%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU162+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:27:06 AM UTC 2025
% Result : Theorem 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU162+1 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 06:09:02 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.38 % SZS status Theorem
% 0.13/0.38 % SZS output start Proof
% 0.13/0.38 tff(disjoint_type, type, (
% 0.13/0.38 disjoint: ( $i * $i ) > $o)).
% 0.13/0.38 tff(singleton_type, type, (
% 0.13/0.38 singleton: $i > $i)).
% 0.13/0.38 tff(tptp_fun_B_0_type, type, (
% 0.13/0.38 tptp_fun_B_0: $i)).
% 0.13/0.38 tff(tptp_fun_A_1_type, type, (
% 0.13/0.38 tptp_fun_A_1: $i)).
% 0.13/0.38 tff(set_difference_type, type, (
% 0.13/0.38 set_difference: ( $i * $i ) > $i)).
% 0.13/0.38 tff(in_type, type, (
% 0.13/0.38 in: ( $i * $i ) > $o)).
% 0.13/0.38 tff(1,assumption,(~(set_difference(A!1, singleton(B!0)) = A!1)), introduced(assumption)).
% 0.13/0.38 tff(2,plain,
% 0.13/0.38 (^[A: $i, B: $i] : refl((disjoint(A, B) <=> (set_difference(A, B) = A)) <=> (disjoint(A, B) <=> (set_difference(A, B) = A)))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(3,plain,
% 0.13/0.38 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A)) <=> ![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.13/0.38 tff(4,plain,
% 0.13/0.38 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A)) <=> ![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(5,axiom,(![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t83_xboole_1')).
% 0.13/0.38 tff(6,plain,
% 0.13/0.38 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.13/0.38 tff(7,plain,(
% 0.13/0.38 ![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 0.13/0.38 inference(skolemize,[status(sab)],[6])).
% 0.13/0.38 tff(8,plain,
% 0.13/0.38 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.13/0.38 tff(9,plain,
% 0.13/0.38 ((~![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))) | (disjoint(A!1, singleton(B!0)) <=> (set_difference(A!1, singleton(B!0)) = A!1))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(10,plain,
% 0.13/0.38 (disjoint(A!1, singleton(B!0)) <=> (set_difference(A!1, singleton(B!0)) = A!1)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.13/0.38 tff(11,plain,
% 0.13/0.38 ((~(disjoint(A!1, singleton(B!0)) <=> (set_difference(A!1, singleton(B!0)) = A!1))) | (~disjoint(A!1, singleton(B!0))) | (set_difference(A!1, singleton(B!0)) = A!1)),
% 0.13/0.38 inference(tautology,[status(thm)],[])).
% 0.13/0.38 tff(12,plain,
% 0.13/0.38 ((~disjoint(A!1, singleton(B!0))) | (set_difference(A!1, singleton(B!0)) = A!1)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.13/0.38 tff(13,plain,
% 0.13/0.38 (~disjoint(A!1, singleton(B!0))),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[12, 1])).
% 0.13/0.38 tff(14,plain,
% 0.13/0.38 ((~![A: $i, B: $i] : (~(in(B, A) <=> (set_difference(A, singleton(B)) = A)))) <=> (~![A: $i, B: $i] : (~(in(B, A) <=> (set_difference(A, singleton(B)) = A))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(15,plain,
% 0.13/0.38 ((~![A: $i, B: $i] : ((set_difference(A, singleton(B)) = A) <=> (~in(B, A)))) <=> (~![A: $i, B: $i] : (~(in(B, A) <=> (set_difference(A, singleton(B)) = A))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(16,axiom,(~![A: $i, B: $i] : ((set_difference(A, singleton(B)) = A) <=> (~in(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t65_zfmisc_1')).
% 0.13/0.38 tff(17,plain,
% 0.13/0.38 (~![A: $i, B: $i] : (~(in(B, A) <=> (set_difference(A, singleton(B)) = A)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.13/0.38 tff(18,plain,
% 0.13/0.38 (~![A: $i, B: $i] : (~(in(B, A) <=> (set_difference(A, singleton(B)) = A)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.13/0.38 tff(19,plain,
% 0.13/0.38 (~![A: $i, B: $i] : (~(in(B, A) <=> (set_difference(A, singleton(B)) = A)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.13/0.38 tff(20,plain,
% 0.13/0.38 (~![A: $i, B: $i] : (~(in(B, A) <=> (set_difference(A, singleton(B)) = A)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.13/0.38 tff(21,plain,(
% 0.13/0.38 in(B!0, A!1) <=> (set_difference(A!1, singleton(B!0)) = A!1)),
% 0.13/0.38 inference(skolemize,[status(sab)],[20])).
% 0.13/0.38 tff(22,plain,
% 0.13/0.38 ((~in(B!0, A!1)) | (set_difference(A!1, singleton(B!0)) = A!1) | (~(in(B!0, A!1) <=> (set_difference(A!1, singleton(B!0)) = A!1)))),
% 0.13/0.38 inference(tautology,[status(thm)],[])).
% 0.13/0.38 tff(23,plain,
% 0.13/0.38 ((~in(B!0, A!1)) | (set_difference(A!1, singleton(B!0)) = A!1)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.13/0.38 tff(24,plain,
% 0.13/0.38 (~in(B!0, A!1)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[23, 1])).
% 0.13/0.38 tff(25,plain,
% 0.13/0.38 (^[A: $i, B: $i] : refl((in(A, B) | disjoint(singleton(A), B)) <=> (in(A, B) | disjoint(singleton(A), B)))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(26,plain,
% 0.13/0.38 (![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B)) <=> ![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[25])).
% 0.13/0.38 tff(27,plain,
% 0.13/0.38 (![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B)) <=> ![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(28,plain,
% 0.13/0.38 (^[A: $i, B: $i] : rewrite(((~in(A, B)) => disjoint(singleton(A), B)) <=> (in(A, B) | disjoint(singleton(A), B)))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(29,plain,
% 0.13/0.38 (![A: $i, B: $i] : ((~in(A, B)) => disjoint(singleton(A), B)) <=> ![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[28])).
% 0.13/0.38 tff(30,axiom,(![A: $i, B: $i] : ((~in(A, B)) => disjoint(singleton(A), B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l28_zfmisc_1')).
% 0.13/0.38 tff(31,plain,
% 0.13/0.38 (![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.13/0.38 tff(32,plain,
% 0.13/0.38 (![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.13/0.38 tff(33,plain,(
% 0.13/0.38 ![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))),
% 0.13/0.38 inference(skolemize,[status(sab)],[32])).
% 0.13/0.38 tff(34,plain,
% 0.13/0.38 (![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.13/0.38 tff(35,plain,
% 0.13/0.38 (((~![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))) | (in(B!0, A!1) | disjoint(singleton(B!0), A!1))) <=> ((~![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))) | in(B!0, A!1) | disjoint(singleton(B!0), A!1))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(36,plain,
% 0.13/0.38 ((~![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))) | (in(B!0, A!1) | disjoint(singleton(B!0), A!1))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(37,plain,
% 0.13/0.38 ((~![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))) | in(B!0, A!1) | disjoint(singleton(B!0), A!1)),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.13/0.38 tff(38,plain,
% 0.13/0.38 (in(B!0, A!1) | disjoint(singleton(B!0), A!1)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[37, 34])).
% 0.13/0.38 tff(39,plain,
% 0.13/0.38 (disjoint(singleton(B!0), A!1)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[38, 24])).
% 0.13/0.38 tff(40,plain,
% 0.13/0.38 (^[A: $i, B: $i] : refl(((~disjoint(A, B)) | disjoint(B, A)) <=> ((~disjoint(A, B)) | disjoint(B, A)))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(41,plain,
% 0.13/0.38 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A)) <=> ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[40])).
% 0.13/0.38 tff(42,plain,
% 0.13/0.38 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A)) <=> ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(43,plain,
% 0.13/0.38 (^[A: $i, B: $i] : rewrite((disjoint(A, B) => disjoint(B, A)) <=> ((~disjoint(A, B)) | disjoint(B, A)))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(44,plain,
% 0.13/0.38 (![A: $i, B: $i] : (disjoint(A, B) => disjoint(B, A)) <=> ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[43])).
% 0.13/0.38 tff(45,axiom,(![A: $i, B: $i] : (disjoint(A, B) => disjoint(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','symmetry_r1_xboole_0')).
% 0.13/0.38 tff(46,plain,
% 0.13/0.38 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.13/0.38 tff(47,plain,
% 0.13/0.38 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.13/0.38 tff(48,plain,(
% 0.13/0.38 ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 0.13/0.38 inference(skolemize,[status(sab)],[47])).
% 0.13/0.38 tff(49,plain,
% 0.13/0.38 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.13/0.39 tff(50,plain,
% 0.13/0.39 (((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | ((~disjoint(singleton(B!0), A!1)) | disjoint(A!1, singleton(B!0)))) <=> ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | (~disjoint(singleton(B!0), A!1)) | disjoint(A!1, singleton(B!0)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(51,plain,
% 0.13/0.39 ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | ((~disjoint(singleton(B!0), A!1)) | disjoint(A!1, singleton(B!0)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(52,plain,
% 0.13/0.39 ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | (~disjoint(singleton(B!0), A!1)) | disjoint(A!1, singleton(B!0))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.13/0.39 tff(53,plain,
% 0.13/0.39 ((~disjoint(singleton(B!0), A!1)) | disjoint(A!1, singleton(B!0))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[52, 49])).
% 0.13/0.39 tff(54,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[53, 39, 13])).
% 0.13/0.39 tff(55,plain,(set_difference(A!1, singleton(B!0)) = A!1), inference(lemma,lemma(discharge,[]))).
% 0.13/0.39 tff(56,plain,
% 0.13/0.39 ((~(disjoint(A!1, singleton(B!0)) <=> (set_difference(A!1, singleton(B!0)) = A!1))) | disjoint(A!1, singleton(B!0)) | (~(set_difference(A!1, singleton(B!0)) = A!1))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(57,plain,
% 0.13/0.39 (disjoint(A!1, singleton(B!0)) | (~(set_difference(A!1, singleton(B!0)) = A!1))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[56, 10])).
% 0.13/0.39 tff(58,plain,
% 0.13/0.39 (disjoint(A!1, singleton(B!0))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[57, 55])).
% 0.13/0.39 tff(59,plain,
% 0.13/0.39 (in(B!0, A!1) | (~(set_difference(A!1, singleton(B!0)) = A!1)) | (~(in(B!0, A!1) <=> (set_difference(A!1, singleton(B!0)) = A!1)))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(60,plain,
% 0.13/0.39 (in(B!0, A!1) | (~(set_difference(A!1, singleton(B!0)) = A!1))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[59, 21])).
% 0.13/0.39 tff(61,plain,
% 0.13/0.39 (in(B!0, A!1)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[60, 55])).
% 0.13/0.39 tff(62,plain,
% 0.13/0.39 (^[A: $i, B: $i] : refl(((~in(A, B)) | (~disjoint(singleton(A), B))) <=> ((~in(A, B)) | (~disjoint(singleton(A), B))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(63,plain,
% 0.13/0.39 (![A: $i, B: $i] : ((~in(A, B)) | (~disjoint(singleton(A), B))) <=> ![A: $i, B: $i] : ((~in(A, B)) | (~disjoint(singleton(A), B)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[62])).
% 0.13/0.39 tff(64,plain,
% 0.13/0.39 (^[A: $i, B: $i] : trans(monotonicity(rewrite((disjoint(singleton(A), B) & in(A, B)) <=> (~((~in(A, B)) | (~disjoint(singleton(A), B))))), ((~(disjoint(singleton(A), B) & in(A, B))) <=> (~(~((~in(A, B)) | (~disjoint(singleton(A), B))))))), rewrite((~(~((~in(A, B)) | (~disjoint(singleton(A), B))))) <=> ((~in(A, B)) | (~disjoint(singleton(A), B)))), ((~(disjoint(singleton(A), B) & in(A, B))) <=> ((~in(A, B)) | (~disjoint(singleton(A), B)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(65,plain,
% 0.13/0.39 (![A: $i, B: $i] : (~(disjoint(singleton(A), B) & in(A, B))) <=> ![A: $i, B: $i] : ((~in(A, B)) | (~disjoint(singleton(A), B)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[64])).
% 0.13/0.39 tff(66,plain,
% 0.13/0.39 (![A: $i, B: $i] : (~(disjoint(singleton(A), B) & in(A, B))) <=> ![A: $i, B: $i] : (~(disjoint(singleton(A), B) & in(A, B)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(67,axiom,(![A: $i, B: $i] : (~(disjoint(singleton(A), B) & in(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l25_zfmisc_1')).
% 0.13/0.39 tff(68,plain,
% 0.13/0.39 (![A: $i, B: $i] : (~(disjoint(singleton(A), B) & in(A, B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.13/0.39 tff(69,plain,(
% 0.13/0.39 ![A: $i, B: $i] : (~(disjoint(singleton(A), B) & in(A, B)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[68])).
% 0.13/0.39 tff(70,plain,
% 0.13/0.39 (![A: $i, B: $i] : ((~in(A, B)) | (~disjoint(singleton(A), B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.13/0.39 tff(71,plain,
% 0.13/0.39 (![A: $i, B: $i] : ((~in(A, B)) | (~disjoint(singleton(A), B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.13/0.39 tff(72,plain,
% 0.13/0.39 (((~![A: $i, B: $i] : ((~in(A, B)) | (~disjoint(singleton(A), B)))) | ((~in(B!0, A!1)) | (~disjoint(singleton(B!0), A!1)))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | (~disjoint(singleton(A), B)))) | (~in(B!0, A!1)) | (~disjoint(singleton(B!0), A!1)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(73,plain,
% 0.13/0.39 ((~![A: $i, B: $i] : ((~in(A, B)) | (~disjoint(singleton(A), B)))) | ((~in(B!0, A!1)) | (~disjoint(singleton(B!0), A!1)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(74,plain,
% 0.13/0.39 ((~![A: $i, B: $i] : ((~in(A, B)) | (~disjoint(singleton(A), B)))) | (~in(B!0, A!1)) | (~disjoint(singleton(B!0), A!1))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.13/0.39 tff(75,plain,
% 0.13/0.39 ((~in(B!0, A!1)) | (~disjoint(singleton(B!0), A!1))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[74, 71])).
% 0.13/0.39 tff(76,plain,
% 0.13/0.39 (~disjoint(singleton(B!0), A!1)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[75, 61])).
% 0.13/0.39 tff(77,plain,
% 0.13/0.39 (((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | ((~disjoint(A!1, singleton(B!0))) | disjoint(singleton(B!0), A!1))) <=> ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | (~disjoint(A!1, singleton(B!0))) | disjoint(singleton(B!0), A!1))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(78,plain,
% 0.13/0.39 ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | ((~disjoint(A!1, singleton(B!0))) | disjoint(singleton(B!0), A!1))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(79,plain,
% 0.13/0.39 ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | (~disjoint(A!1, singleton(B!0))) | disjoint(singleton(B!0), A!1)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.13/0.39 tff(80,plain,
% 0.13/0.39 ((~disjoint(A!1, singleton(B!0))) | disjoint(singleton(B!0), A!1)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[79, 49])).
% 0.13/0.39 tff(81,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[80, 76, 58])).
% 0.13/0.39 % SZS output end Proof
% 0.13/0.39 % E exiting
%------------------------------------------------------------------------------