%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET971+1 : TPTP v9.0.0. Released v3.2.0.
% 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 05:26:44 AM UTC 2025
% Result : Theorem 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET971+1 : TPTP v9.0.0. Released v3.2.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 05:54:23 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.40 % SZS status Theorem
% 0.21/0.40 % SZS output start Proof
% 0.21/0.40 tff(cartesian_product2_type, type, (
% 0.21/0.40 cartesian_product2: ( $i * $i ) > $i)).
% 0.21/0.40 tff(tptp_fun_C_3_type, type, (
% 0.21/0.40 tptp_fun_C_3: $i)).
% 0.21/0.40 tff(tptp_fun_A_5_type, type, (
% 0.21/0.40 tptp_fun_A_5: $i)).
% 0.21/0.40 tff(set_intersection2_type, type, (
% 0.21/0.40 set_intersection2: ( $i * $i ) > $i)).
% 0.21/0.40 tff(tptp_fun_B_4_type, type, (
% 0.21/0.40 tptp_fun_B_4: $i)).
% 0.21/0.40 tff(tptp_fun_D_2_type, type, (
% 0.21/0.40 tptp_fun_D_2: $i)).
% 0.21/0.40 tff(subset_type, type, (
% 0.21/0.40 subset: ( $i * $i ) > $o)).
% 0.21/0.40 tff(1,plain,
% 0.21/0.40 (^[A: $i, B: $i] : refl(((~subset(A, B)) | (set_intersection2(A, B) = A)) <=> ((~subset(A, B)) | (set_intersection2(A, B) = A)))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(2,plain,
% 0.21/0.40 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.40 tff(3,plain,
% 0.21/0.40 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(4,plain,
% 0.21/0.40 (^[A: $i, B: $i] : rewrite((subset(A, B) => (set_intersection2(A, B) = A)) <=> ((~subset(A, B)) | (set_intersection2(A, B) = A)))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(5,plain,
% 0.21/0.40 (![A: $i, B: $i] : (subset(A, B) => (set_intersection2(A, B) = A)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[4])).
% 0.21/0.40 tff(6,axiom,(![A: $i, B: $i] : (subset(A, B) => (set_intersection2(A, B) = A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t28_xboole_1')).
% 0.21/0.40 tff(7,plain,
% 0.21/0.40 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.21/0.40 tff(8,plain,
% 0.21/0.40 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.21/0.40 tff(9,plain,(
% 0.21/0.40 ![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.21/0.40 inference(skolemize,[status(sab)],[8])).
% 0.21/0.40 tff(10,plain,
% 0.21/0.40 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.21/0.40 tff(11,plain,
% 0.21/0.40 ((~![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | (set_intersection2(cartesian_product2(A, D), cartesian_product2(B, C)) = cartesian_product2(A, C)))) <=> (~![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | (set_intersection2(cartesian_product2(A, D), cartesian_product2(B, C)) = cartesian_product2(A, C))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(12,plain,
% 0.21/0.40 ((~![A: $i, B: $i, C: $i, D: $i] : ((subset(A, B) & subset(C, D)) => (set_intersection2(cartesian_product2(A, D), cartesian_product2(B, C)) = cartesian_product2(A, C)))) <=> (~![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | (set_intersection2(cartesian_product2(A, D), cartesian_product2(B, C)) = cartesian_product2(A, C))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(13,axiom,(~![A: $i, B: $i, C: $i, D: $i] : ((subset(A, B) & subset(C, D)) => (set_intersection2(cartesian_product2(A, D), cartesian_product2(B, C)) = cartesian_product2(A, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t124_zfmisc_1')).
% 0.21/0.40 tff(14,plain,
% 0.21/0.40 (~![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | (set_intersection2(cartesian_product2(A, D), cartesian_product2(B, C)) = cartesian_product2(A, C)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.21/0.40 tff(15,plain,
% 0.21/0.40 (~![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | (set_intersection2(cartesian_product2(A, D), cartesian_product2(B, C)) = cartesian_product2(A, C)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[14, 11])).
% 0.21/0.40 tff(16,plain,
% 0.21/0.40 (~![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | (set_intersection2(cartesian_product2(A, D), cartesian_product2(B, C)) = cartesian_product2(A, C)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.21/0.40 tff(17,plain,
% 0.21/0.40 (~![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | (set_intersection2(cartesian_product2(A, D), cartesian_product2(B, C)) = cartesian_product2(A, C)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[16, 11])).
% 0.21/0.40 tff(18,plain,(
% 0.21/0.40 ~((~(subset(A!5, B!4) & subset(C!3, D!2))) | (set_intersection2(cartesian_product2(A!5, D!2), cartesian_product2(B!4, C!3)) = cartesian_product2(A!5, C!3)))),
% 0.21/0.40 inference(skolemize,[status(sab)],[17])).
% 0.21/0.40 tff(19,plain,
% 0.21/0.40 (subset(A!5, B!4) & subset(C!3, D!2)),
% 0.21/0.40 inference(or_elim,[status(thm)],[18])).
% 0.21/0.40 tff(20,plain,
% 0.21/0.40 (subset(C!3, D!2)),
% 0.21/0.40 inference(and_elim,[status(thm)],[19])).
% 0.21/0.40 tff(21,plain,
% 0.21/0.40 (((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | ((~subset(C!3, D!2)) | (set_intersection2(C!3, D!2) = C!3))) <=> ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | (~subset(C!3, D!2)) | (set_intersection2(C!3, D!2) = C!3))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(22,plain,
% 0.21/0.40 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | ((~subset(C!3, D!2)) | (set_intersection2(C!3, D!2) = C!3))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(23,plain,
% 0.21/0.40 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | (~subset(C!3, D!2)) | (set_intersection2(C!3, D!2) = C!3)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.21/0.40 tff(24,plain,
% 0.21/0.40 (set_intersection2(C!3, D!2) = C!3),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[23, 20, 10])).
% 0.21/0.40 tff(25,plain,
% 0.21/0.40 (subset(A!5, B!4)),
% 0.21/0.40 inference(and_elim,[status(thm)],[19])).
% 0.21/0.40 tff(26,plain,
% 0.21/0.40 (((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | ((~subset(A!5, B!4)) | (set_intersection2(A!5, B!4) = A!5))) <=> ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | (~subset(A!5, B!4)) | (set_intersection2(A!5, B!4) = A!5))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(27,plain,
% 0.21/0.40 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | ((~subset(A!5, B!4)) | (set_intersection2(A!5, B!4) = A!5))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(28,plain,
% 0.21/0.40 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | (~subset(A!5, B!4)) | (set_intersection2(A!5, B!4) = A!5)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.21/0.40 tff(29,plain,
% 0.21/0.40 (set_intersection2(A!5, B!4) = A!5),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[28, 25, 10])).
% 0.21/0.40 tff(30,plain,
% 0.21/0.40 (^[A: $i, B: $i] : refl((set_intersection2(A, B) = set_intersection2(B, A)) <=> (set_intersection2(A, B) = set_intersection2(B, A)))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(31,plain,
% 0.21/0.40 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[30])).
% 0.21/0.40 tff(32,plain,
% 0.21/0.40 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(33,axiom,(![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 0.21/0.40 tff(34,plain,
% 0.21/0.40 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.21/0.40 tff(35,plain,(
% 0.21/0.40 ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.21/0.40 inference(skolemize,[status(sab)],[34])).
% 0.21/0.40 tff(36,plain,
% 0.21/0.40 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.21/0.40 tff(37,plain,
% 0.21/0.40 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(A!5, B!4) = set_intersection2(B!4, A!5))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(38,plain,
% 0.21/0.40 (set_intersection2(A!5, B!4) = set_intersection2(B!4, A!5)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.21/0.40 tff(39,plain,
% 0.21/0.40 (set_intersection2(B!4, A!5) = set_intersection2(A!5, B!4)),
% 0.21/0.40 inference(symmetry,[status(thm)],[38])).
% 0.21/0.40 tff(40,plain,
% 0.21/0.40 (set_intersection2(B!4, A!5) = A!5),
% 0.21/0.40 inference(transitivity,[status(thm)],[39, 29])).
% 0.21/0.41 tff(41,plain,
% 0.21/0.41 (cartesian_product2(set_intersection2(B!4, A!5), set_intersection2(C!3, D!2)) = cartesian_product2(A!5, C!3)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[40, 24])).
% 0.21/0.41 tff(42,plain,
% 0.21/0.41 (^[A: $i, B: $i, C: $i, D: $i] : refl((cartesian_product2(set_intersection2(A, B), set_intersection2(C, D)) = set_intersection2(cartesian_product2(A, C), cartesian_product2(B, D))) <=> (cartesian_product2(set_intersection2(A, B), set_intersection2(C, D)) = set_intersection2(cartesian_product2(A, C), cartesian_product2(B, D))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(43,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i, D: $i] : (cartesian_product2(set_intersection2(A, B), set_intersection2(C, D)) = set_intersection2(cartesian_product2(A, C), cartesian_product2(B, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (cartesian_product2(set_intersection2(A, B), set_intersection2(C, D)) = set_intersection2(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[42])).
% 0.21/0.41 tff(44,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i, D: $i] : (cartesian_product2(set_intersection2(A, B), set_intersection2(C, D)) = set_intersection2(cartesian_product2(A, C), cartesian_product2(B, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (cartesian_product2(set_intersection2(A, B), set_intersection2(C, D)) = set_intersection2(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(45,axiom,(![A: $i, B: $i, C: $i, D: $i] : (cartesian_product2(set_intersection2(A, B), set_intersection2(C, D)) = set_intersection2(cartesian_product2(A, C), cartesian_product2(B, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t123_zfmisc_1')).
% 0.21/0.41 tff(46,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i, D: $i] : (cartesian_product2(set_intersection2(A, B), set_intersection2(C, D)) = set_intersection2(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.21/0.41 tff(47,plain,(
% 0.21/0.41 ![A: $i, B: $i, C: $i, D: $i] : (cartesian_product2(set_intersection2(A, B), set_intersection2(C, D)) = set_intersection2(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[46])).
% 0.21/0.41 tff(48,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i, D: $i] : (cartesian_product2(set_intersection2(A, B), set_intersection2(C, D)) = set_intersection2(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.21/0.41 tff(49,plain,
% 0.21/0.41 ((~![A: $i, B: $i, C: $i, D: $i] : (cartesian_product2(set_intersection2(A, B), set_intersection2(C, D)) = set_intersection2(cartesian_product2(A, C), cartesian_product2(B, D)))) | (cartesian_product2(set_intersection2(B!4, A!5), set_intersection2(C!3, D!2)) = set_intersection2(cartesian_product2(B!4, C!3), cartesian_product2(A!5, D!2)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(50,plain,
% 0.21/0.41 (cartesian_product2(set_intersection2(B!4, A!5), set_intersection2(C!3, D!2)) = set_intersection2(cartesian_product2(B!4, C!3), cartesian_product2(A!5, D!2))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.21/0.41 tff(51,plain,
% 0.21/0.41 (set_intersection2(cartesian_product2(B!4, C!3), cartesian_product2(A!5, D!2)) = cartesian_product2(set_intersection2(B!4, A!5), set_intersection2(C!3, D!2))),
% 0.21/0.41 inference(symmetry,[status(thm)],[50])).
% 0.21/0.41 tff(52,plain,
% 0.21/0.41 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(cartesian_product2(A!5, D!2), cartesian_product2(B!4, C!3)) = set_intersection2(cartesian_product2(B!4, C!3), cartesian_product2(A!5, D!2)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(53,plain,
% 0.21/0.41 (set_intersection2(cartesian_product2(A!5, D!2), cartesian_product2(B!4, C!3)) = set_intersection2(cartesian_product2(B!4, C!3), cartesian_product2(A!5, D!2))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[52, 36])).
% 0.21/0.41 tff(54,plain,
% 0.21/0.41 (set_intersection2(cartesian_product2(A!5, D!2), cartesian_product2(B!4, C!3)) = cartesian_product2(A!5, C!3)),
% 0.21/0.41 inference(transitivity,[status(thm)],[53, 51, 41])).
% 0.21/0.41 tff(55,plain,
% 0.21/0.41 (~(set_intersection2(cartesian_product2(A!5, D!2), cartesian_product2(B!4, C!3)) = cartesian_product2(A!5, C!3))),
% 0.21/0.41 inference(or_elim,[status(thm)],[18])).
% 0.21/0.41 tff(56,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.21/0.41 % SZS output end Proof
% 0.21/0.41 % E exiting
%------------------------------------------------------------------------------