%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU112+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:54 AM UTC 2025
% Result : Theorem 0.23s 0.41s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.14 % Problem : SEU112+1 : TPTP v9.0.0. Released v3.2.0.
% 0.05/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n012.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 06:04:25 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.23/0.41 % SZS status Theorem
% 0.23/0.41 % SZS output start Proof
% 0.23/0.41 tff(subset_type, type, (
% 0.23/0.41 subset: ( $i * $i ) > $o)).
% 0.23/0.41 tff(set_union2_type, type, (
% 0.23/0.41 set_union2: ( $i * $i ) > $i)).
% 0.23/0.41 tff(tptp_fun_A_10_type, type, (
% 0.23/0.41 tptp_fun_A_10: $i)).
% 0.23/0.41 tff(tptp_fun_B_9_type, type, (
% 0.23/0.41 tptp_fun_B_9: $i)).
% 0.23/0.41 tff(finite_subsets_type, type, (
% 0.23/0.41 finite_subsets: $i > $i)).
% 0.23/0.41 tff(1,plain,
% 0.23/0.41 (^[A: $i, B: $i] : refl((set_union2(A, B) = set_union2(B, A)) <=> (set_union2(A, B) = set_union2(B, A)))),
% 0.23/0.41 inference(bind,[status(th)],[])).
% 0.23/0.41 tff(2,plain,
% 0.23/0.41 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.23/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.23/0.41 tff(3,plain,
% 0.23/0.41 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(4,axiom,(![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k2_xboole_0')).
% 0.23/0.41 tff(5,plain,
% 0.23/0.41 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.23/0.41 tff(6,plain,(
% 0.23/0.41 ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.23/0.41 inference(skolemize,[status(sab)],[5])).
% 0.23/0.41 tff(7,plain,
% 0.23/0.41 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.23/0.41 tff(8,plain,
% 0.23/0.41 ((~![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))) | (set_union2(A!10, B!9) = set_union2(B!9, A!10))),
% 0.23/0.41 inference(quant_inst,[status(thm)],[])).
% 0.23/0.41 tff(9,plain,
% 0.23/0.41 (set_union2(A!10, B!9) = set_union2(B!9, A!10)),
% 0.23/0.41 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.23/0.41 tff(10,plain,
% 0.23/0.41 (set_union2(B!9, A!10) = set_union2(A!10, B!9)),
% 0.23/0.41 inference(symmetry,[status(thm)],[9])).
% 0.23/0.41 tff(11,plain,
% 0.23/0.41 (subset(B!9, set_union2(B!9, A!10)) <=> subset(B!9, set_union2(A!10, B!9))),
% 0.23/0.41 inference(monotonicity,[status(thm)],[10])).
% 0.23/0.41 tff(12,plain,
% 0.23/0.41 (subset(B!9, set_union2(A!10, B!9)) <=> subset(B!9, set_union2(B!9, A!10))),
% 0.23/0.41 inference(symmetry,[status(thm)],[11])).
% 0.23/0.41 tff(13,plain,
% 0.23/0.41 ((~subset(B!9, set_union2(A!10, B!9))) <=> (~subset(B!9, set_union2(B!9, A!10)))),
% 0.23/0.41 inference(monotonicity,[status(thm)],[12])).
% 0.23/0.41 tff(14,plain,
% 0.23/0.41 (^[A: $i, B: $i] : refl(subset(A, set_union2(A, B)) <=> subset(A, set_union2(A, B)))),
% 0.23/0.41 inference(bind,[status(th)],[])).
% 0.23/0.41 tff(15,plain,
% 0.23/0.41 (![A: $i, B: $i] : subset(A, set_union2(A, B)) <=> ![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.23/0.41 inference(quant_intro,[status(thm)],[14])).
% 0.23/0.41 tff(16,plain,
% 0.23/0.41 (![A: $i, B: $i] : subset(A, set_union2(A, B)) <=> ![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(17,axiom,(![A: $i, B: $i] : subset(A, set_union2(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t7_xboole_1')).
% 0.23/0.41 tff(18,plain,
% 0.23/0.41 (![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.23/0.41 tff(19,plain,(
% 0.23/0.41 ![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.23/0.41 inference(skolemize,[status(sab)],[18])).
% 0.23/0.41 tff(20,plain,
% 0.23/0.41 (![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.23/0.41 tff(21,plain,
% 0.23/0.41 ((~![A: $i, B: $i] : subset(A, set_union2(A, B))) | subset(A!10, set_union2(A!10, B!9))),
% 0.23/0.41 inference(quant_inst,[status(thm)],[])).
% 0.23/0.41 tff(22,plain,
% 0.23/0.41 (subset(A!10, set_union2(A!10, B!9))),
% 0.23/0.41 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.23/0.41 tff(23,plain,
% 0.23/0.41 (^[A: $i, B: $i] : refl(((~subset(A, B)) | subset(finite_subsets(A), finite_subsets(B))) <=> ((~subset(A, B)) | subset(finite_subsets(A), finite_subsets(B))))),
% 0.23/0.41 inference(bind,[status(th)],[])).
% 0.23/0.41 tff(24,plain,
% 0.23/0.41 (![A: $i, B: $i] : ((~subset(A, B)) | subset(finite_subsets(A), finite_subsets(B))) <=> ![A: $i, B: $i] : ((~subset(A, B)) | subset(finite_subsets(A), finite_subsets(B)))),
% 0.23/0.41 inference(quant_intro,[status(thm)],[23])).
% 0.23/0.41 tff(25,plain,
% 0.23/0.41 (![A: $i, B: $i] : ((~subset(A, B)) | subset(finite_subsets(A), finite_subsets(B))) <=> ![A: $i, B: $i] : ((~subset(A, B)) | subset(finite_subsets(A), finite_subsets(B)))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(26,plain,
% 0.23/0.41 (^[A: $i, B: $i] : rewrite((subset(A, B) => subset(finite_subsets(A), finite_subsets(B))) <=> ((~subset(A, B)) | subset(finite_subsets(A), finite_subsets(B))))),
% 0.23/0.41 inference(bind,[status(th)],[])).
% 0.23/0.41 tff(27,plain,
% 0.23/0.41 (![A: $i, B: $i] : (subset(A, B) => subset(finite_subsets(A), finite_subsets(B))) <=> ![A: $i, B: $i] : ((~subset(A, B)) | subset(finite_subsets(A), finite_subsets(B)))),
% 0.23/0.41 inference(quant_intro,[status(thm)],[26])).
% 0.23/0.41 tff(28,axiom,(![A: $i, B: $i] : (subset(A, B) => subset(finite_subsets(A), finite_subsets(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t23_finsub_1')).
% 0.23/0.41 tff(29,plain,
% 0.23/0.41 (![A: $i, B: $i] : ((~subset(A, B)) | subset(finite_subsets(A), finite_subsets(B)))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.23/0.41 tff(30,plain,
% 0.23/0.41 (![A: $i, B: $i] : ((~subset(A, B)) | subset(finite_subsets(A), finite_subsets(B)))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.23/0.41 tff(31,plain,(
% 0.23/0.41 ![A: $i, B: $i] : ((~subset(A, B)) | subset(finite_subsets(A), finite_subsets(B)))),
% 0.23/0.41 inference(skolemize,[status(sab)],[30])).
% 0.23/0.41 tff(32,plain,
% 0.23/0.41 (![A: $i, B: $i] : ((~subset(A, B)) | subset(finite_subsets(A), finite_subsets(B)))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.23/0.41 tff(33,plain,
% 0.23/0.41 (((~![A: $i, B: $i] : ((~subset(A, B)) | subset(finite_subsets(A), finite_subsets(B)))) | ((~subset(A!10, set_union2(A!10, B!9))) | subset(finite_subsets(A!10), finite_subsets(set_union2(A!10, B!9))))) <=> ((~![A: $i, B: $i] : ((~subset(A, B)) | subset(finite_subsets(A), finite_subsets(B)))) | (~subset(A!10, set_union2(A!10, B!9))) | subset(finite_subsets(A!10), finite_subsets(set_union2(A!10, B!9))))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(34,plain,
% 0.23/0.41 ((~![A: $i, B: $i] : ((~subset(A, B)) | subset(finite_subsets(A), finite_subsets(B)))) | ((~subset(A!10, set_union2(A!10, B!9))) | subset(finite_subsets(A!10), finite_subsets(set_union2(A!10, B!9))))),
% 0.23/0.41 inference(quant_inst,[status(thm)],[])).
% 0.23/0.41 tff(35,plain,
% 0.23/0.41 ((~![A: $i, B: $i] : ((~subset(A, B)) | subset(finite_subsets(A), finite_subsets(B)))) | (~subset(A!10, set_union2(A!10, B!9))) | subset(finite_subsets(A!10), finite_subsets(set_union2(A!10, B!9)))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.23/0.41 tff(36,plain,
% 0.23/0.41 (subset(finite_subsets(A!10), finite_subsets(set_union2(A!10, B!9)))),
% 0.23/0.41 inference(unit_resolution,[status(thm)],[35, 32, 22])).
% 0.23/0.41 tff(37,plain,
% 0.23/0.41 (^[A: $i, B: $i, C: $i] : refl((subset(set_union2(A, C), B) | (~subset(A, B)) | (~subset(C, B))) <=> (subset(set_union2(A, C), B) | (~subset(A, B)) | (~subset(C, B))))),
% 0.23/0.41 inference(bind,[status(th)],[])).
% 0.23/0.41 tff(38,plain,
% 0.23/0.41 (![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(A, B)) | (~subset(C, B))) <=> ![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(A, B)) | (~subset(C, B)))),
% 0.23/0.41 inference(quant_intro,[status(thm)],[37])).
% 0.23/0.41 tff(39,plain,
% 0.23/0.41 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((subset(A, B) & subset(C, B)) <=> (~((~subset(A, B)) | (~subset(C, B))))), ((~(subset(A, B) & subset(C, B))) <=> (~(~((~subset(A, B)) | (~subset(C, B))))))), rewrite((~(~((~subset(A, B)) | (~subset(C, B))))) <=> ((~subset(A, B)) | (~subset(C, B)))), ((~(subset(A, B) & subset(C, B))) <=> ((~subset(A, B)) | (~subset(C, B))))), (((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B)) <=> (((~subset(A, B)) | (~subset(C, B))) | subset(set_union2(A, C), B)))), rewrite((((~subset(A, B)) | (~subset(C, B))) | subset(set_union2(A, C), B)) <=> (subset(set_union2(A, C), B) | (~subset(A, B)) | (~subset(C, B)))), (((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B)) <=> (subset(set_union2(A, C), B) | (~subset(A, B)) | (~subset(C, B)))))),
% 0.23/0.41 inference(bind,[status(th)],[])).
% 0.23/0.41 tff(40,plain,
% 0.23/0.41 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B)) <=> ![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(A, B)) | (~subset(C, B)))),
% 0.23/0.41 inference(quant_intro,[status(thm)],[39])).
% 0.23/0.41 tff(41,plain,
% 0.23/0.41 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B)) <=> ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(42,plain,
% 0.23/0.41 (^[A: $i, B: $i, C: $i] : rewrite(((subset(A, B) & subset(C, B)) => subset(set_union2(A, C), B)) <=> ((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B)))),
% 0.23/0.41 inference(bind,[status(th)],[])).
% 0.23/0.41 tff(43,plain,
% 0.23/0.41 (![A: $i, B: $i, C: $i] : ((subset(A, B) & subset(C, B)) => subset(set_union2(A, C), B)) <=> ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B))),
% 0.23/0.41 inference(quant_intro,[status(thm)],[42])).
% 0.23/0.41 tff(44,axiom,(![A: $i, B: $i, C: $i] : ((subset(A, B) & subset(C, B)) => subset(set_union2(A, C), B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t8_xboole_1')).
% 0.23/0.41 tff(45,plain,
% 0.23/0.41 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.23/0.41 tff(46,plain,
% 0.23/0.41 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.23/0.41 tff(47,plain,(
% 0.23/0.41 ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B))),
% 0.23/0.41 inference(skolemize,[status(sab)],[46])).
% 0.23/0.41 tff(48,plain,
% 0.23/0.41 (![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(A, B)) | (~subset(C, B)))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.23/0.41 tff(49,plain,
% 0.23/0.41 (![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(A, B)) | (~subset(C, B)))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[48, 38])).
% 0.23/0.41 tff(50,plain,
% 0.23/0.41 ((~![A: $i, B: $i] : subset(set_union2(finite_subsets(A), finite_subsets(B)), finite_subsets(set_union2(A, B)))) <=> (~![A: $i, B: $i] : subset(set_union2(finite_subsets(A), finite_subsets(B)), finite_subsets(set_union2(A, B))))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(51,axiom,(~![A: $i, B: $i] : subset(set_union2(finite_subsets(A), finite_subsets(B)), finite_subsets(set_union2(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t25_finsub_1')).
% 0.23/0.41 tff(52,plain,
% 0.23/0.41 (~![A: $i, B: $i] : subset(set_union2(finite_subsets(A), finite_subsets(B)), finite_subsets(set_union2(A, B)))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.23/0.41 tff(53,plain,
% 0.23/0.41 (~![A: $i, B: $i] : subset(set_union2(finite_subsets(A), finite_subsets(B)), finite_subsets(set_union2(A, B)))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[52, 50])).
% 0.23/0.41 tff(54,plain,
% 0.23/0.41 (~![A: $i, B: $i] : subset(set_union2(finite_subsets(A), finite_subsets(B)), finite_subsets(set_union2(A, B)))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[53, 50])).
% 0.23/0.41 tff(55,plain,
% 0.23/0.41 (~![A: $i, B: $i] : subset(set_union2(finite_subsets(A), finite_subsets(B)), finite_subsets(set_union2(A, B)))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.23/0.41 tff(56,plain,(
% 0.23/0.41 ~subset(set_union2(finite_subsets(A!10), finite_subsets(B!9)), finite_subsets(set_union2(A!10, B!9)))),
% 0.23/0.41 inference(skolemize,[status(sab)],[55])).
% 0.23/0.41 tff(57,plain,
% 0.23/0.41 (((~![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(A, B)) | (~subset(C, B)))) | (subset(set_union2(finite_subsets(A!10), finite_subsets(B!9)), finite_subsets(set_union2(A!10, B!9))) | (~subset(finite_subsets(A!10), finite_subsets(set_union2(A!10, B!9)))) | (~subset(finite_subsets(B!9), finite_subsets(set_union2(A!10, B!9)))))) <=> ((~![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(A, B)) | (~subset(C, B)))) | subset(set_union2(finite_subsets(A!10), finite_subsets(B!9)), finite_subsets(set_union2(A!10, B!9))) | (~subset(finite_subsets(A!10), finite_subsets(set_union2(A!10, B!9)))) | (~subset(finite_subsets(B!9), finite_subsets(set_union2(A!10, B!9)))))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(58,plain,
% 0.23/0.41 ((~![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(A, B)) | (~subset(C, B)))) | (subset(set_union2(finite_subsets(A!10), finite_subsets(B!9)), finite_subsets(set_union2(A!10, B!9))) | (~subset(finite_subsets(A!10), finite_subsets(set_union2(A!10, B!9)))) | (~subset(finite_subsets(B!9), finite_subsets(set_union2(A!10, B!9)))))),
% 0.23/0.42 inference(quant_inst,[status(thm)],[])).
% 0.23/0.42 tff(59,plain,
% 0.23/0.42 ((~![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(A, B)) | (~subset(C, B)))) | subset(set_union2(finite_subsets(A!10), finite_subsets(B!9)), finite_subsets(set_union2(A!10, B!9))) | (~subset(finite_subsets(A!10), finite_subsets(set_union2(A!10, B!9)))) | (~subset(finite_subsets(B!9), finite_subsets(set_union2(A!10, B!9))))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.23/0.42 tff(60,plain,
% 0.23/0.42 (~subset(finite_subsets(B!9), finite_subsets(set_union2(A!10, B!9)))),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[59, 56, 49, 36])).
% 0.23/0.42 tff(61,plain,
% 0.23/0.42 (((~![A: $i, B: $i] : ((~subset(A, B)) | subset(finite_subsets(A), finite_subsets(B)))) | ((~subset(B!9, set_union2(A!10, B!9))) | subset(finite_subsets(B!9), finite_subsets(set_union2(A!10, B!9))))) <=> ((~![A: $i, B: $i] : ((~subset(A, B)) | subset(finite_subsets(A), finite_subsets(B)))) | (~subset(B!9, set_union2(A!10, B!9))) | subset(finite_subsets(B!9), finite_subsets(set_union2(A!10, B!9))))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(62,plain,
% 0.23/0.42 ((~![A: $i, B: $i] : ((~subset(A, B)) | subset(finite_subsets(A), finite_subsets(B)))) | ((~subset(B!9, set_union2(A!10, B!9))) | subset(finite_subsets(B!9), finite_subsets(set_union2(A!10, B!9))))),
% 0.23/0.42 inference(quant_inst,[status(thm)],[])).
% 0.23/0.42 tff(63,plain,
% 0.23/0.42 ((~![A: $i, B: $i] : ((~subset(A, B)) | subset(finite_subsets(A), finite_subsets(B)))) | (~subset(B!9, set_union2(A!10, B!9))) | subset(finite_subsets(B!9), finite_subsets(set_union2(A!10, B!9)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.23/0.42 tff(64,plain,
% 0.23/0.42 ((~subset(B!9, set_union2(A!10, B!9))) | subset(finite_subsets(B!9), finite_subsets(set_union2(A!10, B!9)))),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[63, 32])).
% 0.23/0.42 tff(65,plain,
% 0.23/0.42 (~subset(B!9, set_union2(A!10, B!9))),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[64, 60])).
% 0.23/0.42 tff(66,plain,
% 0.23/0.42 (~subset(B!9, set_union2(B!9, A!10))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[65, 13])).
% 0.23/0.42 tff(67,plain,
% 0.23/0.42 ((~![A: $i, B: $i] : subset(A, set_union2(A, B))) | subset(B!9, set_union2(B!9, A!10))),
% 0.23/0.42 inference(quant_inst,[status(thm)],[])).
% 0.23/0.42 tff(68,plain,
% 0.23/0.42 (subset(B!9, set_union2(B!9, A!10))),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[67, 20])).
% 0.23/0.42 tff(69,plain,
% 0.23/0.42 ($false),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[68, 66])).
% 0.23/0.42 % SZS output end Proof
% 0.23/0.42 % E exiting
%------------------------------------------------------------------------------