%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU141+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:27:00 AM UTC 2025
% Result : Theorem 0.22s 0.49s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU141+2 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n015.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Jun 20 06:07:41 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.22/0.49 % SZS status Theorem
% 0.22/0.49 % SZS output start Proof
% 0.22/0.49 tff(empty_set_type, type, (
% 0.22/0.49 empty_set: $i)).
% 0.22/0.49 tff(set_intersection2_type, type, (
% 0.22/0.49 set_intersection2: ( $i * $i ) > $i)).
% 0.22/0.49 tff(tptp_fun_B_10_type, type, (
% 0.22/0.49 tptp_fun_B_10: $i)).
% 0.22/0.49 tff(tptp_fun_A_11_type, type, (
% 0.22/0.49 tptp_fun_A_11: $i)).
% 0.22/0.49 tff(set_difference_type, type, (
% 0.22/0.49 set_difference: ( $i * $i ) > $i)).
% 0.22/0.49 tff(subset_type, type, (
% 0.22/0.49 subset: ( $i * $i ) > $o)).
% 0.22/0.49 tff(set_union2_type, type, (
% 0.22/0.49 set_union2: ( $i * $i ) > $i)).
% 0.22/0.49 tff(disjoint_type, type, (
% 0.22/0.49 disjoint: ( $i * $i ) > $o)).
% 0.22/0.49 tff(1,plain,
% 0.22/0.49 (^[A: $i, B: $i] : refl(((set_difference(A, B) = empty_set) <=> subset(A, B)) <=> ((set_difference(A, B) = empty_set) <=> subset(A, B)))),
% 0.22/0.49 inference(bind,[status(th)],[])).
% 0.22/0.49 tff(2,plain,
% 0.22/0.49 (![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B)) <=> ![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 0.22/0.49 inference(quant_intro,[status(thm)],[1])).
% 0.22/0.49 tff(3,plain,
% 0.22/0.49 (![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B)) <=> ![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(4,axiom,(![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l32_xboole_1')).
% 0.22/0.49 tff(5,plain,
% 0.22/0.49 (![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.22/0.49 tff(6,plain,(
% 0.22/0.49 ![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 0.22/0.49 inference(skolemize,[status(sab)],[5])).
% 0.22/0.49 tff(7,plain,
% 0.22/0.49 (![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.22/0.49 tff(8,plain,
% 0.22/0.49 ((~![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))) | ((set_difference(set_difference(A!11, B!10), A!11) = empty_set) <=> subset(set_difference(A!11, B!10), A!11))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(9,plain,
% 0.22/0.49 ((set_difference(set_difference(A!11, B!10), A!11) = empty_set) <=> subset(set_difference(A!11, B!10), A!11)),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.22/0.49 tff(10,plain,
% 0.22/0.49 (^[A: $i, B: $i] : refl(subset(set_difference(A, B), A) <=> subset(set_difference(A, B), A))),
% 0.22/0.49 inference(bind,[status(th)],[])).
% 0.22/0.49 tff(11,plain,
% 0.22/0.49 (![A: $i, B: $i] : subset(set_difference(A, B), A) <=> ![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 0.22/0.49 inference(quant_intro,[status(thm)],[10])).
% 0.22/0.49 tff(12,plain,
% 0.22/0.49 (![A: $i, B: $i] : subset(set_difference(A, B), A) <=> ![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(13,axiom,(![A: $i, B: $i] : subset(set_difference(A, B), A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t36_xboole_1')).
% 0.22/0.49 tff(14,plain,
% 0.22/0.49 (![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.22/0.49 tff(15,plain,(
% 0.22/0.49 ![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 0.22/0.49 inference(skolemize,[status(sab)],[14])).
% 0.22/0.49 tff(16,plain,
% 0.22/0.49 (![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.22/0.49 tff(17,plain,
% 0.22/0.49 ((~![A: $i, B: $i] : subset(set_difference(A, B), A)) | subset(set_difference(A!11, B!10), A!11)),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(18,plain,
% 0.22/0.49 (subset(set_difference(A!11, B!10), A!11)),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.22/0.49 tff(19,plain,
% 0.22/0.49 ((~((set_difference(set_difference(A!11, B!10), A!11) = empty_set) <=> subset(set_difference(A!11, B!10), A!11))) | (set_difference(set_difference(A!11, B!10), A!11) = empty_set) | (~subset(set_difference(A!11, B!10), A!11))),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(20,plain,
% 0.22/0.49 ((~((set_difference(set_difference(A!11, B!10), A!11) = empty_set) <=> subset(set_difference(A!11, B!10), A!11))) | (set_difference(set_difference(A!11, B!10), A!11) = empty_set)),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.22/0.49 tff(21,plain,
% 0.22/0.49 (set_difference(set_difference(A!11, B!10), A!11) = empty_set),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[20, 9])).
% 0.22/0.50 tff(22,plain,
% 0.22/0.50 (^[A: $i, B: $i] : refl(((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))) <=> ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))))),
% 0.22/0.50 inference(bind,[status(th)],[])).
% 0.22/0.50 tff(23,plain,
% 0.22/0.50 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 0.22/0.50 inference(quant_intro,[status(thm)],[22])).
% 0.22/0.50 tff(24,plain,
% 0.22/0.50 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(25,plain,
% 0.22/0.50 (^[A: $i, B: $i] : rewrite((subset(A, B) => (B = set_union2(A, set_difference(B, A)))) <=> ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))))),
% 0.22/0.50 inference(bind,[status(th)],[])).
% 0.22/0.50 tff(26,plain,
% 0.22/0.50 (![A: $i, B: $i] : (subset(A, B) => (B = set_union2(A, set_difference(B, A)))) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 0.22/0.50 inference(quant_intro,[status(thm)],[25])).
% 0.22/0.50 tff(27,axiom,(![A: $i, B: $i] : (subset(A, B) => (B = set_union2(A, set_difference(B, A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t45_xboole_1')).
% 0.22/0.50 tff(28,plain,
% 0.22/0.50 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.22/0.50 tff(29,plain,
% 0.22/0.50 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.22/0.50 tff(30,plain,(
% 0.22/0.50 ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 0.22/0.50 inference(skolemize,[status(sab)],[29])).
% 0.22/0.50 tff(31,plain,
% 0.22/0.50 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.22/0.50 tff(32,plain,
% 0.22/0.50 (((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | ((~subset(set_difference(A!11, B!10), A!11)) | (A!11 = set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10)))))) <=> ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | (~subset(set_difference(A!11, B!10), A!11)) | (A!11 = set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10)))))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(33,plain,
% 0.22/0.50 ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | ((~subset(set_difference(A!11, B!10), A!11)) | (A!11 = set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10)))))),
% 0.22/0.50 inference(quant_inst,[status(thm)],[])).
% 0.22/0.50 tff(34,plain,
% 0.22/0.50 ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | (~subset(set_difference(A!11, B!10), A!11)) | (A!11 = set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10))))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.22/0.50 tff(35,plain,
% 0.22/0.50 (A!11 = set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10)))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[34, 31, 18])).
% 0.22/0.50 tff(36,plain,
% 0.22/0.50 (set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10))) = A!11),
% 0.22/0.50 inference(symmetry,[status(thm)],[35])).
% 0.22/0.50 tff(37,plain,
% 0.22/0.50 (set_difference(set_difference(A!11, B!10), set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10)))) = set_difference(set_difference(A!11, B!10), A!11)),
% 0.22/0.50 inference(monotonicity,[status(thm)],[36])).
% 0.22/0.50 tff(38,plain,
% 0.22/0.50 (^[A: $i, B: $i] : refl((set_difference(set_union2(A, B), B) = set_difference(A, B)) <=> (set_difference(set_union2(A, B), B) = set_difference(A, B)))),
% 0.22/0.50 inference(bind,[status(th)],[])).
% 0.22/0.50 tff(39,plain,
% 0.22/0.50 (![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B)) <=> ![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 0.22/0.50 inference(quant_intro,[status(thm)],[38])).
% 0.22/0.50 tff(40,plain,
% 0.22/0.50 (![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B)) <=> ![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(41,axiom,(![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t40_xboole_1')).
% 0.22/0.50 tff(42,plain,
% 0.22/0.50 (![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.22/0.50 tff(43,plain,(
% 0.22/0.50 ![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 0.22/0.50 inference(skolemize,[status(sab)],[42])).
% 0.22/0.50 tff(44,plain,
% 0.22/0.50 (![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.22/0.50 tff(45,plain,
% 0.22/0.50 ((~![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))) | (set_difference(set_union2(set_difference(A!11, B!10), set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10)))), set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10)))) = set_difference(set_difference(A!11, B!10), set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10)))))),
% 0.22/0.50 inference(quant_inst,[status(thm)],[])).
% 0.22/0.50 tff(46,plain,
% 0.22/0.50 (set_difference(set_union2(set_difference(A!11, B!10), set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10)))), set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10)))) = set_difference(set_difference(A!11, B!10), set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10))))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.22/0.50 tff(47,plain,
% 0.22/0.50 (^[A: $i, B: $i] : refl((set_difference(A, set_difference(A, B)) = set_intersection2(A, B)) <=> (set_difference(A, set_difference(A, B)) = set_intersection2(A, B)))),
% 0.22/0.50 inference(bind,[status(th)],[])).
% 0.22/0.50 tff(48,plain,
% 0.22/0.50 (![A: $i, B: $i] : (set_difference(A, set_difference(A, B)) = set_intersection2(A, B)) <=> ![A: $i, B: $i] : (set_difference(A, set_difference(A, B)) = set_intersection2(A, B))),
% 0.22/0.50 inference(quant_intro,[status(thm)],[47])).
% 0.22/0.50 tff(49,plain,
% 0.22/0.50 (![A: $i, B: $i] : (set_difference(A, set_difference(A, B)) = set_intersection2(A, B)) <=> ![A: $i, B: $i] : (set_difference(A, set_difference(A, B)) = set_intersection2(A, B))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(50,axiom,(![A: $i, B: $i] : (set_difference(A, set_difference(A, B)) = set_intersection2(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t48_xboole_1')).
% 0.22/0.50 tff(51,plain,
% 0.22/0.50 (![A: $i, B: $i] : (set_difference(A, set_difference(A, B)) = set_intersection2(A, B))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.22/0.50 tff(52,plain,(
% 0.22/0.50 ![A: $i, B: $i] : (set_difference(A, set_difference(A, B)) = set_intersection2(A, B))),
% 0.22/0.50 inference(skolemize,[status(sab)],[51])).
% 0.22/0.50 tff(53,plain,
% 0.22/0.50 (![A: $i, B: $i] : (set_difference(A, set_difference(A, B)) = set_intersection2(A, B))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.22/0.50 tff(54,plain,
% 0.22/0.50 ((~![A: $i, B: $i] : (set_difference(A, set_difference(A, B)) = set_intersection2(A, B))) | (set_difference(A!11, set_difference(A!11, B!10)) = set_intersection2(A!11, B!10))),
% 0.22/0.50 inference(quant_inst,[status(thm)],[])).
% 0.22/0.50 tff(55,plain,
% 0.22/0.50 (set_difference(A!11, set_difference(A!11, B!10)) = set_intersection2(A!11, B!10)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.22/0.50 tff(56,plain,
% 0.22/0.50 (set_intersection2(A!11, B!10) = set_difference(A!11, set_difference(A!11, B!10))),
% 0.22/0.50 inference(symmetry,[status(thm)],[55])).
% 0.22/0.50 tff(57,assumption,(~(set_difference(A!11, B!10) = A!11)), introduced(assumption)).
% 0.22/0.50 tff(58,plain,
% 0.22/0.50 ((~(disjoint(A!11, B!10) <=> (set_difference(A!11, B!10) = A!11))) <=> (~(disjoint(A!11, B!10) <=> (set_difference(A!11, B!10) = A!11)))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(59,plain,
% 0.22/0.50 ((~![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))) <=> (~![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A)))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(60,axiom,(~![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t83_xboole_1')).
% 0.22/0.50 tff(61,plain,
% 0.22/0.50 (~![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.22/0.50 tff(62,plain,
% 0.22/0.50 (~![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[61, 59])).
% 0.22/0.50 tff(63,plain,
% 0.22/0.50 (~![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[62, 59])).
% 0.22/0.50 tff(64,plain,
% 0.22/0.50 (~![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.22/0.50 tff(65,plain,(
% 0.22/0.50 ~(disjoint(A!11, B!10) <=> (set_difference(A!11, B!10) = A!11))),
% 0.22/0.50 inference(skolemize,[status(sab)],[64])).
% 0.22/0.50 tff(66,plain,
% 0.22/0.50 (~(disjoint(A!11, B!10) <=> (set_difference(A!11, B!10) = A!11))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.22/0.50 tff(67,plain,
% 0.22/0.50 ((disjoint(A!11, B!10) <=> (set_difference(A!11, B!10) = A!11)) | disjoint(A!11, B!10) | (set_difference(A!11, B!10) = A!11)),
% 0.22/0.50 inference(tautology,[status(thm)],[])).
% 0.22/0.50 tff(68,plain,
% 0.22/0.50 (disjoint(A!11, B!10) | (set_difference(A!11, B!10) = A!11)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.22/0.50 tff(69,plain,
% 0.22/0.50 (disjoint(A!11, B!10)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[68, 57])).
% 0.22/0.50 tff(70,plain,
% 0.22/0.50 (^[A: $i, B: $i] : refl((disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)) <=> (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)))),
% 0.22/0.50 inference(bind,[status(th)],[])).
% 0.22/0.50 tff(71,plain,
% 0.22/0.50 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)) <=> ![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 0.22/0.50 inference(quant_intro,[status(thm)],[70])).
% 0.22/0.50 tff(72,plain,
% 0.22/0.50 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)) <=> ![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(73,axiom,(![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d7_xboole_0')).
% 0.22/0.50 tff(74,plain,
% 0.22/0.50 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.22/0.50 tff(75,plain,(
% 0.22/0.50 ![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 0.22/0.50 inference(skolemize,[status(sab)],[74])).
% 0.22/0.50 tff(76,plain,
% 0.22/0.50 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.22/0.50 tff(77,plain,
% 0.22/0.50 ((~![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))) | (disjoint(A!11, B!10) <=> (set_intersection2(A!11, B!10) = empty_set))),
% 0.22/0.50 inference(quant_inst,[status(thm)],[])).
% 0.22/0.50 tff(78,plain,
% 0.22/0.50 (disjoint(A!11, B!10) <=> (set_intersection2(A!11, B!10) = empty_set)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.22/0.50 tff(79,plain,
% 0.22/0.50 ((~(disjoint(A!11, B!10) <=> (set_intersection2(A!11, B!10) = empty_set))) | (~disjoint(A!11, B!10)) | (set_intersection2(A!11, B!10) = empty_set)),
% 0.22/0.50 inference(tautology,[status(thm)],[])).
% 0.22/0.50 tff(80,plain,
% 0.22/0.50 ((~disjoint(A!11, B!10)) | (set_intersection2(A!11, B!10) = empty_set)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.22/0.50 tff(81,plain,
% 0.22/0.50 (set_intersection2(A!11, B!10) = empty_set),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[80, 69])).
% 0.22/0.50 tff(82,plain,
% 0.22/0.50 (empty_set = set_intersection2(A!11, B!10)),
% 0.22/0.50 inference(symmetry,[status(thm)],[81])).
% 0.22/0.50 tff(83,plain,
% 0.22/0.50 ((~![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))) | ((set_difference(set_difference(A!11, B!10), set_difference(A!11, B!10)) = empty_set) <=> subset(set_difference(A!11, B!10), set_difference(A!11, B!10)))),
% 0.22/0.50 inference(quant_inst,[status(thm)],[])).
% 0.22/0.50 tff(84,plain,
% 0.22/0.50 ((set_difference(set_difference(A!11, B!10), set_difference(A!11, B!10)) = empty_set) <=> subset(set_difference(A!11, B!10), set_difference(A!11, B!10))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[83, 7])).
% 0.22/0.50 tff(85,plain,
% 0.22/0.50 (^[A: $i, B: $i] : refl(((~subset(A, B)) | (set_intersection2(A, B) = A)) <=> ((~subset(A, B)) | (set_intersection2(A, B) = A)))),
% 0.22/0.50 inference(bind,[status(th)],[])).
% 0.22/0.50 tff(86,plain,
% 0.22/0.50 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.22/0.50 inference(quant_intro,[status(thm)],[85])).
% 0.22/0.50 tff(87,plain,
% 0.22/0.50 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(88,plain,
% 0.22/0.50 (^[A: $i, B: $i] : rewrite((subset(A, B) => (set_intersection2(A, B) = A)) <=> ((~subset(A, B)) | (set_intersection2(A, B) = A)))),
% 0.22/0.50 inference(bind,[status(th)],[])).
% 0.22/0.50 tff(89,plain,
% 0.22/0.50 (![A: $i, B: $i] : (subset(A, B) => (set_intersection2(A, B) = A)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.22/0.50 inference(quant_intro,[status(thm)],[88])).
% 0.22/0.50 tff(90,axiom,(![A: $i, B: $i] : (subset(A, B) => (set_intersection2(A, B) = A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t28_xboole_1')).
% 0.22/0.50 tff(91,plain,
% 0.22/0.50 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.22/0.50 tff(92,plain,
% 0.22/0.50 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.22/0.50 tff(93,plain,(
% 0.22/0.50 ![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.22/0.50 inference(skolemize,[status(sab)],[92])).
% 0.22/0.50 tff(94,plain,
% 0.22/0.50 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.22/0.50 tff(95,plain,
% 0.22/0.50 (((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | ((~subset(set_difference(A!11, B!10), A!11)) | (set_intersection2(set_difference(A!11, B!10), A!11) = set_difference(A!11, B!10)))) <=> ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | (~subset(set_difference(A!11, B!10), A!11)) | (set_intersection2(set_difference(A!11, B!10), A!11) = set_difference(A!11, B!10)))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(96,plain,
% 0.22/0.50 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | ((~subset(set_difference(A!11, B!10), A!11)) | (set_intersection2(set_difference(A!11, B!10), A!11) = set_difference(A!11, B!10)))),
% 0.22/0.50 inference(quant_inst,[status(thm)],[])).
% 0.22/0.50 tff(97,plain,
% 0.22/0.50 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | (~subset(set_difference(A!11, B!10), A!11)) | (set_intersection2(set_difference(A!11, B!10), A!11) = set_difference(A!11, B!10))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.22/0.50 tff(98,plain,
% 0.22/0.50 (set_intersection2(set_difference(A!11, B!10), A!11) = set_difference(A!11, B!10)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[97, 94, 18])).
% 0.22/0.50 tff(99,plain,
% 0.22/0.50 (set_intersection2(set_difference(A!11, B!10), set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10)))) = set_intersection2(set_difference(A!11, B!10), A!11)),
% 0.22/0.50 inference(monotonicity,[status(thm)],[36])).
% 0.22/0.50 tff(100,plain,
% 0.22/0.50 (set_intersection2(set_difference(A!11, B!10), set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10)))) = set_difference(A!11, B!10)),
% 0.22/0.50 inference(transitivity,[status(thm)],[99, 98])).
% 0.22/0.50 tff(101,plain,
% 0.22/0.50 (subset(set_intersection2(set_difference(A!11, B!10), set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10)))), set_difference(A!11, B!10)) <=> subset(set_difference(A!11, B!10), set_difference(A!11, B!10))),
% 0.22/0.50 inference(monotonicity,[status(thm)],[100])).
% 0.22/0.50 tff(102,plain,
% 0.22/0.50 (^[A: $i, B: $i] : refl(subset(set_intersection2(A, B), A) <=> subset(set_intersection2(A, B), A))),
% 0.22/0.50 inference(bind,[status(th)],[])).
% 0.22/0.50 tff(103,plain,
% 0.22/0.50 (![A: $i, B: $i] : subset(set_intersection2(A, B), A) <=> ![A: $i, B: $i] : subset(set_intersection2(A, B), A)),
% 0.22/0.50 inference(quant_intro,[status(thm)],[102])).
% 0.22/0.50 tff(104,plain,
% 0.22/0.50 (![A: $i, B: $i] : subset(set_intersection2(A, B), A) <=> ![A: $i, B: $i] : subset(set_intersection2(A, B), A)),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(105,axiom,(![A: $i, B: $i] : subset(set_intersection2(A, B), A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t17_xboole_1')).
% 0.22/0.50 tff(106,plain,
% 0.22/0.50 (![A: $i, B: $i] : subset(set_intersection2(A, B), A)),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.22/0.50 tff(107,plain,(
% 0.22/0.50 ![A: $i, B: $i] : subset(set_intersection2(A, B), A)),
% 0.22/0.50 inference(skolemize,[status(sab)],[106])).
% 0.22/0.50 tff(108,plain,
% 0.22/0.50 (![A: $i, B: $i] : subset(set_intersection2(A, B), A)),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.22/0.50 tff(109,plain,
% 0.22/0.50 ((~![A: $i, B: $i] : subset(set_intersection2(A, B), A)) | subset(set_intersection2(set_difference(A!11, B!10), set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10)))), set_difference(A!11, B!10))),
% 0.22/0.50 inference(quant_inst,[status(thm)],[])).
% 0.22/0.50 tff(110,plain,
% 0.22/0.50 (subset(set_intersection2(set_difference(A!11, B!10), set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10)))), set_difference(A!11, B!10))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.22/0.50 tff(111,plain,
% 0.22/0.50 (subset(set_difference(A!11, B!10), set_difference(A!11, B!10))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[110, 101])).
% 0.22/0.50 tff(112,plain,
% 0.22/0.50 ((~((set_difference(set_difference(A!11, B!10), set_difference(A!11, B!10)) = empty_set) <=> subset(set_difference(A!11, B!10), set_difference(A!11, B!10)))) | (set_difference(set_difference(A!11, B!10), set_difference(A!11, B!10)) = empty_set) | (~subset(set_difference(A!11, B!10), set_difference(A!11, B!10)))),
% 0.22/0.50 inference(tautology,[status(thm)],[])).
% 0.22/0.50 tff(113,plain,
% 0.22/0.50 ((~((set_difference(set_difference(A!11, B!10), set_difference(A!11, B!10)) = empty_set) <=> subset(set_difference(A!11, B!10), set_difference(A!11, B!10)))) | (set_difference(set_difference(A!11, B!10), set_difference(A!11, B!10)) = empty_set)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.22/0.50 tff(114,plain,
% 0.22/0.50 (set_difference(set_difference(A!11, B!10), set_difference(A!11, B!10)) = empty_set),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[113, 84])).
% 0.22/0.50 tff(115,plain,
% 0.22/0.50 (set_difference(set_difference(A!11, B!10), set_difference(A!11, B!10)) = set_difference(A!11, set_difference(A!11, B!10))),
% 0.22/0.50 inference(transitivity,[status(thm)],[114, 82, 56])).
% 0.22/0.50 tff(116,plain,
% 0.22/0.50 (set_union2(set_difference(A!11, B!10), set_difference(set_difference(A!11, B!10), set_difference(A!11, B!10))) = set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10)))),
% 0.22/0.50 inference(monotonicity,[status(thm)],[115])).
% 0.22/0.50 tff(117,plain,
% 0.22/0.50 (((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | ((~subset(set_difference(A!11, B!10), set_difference(A!11, B!10))) | (set_difference(A!11, B!10) = set_union2(set_difference(A!11, B!10), set_difference(set_difference(A!11, B!10), set_difference(A!11, B!10)))))) <=> ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | (~subset(set_difference(A!11, B!10), set_difference(A!11, B!10))) | (set_difference(A!11, B!10) = set_union2(set_difference(A!11, B!10), set_difference(set_difference(A!11, B!10), set_difference(A!11, B!10)))))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(118,plain,
% 0.22/0.50 ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | ((~subset(set_difference(A!11, B!10), set_difference(A!11, B!10))) | (set_difference(A!11, B!10) = set_union2(set_difference(A!11, B!10), set_difference(set_difference(A!11, B!10), set_difference(A!11, B!10)))))),
% 0.22/0.50 inference(quant_inst,[status(thm)],[])).
% 0.22/0.50 tff(119,plain,
% 0.22/0.50 ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | (~subset(set_difference(A!11, B!10), set_difference(A!11, B!10))) | (set_difference(A!11, B!10) = set_union2(set_difference(A!11, B!10), set_difference(set_difference(A!11, B!10), set_difference(A!11, B!10))))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.22/0.50 tff(120,plain,
% 0.22/0.50 (set_difference(A!11, B!10) = set_union2(set_difference(A!11, B!10), set_difference(set_difference(A!11, B!10), set_difference(A!11, B!10)))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[119, 31, 111])).
% 0.22/0.50 tff(121,plain,
% 0.22/0.50 (set_difference(A!11, B!10) = A!11),
% 0.22/0.50 inference(transitivity,[status(thm)],[120, 116, 36])).
% 0.22/0.50 tff(122,plain,
% 0.22/0.50 ($false),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[57, 121])).
% 0.22/0.50 tff(123,plain,(set_difference(A!11, B!10) = A!11), inference(lemma,lemma(discharge,[]))).
% 0.22/0.50 tff(124,plain,
% 0.22/0.50 (set_difference(A!11, B!10) = set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10)))),
% 0.22/0.50 inference(transitivity,[status(thm)],[123, 35])).
% 0.22/0.50 tff(125,plain,
% 0.22/0.50 (set_union2(set_difference(A!11, B!10), set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10)))) = set_union2(set_difference(A!11, B!10), A!11)),
% 0.22/0.50 inference(monotonicity,[status(thm)],[36])).
% 0.22/0.50 tff(126,plain,
% 0.22/0.50 (set_union2(set_difference(A!11, B!10), A!11) = set_union2(set_difference(A!11, B!10), set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10))))),
% 0.22/0.50 inference(symmetry,[status(thm)],[125])).
% 0.22/0.50 tff(127,plain,
% 0.22/0.50 (^[A: $i, B: $i] : refl(((~subset(A, B)) | (set_union2(A, B) = B)) <=> ((~subset(A, B)) | (set_union2(A, B) = B)))),
% 0.22/0.50 inference(bind,[status(th)],[])).
% 0.22/0.50 tff(128,plain,
% 0.22/0.50 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.22/0.50 inference(quant_intro,[status(thm)],[127])).
% 0.22/0.50 tff(129,plain,
% 0.22/0.50 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(130,plain,
% 0.22/0.50 (^[A: $i, B: $i] : rewrite((subset(A, B) => (set_union2(A, B) = B)) <=> ((~subset(A, B)) | (set_union2(A, B) = B)))),
% 0.22/0.50 inference(bind,[status(th)],[])).
% 0.22/0.50 tff(131,plain,
% 0.22/0.50 (![A: $i, B: $i] : (subset(A, B) => (set_union2(A, B) = B)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.22/0.50 inference(quant_intro,[status(thm)],[130])).
% 0.22/0.50 tff(132,axiom,(![A: $i, B: $i] : (subset(A, B) => (set_union2(A, B) = B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t12_xboole_1')).
% 0.22/0.50 tff(133,plain,
% 0.22/0.50 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.22/0.50 tff(134,plain,
% 0.22/0.50 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[133, 129])).
% 0.22/0.50 tff(135,plain,(
% 0.22/0.50 ![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.22/0.50 inference(skolemize,[status(sab)],[134])).
% 0.22/0.50 tff(136,plain,
% 0.22/0.50 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[135, 128])).
% 0.22/0.50 tff(137,plain,
% 0.22/0.50 (((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | ((~subset(set_difference(A!11, B!10), A!11)) | (set_union2(set_difference(A!11, B!10), A!11) = A!11))) <=> ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | (~subset(set_difference(A!11, B!10), A!11)) | (set_union2(set_difference(A!11, B!10), A!11) = A!11))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(138,plain,
% 0.22/0.50 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | ((~subset(set_difference(A!11, B!10), A!11)) | (set_union2(set_difference(A!11, B!10), A!11) = A!11))),
% 0.22/0.50 inference(quant_inst,[status(thm)],[])).
% 0.22/0.50 tff(139,plain,
% 0.22/0.50 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | (~subset(set_difference(A!11, B!10), A!11)) | (set_union2(set_difference(A!11, B!10), A!11) = A!11)),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.22/0.50 tff(140,plain,
% 0.22/0.50 (set_union2(set_difference(A!11, B!10), A!11) = A!11),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[139, 136, 18])).
% 0.22/0.50 tff(141,plain,
% 0.22/0.50 (A!11 = set_union2(set_difference(A!11, B!10), A!11)),
% 0.22/0.50 inference(symmetry,[status(thm)],[140])).
% 0.22/0.51 tff(142,plain,
% 0.22/0.51 (A!11 = set_union2(set_difference(A!11, B!10), set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10))))),
% 0.22/0.51 inference(transitivity,[status(thm)],[141, 126])).
% 0.22/0.51 tff(143,plain,
% 0.22/0.51 (set_difference(A!11, set_difference(A!11, B!10)) = set_difference(set_union2(set_difference(A!11, B!10), set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10)))), set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10))))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[142, 124])).
% 0.22/0.51 tff(144,plain,
% 0.22/0.51 (set_intersection2(A!11, B!10) = empty_set),
% 0.22/0.51 inference(transitivity,[status(thm)],[56, 143, 46, 37, 21])).
% 0.22/0.51 tff(145,plain,
% 0.22/0.51 ((disjoint(A!11, B!10) <=> (set_difference(A!11, B!10) = A!11)) | (~disjoint(A!11, B!10)) | (~(set_difference(A!11, B!10) = A!11))),
% 0.22/0.51 inference(tautology,[status(thm)],[])).
% 0.22/0.51 tff(146,plain,
% 0.22/0.51 ((~disjoint(A!11, B!10)) | (~(set_difference(A!11, B!10) = A!11))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[145, 66])).
% 0.22/0.51 tff(147,plain,
% 0.22/0.51 (~disjoint(A!11, B!10)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[146, 123])).
% 0.22/0.51 tff(148,plain,
% 0.22/0.51 ((~(disjoint(A!11, B!10) <=> (set_intersection2(A!11, B!10) = empty_set))) | disjoint(A!11, B!10) | (~(set_intersection2(A!11, B!10) = empty_set))),
% 0.22/0.51 inference(tautology,[status(thm)],[])).
% 0.22/0.51 tff(149,plain,
% 0.22/0.51 (disjoint(A!11, B!10) | (~(set_intersection2(A!11, B!10) = empty_set))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[148, 78])).
% 0.22/0.51 tff(150,plain,
% 0.22/0.51 (~(set_intersection2(A!11, B!10) = empty_set)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[149, 147])).
% 0.22/0.51 tff(151,plain,
% 0.22/0.51 ($false),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[150, 144])).
% 0.22/0.51 % SZS output end Proof
% 0.22/0.51 % E exiting
%------------------------------------------------------------------------------