%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU137+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:26:59 AM UTC 2025
% Result : Theorem 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SEU137+2 : TPTP v9.0.0. Released v3.3.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n011.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 06:07:26 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.21/0.40 % SZS status Theorem
% 0.21/0.40 % SZS output start Proof
% 0.21/0.40 tff(set_union2_type, type, (
% 0.21/0.40 set_union2: ( $i * $i ) > $i)).
% 0.21/0.40 tff(set_difference_type, type, (
% 0.21/0.40 set_difference: ( $i * $i ) > $i)).
% 0.21/0.40 tff(tptp_fun_A_10_type, type, (
% 0.21/0.40 tptp_fun_A_10: $i)).
% 0.21/0.40 tff(tptp_fun_B_9_type, type, (
% 0.21/0.40 tptp_fun_B_9: $i)).
% 0.21/0.40 tff(subset_type, type, (
% 0.21/0.40 subset: ( $i * $i ) > $o)).
% 0.21/0.40 tff(1,plain,
% 0.21/0.40 (^[A: $i, B: $i] : refl((set_union2(A, set_difference(B, A)) = set_union2(A, B)) <=> (set_union2(A, set_difference(B, A)) = set_union2(A, B)))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(2,plain,
% 0.21/0.40 (![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B)) <=> ![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.40 tff(3,plain,
% 0.21/0.40 (![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B)) <=> ![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(4,axiom,(![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t39_xboole_1')).
% 0.21/0.40 tff(5,plain,
% 0.21/0.40 (![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.40 tff(6,plain,(
% 0.21/0.40 ![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B))),
% 0.21/0.40 inference(skolemize,[status(sab)],[5])).
% 0.21/0.40 tff(7,plain,
% 0.21/0.40 (![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.40 tff(8,plain,
% 0.21/0.40 ((~![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B))) | (set_union2(A!10, set_difference(B!9, A!10)) = set_union2(A!10, B!9))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(9,plain,
% 0.21/0.40 (set_union2(A!10, set_difference(B!9, A!10)) = set_union2(A!10, B!9)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.40 tff(10,plain,
% 0.21/0.40 (set_union2(A!10, B!9) = set_union2(A!10, set_difference(B!9, A!10))),
% 0.21/0.40 inference(symmetry,[status(thm)],[9])).
% 0.21/0.40 tff(11,plain,
% 0.21/0.40 ((~![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)))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(12,plain,
% 0.21/0.40 ((~![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)))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(13,axiom,(~![A: $i, B: $i] : (subset(A, B) => (B = set_union2(A, set_difference(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t45_xboole_1')).
% 0.21/0.40 tff(14,plain,
% 0.21/0.40 (~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.21/0.40 tff(15,plain,
% 0.21/0.40 (~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[14, 11])).
% 0.21/0.40 tff(16,plain,
% 0.21/0.40 (~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.21/0.40 tff(17,plain,
% 0.21/0.40 (~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[16, 11])).
% 0.21/0.40 tff(18,plain,(
% 0.21/0.40 ~((~subset(A!10, B!9)) | (B!9 = set_union2(A!10, set_difference(B!9, A!10))))),
% 0.21/0.40 inference(skolemize,[status(sab)],[17])).
% 0.21/0.40 tff(19,plain,
% 0.21/0.40 (subset(A!10, B!9)),
% 0.21/0.40 inference(or_elim,[status(thm)],[18])).
% 0.21/0.40 tff(20,plain,
% 0.21/0.40 (^[A: $i, B: $i] : refl(((~subset(A, B)) | (set_union2(A, B) = B)) <=> ((~subset(A, B)) | (set_union2(A, B) = B)))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(21,plain,
% 0.21/0.40 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[20])).
% 0.21/0.40 tff(22,plain,
% 0.21/0.40 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(23,plain,
% 0.21/0.40 (^[A: $i, B: $i] : rewrite((subset(A, B) => (set_union2(A, B) = B)) <=> ((~subset(A, B)) | (set_union2(A, B) = B)))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(24,plain,
% 0.21/0.40 (![A: $i, B: $i] : (subset(A, B) => (set_union2(A, B) = B)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[23])).
% 0.21/0.40 tff(25,axiom,(![A: $i, B: $i] : (subset(A, B) => (set_union2(A, B) = B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t12_xboole_1')).
% 0.21/0.40 tff(26,plain,
% 0.21/0.40 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.21/0.40 tff(27,plain,
% 0.21/0.40 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.21/0.40 tff(28,plain,(
% 0.21/0.40 ![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.21/0.40 inference(skolemize,[status(sab)],[27])).
% 0.21/0.40 tff(29,plain,
% 0.21/0.40 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.21/0.40 tff(30,plain,
% 0.21/0.40 (((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | ((~subset(A!10, B!9)) | (set_union2(A!10, B!9) = B!9))) <=> ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | (~subset(A!10, B!9)) | (set_union2(A!10, B!9) = B!9))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(31,plain,
% 0.21/0.40 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | ((~subset(A!10, B!9)) | (set_union2(A!10, B!9) = B!9))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(32,plain,
% 0.21/0.40 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | (~subset(A!10, B!9)) | (set_union2(A!10, B!9) = B!9)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.21/0.40 tff(33,plain,
% 0.21/0.40 (set_union2(A!10, B!9) = B!9),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[32, 29, 19])).
% 0.21/0.40 tff(34,plain,
% 0.21/0.40 (B!9 = set_union2(A!10, B!9)),
% 0.21/0.40 inference(symmetry,[status(thm)],[33])).
% 0.21/0.40 tff(35,plain,
% 0.21/0.40 (B!9 = set_union2(A!10, set_difference(B!9, A!10))),
% 0.21/0.40 inference(transitivity,[status(thm)],[34, 10])).
% 0.21/0.40 tff(36,plain,
% 0.21/0.40 (~(B!9 = set_union2(A!10, set_difference(B!9, A!10)))),
% 0.21/0.40 inference(or_elim,[status(thm)],[18])).
% 0.21/0.40 tff(37,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.21/0.40 % SZS output end Proof
% 0.21/0.40 % E exiting
%------------------------------------------------------------------------------