94,plain,
% 0.19/0.42 ((~in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7)))) <=> ((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[93, 67])).
% 0.19/0.42 tff(95,plain,
% 0.19/0.42 ((~((~in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7)))) <=> ((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))))) | in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))) | ((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(96,plain,
% 0.19/0.42 (in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))) | ((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.19/0.42 tff(97,plain,
% 0.19/0.42 (in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[96, 36])).
% 0.19/0.42 tff(98,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[97, 46])).
% 0.19/0.42 tff(99,plain,((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(100,plain,
% 0.19/0.42 (in(A!8, relation_restriction(C!6, B!7)) | (~((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7))))) | (~(in(A!8, relation_restriction(C!6, B!7)) <=> ((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7))))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(101,plain,
% 0.19/0.42 (in(A!8, relation_restriction(C!6, B!7)) | (~((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[100, 42])).
% 0.19/0.42 tff(102,plain,
% 0.19/0.42 (in(A!8, relation_restriction(C!6, B!7))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[101, 99])).
% 0.19/0.42 tff(103,plain,
% 0.19/0.42 (in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[102, 34])).
% 0.19/0.42 tff(104,plain,
% 0.19/0.42 ((~((~in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7)))) <=> ((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))))) | (~in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7)))) | (~((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(105,plain,
% 0.19/0.42 ((~in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7)))) | (~((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[104, 94])).
% 0.19/0.42 tff(106,plain,
% 0.19/0.42 (~in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[105, 99])).
% 0.19/0.42 tff(107,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[106, 103])).
% 0.19/0.42 % SZS output end Proof
%------------------------------------------------------------------------------