%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU128+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:57 AM UTC 2025
% Result : Theorem 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU128+1 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n012.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 06:05:40 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.21/0.39 % SZS status Theorem
% 0.21/0.39 % SZS output start Proof
% 0.21/0.39 tff(in_type, type, (
% 0.21/0.39 in: ( $i * $i ) > $o)).
% 0.21/0.39 tff(set_intersection2_type, type, (
% 0.21/0.39 set_intersection2: ( $i * $i ) > $i)).
% 0.21/0.39 tff(tptp_fun_B_5_type, type, (
% 0.21/0.39 tptp_fun_B_5: $i)).
% 0.21/0.39 tff(tptp_fun_C_4_type, type, (
% 0.21/0.39 tptp_fun_C_4: $i)).
% 0.21/0.39 tff(tptp_fun_C_0_type, type, (
% 0.21/0.39 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.21/0.39 tff(tptp_fun_A_6_type, type, (
% 0.21/0.39 tptp_fun_A_6: $i)).
% 0.21/0.39 tff(subset_type, type, (
% 0.21/0.39 subset: ( $i * $i ) > $o)).
% 0.21/0.39 tff(tptp_fun_D_1_type, type, (
% 0.21/0.39 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 0.21/0.39 tff(1,plain,
% 0.21/0.39 (^[A: $i, B: $i] : refl((set_intersection2(A, B) = set_intersection2(B, A)) <=> (set_intersection2(A, B) = set_intersection2(B, A)))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(2,plain,
% 0.21/0.39 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.39 tff(3,plain,
% 0.21/0.39 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(4,axiom,(![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 0.21/0.39 tff(5,plain,
% 0.21/0.39 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.39 tff(6,plain,(
% 0.21/0.39 ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.21/0.39 inference(skolemize,[status(sab)],[5])).
% 0.21/0.39 tff(7,plain,
% 0.21/0.39 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.39 tff(8,plain,
% 0.21/0.39 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(B!5, C!4) = set_intersection2(C!4, B!5))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(9,plain,
% 0.21/0.39 (set_intersection2(B!5, C!4) = set_intersection2(C!4, B!5)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.39 tff(10,plain,
% 0.21/0.39 (set_intersection2(C!4, B!5) = set_intersection2(B!5, C!4)),
% 0.21/0.39 inference(symmetry,[status(thm)],[9])).
% 0.21/0.39 tff(11,plain,
% 0.21/0.39 (in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(C!4, B!5)) <=> in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(B!5, C!4))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[10])).
% 0.21/0.39 tff(12,plain,
% 0.21/0.39 (in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(B!5, C!4)) <=> in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(C!4, B!5))),
% 0.21/0.39 inference(symmetry,[status(thm)],[11])).
% 0.21/0.39 tff(13,plain,
% 0.21/0.39 ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(B!5, C!4))) <=> (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(C!4, B!5)))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[12])).
% 0.21/0.39 tff(14,plain,
% 0.21/0.39 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(15,plain,
% 0.21/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(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_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[14])).
% 0.21/0.39 tff(16,plain,
% 0.21/0.39 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(17,plain,
% 0.21/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(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_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[16])).
% 0.21/0.39 tff(18,plain,
% 0.21/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(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_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.21/0.39 inference(transitivity,[status(thm)],[17, 15])).
% 0.21/0.39 tff(19,plain,
% 0.21/0.39 (^[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_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(20,plain,
% 0.21/0.39 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(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_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[19])).
% 0.21/0.39 tff(21,plain,
% 0.21/0.39 (![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)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(22,plain,
% 0.21/0.39 (^[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))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(23,plain,
% 0.21/0.39 (![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)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[22])).
% 0.21/0.39 tff(24,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_tarski')).
% 0.21/0.39 tff(25,plain,
% 0.21/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.21/0.39 tff(26,plain,
% 0.21/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.21/0.39 tff(27,plain,(
% 0.21/0.39 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))),
% 0.21/0.39 inference(skolemize,[status(sab)],[26])).
% 0.21/0.39 tff(28,plain,
% 0.21/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.21/0.39 tff(29,plain,
% 0.21/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.21/0.39 tff(30,plain,
% 0.21/0.39 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))) | (~((~((~subset(A!6, set_intersection2(B!5, C!4))) | ![C: $i] : ((~in(C, A!6)) | in(C, set_intersection2(B!5, C!4))))) | (~(subset(A!6, set_intersection2(B!5, C!4)) | (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), A!6)) | in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(B!5, C!4))))))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(31,plain,
% 0.21/0.39 (~((~((~subset(A!6, set_intersection2(B!5, C!4))) | ![C: $i] : ((~in(C, A!6)) | in(C, set_intersection2(B!5, C!4))))) | (~(subset(A!6, set_intersection2(B!5, C!4)) | (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), A!6)) | in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(B!5, C!4)))))))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.21/0.39 tff(32,plain,
% 0.21/0.39 (((~((~subset(A!6, set_intersection2(B!5, C!4))) | ![C: $i] : ((~in(C, A!6)) | in(C, set_intersection2(B!5, C!4))))) | (~(subset(A!6, set_intersection2(B!5, C!4)) | (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), A!6)) | in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(B!5, C!4))))))) | (subset(A!6, set_intersection2(B!5, C!4)) | (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), A!6)) | in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(B!5, C!4)))))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(33,plain,
% 0.21/0.39 (subset(A!6, set_intersection2(B!5, C!4)) | (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), A!6)) | in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(B!5, C!4))))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.21/0.39 tff(34,plain,
% 0.21/0.39 ((~![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))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(35,plain,
% 0.21/0.39 ((~![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))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(36,axiom,(~![A: $i, B: $i, C: $i] : ((subset(A, B) & subset(A, C)) => subset(A, set_intersection2(B, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t19_xboole_1')).
% 0.21/0.39 tff(37,plain,
% 0.21/0.39 (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(A, C))) | subset(A, set_intersection2(B, C)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.21/0.39 tff(38,plain,
% 0.21/0.39 (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(A, C))) | subset(A, set_intersection2(B, C)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[37, 34])).
% 0.21/0.39 tff(39,plain,
% 0.21/0.39 (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(A, C))) | subset(A, set_intersection2(B, C)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.21/0.39 tff(40,plain,
% 0.21/0.39 (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(A, C))) | subset(A, set_intersection2(B, C)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[39, 34])).
% 0.21/0.39 tff(41,plain,(
% 0.21/0.39 ~((~(subset(A!6, B!5) & subset(A!6, C!4))) | subset(A!6, set_intersection2(B!5, C!4)))),
% 0.21/0.39 inference(skolemize,[status(sab)],[40])).
% 0.21/0.39 tff(42,plain,
% 0.21/0.39 (~subset(A!6, set_intersection2(B!5, C!4))),
% 0.21/0.39 inference(or_elim,[status(thm)],[41])).
% 0.21/0.39 tff(43,plain,
% 0.21/0.39 ((~(subset(A!6, set_intersection2(B!5, C!4)) | (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), A!6)) | in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(B!5, C!4)))))) | subset(A!6, set_intersection2(B!5, C!4)) | (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), A!6)) | in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(B!5, C!4))))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(44,plain,
% 0.21/0.39 ((~(subset(A!6, set_intersection2(B!5, C!4)) | (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), A!6)) | in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(B!5, C!4)))))) | (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), A!6)) | in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(B!5, C!4))))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.21/0.40 tff(45,plain,
% 0.21/0.40 (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), A!6)) | in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(B!5, C!4)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[44, 33])).
% 0.21/0.40 tff(46,plain,
% 0.21/0.40 (((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), A!6)) | in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(B!5, C!4))) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(B!5, C!4)))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(47,plain,
% 0.21/0.40 (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(B!5, C!4))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.21/0.40 tff(48,plain,
% 0.21/0.40 (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(C!4, B!5))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[47, 13])).
% 0.21/0.40 tff(49,plain,
% 0.21/0.40 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(50,plain,
% 0.21/0.40 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[49])).
% 0.21/0.40 tff(51,plain,
% 0.21/0.40 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.21/0.40 inference(pull_quant,[status(thm)],[])).
% 0.21/0.40 tff(52,plain,
% 0.21/0.40 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C)))) <=> ![D: $i] : ((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))), ((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) <=> (~![D: $i] : ((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))))), pull_quant((~![D: $i] : ((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C)))))), ((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))))), (((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))) <=> (?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))), pull_quant((?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))), (((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))), ((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> (~?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))))), pull_quant((~?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))), ((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(53,plain,
% 0.21/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[52])).
% 0.21/0.40 tff(54,plain,
% 0.21/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[53, 51])).
% 0.21/0.40 tff(55,plain,
% 0.21/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[54, 50])).
% 0.21/0.40 tff(56,plain,
% 0.21/0.40 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(57,plain,
% 0.21/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[56])).
% 0.21/0.40 tff(58,plain,
% 0.21/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[57, 55])).
% 0.21/0.40 tff(59,plain,
% 0.21/0.40 (^[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, B)) | (~in(D, A))) <=> in(D, C))))), rewrite(((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & in(tptp_fun_D_1(C, B, A), B))))) <=> ((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))), ((((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & in(tptp_fun_D_1(C, B, A), B)))))) <=> (((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C)))) & ((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))), rewrite((((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C)))) & ((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))), ((((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & in(tptp_fun_D_1(C, B, A), B)))))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(60,plain,
% 0.21/0.40 (![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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & in(tptp_fun_D_1(C, B, A), B)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[59])).
% 0.21/0.40 tff(61,plain,
% 0.21/0.40 (![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))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 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/sandbox/benchmark/theBenchmark.p','d3_xboole_0')).
% 0.21/0.40 tff(63,plain,
% 0.21/0.40 (![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.21/0.40 tff(64,plain,(
% 0.21/0.40 ![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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & in(tptp_fun_D_1(C, B, A), B))))))),
% 0.21/0.40 inference(skolemize,[status(sab)],[63])).
% 0.21/0.40 tff(65,plain,
% 0.21/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.21/0.40 tff(66,plain,
% 0.21/0.40 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.21/0.40 tff(67,plain,
% 0.21/0.40 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~(((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4))) <=> in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(C!4, B!5))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~(((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4))) <=> in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(C!4, B!5)))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(68,plain,
% 0.21/0.40 ((~(((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4))) <=> in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(C!4, B!5)))) <=> (~(((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4))) <=> in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(C!4, B!5))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(69,plain,
% 0.21/0.40 (((((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4))) <=> in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(C!4, B!5))) | $false) <=> (((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4))) <=> in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(C!4, B!5)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(70,plain,
% 0.21/0.41 ((~$true) <=> $false),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(71,plain,
% 0.21/0.41 (($true | (((~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), B!5))) <=> in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), set_intersection2(C!4, B!5)))) <=> $true),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(72,plain,
% 0.21/0.41 ((((~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), B!5))) <=> in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), set_intersection2(C!4, B!5))) <=> (((~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), B!5))) <=> in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), set_intersection2(C!4, B!5)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(73,plain,
% 0.21/0.41 ((set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5)) <=> $true),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(74,plain,
% 0.21/0.41 (((set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5)) | (((~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), B!5))) <=> in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), set_intersection2(C!4, B!5)))) <=> ($true | (((~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), B!5))) <=> in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), set_intersection2(C!4, B!5))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[73, 72])).
% 0.21/0.41 tff(75,plain,
% 0.21/0.41 (((set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5)) | (((~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), B!5))) <=> in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), set_intersection2(C!4, B!5)))) <=> $true),
% 0.21/0.41 inference(transitivity,[status(thm)],[74, 71])).
% 0.21/0.41 tff(76,plain,
% 0.21/0.41 ((~((set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5)) | (((~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), B!5))) <=> in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), set_intersection2(C!4, B!5))))) <=> (~$true)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[75])).
% 0.21/0.41 tff(77,plain,
% 0.21/0.41 ((~((set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5)) | (((~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), B!5))) <=> in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), set_intersection2(C!4, B!5))))) <=> $false),
% 0.21/0.41 inference(transitivity,[status(thm)],[76, 70])).
% 0.21/0.41 tff(78,plain,
% 0.21/0.41 ((~(~(((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4))) <=> in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(C!4, B!5))))) <=> (((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4))) <=> in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(C!4, B!5)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(79,plain,
% 0.21/0.41 (($false | (~(((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4))) <=> in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(C!4, B!5))))) <=> (~(((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4))) <=> in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(C!4, B!5))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(80,plain,
% 0.21/0.41 ((~(set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5))) <=> (~$true)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[73])).
% 0.21/0.41 tff(81,plain,
% 0.21/0.41 ((~(set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5))) <=> $false),
% 0.21/0.41 inference(transitivity,[status(thm)],[80, 70])).
% 0.21/0.41 tff(82,plain,
% 0.21/0.41 (((~(set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5))) | (~(((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4))) <=> in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(C!4, B!5))))) <=> ($false | (~(((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4))) <=> in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(C!4, B!5)))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[81, 68])).
% 0.21/0.41 tff(83,plain,
% 0.21/0.41 (((~(set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5))) | (~(((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4))) <=> in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(C!4, B!5))))) <=> (~(((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4))) <=> in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(C!4, B!5))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[82, 79])).
% 0.21/0.41 tff(84,plain,
% 0.21/0.41 ((~((~(set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5))) | (~(((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4))) <=> in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(C!4, B!5)))))) <=> (~(~(((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4))) <=> in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(C!4, B!5)))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[83])).
% 0.21/0.41 tff(85,plain,
% 0.21/0.41 ((~((~(set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5))) | (~(((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4))) <=> in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(C!4, B!5)))))) <=> (((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4))) <=> in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(C!4, B!5)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[84, 78])).
% 0.21/0.41 tff(86,plain,
% 0.21/0.41 (((~((~(set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5))) | (~(((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4))) <=> in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(C!4, B!5)))))) | (~((set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5)) | (((~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), B!5))) <=> in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), set_intersection2(C!4, B!5)))))) <=> ((((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4))) <=> in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(C!4, B!5))) | $false)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[85, 77])).
% 0.21/0.41 tff(87,plain,
% 0.21/0.41 (((~((~(set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5))) | (~(((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4))) <=> in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(C!4, B!5)))))) | (~((set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5)) | (((~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), B!5))) <=> in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), set_intersection2(C!4, B!5)))))) <=> (((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4))) <=> in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(C!4, B!5)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[86, 69])).
% 0.21/0.41 tff(88,plain,
% 0.21/0.41 ((~((~((~(set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5))) | (~(((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4))) <=> in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(C!4, B!5)))))) | (~((set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5)) | (((~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), B!5))) <=> in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), set_intersection2(C!4, B!5))))))) <=> (~(((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4))) <=> in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(C!4, B!5))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[87])).
% 0.21/0.41 tff(89,plain,
% 0.21/0.41 ((~((~((~(set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5))) | (~(((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4))) <=> in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(C!4, B!5)))))) | (~((set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5)) | (((~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), B!5))) <=> in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), set_intersection2(C!4, B!5))))))) <=> (~(((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4))) <=> in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(C!4, B!5))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[88, 68])).
% 0.21/0.41 tff(90,plain,
% 0.21/0.41 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~((~((~(set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5))) | (~(((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4))) <=> in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(C!4, B!5)))))) | (~((set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5)) | (((~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), B!5))) <=> in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), set_intersection2(C!4, B!5)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~(((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4))) <=> in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(C!4, B!5)))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[89])).
% 0.21/0.41 tff(91,plain,
% 0.21/0.41 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~((~((~(set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5))) | (~(((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4))) <=> in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(C!4, B!5)))))) | (~((set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5)) | (((~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), B!5))) <=> in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), set_intersection2(C!4, B!5)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~(((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4))) <=> in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(C!4, B!5)))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[90, 67])).
% 0.21/0.42 tff(92,plain,
% 0.21/0.42 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~((~((~(set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5))) | (~(((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4))) <=> in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(C!4, B!5)))))) | (~((set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5)) | (((~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), B!5))) <=> in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), set_intersection2(C!4, B!5)))))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(93,plain,
% 0.21/0.42 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~(((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4))) <=> in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(C!4, B!5))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.21/0.42 tff(94,plain,
% 0.21/0.42 (~(((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4))) <=> in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(C!4, B!5)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[93, 66])).
% 0.21/0.42 tff(95,plain,
% 0.21/0.42 (((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), A!6)) | in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(B!5, C!4))) | in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), A!6)),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(96,plain,
% 0.21/0.42 (in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), A!6)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[95, 45])).
% 0.21/0.42 tff(97,plain,
% 0.21/0.42 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))) | (~((~((~subset(A!6, C!4)) | ![C: $i] : ((~in(C, A!6)) | in(C, C!4)))) | (~(subset(A!6, C!4) | (~((~in(tptp_fun_C_0(C!4, A!6), A!6)) | in(tptp_fun_C_0(C!4, A!6), C!4)))))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(98,plain,
% 0.21/0.42 (~((~((~subset(A!6, C!4)) | ![C: $i] : ((~in(C, A!6)) | in(C, C!4)))) | (~(subset(A!6, C!4) | (~((~in(tptp_fun_C_0(C!4, A!6), A!6)) | in(tptp_fun_C_0(C!4, A!6), C!4))))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[97, 29])).
% 0.21/0.42 tff(99,plain,
% 0.21/0.42 (((~((~subset(A!6, C!4)) | ![C: $i] : ((~in(C, A!6)) | in(C, C!4)))) | (~(subset(A!6, C!4) | (~((~in(tptp_fun_C_0(C!4, A!6), A!6)) | in(tptp_fun_C_0(C!4, A!6), C!4)))))) | ((~subset(A!6, C!4)) | ![C: $i] : ((~in(C, A!6)) | in(C, C!4)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(100,plain,
% 0.21/0.42 ((~subset(A!6, C!4)) | ![C: $i] : ((~in(C, A!6)) | in(C, C!4))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.21/0.42 tff(101,plain,
% 0.21/0.42 (subset(A!6, B!5) & subset(A!6, C!4)),
% 0.21/0.42 inference(or_elim,[status(thm)],[41])).
% 0.21/0.42 tff(102,plain,
% 0.21/0.42 (subset(A!6, C!4)),
% 0.21/0.42 inference(and_elim,[status(thm)],[101])).
% 0.21/0.42 tff(103,plain,
% 0.21/0.42 ((~((~subset(A!6, C!4)) | ![C: $i] : ((~in(C, A!6)) | in(C, C!4)))) | (~subset(A!6, C!4)) | ![C: $i] : ((~in(C, A!6)) | in(C, C!4))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(104,plain,
% 0.21/0.42 ((~((~subset(A!6, C!4)) | ![C: $i] : ((~in(C, A!6)) | in(C, C!4)))) | ![C: $i] : ((~in(C, A!6)) | in(C, C!4))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.21/0.42 tff(105,plain,
% 0.21/0.42 (![C: $i] : ((~in(C, A!6)) | in(C, C!4))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[104, 100])).
% 0.21/0.42 tff(106,plain,
% 0.21/0.42 (((~![C: $i] : ((~in(C, A!6)) | in(C, C!4))) | ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), A!6)) | in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4))) <=> ((~![C: $i] : ((~in(C, A!6)) | in(C, C!4))) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), A!6)) | in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(107,plain,
% 0.21/0.42 ((~![C: $i] : ((~in(C, A!6)) | in(C, C!4))) | ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), A!6)) | in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(108,plain,
% 0.21/0.42 ((~![C: $i] : ((~in(C, A!6)) | in(C, C!4))) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), A!6)) | in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.21/0.42 tff(109,plain,
% 0.21/0.42 (in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[108, 105, 96])).
% 0.21/0.42 tff(110,plain,
% 0.21/0.42 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))) | (~((~((~subset(A!6, B!5)) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5)))) | (~(subset(A!6, B!5) | (~((~in(tptp_fun_C_0(B!5, A!6), A!6)) | in(tptp_fun_C_0(B!5, A!6), B!5)))))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(111,plain,
% 0.21/0.42 (~((~((~subset(A!6, B!5)) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5)))) | (~(subset(A!6, B!5) | (~((~in(tptp_fun_C_0(B!5, A!6), A!6)) | in(tptp_fun_C_0(B!5, A!6), B!5))))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[110, 29])).
% 0.21/0.42 tff(112,plain,
% 0.21/0.42 (((~((~subset(A!6, B!5)) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5)))) | (~(subset(A!6, B!5) | (~((~in(tptp_fun_C_0(B!5, A!6), A!6)) | in(tptp_fun_C_0(B!5, A!6), B!5)))))) | ((~subset(A!6, B!5)) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(113,plain,
% 0.21/0.42 ((~subset(A!6, B!5)) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.21/0.42 tff(114,plain,
% 0.21/0.42 (subset(A!6, B!5)),
% 0.21/0.42 inference(and_elim,[status(thm)],[101])).
% 0.21/0.42 tff(115,plain,
% 0.21/0.42 ((~((~subset(A!6, B!5)) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5)))) | (~subset(A!6, B!5)) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(116,plain,
% 0.21/0.42 ((~((~subset(A!6, B!5)) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5)))) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[115, 114])).
% 0.21/0.42 tff(117,plain,
% 0.21/0.42 (![C: $i] : ((~in(C, A!6)) | in(C, B!5))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[116, 113])).
% 0.21/0.42 tff(118,plain,
% 0.21/0.42 (((~![C: $i] : ((~in(C, A!6)) | in(C, B!5))) | ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), A!6)) | in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5))) <=> ((~![C: $i] : ((~in(C, A!6)) | in(C, B!5))) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), A!6)) | in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(119,plain,
% 0.21/0.42 ((~![C: $i] : ((~in(C, A!6)) | in(C, B!5))) | ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), A!6)) | in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(120,plain,
% 0.21/0.42 ((~![C: $i] : ((~in(C, A!6)) | in(C, B!5))) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), A!6)) | in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.21/0.42 tff(121,plain,
% 0.21/0.42 (in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[120, 117, 96])).
% 0.21/0.42 tff(122,plain,
% 0.21/0.42 ((~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4)))) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(123,plain,
% 0.21/0.42 (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[122, 121, 109])).
% 0.21/0.42 tff(124,plain,
% 0.21/0.42 ((((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4))) <=> in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(C!4, B!5))) | ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4))) | in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(C!4, B!5))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(125,plain,
% 0.21/0.43 ((((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), C!4))) <=> in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(C!4, B!5))) | in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(C!4, B!5))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[124, 123])).
% 0.21/0.43 tff(126,plain,
% 0.21/0.43 (in(tptp_fun_C_0(set_intersection2(B!5, C!4), A!6), set_intersection2(C!4, B!5))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[125, 94])).
% 0.21/0.43 tff(127,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[126, 48])).
% 0.21/0.43 % SZS output end Proof
% 0.21/0.43 % E exiting
%------------------------------------------------------------------------------