TSTP Solution File: SEU128+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU128+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 07:27:37 EDT 2022
% Result : Theorem 0.12s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU128+2 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n004.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 09:31:04 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.
% 0.12/0.40 % SZS status Theorem
% 0.12/0.40 % SZS output start Proof
% 0.12/0.40 tff(in_type, type, (
% 0.12/0.40 in: ( $i * $i ) > $o)).
% 0.12/0.40 tff(set_intersection2_type, type, (
% 0.12/0.40 set_intersection2: ( $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_B_7_type, type, (
% 0.12/0.40 tptp_fun_B_7: $i)).
% 0.12/0.40 tff(tptp_fun_C_6_type, type, (
% 0.12/0.40 tptp_fun_C_6: $i)).
% 0.12/0.40 tff(tptp_fun_C_2_type, type, (
% 0.12/0.40 tptp_fun_C_2: ( $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_A_8_type, type, (
% 0.12/0.40 tptp_fun_A_8: $i)).
% 0.12/0.40 tff(subset_type, type, (
% 0.12/0.40 subset: ( $i * $i ) > $o)).
% 0.12/0.40 tff(tptp_fun_D_3_type, type, (
% 0.12/0.40 tptp_fun_D_3: ( $i * $i * $i ) > $i)).
% 0.12/0.40 tff(1,plain,
% 0.12/0.40 (^[A: $i, B: $i] : refl((set_intersection2(A, B) = set_intersection2(B, A)) <=> (set_intersection2(A, B) = set_intersection2(B, A)))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(2,plain,
% 0.12/0.40 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.40 tff(3,plain,
% 0.12/0.40 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(4,axiom,(![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 0.12/0.40 tff(5,plain,
% 0.12/0.40 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.40 tff(6,plain,(
% 0.12/0.40 ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.12/0.40 inference(skolemize,[status(sab)],[5])).
% 0.12/0.40 tff(7,plain,
% 0.12/0.40 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.40 tff(8,plain,
% 0.12/0.40 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(B!7, C!6) = set_intersection2(C!6, B!7))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(9,plain,
% 0.12/0.40 (set_intersection2(B!7, C!6) = set_intersection2(C!6, B!7)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.12/0.40 tff(10,plain,
% 0.12/0.40 (set_intersection2(C!6, B!7) = set_intersection2(B!7, C!6)),
% 0.12/0.40 inference(symmetry,[status(thm)],[9])).
% 0.12/0.40 tff(11,plain,
% 0.12/0.40 (in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(C!6, B!7)) <=> in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(B!7, C!6))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[10])).
% 0.12/0.40 tff(12,plain,
% 0.12/0.40 (in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(B!7, C!6)) <=> in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(C!6, B!7))),
% 0.12/0.40 inference(symmetry,[status(thm)],[11])).
% 0.12/0.40 tff(13,plain,
% 0.12/0.40 ((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(B!7, C!6))) <=> (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(C!6, B!7)))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[12])).
% 0.12/0.40 tff(14,plain,
% 0.12/0.40 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(15,plain,
% 0.12/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[14])).
% 0.12/0.40 tff(16,plain,
% 0.12/0.40 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(17,plain,
% 0.12/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[16])).
% 0.12/0.40 tff(18,plain,
% 0.12/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[17, 15])).
% 0.12/0.40 tff(19,plain,
% 0.12/0.40 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))), rewrite((subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(20,plain,
% 0.12/0.40 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[19])).
% 0.12/0.40 tff(21,plain,
% 0.12/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(22,plain,
% 0.12/0.40 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(23,plain,
% 0.12/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[22])).
% 0.12/0.40 tff(24,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_tarski')).
% 0.12/0.40 tff(25,plain,
% 0.12/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.12/0.40 tff(26,plain,
% 0.12/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.12/0.40 tff(27,plain,(
% 0.12/0.40 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))),
% 0.12/0.40 inference(skolemize,[status(sab)],[26])).
% 0.12/0.40 tff(28,plain,
% 0.12/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.12/0.40 tff(29,plain,
% 0.12/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.19/0.40 tff(30,plain,
% 0.19/0.40 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))) | (~((~((~subset(A!8, set_intersection2(B!7, C!6))) | ![C: $i] : ((~in(C, A!8)) | in(C, set_intersection2(B!7, C!6))))) | (~(subset(A!8, set_intersection2(B!7, C!6)) | (~((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), A!8)) | in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(B!7, C!6))))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(31,plain,
% 0.19/0.40 (~((~((~subset(A!8, set_intersection2(B!7, C!6))) | ![C: $i] : ((~in(C, A!8)) | in(C, set_intersection2(B!7, C!6))))) | (~(subset(A!8, set_intersection2(B!7, C!6)) | (~((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), A!8)) | in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(B!7, C!6)))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.19/0.40 tff(32,plain,
% 0.19/0.40 (((~((~subset(A!8, set_intersection2(B!7, C!6))) | ![C: $i] : ((~in(C, A!8)) | in(C, set_intersection2(B!7, C!6))))) | (~(subset(A!8, set_intersection2(B!7, C!6)) | (~((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), A!8)) | in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(B!7, C!6))))))) | (subset(A!8, set_intersection2(B!7, C!6)) | (~((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), A!8)) | in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(B!7, C!6)))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(33,plain,
% 0.19/0.40 (subset(A!8, set_intersection2(B!7, C!6)) | (~((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), A!8)) | in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(B!7, C!6))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.19/0.40 tff(34,plain,
% 0.19/0.40 ((~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(A, C))) | subset(A, set_intersection2(B, C)))) <=> (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(A, C))) | subset(A, set_intersection2(B, C))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(35,plain,
% 0.19/0.40 ((~![A: $i, B: $i, C: $i] : ((subset(A, B) & subset(A, C)) => subset(A, set_intersection2(B, C)))) <=> (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(A, C))) | subset(A, set_intersection2(B, C))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(36,axiom,(~![A: $i, B: $i, C: $i] : ((subset(A, B) & subset(A, C)) => subset(A, set_intersection2(B, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t19_xboole_1')).
% 0.19/0.40 tff(37,plain,
% 0.19/0.40 (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(A, C))) | subset(A, set_intersection2(B, C)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.19/0.40 tff(38,plain,
% 0.19/0.40 (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(A, C))) | subset(A, set_intersection2(B, C)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[37, 34])).
% 0.19/0.40 tff(39,plain,
% 0.19/0.40 (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(A, C))) | subset(A, set_intersection2(B, C)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(A, C))) | subset(A, set_intersection2(B, C)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[39, 34])).
% 0.19/0.40 tff(41,plain,
% 0.19/0.40 (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(A, C))) | subset(A, set_intersection2(B, C)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[40, 34])).
% 0.19/0.40 tff(42,plain,
% 0.19/0.40 (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(A, C))) | subset(A, set_intersection2(B, C)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.19/0.40 tff(43,plain,
% 0.19/0.40 (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(A, C))) | subset(A, set_intersection2(B, C)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[42, 34])).
% 0.19/0.40 tff(44,plain,(
% 0.19/0.40 ~((~(subset(A!8, B!7) & subset(A!8, C!6))) | subset(A!8, set_intersection2(B!7, C!6)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[43])).
% 0.19/0.40 tff(45,plain,
% 0.19/0.40 (~subset(A!8, set_intersection2(B!7, C!6))),
% 0.19/0.40 inference(or_elim,[status(thm)],[44])).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 ((~(subset(A!8, set_intersection2(B!7, C!6)) | (~((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), A!8)) | in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(B!7, C!6)))))) | subset(A!8, set_intersection2(B!7, C!6)) | (~((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), A!8)) | in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(B!7, C!6))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 ((~(subset(A!8, set_intersection2(B!7, C!6)) | (~((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), A!8)) | in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(B!7, C!6)))))) | (~((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), A!8)) | in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(B!7, C!6))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 (~((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), A!8)) | in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(B!7, C!6)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[47, 33])).
% 0.19/0.40 tff(49,plain,
% 0.19/0.40 (((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), A!8)) | in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(B!7, C!6))) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(B!7, C!6)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(B!7, C!6))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.19/0.40 tff(51,plain,
% 0.19/0.40 (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(C!6, B!7))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[50, 13])).
% 0.19/0.40 tff(52,plain,
% 0.19/0.40 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B)))))))) <=> (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B)))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B))))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[52])).
% 0.19/0.40 tff(54,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B))))))))),
% 0.19/0.40 inference(pull_quant,[status(thm)],[])).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 (^[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, B)) | (~in(D, A)))))) <=> ![D: $i] : ((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))), ((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) <=> (~![D: $i] : ((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))))), pull_quant((~![D: $i] : ((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) <=> ?[D: $i] : (~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A)))))))), ((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) <=> ?[D: $i] : (~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))))), (((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B))))))) <=> (?[D: $i] : (~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B))))))))), pull_quant((?[D: $i] : (~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B))))))) <=> ?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B)))))))), (((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B))))))) <=> ?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B))))))))), ((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B)))))))) <=> (~?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B)))))))))), pull_quant((~?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B)))))))) <=> ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B))))))))), ((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B)))))))) <=> ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B))))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(56,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B))))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[55])).
% 0.19/0.40 tff(57,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B))))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[56, 54])).
% 0.19/0.41 tff(58,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B))))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[57, 53])).
% 0.19/0.41 tff(59,plain,
% 0.19/0.41 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B)))))))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B)))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(60,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B))))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[59])).
% 0.19/0.41 tff(61,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B))))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[60, 58])).
% 0.19/0.41 tff(62,plain,
% 0.19/0.41 (^[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, B)) | (~in(D, A))))))), rewrite(((C = set_intersection2(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) & in(tptp_fun_D_3(C, B, A), B)))) <=> ((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) & in(tptp_fun_D_3(C, B, A), B))))) <=> (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A)))))) & ((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B)))))))), rewrite((((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A)))))) & ((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B)))))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) & in(tptp_fun_D_3(C, B, A), B))))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B))))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(63,plain,
% 0.19/0.41 (![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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) & in(tptp_fun_D_3(C, B, A), B))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B))))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[62])).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 (^[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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) & in(tptp_fun_D_3(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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) & in(tptp_fun_D_3(C, B, A), B))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(65,plain,
% 0.19/0.41 (![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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) & in(tptp_fun_D_3(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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) & in(tptp_fun_D_3(C, B, A), B)))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[64])).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 (![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))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(67,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')).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.19/0.41 tff(69,plain,(
% 0.19/0.41 ![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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) & in(tptp_fun_D_3(C, B, A), B))))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[68])).
% 0.19/0.41 tff(70,plain,
% 0.19/0.41 (![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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) & in(tptp_fun_D_3(C, B, A), B)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.19/0.41 tff(71,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B))))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.19/0.41 tff(72,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B))))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[71, 61])).
% 0.19/0.41 tff(73,plain,
% 0.19/0.41 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B))))))))) | ((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(C!6, B!7))) <=> ((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), B!7)) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), C!6))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B))))))))) | ((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(C!6, B!7))) <=> ((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), B!7)) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), C!6)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(74,plain,
% 0.19/0.41 ((~(in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(C!6, B!7)) <=> ((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), B!7)) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), C!6))))) <=> ((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(C!6, B!7))) <=> ((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), B!7)) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), C!6))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(75,plain,
% 0.19/0.41 (((in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(C!6, B!7)) <=> ((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), B!7)) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), C!6)))) | $false) <=> (in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(C!6, B!7)) <=> ((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), B!7)) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), C!6))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(76,plain,
% 0.19/0.41 ((~$true) <=> $false),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(77,plain,
% 0.19/0.41 (($true | (in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), set_intersection2(C!6, B!7)) <=> ((~in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), C!6)) | (~in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), B!7))))) <=> $true),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(78,plain,
% 0.19/0.41 ((in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), set_intersection2(C!6, B!7)) <=> ((~in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), C!6)) | (~in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), B!7)))) <=> (in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), set_intersection2(C!6, B!7)) <=> ((~in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), C!6)) | (~in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), B!7))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(79,plain,
% 0.19/0.41 ((set_intersection2(C!6, B!7) = set_intersection2(C!6, B!7)) <=> $true),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(80,plain,
% 0.19/0.41 (((set_intersection2(C!6, B!7) = set_intersection2(C!6, B!7)) | (in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), set_intersection2(C!6, B!7)) <=> ((~in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), C!6)) | (~in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), B!7))))) <=> ($true | (in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), set_intersection2(C!6, B!7)) <=> ((~in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), C!6)) | (~in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), B!7)))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[79, 78])).
% 0.19/0.41 tff(81,plain,
% 0.19/0.41 (((set_intersection2(C!6, B!7) = set_intersection2(C!6, B!7)) | (in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), set_intersection2(C!6, B!7)) <=> ((~in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), C!6)) | (~in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), B!7))))) <=> $true),
% 0.19/0.42 inference(transitivity,[status(thm)],[80, 77])).
% 0.19/0.42 tff(82,plain,
% 0.19/0.42 ((~((set_intersection2(C!6, B!7) = set_intersection2(C!6, B!7)) | (in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), set_intersection2(C!6, B!7)) <=> ((~in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), C!6)) | (~in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), B!7)))))) <=> (~$true)),
% 0.19/0.42 inference(monotonicity,[status(thm)],[81])).
% 0.19/0.42 tff(83,plain,
% 0.19/0.42 ((~((set_intersection2(C!6, B!7) = set_intersection2(C!6, B!7)) | (in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), set_intersection2(C!6, B!7)) <=> ((~in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), C!6)) | (~in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), B!7)))))) <=> $false),
% 0.19/0.42 inference(transitivity,[status(thm)],[82, 76])).
% 0.19/0.42 tff(84,plain,
% 0.19/0.42 ((~(in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(C!6, B!7)) <=> (~((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), B!7)) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), C!6)))))) <=> (in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(C!6, B!7)) <=> ((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), B!7)) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), C!6))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(85,plain,
% 0.19/0.42 (($false | (in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(C!6, B!7)) <=> (~((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), B!7)) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), C!6)))))) <=> (in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(C!6, B!7)) <=> (~((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), B!7)) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), C!6)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(86,plain,
% 0.19/0.42 ((~(set_intersection2(C!6, B!7) = set_intersection2(C!6, B!7))) <=> (~$true)),
% 0.19/0.42 inference(monotonicity,[status(thm)],[79])).
% 0.19/0.42 tff(87,plain,
% 0.19/0.42 ((~(set_intersection2(C!6, B!7) = set_intersection2(C!6, B!7))) <=> $false),
% 0.19/0.42 inference(transitivity,[status(thm)],[86, 76])).
% 0.19/0.42 tff(88,plain,
% 0.19/0.42 (((~(set_intersection2(C!6, B!7) = set_intersection2(C!6, B!7))) | (in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(C!6, B!7)) <=> (~((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), B!7)) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), C!6)))))) <=> ($false | (in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(C!6, B!7)) <=> (~((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), B!7)) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), C!6))))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[87])).
% 0.19/0.42 tff(89,plain,
% 0.19/0.42 (((~(set_intersection2(C!6, B!7) = set_intersection2(C!6, B!7))) | (in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(C!6, B!7)) <=> (~((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), B!7)) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), C!6)))))) <=> (in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(C!6, B!7)) <=> (~((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), B!7)) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), C!6)))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[88, 85])).
% 0.19/0.42 tff(90,plain,
% 0.19/0.42 ((~((~(set_intersection2(C!6, B!7) = set_intersection2(C!6, B!7))) | (in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(C!6, B!7)) <=> (~((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), B!7)) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), C!6))))))) <=> (~(in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(C!6, B!7)) <=> (~((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), B!7)) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), C!6))))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[89])).
% 0.19/0.42 tff(91,plain,
% 0.19/0.42 ((~((~(set_intersection2(C!6, B!7) = set_intersection2(C!6, B!7))) | (in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(C!6, B!7)) <=> (~((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), B!7)) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), C!6))))))) <=> (in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(C!6, B!7)) <=> ((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), B!7)) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), C!6))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[90, 84])).
% 0.19/0.42 tff(92,plain,
% 0.19/0.42 (((~((~(set_intersection2(C!6, B!7) = set_intersection2(C!6, B!7))) | (in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(C!6, B!7)) <=> (~((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), B!7)) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), C!6))))))) | (~((set_intersection2(C!6, B!7) = set_intersection2(C!6, B!7)) | (in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), set_intersection2(C!6, B!7)) <=> ((~in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), C!6)) | (~in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), B!7))))))) <=> ((in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(C!6, B!7)) <=> ((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), B!7)) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), C!6)))) | $false)),
% 0.19/0.42 inference(monotonicity,[status(thm)],[91, 83])).
% 0.19/0.42 tff(93,plain,
% 0.19/0.42 (((~((~(set_intersection2(C!6, B!7) = set_intersection2(C!6, B!7))) | (in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(C!6, B!7)) <=> (~((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), B!7)) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), C!6))))))) | (~((set_intersection2(C!6, B!7) = set_intersection2(C!6, B!7)) | (in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), set_intersection2(C!6, B!7)) <=> ((~in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), C!6)) | (~in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), B!7))))))) <=> (in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(C!6, B!7)) <=> ((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), B!7)) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), C!6))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[92, 75])).
% 0.19/0.42 tff(94,plain,
% 0.19/0.42 ((~((~((~(set_intersection2(C!6, B!7) = set_intersection2(C!6, B!7))) | (in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(C!6, B!7)) <=> (~((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), B!7)) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), C!6))))))) | (~((set_intersection2(C!6, B!7) = set_intersection2(C!6, B!7)) | (in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), set_intersection2(C!6, B!7)) <=> ((~in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), C!6)) | (~in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), B!7)))))))) <=> (~(in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(C!6, B!7)) <=> ((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), B!7)) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), C!6)))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[93])).
% 0.19/0.42 tff(95,plain,
% 0.19/0.42 ((~((~((~(set_intersection2(C!6, B!7) = set_intersection2(C!6, B!7))) | (in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(C!6, B!7)) <=> (~((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), B!7)) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), C!6))))))) | (~((set_intersection2(C!6, B!7) = set_intersection2(C!6, B!7)) | (in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), set_intersection2(C!6, B!7)) <=> ((~in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), C!6)) | (~in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), B!7)))))))) <=> ((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(C!6, B!7))) <=> ((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), B!7)) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), C!6))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[94, 74])).
% 0.19/0.42 tff(96,plain,
% 0.19/0.42 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B))))))))) | (~((~((~(set_intersection2(C!6, B!7) = set_intersection2(C!6, B!7))) | (in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(C!6, B!7)) <=> (~((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), B!7)) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), C!6))))))) | (~((set_intersection2(C!6, B!7) = set_intersection2(C!6, B!7)) | (in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), set_intersection2(C!6, B!7)) <=> ((~in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), C!6)) | (~in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), B!7))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B))))))))) | ((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(C!6, B!7))) <=> ((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), B!7)) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), C!6)))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[95])).
% 0.19/0.42 tff(97,plain,
% 0.19/0.42 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B))))))))) | (~((~((~(set_intersection2(C!6, B!7) = set_intersection2(C!6, B!7))) | (in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(C!6, B!7)) <=> (~((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), B!7)) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), C!6))))))) | (~((set_intersection2(C!6, B!7) = set_intersection2(C!6, B!7)) | (in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), set_intersection2(C!6, B!7)) <=> ((~in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), C!6)) | (~in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), B!7))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B))))))))) | ((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(C!6, B!7))) <=> ((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), B!7)) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), C!6)))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[96, 73])).
% 0.19/0.42 tff(98,plain,
% 0.19/0.42 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B))))))))) | (~((~((~(set_intersection2(C!6, B!7) = set_intersection2(C!6, B!7))) | (in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(C!6, B!7)) <=> (~((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), B!7)) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), C!6))))))) | (~((set_intersection2(C!6, B!7) = set_intersection2(C!6, B!7)) | (in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), set_intersection2(C!6, B!7)) <=> ((~in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), C!6)) | (~in(tptp_fun_D_3(set_intersection2(C!6, B!7), B!7, C!6), B!7))))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(99,plain,
% 0.19/0.42 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B))))))))) | ((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(C!6, B!7))) <=> ((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), B!7)) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), C!6))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.19/0.43 tff(100,plain,
% 0.19/0.43 ((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(C!6, B!7))) <=> ((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), B!7)) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), C!6)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[99, 72])).
% 0.19/0.43 tff(101,plain,
% 0.19/0.43 (((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), A!8)) | in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(B!7, C!6))) | in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), A!8)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(102,plain,
% 0.19/0.43 (in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), A!8)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[101, 48])).
% 0.19/0.43 tff(103,plain,
% 0.19/0.43 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))) | (~((~((~subset(A!8, B!7)) | ![C: $i] : ((~in(C, A!8)) | in(C, B!7)))) | (~(subset(A!8, B!7) | (~((~in(tptp_fun_C_2(B!7, A!8), A!8)) | in(tptp_fun_C_2(B!7, A!8), B!7)))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(104,plain,
% 0.19/0.43 (~((~((~subset(A!8, B!7)) | ![C: $i] : ((~in(C, A!8)) | in(C, B!7)))) | (~(subset(A!8, B!7) | (~((~in(tptp_fun_C_2(B!7, A!8), A!8)) | in(tptp_fun_C_2(B!7, A!8), B!7))))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[103, 29])).
% 0.19/0.43 tff(105,plain,
% 0.19/0.43 (((~((~subset(A!8, B!7)) | ![C: $i] : ((~in(C, A!8)) | in(C, B!7)))) | (~(subset(A!8, B!7) | (~((~in(tptp_fun_C_2(B!7, A!8), A!8)) | in(tptp_fun_C_2(B!7, A!8), B!7)))))) | ((~subset(A!8, B!7)) | ![C: $i] : ((~in(C, A!8)) | in(C, B!7)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(106,plain,
% 0.19/0.43 ((~subset(A!8, B!7)) | ![C: $i] : ((~in(C, A!8)) | in(C, B!7))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.19/0.43 tff(107,plain,
% 0.19/0.43 (subset(A!8, B!7) & subset(A!8, C!6)),
% 0.19/0.43 inference(or_elim,[status(thm)],[44])).
% 0.19/0.43 tff(108,plain,
% 0.19/0.43 (subset(A!8, B!7)),
% 0.19/0.43 inference(and_elim,[status(thm)],[107])).
% 0.19/0.43 tff(109,plain,
% 0.19/0.43 ((~((~subset(A!8, B!7)) | ![C: $i] : ((~in(C, A!8)) | in(C, B!7)))) | (~subset(A!8, B!7)) | ![C: $i] : ((~in(C, A!8)) | in(C, B!7))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(110,plain,
% 0.19/0.43 ((~((~subset(A!8, B!7)) | ![C: $i] : ((~in(C, A!8)) | in(C, B!7)))) | ![C: $i] : ((~in(C, A!8)) | in(C, B!7))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.19/0.43 tff(111,plain,
% 0.19/0.43 (![C: $i] : ((~in(C, A!8)) | in(C, B!7))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[110, 106])).
% 0.19/0.43 tff(112,plain,
% 0.19/0.43 (((~![C: $i] : ((~in(C, A!8)) | in(C, B!7))) | ((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), A!8)) | in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), B!7))) <=> ((~![C: $i] : ((~in(C, A!8)) | in(C, B!7))) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), A!8)) | in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), B!7))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(113,plain,
% 0.19/0.43 ((~![C: $i] : ((~in(C, A!8)) | in(C, B!7))) | ((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), A!8)) | in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), B!7))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(114,plain,
% 0.19/0.43 ((~![C: $i] : ((~in(C, A!8)) | in(C, B!7))) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), A!8)) | in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), B!7)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.19/0.43 tff(115,plain,
% 0.19/0.43 (in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), B!7)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[114, 111, 102])).
% 0.19/0.43 tff(116,plain,
% 0.19/0.43 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))) | (~((~((~subset(A!8, C!6)) | ![C: $i] : ((~in(C, A!8)) | in(C, C!6)))) | (~(subset(A!8, C!6) | (~((~in(tptp_fun_C_2(C!6, A!8), A!8)) | in(tptp_fun_C_2(C!6, A!8), C!6)))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(117,plain,
% 0.19/0.43 (~((~((~subset(A!8, C!6)) | ![C: $i] : ((~in(C, A!8)) | in(C, C!6)))) | (~(subset(A!8, C!6) | (~((~in(tptp_fun_C_2(C!6, A!8), A!8)) | in(tptp_fun_C_2(C!6, A!8), C!6))))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[116, 29])).
% 0.19/0.43 tff(118,plain,
% 0.19/0.43 (((~((~subset(A!8, C!6)) | ![C: $i] : ((~in(C, A!8)) | in(C, C!6)))) | (~(subset(A!8, C!6) | (~((~in(tptp_fun_C_2(C!6, A!8), A!8)) | in(tptp_fun_C_2(C!6, A!8), C!6)))))) | ((~subset(A!8, C!6)) | ![C: $i] : ((~in(C, A!8)) | in(C, C!6)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(119,plain,
% 0.19/0.43 ((~subset(A!8, C!6)) | ![C: $i] : ((~in(C, A!8)) | in(C, C!6))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[118, 117])).
% 0.19/0.43 tff(120,plain,
% 0.19/0.43 (subset(A!8, C!6)),
% 0.19/0.43 inference(and_elim,[status(thm)],[107])).
% 0.19/0.43 tff(121,plain,
% 0.19/0.43 ((~((~subset(A!8, C!6)) | ![C: $i] : ((~in(C, A!8)) | in(C, C!6)))) | (~subset(A!8, C!6)) | ![C: $i] : ((~in(C, A!8)) | in(C, C!6))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(122,plain,
% 0.19/0.43 ((~((~subset(A!8, C!6)) | ![C: $i] : ((~in(C, A!8)) | in(C, C!6)))) | ![C: $i] : ((~in(C, A!8)) | in(C, C!6))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.19/0.43 tff(123,plain,
% 0.19/0.43 (![C: $i] : ((~in(C, A!8)) | in(C, C!6))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[122, 119])).
% 0.19/0.43 tff(124,plain,
% 0.19/0.43 (((~![C: $i] : ((~in(C, A!8)) | in(C, C!6))) | ((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), A!8)) | in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), C!6))) <=> ((~![C: $i] : ((~in(C, A!8)) | in(C, C!6))) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), A!8)) | in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), C!6))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(125,plain,
% 0.19/0.43 ((~![C: $i] : ((~in(C, A!8)) | in(C, C!6))) | ((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), A!8)) | in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), C!6))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(126,plain,
% 0.19/0.43 ((~![C: $i] : ((~in(C, A!8)) | in(C, C!6))) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), A!8)) | in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), C!6)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.19/0.43 tff(127,plain,
% 0.19/0.43 (in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), C!6)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[126, 123, 102])).
% 0.19/0.43 tff(128,plain,
% 0.19/0.43 ((~((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), B!7)) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), C!6)))) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), B!7)) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), C!6))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(129,plain,
% 0.19/0.43 (~((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), B!7)) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), C!6)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[128, 127, 115])).
% 0.19/0.43 tff(130,plain,
% 0.19/0.43 ((~((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(C!6, B!7))) <=> ((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), B!7)) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), C!6))))) | in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(C!6, B!7)) | ((~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), B!7)) | (~in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), C!6)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(131,plain,
% 0.19/0.43 (in(tptp_fun_C_2(set_intersection2(B!7, C!6), A!8), set_intersection2(C!6, B!7))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[130, 129, 100])).
% 0.19/0.43 tff(132,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[131, 51])).
% 0.19/0.43 % SZS output end Proof
%------------------------------------------------------------------------------