%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU130+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:26:58 AM UTC 2025
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU130+1 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n013.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 : Fri Jun 20 06:06:53 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(in_type, type, (
% 0.12/0.38 in: ( $i * $i ) > $o)).
% 0.12/0.38 tff(tptp_fun_B_4_type, type, (
% 0.12/0.38 tptp_fun_B_4: $i)).
% 0.12/0.38 tff(tptp_fun_C_0_type, type, (
% 0.12/0.38 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.12/0.38 tff(tptp_fun_A_5_type, type, (
% 0.12/0.38 tptp_fun_A_5: $i)).
% 0.12/0.38 tff(set_intersection2_type, type, (
% 0.12/0.38 set_intersection2: ( $i * $i ) > $i)).
% 0.12/0.38 tff(subset_type, type, (
% 0.12/0.38 subset: ( $i * $i ) > $o)).
% 0.12/0.38 tff(tptp_fun_D_1_type, type, (
% 0.12/0.38 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 (^[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))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (![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)))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (^[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))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (![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)))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (![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)))))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[4, 2])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (^[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)))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (![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)))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[6])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (![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)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (^[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))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (![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)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[9])).
% 0.12/0.38 tff(11,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')).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.12/0.38 tff(14,plain,(
% 0.12/0.38 ![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)))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[13])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (![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)))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (![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)))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 ((~![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!5, set_intersection2(B!4, A!5))) | ![C: $i] : ((~in(C, A!5)) | in(C, set_intersection2(B!4, A!5))))) | (~(subset(A!5, set_intersection2(B!4, A!5)) | (~((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5))))))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (~((~((~subset(A!5, set_intersection2(B!4, A!5))) | ![C: $i] : ((~in(C, A!5)) | in(C, set_intersection2(B!4, A!5))))) | (~(subset(A!5, set_intersection2(B!4, A!5)) | (~((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5)))))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (((~((~subset(A!5, set_intersection2(B!4, A!5))) | ![C: $i] : ((~in(C, A!5)) | in(C, set_intersection2(B!4, A!5))))) | (~(subset(A!5, set_intersection2(B!4, A!5)) | (~((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5))))))) | (subset(A!5, set_intersection2(B!4, A!5)) | (~((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5)))))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (subset(A!5, set_intersection2(B!4, A!5)) | (~((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (^[A: $i, B: $i] : refl((set_intersection2(A, B) = set_intersection2(B, A)) <=> (set_intersection2(A, B) = set_intersection2(B, A)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[21])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(24,axiom,(![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.12/0.38 tff(26,plain,(
% 0.12/0.38 ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.12/0.38 inference(skolemize,[status(sab)],[25])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(A!5, B!4) = set_intersection2(B!4, A!5))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (set_intersection2(A!5, B!4) = set_intersection2(B!4, A!5)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (set_intersection2(B!4, A!5) = set_intersection2(A!5, B!4)),
% 0.12/0.38 inference(symmetry,[status(thm)],[29])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 (subset(set_intersection2(B!4, A!5), A!5) <=> subset(set_intersection2(A!5, B!4), A!5)),
% 0.12/0.38 inference(monotonicity,[status(thm)],[30])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 (subset(set_intersection2(A!5, B!4), A!5) <=> subset(set_intersection2(B!4, A!5), A!5)),
% 0.12/0.38 inference(symmetry,[status(thm)],[31])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 (^[A: $i, B: $i] : refl(subset(set_intersection2(A, B), A) <=> subset(set_intersection2(A, B), A))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 (![A: $i, B: $i] : subset(set_intersection2(A, B), A) <=> ![A: $i, B: $i] : subset(set_intersection2(A, B), A)),
% 0.12/0.38 inference(quant_intro,[status(thm)],[33])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 (![A: $i, B: $i] : subset(set_intersection2(A, B), A) <=> ![A: $i, B: $i] : subset(set_intersection2(A, B), A)),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(36,axiom,(![A: $i, B: $i] : subset(set_intersection2(A, B), A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t17_xboole_1')).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 (![A: $i, B: $i] : subset(set_intersection2(A, B), A)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.12/0.38 tff(38,plain,(
% 0.12/0.38 ![A: $i, B: $i] : subset(set_intersection2(A, B), A)),
% 0.12/0.38 inference(skolemize,[status(sab)],[37])).
% 0.12/0.38 tff(39,plain,
% 0.12/0.38 (![A: $i, B: $i] : subset(set_intersection2(A, B), A)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 ((~![A: $i, B: $i] : subset(set_intersection2(A, B), A)) | subset(set_intersection2(A!5, B!4), A!5)),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 (subset(set_intersection2(A!5, B!4), A!5)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.12/0.38 tff(42,plain,
% 0.12/0.38 (subset(set_intersection2(B!4, A!5), A!5)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[41, 32])).
% 0.12/0.38 tff(43,plain,
% 0.12/0.38 (^[A: $i, B: $i] : refl((~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(44,plain,
% 0.12/0.38 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[43])).
% 0.12/0.38 tff(45,plain,
% 0.12/0.38 (^[A: $i, B: $i] : trans(trans(monotonicity(rewrite((subset(A, B) & subset(B, A)) <=> (~((~subset(A, B)) | (~subset(B, A))))), (((A = B) <=> (subset(A, B) & subset(B, A))) <=> ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))))), rewrite(((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))), (((A = B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))))), rewrite((~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))), (((A = B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(46,plain,
% 0.12/0.38 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[45])).
% 0.21/0.38 tff(47,plain,
% 0.21/0.38 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(48,axiom,(![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d10_xboole_0')).
% 0.21/0.38 tff(49,plain,
% 0.21/0.38 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.21/0.38 tff(50,plain,(
% 0.21/0.38 ![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.21/0.38 inference(skolemize,[status(sab)],[49])).
% 0.21/0.38 tff(51,plain,
% 0.21/0.38 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.21/0.38 tff(52,plain,
% 0.21/0.38 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.21/0.38 tff(53,plain,
% 0.21/0.38 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))) | (~(((~subset(set_intersection2(B!4, A!5), A!5)) | (~subset(A!5, set_intersection2(B!4, A!5)))) <=> (set_intersection2(B!4, A!5) = A!5)))),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(54,plain,
% 0.21/0.38 (~(((~subset(set_intersection2(B!4, A!5), A!5)) | (~subset(A!5, set_intersection2(B!4, A!5)))) <=> (set_intersection2(B!4, A!5) = A!5))),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.21/0.38 tff(55,plain,
% 0.21/0.38 ((set_intersection2(B!4, A!5) = A!5) <=> (set_intersection2(A!5, B!4) = A!5)),
% 0.21/0.38 inference(monotonicity,[status(thm)],[30])).
% 0.21/0.38 tff(56,plain,
% 0.21/0.38 ((set_intersection2(A!5, B!4) = A!5) <=> (set_intersection2(B!4, A!5) = A!5)),
% 0.21/0.38 inference(symmetry,[status(thm)],[55])).
% 0.21/0.38 tff(57,plain,
% 0.21/0.38 ((~(set_intersection2(A!5, B!4) = A!5)) <=> (~(set_intersection2(B!4, A!5) = A!5))),
% 0.21/0.38 inference(monotonicity,[status(thm)],[56])).
% 0.21/0.38 tff(58,plain,
% 0.21/0.38 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) <=> (~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A)))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(59,plain,
% 0.21/0.38 ((~![A: $i, B: $i] : (subset(A, B) => (set_intersection2(A, B) = A))) <=> (~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A)))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(60,axiom,(~![A: $i, B: $i] : (subset(A, B) => (set_intersection2(A, B) = A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t28_xboole_1')).
% 0.21/0.38 tff(61,plain,
% 0.21/0.38 (~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.21/0.38 tff(62,plain,
% 0.21/0.38 (~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[61, 58])).
% 0.21/0.38 tff(63,plain,
% 0.21/0.38 (~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.21/0.38 tff(64,plain,
% 0.21/0.38 (~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[63, 58])).
% 0.21/0.38 tff(65,plain,(
% 0.21/0.38 ~((~subset(A!5, B!4)) | (set_intersection2(A!5, B!4) = A!5))),
% 0.21/0.38 inference(skolemize,[status(sab)],[64])).
% 0.21/0.38 tff(66,plain,
% 0.21/0.38 (~(set_intersection2(A!5, B!4) = A!5)),
% 0.21/0.38 inference(or_elim,[status(thm)],[65])).
% 0.21/0.38 tff(67,plain,
% 0.21/0.38 (~(set_intersection2(B!4, A!5) = A!5)),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[66, 57])).
% 0.21/0.38 tff(68,plain,
% 0.21/0.38 ((((~subset(set_intersection2(B!4, A!5), A!5)) | (~subset(A!5, set_intersection2(B!4, A!5)))) <=> (set_intersection2(B!4, A!5) = A!5)) | ((~subset(set_intersection2(B!4, A!5), A!5)) | (~subset(A!5, set_intersection2(B!4, A!5)))) | (set_intersection2(B!4, A!5) = A!5)),
% 0.21/0.38 inference(tautology,[status(thm)],[])).
% 0.21/0.38 tff(69,plain,
% 0.21/0.38 ((~subset(set_intersection2(B!4, A!5), A!5)) | (~subset(A!5, set_intersection2(B!4, A!5)))),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[68, 67, 54])).
% 0.21/0.38 tff(70,plain,
% 0.21/0.38 ((~((~subset(set_intersection2(B!4, A!5), A!5)) | (~subset(A!5, set_intersection2(B!4, A!5))))) | (~subset(set_intersection2(B!4, A!5), A!5)) | (~subset(A!5, set_intersection2(B!4, A!5)))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(71,plain,
% 0.21/0.39 (~subset(A!5, set_intersection2(B!4, A!5))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[70, 69, 42])).
% 0.21/0.39 tff(72,plain,
% 0.21/0.39 ((~(subset(A!5, set_intersection2(B!4, A!5)) | (~((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5)))))) | subset(A!5, set_intersection2(B!4, A!5)) | (~((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5))))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(73,plain,
% 0.21/0.39 ((~(subset(A!5, set_intersection2(B!4, A!5)) | (~((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5)))))) | (~((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5))))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.21/0.39 tff(74,plain,
% 0.21/0.39 (~((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[73, 20])).
% 0.21/0.39 tff(75,plain,
% 0.21/0.39 (((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5))) | in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(76,plain,
% 0.21/0.39 (in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.21/0.39 tff(77,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!5, B!4)) | ![C: $i] : ((~in(C, A!5)) | in(C, B!4)))) | (~(subset(A!5, B!4) | (~((~in(tptp_fun_C_0(B!4, A!5), A!5)) | in(tptp_fun_C_0(B!4, A!5), B!4)))))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(78,plain,
% 0.21/0.39 (~((~((~subset(A!5, B!4)) | ![C: $i] : ((~in(C, A!5)) | in(C, B!4)))) | (~(subset(A!5, B!4) | (~((~in(tptp_fun_C_0(B!4, A!5), A!5)) | in(tptp_fun_C_0(B!4, A!5), B!4))))))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[77, 16])).
% 0.21/0.39 tff(79,plain,
% 0.21/0.39 (((~((~subset(A!5, B!4)) | ![C: $i] : ((~in(C, A!5)) | in(C, B!4)))) | (~(subset(A!5, B!4) | (~((~in(tptp_fun_C_0(B!4, A!5), A!5)) | in(tptp_fun_C_0(B!4, A!5), B!4)))))) | ((~subset(A!5, B!4)) | ![C: $i] : ((~in(C, A!5)) | in(C, B!4)))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(80,plain,
% 0.21/0.39 ((~subset(A!5, B!4)) | ![C: $i] : ((~in(C, A!5)) | in(C, B!4))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.21/0.39 tff(81,plain,
% 0.21/0.39 (subset(A!5, B!4)),
% 0.21/0.39 inference(or_elim,[status(thm)],[65])).
% 0.21/0.39 tff(82,plain,
% 0.21/0.39 ((~((~subset(A!5, B!4)) | ![C: $i] : ((~in(C, A!5)) | in(C, B!4)))) | (~subset(A!5, B!4)) | ![C: $i] : ((~in(C, A!5)) | in(C, B!4))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(83,plain,
% 0.21/0.39 ((~((~subset(A!5, B!4)) | ![C: $i] : ((~in(C, A!5)) | in(C, B!4)))) | ![C: $i] : ((~in(C, A!5)) | in(C, B!4))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.21/0.39 tff(84,plain,
% 0.21/0.39 (![C: $i] : ((~in(C, A!5)) | in(C, B!4))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[83, 80])).
% 0.21/0.39 tff(85,plain,
% 0.21/0.39 (((~![C: $i] : ((~in(C, A!5)) | in(C, B!4))) | ((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4))) <=> ((~![C: $i] : ((~in(C, A!5)) | in(C, B!4))) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(86,plain,
% 0.21/0.39 ((~![C: $i] : ((~in(C, A!5)) | in(C, B!4))) | ((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(87,plain,
% 0.21/0.39 ((~![C: $i] : ((~in(C, A!5)) | in(C, B!4))) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.21/0.39 tff(88,plain,
% 0.21/0.39 (in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[87, 84, 76])).
% 0.21/0.39 tff(89,plain,
% 0.21/0.39 (^[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)))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(90,plain,
% 0.21/0.39 (![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))))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[89])).
% 0.21/0.39 tff(91,plain,
% 0.21/0.39 (![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))))))),
% 0.21/0.39 inference(pull_quant,[status(thm)],[])).
% 0.21/0.39 tff(92,plain,
% 0.21/0.39 (^[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))))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(93,plain,
% 0.21/0.39 (![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))))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[92])).
% 0.21/0.39 tff(94,plain,
% 0.21/0.39 (![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))))))),
% 0.21/0.39 inference(transitivity,[status(thm)],[93, 91])).
% 0.21/0.39 tff(95,plain,
% 0.21/0.39 (![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))))))),
% 0.21/0.39 inference(transitivity,[status(thm)],[94, 90])).
% 0.21/0.39 tff(96,plain,
% 0.21/0.39 (^[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)))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(97,plain,
% 0.21/0.39 (![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))))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[96])).
% 0.21/0.39 tff(98,plain,
% 0.21/0.39 (![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))))))),
% 0.21/0.39 inference(transitivity,[status(thm)],[97, 95])).
% 0.21/0.39 tff(99,plain,
% 0.21/0.39 (^[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))))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(100,plain,
% 0.21/0.39 (![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))))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[99])).
% 0.21/0.39 tff(101,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(102,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(103,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)],[102, 101])).
% 0.21/0.40 tff(104,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)],[103])).
% 0.21/0.40 tff(105,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)],[104, 100])).
% 0.21/0.40 tff(106,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)],[105, 98])).
% 0.21/0.40 tff(107,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!4, A!5), A!5), A!5)) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4))) <=> in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!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!4, A!5), A!5), A!5)) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4))) <=> in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5)))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(108,plain,
% 0.21/0.40 ((~(((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4))) <=> in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5)))) <=> (~(((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4))) <=> in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(109,plain,
% 0.21/0.40 (((((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4))) <=> in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5))) | $false) <=> (((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4))) <=> in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(110,plain,
% 0.21/0.40 ((~$true) <=> $false),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(111,plain,
% 0.21/0.40 (($true | (((~in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), B!4)) | (~in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), A!5))) <=> in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), set_intersection2(B!4, A!5)))) <=> $true),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(112,plain,
% 0.21/0.40 ((((~in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), B!4)) | (~in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), A!5))) <=> in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), set_intersection2(B!4, A!5))) <=> (((~in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), B!4)) | (~in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), A!5))) <=> in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), set_intersection2(B!4, A!5)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(113,plain,
% 0.21/0.40 ((set_intersection2(B!4, A!5) = set_intersection2(B!4, A!5)) <=> $true),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(114,plain,
% 0.21/0.40 (((set_intersection2(B!4, A!5) = set_intersection2(B!4, A!5)) | (((~in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), B!4)) | (~in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), A!5))) <=> in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), set_intersection2(B!4, A!5)))) <=> ($true | (((~in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), B!4)) | (~in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), A!5))) <=> in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), set_intersection2(B!4, A!5))))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[113, 112])).
% 0.21/0.40 tff(115,plain,
% 0.21/0.40 (((set_intersection2(B!4, A!5) = set_intersection2(B!4, A!5)) | (((~in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), B!4)) | (~in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), A!5))) <=> in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), set_intersection2(B!4, A!5)))) <=> $true),
% 0.21/0.40 inference(transitivity,[status(thm)],[114, 111])).
% 0.21/0.40 tff(116,plain,
% 0.21/0.40 ((~((set_intersection2(B!4, A!5) = set_intersection2(B!4, A!5)) | (((~in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), B!4)) | (~in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), A!5))) <=> in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), set_intersection2(B!4, A!5))))) <=> (~$true)),
% 0.21/0.40 inference(monotonicity,[status(thm)],[115])).
% 0.21/0.40 tff(117,plain,
% 0.21/0.40 ((~((set_intersection2(B!4, A!5) = set_intersection2(B!4, A!5)) | (((~in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), B!4)) | (~in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), A!5))) <=> in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), set_intersection2(B!4, A!5))))) <=> $false),
% 0.21/0.40 inference(transitivity,[status(thm)],[116, 110])).
% 0.21/0.40 tff(118,plain,
% 0.21/0.40 ((~(~(((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4))) <=> in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5))))) <=> (((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4))) <=> in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(119,plain,
% 0.21/0.40 (($false | (~(((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4))) <=> in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5))))) <=> (~(((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4))) <=> in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(120,plain,
% 0.21/0.40 ((~(set_intersection2(B!4, A!5) = set_intersection2(B!4, A!5))) <=> (~$true)),
% 0.21/0.40 inference(monotonicity,[status(thm)],[113])).
% 0.21/0.40 tff(121,plain,
% 0.21/0.40 ((~(set_intersection2(B!4, A!5) = set_intersection2(B!4, A!5))) <=> $false),
% 0.21/0.40 inference(transitivity,[status(thm)],[120, 110])).
% 0.21/0.40 tff(122,plain,
% 0.21/0.40 (((~(set_intersection2(B!4, A!5) = set_intersection2(B!4, A!5))) | (~(((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4))) <=> in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5))))) <=> ($false | (~(((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4))) <=> in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5)))))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[121, 108])).
% 0.21/0.40 tff(123,plain,
% 0.21/0.40 (((~(set_intersection2(B!4, A!5) = set_intersection2(B!4, A!5))) | (~(((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4))) <=> in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5))))) <=> (~(((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4))) <=> in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[122, 119])).
% 0.21/0.40 tff(124,plain,
% 0.21/0.40 ((~((~(set_intersection2(B!4, A!5) = set_intersection2(B!4, A!5))) | (~(((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4))) <=> in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5)))))) <=> (~(~(((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4))) <=> in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5)))))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[123])).
% 0.21/0.40 tff(125,plain,
% 0.21/0.40 ((~((~(set_intersection2(B!4, A!5) = set_intersection2(B!4, A!5))) | (~(((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4))) <=> in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5)))))) <=> (((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4))) <=> in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5)))),
% 0.21/0.40 inference(transitivity,[status(thm)],[124, 118])).
% 0.21/0.40 tff(126,plain,
% 0.21/0.40 (((~((~(set_intersection2(B!4, A!5) = set_intersection2(B!4, A!5))) | (~(((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4))) <=> in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5)))))) | (~((set_intersection2(B!4, A!5) = set_intersection2(B!4, A!5)) | (((~in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), B!4)) | (~in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), A!5))) <=> in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), set_intersection2(B!4, A!5)))))) <=> ((((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4))) <=> in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5))) | $false)),
% 0.21/0.40 inference(monotonicity,[status(thm)],[125, 117])).
% 0.21/0.40 tff(127,plain,
% 0.21/0.40 (((~((~(set_intersection2(B!4, A!5) = set_intersection2(B!4, A!5))) | (~(((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4))) <=> in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5)))))) | (~((set_intersection2(B!4, A!5) = set_intersection2(B!4, A!5)) | (((~in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), B!4)) | (~in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), A!5))) <=> in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), set_intersection2(B!4, A!5)))))) <=> (((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4))) <=> in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5)))),
% 0.21/0.40 inference(transitivity,[status(thm)],[126, 109])).
% 0.21/0.40 tff(128,plain,
% 0.21/0.40 ((~((~((~(set_intersection2(B!4, A!5) = set_intersection2(B!4, A!5))) | (~(((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4))) <=> in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5)))))) | (~((set_intersection2(B!4, A!5) = set_intersection2(B!4, A!5)) | (((~in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), B!4)) | (~in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), A!5))) <=> in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), set_intersection2(B!4, A!5))))))) <=> (~(((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4))) <=> in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[127])).
% 0.21/0.41 tff(129,plain,
% 0.21/0.41 ((~((~((~(set_intersection2(B!4, A!5) = set_intersection2(B!4, A!5))) | (~(((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4))) <=> in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5)))))) | (~((set_intersection2(B!4, A!5) = set_intersection2(B!4, A!5)) | (((~in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), B!4)) | (~in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), A!5))) <=> in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), set_intersection2(B!4, A!5))))))) <=> (~(((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4))) <=> in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[128, 108])).
% 0.21/0.41 tff(130,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(B!4, A!5) = set_intersection2(B!4, A!5))) | (~(((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4))) <=> in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5)))))) | (~((set_intersection2(B!4, A!5) = set_intersection2(B!4, A!5)) | (((~in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), B!4)) | (~in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), A!5))) <=> in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), set_intersection2(B!4, A!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!4, A!5), A!5), A!5)) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4))) <=> in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5)))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[129])).
% 0.21/0.41 tff(131,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(B!4, A!5) = set_intersection2(B!4, A!5))) | (~(((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4))) <=> in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5)))))) | (~((set_intersection2(B!4, A!5) = set_intersection2(B!4, A!5)) | (((~in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), B!4)) | (~in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), A!5))) <=> in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), set_intersection2(B!4, A!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!4, A!5), A!5), A!5)) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4))) <=> in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5)))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[130, 107])).
% 0.21/0.41 tff(132,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(B!4, A!5) = set_intersection2(B!4, A!5))) | (~(((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4))) <=> in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5)))))) | (~((set_intersection2(B!4, A!5) = set_intersection2(B!4, A!5)) | (((~in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), B!4)) | (~in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), A!5))) <=> in(tptp_fun_D_1(set_intersection2(B!4, A!5), A!5, B!4), set_intersection2(B!4, A!5)))))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(133,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))))))) | (~(((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4))) <=> in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.21/0.41 tff(134,plain,
% 0.21/0.41 (~(((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4))) <=> in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[133, 106])).
% 0.21/0.41 tff(135,plain,
% 0.21/0.41 (((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5))) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(136,plain,
% 0.21/0.41 (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[135, 74])).
% 0.21/0.41 tff(137,plain,
% 0.21/0.41 ((((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4))) <=> in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5))) | ((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4))) | in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(138,plain,
% 0.21/0.41 ((((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4))) <=> in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), set_intersection2(B!4, A!5))) | ((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.21/0.41 tff(139,plain,
% 0.21/0.41 ((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[138, 134])).
% 0.21/0.41 tff(140,plain,
% 0.21/0.41 ((~((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4)))) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(141,plain,
% 0.21/0.41 ((~((~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), A!5)) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4)))) | (~in(tptp_fun_C_0(set_intersection2(B!4, A!5), A!5), B!4))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[140, 76])).
% 0.21/0.41 tff(142,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[141, 139, 88])).
% 0.21/0.41 % SZS output end Proof
% 0.21/0.41 % E exiting
%------------------------------------------------------------------------------