TSTP Solution File: SEU162+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU162+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 : Tue Sep 20 07:27:54 EDT 2022
% Result : Theorem 0.21s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU162+3 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n022.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Sep 3 09:48:40 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 0.21/0.41 % SZS status Theorem
% 0.21/0.41 % SZS output start Proof
% 0.21/0.41 tff(disjoint_type, type, (
% 0.21/0.41 disjoint: ( $i * $i ) > $o)).
% 0.21/0.41 tff(tptp_fun_A_3_type, type, (
% 0.21/0.41 tptp_fun_A_3: $i)).
% 0.21/0.41 tff(singleton_type, type, (
% 0.21/0.41 singleton: $i > $i)).
% 0.21/0.41 tff(tptp_fun_B_2_type, type, (
% 0.21/0.41 tptp_fun_B_2: $i)).
% 0.21/0.41 tff(in_type, type, (
% 0.21/0.41 in: ( $i * $i ) > $o)).
% 0.21/0.41 tff(set_difference_type, type, (
% 0.21/0.41 set_difference: ( $i * $i ) > $i)).
% 0.21/0.41 tff(1,assumption,(~in(B!2, A!3)), introduced(assumption)).
% 0.21/0.41 tff(2,plain,
% 0.21/0.41 (^[A: $i, B: $i] : refl((in(A, B) | disjoint(singleton(A), B)) <=> (in(A, B) | disjoint(singleton(A), B)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(3,plain,
% 0.21/0.41 (![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B)) <=> ![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[2])).
% 0.21/0.41 tff(4,plain,
% 0.21/0.41 (![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B)) <=> ![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(5,plain,
% 0.21/0.41 (^[A: $i, B: $i] : rewrite(((~in(A, B)) => disjoint(singleton(A), B)) <=> (in(A, B) | disjoint(singleton(A), B)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(6,plain,
% 0.21/0.41 (![A: $i, B: $i] : ((~in(A, B)) => disjoint(singleton(A), B)) <=> ![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[5])).
% 0.21/0.41 tff(7,axiom,(![A: $i, B: $i] : ((~in(A, B)) => disjoint(singleton(A), B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l28_zfmisc_1')).
% 0.21/0.41 tff(8,plain,
% 0.21/0.41 (![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.21/0.41 tff(9,plain,
% 0.21/0.41 (![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.21/0.41 tff(10,plain,(
% 0.21/0.41 ![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))),
% 0.21/0.41 inference(skolemize,[status(sab)],[9])).
% 0.21/0.41 tff(11,plain,
% 0.21/0.41 (![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.21/0.41 tff(12,plain,
% 0.21/0.41 (((~![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))) | (in(B!2, A!3) | disjoint(singleton(B!2), A!3))) <=> ((~![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))) | in(B!2, A!3) | disjoint(singleton(B!2), A!3))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(13,plain,
% 0.21/0.41 ((~![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))) | (in(B!2, A!3) | disjoint(singleton(B!2), A!3))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(14,plain,
% 0.21/0.41 ((~![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))) | in(B!2, A!3) | disjoint(singleton(B!2), A!3)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.21/0.41 tff(15,plain,
% 0.21/0.41 (in(B!2, A!3) | disjoint(singleton(B!2), A!3)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[14, 11])).
% 0.21/0.41 tff(16,plain,
% 0.21/0.41 (disjoint(singleton(B!2), A!3)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[15, 1])).
% 0.21/0.41 tff(17,plain,
% 0.21/0.41 ((~((set_difference(A!3, singleton(B!2)) = A!3) <=> (~in(B!2, A!3)))) <=> ((set_difference(A!3, singleton(B!2)) = A!3) <=> in(B!2, A!3))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(18,plain,
% 0.21/0.41 ((~![A: $i, B: $i] : ((set_difference(A, singleton(B)) = A) <=> (~in(B, A)))) <=> (~![A: $i, B: $i] : ((set_difference(A, singleton(B)) = A) <=> (~in(B, A))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(19,axiom,(~![A: $i, B: $i] : ((set_difference(A, singleton(B)) = A) <=> (~in(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t65_zfmisc_1')).
% 0.21/0.41 tff(20,plain,
% 0.21/0.41 (~![A: $i, B: $i] : ((set_difference(A, singleton(B)) = A) <=> (~in(B, A)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.21/0.41 tff(21,plain,
% 0.21/0.41 (~![A: $i, B: $i] : ((set_difference(A, singleton(B)) = A) <=> (~in(B, A)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[20, 18])).
% 0.21/0.41 tff(22,plain,
% 0.21/0.41 (~![A: $i, B: $i] : ((set_difference(A, singleton(B)) = A) <=> (~in(B, A)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[21, 18])).
% 0.21/0.41 tff(23,plain,
% 0.21/0.41 (~![A: $i, B: $i] : ((set_difference(A, singleton(B)) = A) <=> (~in(B, A)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.21/0.41 tff(24,plain,
% 0.21/0.41 (~![A: $i, B: $i] : ((set_difference(A, singleton(B)) = A) <=> (~in(B, A)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[23, 18])).
% 0.21/0.41 tff(25,plain,
% 0.21/0.41 (~![A: $i, B: $i] : ((set_difference(A, singleton(B)) = A) <=> (~in(B, A)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[24, 18])).
% 0.21/0.41 tff(26,plain,
% 0.21/0.41 (~![A: $i, B: $i] : ((set_difference(A, singleton(B)) = A) <=> (~in(B, A)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.21/0.41 tff(27,plain,(
% 0.21/0.41 ~((set_difference(A!3, singleton(B!2)) = A!3) <=> (~in(B!2, A!3)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[26])).
% 0.21/0.41 tff(28,plain,
% 0.21/0.41 ((set_difference(A!3, singleton(B!2)) = A!3) <=> in(B!2, A!3)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.21/0.41 tff(29,plain,
% 0.21/0.41 ((~(set_difference(A!3, singleton(B!2)) = A!3)) | in(B!2, A!3) | (~((set_difference(A!3, singleton(B!2)) = A!3) <=> in(B!2, A!3)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(30,plain,
% 0.21/0.41 ((~(set_difference(A!3, singleton(B!2)) = A!3)) | in(B!2, A!3)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.21/0.41 tff(31,plain,
% 0.21/0.41 (~(set_difference(A!3, singleton(B!2)) = A!3)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[30, 1])).
% 0.21/0.41 tff(32,plain,
% 0.21/0.41 (^[A: $i, B: $i] : refl((disjoint(A, B) <=> (set_difference(A, B) = A)) <=> (disjoint(A, B) <=> (set_difference(A, B) = A)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(33,plain,
% 0.21/0.41 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A)) <=> ![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[32])).
% 0.21/0.41 tff(34,plain,
% 0.21/0.41 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A)) <=> ![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(35,axiom,(![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t83_xboole_1')).
% 0.21/0.41 tff(36,plain,
% 0.21/0.41 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.21/0.41 tff(37,plain,(
% 0.21/0.41 ![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 0.21/0.41 inference(skolemize,[status(sab)],[36])).
% 0.21/0.41 tff(38,plain,
% 0.21/0.41 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.21/0.41 tff(39,plain,
% 0.21/0.41 ((~![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))) | (disjoint(A!3, singleton(B!2)) <=> (set_difference(A!3, singleton(B!2)) = A!3))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(40,plain,
% 0.21/0.41 (disjoint(A!3, singleton(B!2)) <=> (set_difference(A!3, singleton(B!2)) = A!3)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.21/0.41 tff(41,plain,
% 0.21/0.41 ((~(disjoint(A!3, singleton(B!2)) <=> (set_difference(A!3, singleton(B!2)) = A!3))) | (~disjoint(A!3, singleton(B!2))) | (set_difference(A!3, singleton(B!2)) = A!3)),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(42,plain,
% 0.21/0.41 ((~disjoint(A!3, singleton(B!2))) | (set_difference(A!3, singleton(B!2)) = A!3)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.21/0.41 tff(43,plain,
% 0.21/0.41 (~disjoint(A!3, singleton(B!2))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[42, 31])).
% 0.21/0.41 tff(44,plain,
% 0.21/0.41 (^[A: $i, B: $i] : refl(((~disjoint(A, B)) | disjoint(B, A)) <=> ((~disjoint(A, B)) | disjoint(B, A)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(45,plain,
% 0.21/0.41 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A)) <=> ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[44])).
% 0.21/0.41 tff(46,plain,
% 0.21/0.41 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A)) <=> ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(47,plain,
% 0.21/0.41 (^[A: $i, B: $i] : rewrite((disjoint(A, B) => disjoint(B, A)) <=> ((~disjoint(A, B)) | disjoint(B, A)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(48,plain,
% 0.21/0.41 (![A: $i, B: $i] : (disjoint(A, B) => disjoint(B, A)) <=> ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[47])).
% 0.21/0.41 tff(49,axiom,(![A: $i, B: $i] : (disjoint(A, B) => disjoint(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','symmetry_r1_xboole_0')).
% 0.21/0.41 tff(50,plain,
% 0.21/0.41 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.21/0.41 tff(51,plain,
% 0.21/0.41 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.21/0.41 tff(52,plain,(
% 0.21/0.41 ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 0.21/0.41 inference(skolemize,[status(sab)],[51])).
% 0.21/0.41 tff(53,plain,
% 0.21/0.41 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.21/0.41 tff(54,plain,
% 0.21/0.41 (((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | ((~disjoint(singleton(B!2), A!3)) | disjoint(A!3, singleton(B!2)))) <=> ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | (~disjoint(singleton(B!2), A!3)) | disjoint(A!3, singleton(B!2)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(55,plain,
% 0.21/0.41 ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | ((~disjoint(singleton(B!2), A!3)) | disjoint(A!3, singleton(B!2)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(56,plain,
% 0.21/0.41 ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | (~disjoint(singleton(B!2), A!3)) | disjoint(A!3, singleton(B!2))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.21/0.41 tff(57,plain,
% 0.21/0.41 ((~disjoint(singleton(B!2), A!3)) | disjoint(A!3, singleton(B!2))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[56, 53])).
% 0.21/0.41 tff(58,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[57, 43, 16])).
% 0.21/0.41 tff(59,plain,(in(B!2, A!3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(60,plain,
% 0.21/0.41 (^[A: $i, B: $i] : refl(((~in(A, B)) | (~disjoint(singleton(A), B))) <=> ((~in(A, B)) | (~disjoint(singleton(A), B))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(61,plain,
% 0.21/0.41 (![A: $i, B: $i] : ((~in(A, B)) | (~disjoint(singleton(A), B))) <=> ![A: $i, B: $i] : ((~in(A, B)) | (~disjoint(singleton(A), B)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[60])).
% 0.21/0.41 tff(62,plain,
% 0.21/0.41 (^[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)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(63,plain,
% 0.21/0.41 (![A: $i, B: $i] : (~(disjoint(singleton(A), B) & in(A, B))) <=> ![A: $i, B: $i] : ((~in(A, B)) | (~disjoint(singleton(A), B)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[62])).
% 0.21/0.41 tff(64,plain,
% 0.21/0.41 (![A: $i, B: $i] : (~(disjoint(singleton(A), B) & in(A, B))) <=> ![A: $i, B: $i] : (~(disjoint(singleton(A), B) & in(A, B)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(65,axiom,(![A: $i, B: $i] : (~(disjoint(singleton(A), B) & in(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l25_zfmisc_1')).
% 0.21/0.41 tff(66,plain,
% 0.21/0.41 (![A: $i, B: $i] : (~(disjoint(singleton(A), B) & in(A, B)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.21/0.41 tff(67,plain,(
% 0.21/0.41 ![A: $i, B: $i] : (~(disjoint(singleton(A), B) & in(A, B)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[66])).
% 0.21/0.41 tff(68,plain,
% 0.21/0.41 (![A: $i, B: $i] : ((~in(A, B)) | (~disjoint(singleton(A), B)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.21/0.41 tff(69,plain,
% 0.21/0.41 (![A: $i, B: $i] : ((~in(A, B)) | (~disjoint(singleton(A), B)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.21/0.41 tff(70,plain,
% 0.21/0.41 (((~![A: $i, B: $i] : ((~in(A, B)) | (~disjoint(singleton(A), B)))) | ((~in(B!2, A!3)) | (~disjoint(singleton(B!2), A!3)))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | (~disjoint(singleton(A), B)))) | (~in(B!2, A!3)) | (~disjoint(singleton(B!2), A!3)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(71,plain,
% 0.21/0.41 ((~![A: $i, B: $i] : ((~in(A, B)) | (~disjoint(singleton(A), B)))) | ((~in(B!2, A!3)) | (~disjoint(singleton(B!2), A!3)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(72,plain,
% 0.21/0.41 ((~![A: $i, B: $i] : ((~in(A, B)) | (~disjoint(singleton(A), B)))) | (~in(B!2, A!3)) | (~disjoint(singleton(B!2), A!3))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.21/0.41 tff(73,plain,
% 0.21/0.41 ((~in(B!2, A!3)) | (~disjoint(singleton(B!2), A!3))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[72, 69])).
% 0.21/0.41 tff(74,plain,
% 0.21/0.41 (~disjoint(singleton(B!2), A!3)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[73, 59])).
% 0.21/0.41 tff(75,plain,
% 0.21/0.41 ((set_difference(A!3, singleton(B!2)) = A!3) | (~in(B!2, A!3)) | (~((set_difference(A!3, singleton(B!2)) = A!3) <=> in(B!2, A!3)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(76,plain,
% 0.21/0.41 ((set_difference(A!3, singleton(B!2)) = A!3) | (~in(B!2, A!3))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[75, 28])).
% 0.21/0.41 tff(77,plain,
% 0.21/0.41 (set_difference(A!3, singleton(B!2)) = A!3),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[76, 59])).
% 0.21/0.41 tff(78,plain,
% 0.21/0.41 ((~(disjoint(A!3, singleton(B!2)) <=> (set_difference(A!3, singleton(B!2)) = A!3))) | disjoint(A!3, singleton(B!2)) | (~(set_difference(A!3, singleton(B!2)) = A!3))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(79,plain,
% 0.21/0.41 (disjoint(A!3, singleton(B!2)) | (~(set_difference(A!3, singleton(B!2)) = A!3))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[78, 40])).
% 0.21/0.41 tff(80,plain,
% 0.21/0.41 (disjoint(A!3, singleton(B!2))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[79, 77])).
% 0.21/0.41 tff(81,plain,
% 0.21/0.41 (((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | ((~disjoint(A!3, singleton(B!2))) | disjoint(singleton(B!2), A!3))) <=> ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | (~disjoint(A!3, singleton(B!2))) | disjoint(singleton(B!2), A!3))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(82,plain,
% 0.21/0.41 ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | ((~disjoint(A!3, singleton(B!2))) | disjoint(singleton(B!2), A!3))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(83,plain,
% 0.21/0.41 ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | (~disjoint(A!3, singleton(B!2))) | disjoint(singleton(B!2), A!3)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.21/0.41 tff(84,plain,
% 0.21/0.41 ((~disjoint(A!3, singleton(B!2))) | disjoint(singleton(B!2), A!3)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[83, 53])).
% 0.21/0.41 tff(85,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[84, 80, 74])).
% 0.21/0.41 % SZS output end Proof
%------------------------------------------------------------------------------