%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET917+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 05:26:39 AM UTC 2025
% Result : Theorem 0.24s 0.41s
% Output : Proof 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.15 % Problem : SET917+1 : TPTP v9.0.0. Released v3.2.0.
% 0.09/0.15 % Command : run_E %s %d THM
% 0.15/0.37 % Computer : n012.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Fri Jun 20 05:49:55 EDT 2025
% 0.15/0.37 % CPUTime :
% 0.24/0.41 % SZS status Theorem
% 0.24/0.41 % SZS output start Proof
% 0.24/0.41 tff(singleton_type, type, (
% 0.24/0.41 singleton: $i > $i)).
% 0.24/0.41 tff(tptp_fun_A_3_type, type, (
% 0.24/0.41 tptp_fun_A_3: $i)).
% 0.24/0.41 tff(set_intersection2_type, type, (
% 0.24/0.41 set_intersection2: ( $i * $i ) > $i)).
% 0.24/0.41 tff(tptp_fun_B_2_type, type, (
% 0.24/0.41 tptp_fun_B_2: $i)).
% 0.24/0.41 tff(in_type, type, (
% 0.24/0.41 in: ( $i * $i ) > $o)).
% 0.24/0.41 tff(disjoint_type, type, (
% 0.24/0.41 disjoint: ( $i * $i ) > $o)).
% 0.24/0.41 tff(1,plain,
% 0.24/0.41 ((~![A: $i, B: $i] : (disjoint(singleton(A), B) | (set_intersection2(singleton(A), B) = singleton(A)))) <=> (~![A: $i, B: $i] : (disjoint(singleton(A), B) | (set_intersection2(singleton(A), B) = singleton(A))))),
% 0.24/0.41 inference(rewrite,[status(thm)],[])).
% 0.24/0.41 tff(2,axiom,(~![A: $i, B: $i] : (disjoint(singleton(A), B) | (set_intersection2(singleton(A), B) = singleton(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t58_zfmisc_1')).
% 0.24/0.41 tff(3,plain,
% 0.24/0.41 (~![A: $i, B: $i] : (disjoint(singleton(A), B) | (set_intersection2(singleton(A), B) = singleton(A)))),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.24/0.41 tff(4,plain,
% 0.24/0.41 (~![A: $i, B: $i] : (disjoint(singleton(A), B) | (set_intersection2(singleton(A), B) = singleton(A)))),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[3, 1])).
% 0.24/0.41 tff(5,plain,
% 0.24/0.41 (~![A: $i, B: $i] : (disjoint(singleton(A), B) | (set_intersection2(singleton(A), B) = singleton(A)))),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.24/0.41 tff(6,plain,
% 0.24/0.41 (~![A: $i, B: $i] : (disjoint(singleton(A), B) | (set_intersection2(singleton(A), B) = singleton(A)))),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.24/0.41 tff(7,plain,(
% 0.24/0.41 ~(disjoint(singleton(A!3), B!2) | (set_intersection2(singleton(A!3), B!2) = singleton(A!3)))),
% 0.24/0.41 inference(skolemize,[status(sab)],[6])).
% 0.24/0.41 tff(8,plain,
% 0.24/0.41 (~disjoint(singleton(A!3), B!2)),
% 0.24/0.41 inference(or_elim,[status(thm)],[7])).
% 0.24/0.41 tff(9,plain,
% 0.24/0.41 (^[A: $i, B: $i] : refl((in(A, B) | disjoint(singleton(A), B)) <=> (in(A, B) | disjoint(singleton(A), B)))),
% 0.24/0.41 inference(bind,[status(th)],[])).
% 0.24/0.41 tff(10,plain,
% 0.24/0.41 (![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B)) <=> ![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))),
% 0.24/0.41 inference(quant_intro,[status(thm)],[9])).
% 0.24/0.41 tff(11,plain,
% 0.24/0.41 (![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B)) <=> ![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))),
% 0.24/0.41 inference(rewrite,[status(thm)],[])).
% 0.24/0.41 tff(12,plain,
% 0.24/0.41 (^[A: $i, B: $i] : rewrite(((~in(A, B)) => disjoint(singleton(A), B)) <=> (in(A, B) | disjoint(singleton(A), B)))),
% 0.24/0.41 inference(bind,[status(th)],[])).
% 0.24/0.41 tff(13,plain,
% 0.24/0.41 (![A: $i, B: $i] : ((~in(A, B)) => disjoint(singleton(A), B)) <=> ![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))),
% 0.24/0.41 inference(quant_intro,[status(thm)],[12])).
% 0.24/0.41 tff(14,axiom,(![A: $i, B: $i] : ((~in(A, B)) => disjoint(singleton(A), B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l28_zfmisc_1')).
% 0.24/0.41 tff(15,plain,
% 0.24/0.41 (![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.24/0.41 tff(16,plain,
% 0.24/0.41 (![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.24/0.41 tff(17,plain,(
% 0.24/0.41 ![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))),
% 0.24/0.41 inference(skolemize,[status(sab)],[16])).
% 0.24/0.41 tff(18,plain,
% 0.24/0.41 (![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.24/0.41 tff(19,plain,
% 0.24/0.41 (((~![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))) | (in(A!3, B!2) | disjoint(singleton(A!3), B!2))) <=> ((~![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))) | in(A!3, B!2) | disjoint(singleton(A!3), B!2))),
% 0.24/0.41 inference(rewrite,[status(thm)],[])).
% 0.24/0.41 tff(20,plain,
% 0.24/0.41 ((~![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))) | (in(A!3, B!2) | disjoint(singleton(A!3), B!2))),
% 0.24/0.41 inference(quant_inst,[status(thm)],[])).
% 0.24/0.41 tff(21,plain,
% 0.24/0.41 ((~![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))) | in(A!3, B!2) | disjoint(singleton(A!3), B!2)),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.24/0.41 tff(22,plain,
% 0.24/0.41 (in(A!3, B!2)),
% 0.24/0.41 inference(unit_resolution,[status(thm)],[21, 18, 8])).
% 0.24/0.41 tff(23,plain,
% 0.24/0.41 (^[A: $i, B: $i] : refl(((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A))) <=> ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A))))),
% 0.24/0.41 inference(bind,[status(th)],[])).
% 0.24/0.41 tff(24,plain,
% 0.24/0.41 (![A: $i, B: $i] : ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A))) <=> ![A: $i, B: $i] : ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A)))),
% 0.24/0.41 inference(quant_intro,[status(thm)],[23])).
% 0.24/0.41 tff(25,plain,
% 0.24/0.41 (![A: $i, B: $i] : ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A))) <=> ![A: $i, B: $i] : ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A)))),
% 0.24/0.41 inference(rewrite,[status(thm)],[])).
% 0.24/0.41 tff(26,plain,
% 0.24/0.41 (^[A: $i, B: $i] : rewrite((in(A, B) => (set_intersection2(B, singleton(A)) = singleton(A))) <=> ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A))))),
% 0.24/0.41 inference(bind,[status(th)],[])).
% 0.24/0.41 tff(27,plain,
% 0.24/0.41 (![A: $i, B: $i] : (in(A, B) => (set_intersection2(B, singleton(A)) = singleton(A))) <=> ![A: $i, B: $i] : ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A)))),
% 0.24/0.41 inference(quant_intro,[status(thm)],[26])).
% 0.24/0.41 tff(28,axiom,(![A: $i, B: $i] : (in(A, B) => (set_intersection2(B, singleton(A)) = singleton(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l32_zfmisc_1')).
% 0.24/0.41 tff(29,plain,
% 0.24/0.41 (![A: $i, B: $i] : ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A)))),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.24/0.41 tff(30,plain,
% 0.24/0.41 (![A: $i, B: $i] : ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A)))),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.24/0.41 tff(31,plain,(
% 0.24/0.41 ![A: $i, B: $i] : ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A)))),
% 0.24/0.41 inference(skolemize,[status(sab)],[30])).
% 0.24/0.41 tff(32,plain,
% 0.24/0.41 (![A: $i, B: $i] : ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A)))),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.24/0.41 tff(33,plain,
% 0.24/0.41 (((~![A: $i, B: $i] : ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A)))) | ((~in(A!3, B!2)) | (set_intersection2(B!2, singleton(A!3)) = singleton(A!3)))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A)))) | (~in(A!3, B!2)) | (set_intersection2(B!2, singleton(A!3)) = singleton(A!3)))),
% 0.24/0.41 inference(rewrite,[status(thm)],[])).
% 0.24/0.41 tff(34,plain,
% 0.24/0.41 ((~![A: $i, B: $i] : ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A)))) | ((~in(A!3, B!2)) | (set_intersection2(B!2, singleton(A!3)) = singleton(A!3)))),
% 0.24/0.41 inference(quant_inst,[status(thm)],[])).
% 0.24/0.41 tff(35,plain,
% 0.24/0.41 ((~![A: $i, B: $i] : ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A)))) | (~in(A!3, B!2)) | (set_intersection2(B!2, singleton(A!3)) = singleton(A!3))),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.24/0.41 tff(36,plain,
% 0.24/0.41 (set_intersection2(B!2, singleton(A!3)) = singleton(A!3)),
% 0.24/0.41 inference(unit_resolution,[status(thm)],[35, 32, 22])).
% 0.24/0.41 tff(37,plain,
% 0.24/0.41 (^[A: $i, B: $i] : refl((set_intersection2(A, B) = set_intersection2(B, A)) <=> (set_intersection2(A, B) = set_intersection2(B, A)))),
% 0.24/0.41 inference(bind,[status(th)],[])).
% 0.24/0.41 tff(38,plain,
% 0.24/0.41 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.24/0.41 inference(quant_intro,[status(thm)],[37])).
% 0.24/0.41 tff(39,plain,
% 0.24/0.41 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.24/0.41 inference(rewrite,[status(thm)],[])).
% 0.24/0.41 tff(40,axiom,(![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 0.24/0.41 tff(41,plain,
% 0.24/0.41 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.24/0.41 tff(42,plain,(
% 0.24/0.41 ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.24/0.41 inference(skolemize,[status(sab)],[41])).
% 0.24/0.41 tff(43,plain,
% 0.24/0.41 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.24/0.41 tff(44,plain,
% 0.24/0.41 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(singleton(A!3), B!2) = set_intersection2(B!2, singleton(A!3)))),
% 0.24/0.41 inference(quant_inst,[status(thm)],[])).
% 0.24/0.41 tff(45,plain,
% 0.24/0.41 (set_intersection2(singleton(A!3), B!2) = set_intersection2(B!2, singleton(A!3))),
% 0.24/0.41 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.24/0.41 tff(46,plain,
% 0.24/0.41 (set_intersection2(singleton(A!3), B!2) = singleton(A!3)),
% 0.24/0.41 inference(transitivity,[status(thm)],[45, 36])).
% 0.24/0.41 tff(47,plain,
% 0.24/0.41 (~(set_intersection2(singleton(A!3), B!2) = singleton(A!3))),
% 0.24/0.41 inference(or_elim,[status(thm)],[7])).
% 0.24/0.41 tff(48,plain,
% 0.24/0.41 ($false),
% 0.24/0.41 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.24/0.41 % SZS output end Proof
% 0.24/0.41 % E exiting
%------------------------------------------------------------------------------