%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU097+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:26:53 AM UTC 2025
% Result : Theorem 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU097+1 : TPTP v9.0.0. Released v3.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 06:03:33 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.39 % SZS status Theorem
% 0.20/0.39 % SZS output start Proof
% 0.20/0.39 tff(finite_type, type, (
% 0.20/0.39 finite: $i > $o)).
% 0.20/0.39 tff(set_union2_type, type, (
% 0.20/0.39 set_union2: ( $i * $i ) > $i)).
% 0.20/0.39 tff(set_difference_type, type, (
% 0.20/0.39 set_difference: ( $i * $i ) > $i)).
% 0.20/0.39 tff(tptp_fun_A_27_type, type, (
% 0.20/0.39 tptp_fun_A_27: $i)).
% 0.20/0.39 tff(tptp_fun_B_26_type, type, (
% 0.20/0.39 tptp_fun_B_26: $i)).
% 0.20/0.39 tff(symmetric_difference_type, type, (
% 0.20/0.39 symmetric_difference: ( $i * $i ) > $i)).
% 0.20/0.39 tff(1,plain,
% 0.20/0.39 (^[A: $i, B: $i] : refl((symmetric_difference(A, B) = set_union2(set_difference(A, B), set_difference(B, A))) <=> (symmetric_difference(A, B) = set_union2(set_difference(A, B), set_difference(B, A))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(2,plain,
% 0.20/0.39 (![A: $i, B: $i] : (symmetric_difference(A, B) = set_union2(set_difference(A, B), set_difference(B, A))) <=> ![A: $i, B: $i] : (symmetric_difference(A, B) = set_union2(set_difference(A, B), set_difference(B, A)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.39 tff(3,plain,
% 0.20/0.39 (![A: $i, B: $i] : (symmetric_difference(A, B) = set_union2(set_difference(A, B), set_difference(B, A))) <=> ![A: $i, B: $i] : (symmetric_difference(A, B) = set_union2(set_difference(A, B), set_difference(B, A)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(4,axiom,(![A: $i, B: $i] : (symmetric_difference(A, B) = set_union2(set_difference(A, B), set_difference(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d6_xboole_0')).
% 0.20/0.39 tff(5,plain,
% 0.20/0.39 (![A: $i, B: $i] : (symmetric_difference(A, B) = set_union2(set_difference(A, B), set_difference(B, A)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.39 tff(6,plain,(
% 0.20/0.39 ![A: $i, B: $i] : (symmetric_difference(A, B) = set_union2(set_difference(A, B), set_difference(B, A)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[5])).
% 0.20/0.39 tff(7,plain,
% 0.20/0.39 (![A: $i, B: $i] : (symmetric_difference(A, B) = set_union2(set_difference(A, B), set_difference(B, A)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.39 tff(8,plain,
% 0.20/0.39 ((~![A: $i, B: $i] : (symmetric_difference(A, B) = set_union2(set_difference(A, B), set_difference(B, A)))) | (symmetric_difference(A!27, B!26) = set_union2(set_difference(A!27, B!26), set_difference(B!26, A!27)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(9,plain,
% 0.20/0.39 (symmetric_difference(A!27, B!26) = set_union2(set_difference(A!27, B!26), set_difference(B!26, A!27))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.39 tff(10,plain,
% 0.20/0.39 (set_union2(set_difference(A!27, B!26), set_difference(B!26, A!27)) = symmetric_difference(A!27, B!26)),
% 0.20/0.39 inference(symmetry,[status(thm)],[9])).
% 0.20/0.39 tff(11,plain,
% 0.20/0.39 (finite(set_union2(set_difference(A!27, B!26), set_difference(B!26, A!27))) <=> finite(symmetric_difference(A!27, B!26))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[10])).
% 0.20/0.39 tff(12,plain,
% 0.20/0.39 (finite(symmetric_difference(A!27, B!26)) <=> finite(set_union2(set_difference(A!27, B!26), set_difference(B!26, A!27)))),
% 0.20/0.39 inference(symmetry,[status(thm)],[11])).
% 0.20/0.39 tff(13,plain,
% 0.20/0.39 ((~finite(symmetric_difference(A!27, B!26))) <=> (~finite(set_union2(set_difference(A!27, B!26), set_difference(B!26, A!27))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[12])).
% 0.20/0.39 tff(14,plain,
% 0.20/0.39 ((~![A: $i, B: $i] : (finite(symmetric_difference(A, B)) | (~(finite(A) & finite(B))))) <=> (~![A: $i, B: $i] : (finite(symmetric_difference(A, B)) | (~(finite(A) & finite(B)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(15,plain,
% 0.20/0.39 ((~![A: $i, B: $i] : ((finite(A) & finite(B)) => finite(symmetric_difference(A, B)))) <=> (~![A: $i, B: $i] : (finite(symmetric_difference(A, B)) | (~(finite(A) & finite(B)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(16,axiom,(~![A: $i, B: $i] : ((finite(A) & finite(B)) => finite(symmetric_difference(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t28_finset_1')).
% 0.20/0.39 tff(17,plain,
% 0.20/0.39 (~![A: $i, B: $i] : (finite(symmetric_difference(A, B)) | (~(finite(A) & finite(B))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.39 tff(18,plain,
% 0.20/0.39 (~![A: $i, B: $i] : (finite(symmetric_difference(A, B)) | (~(finite(A) & finite(B))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.20/0.39 tff(19,plain,
% 0.20/0.39 (~![A: $i, B: $i] : (finite(symmetric_difference(A, B)) | (~(finite(A) & finite(B))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.39 tff(20,plain,
% 0.20/0.39 (~![A: $i, B: $i] : (finite(symmetric_difference(A, B)) | (~(finite(A) & finite(B))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.20/0.39 tff(21,plain,(
% 0.20/0.39 ~(finite(symmetric_difference(A!27, B!26)) | (~(finite(A!27) & finite(B!26))))),
% 0.20/0.39 inference(skolemize,[status(sab)],[20])).
% 0.20/0.39 tff(22,plain,
% 0.20/0.39 (~finite(symmetric_difference(A!27, B!26))),
% 0.20/0.39 inference(or_elim,[status(thm)],[21])).
% 0.20/0.39 tff(23,plain,
% 0.20/0.39 (~finite(set_union2(set_difference(A!27, B!26), set_difference(B!26, A!27)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[22, 13])).
% 0.20/0.39 tff(24,plain,
% 0.20/0.39 (finite(A!27) & finite(B!26)),
% 0.20/0.39 inference(or_elim,[status(thm)],[21])).
% 0.20/0.39 tff(25,plain,
% 0.20/0.39 (finite(A!27)),
% 0.20/0.39 inference(and_elim,[status(thm)],[24])).
% 0.20/0.39 tff(26,plain,
% 0.20/0.39 (^[A: $i, B: $i] : refl((finite(set_difference(A, B)) | (~finite(A))) <=> (finite(set_difference(A, B)) | (~finite(A))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(27,plain,
% 0.20/0.39 (![A: $i, B: $i] : (finite(set_difference(A, B)) | (~finite(A))) <=> ![A: $i, B: $i] : (finite(set_difference(A, B)) | (~finite(A)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[26])).
% 0.20/0.39 tff(28,plain,
% 0.20/0.39 (![A: $i, B: $i] : (finite(set_difference(A, B)) | (~finite(A))) <=> ![A: $i, B: $i] : (finite(set_difference(A, B)) | (~finite(A)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(29,plain,
% 0.20/0.39 (^[A: $i, B: $i] : rewrite((finite(A) => finite(set_difference(A, B))) <=> (finite(set_difference(A, B)) | (~finite(A))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(30,plain,
% 0.20/0.39 (![A: $i, B: $i] : (finite(A) => finite(set_difference(A, B))) <=> ![A: $i, B: $i] : (finite(set_difference(A, B)) | (~finite(A)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[29])).
% 0.20/0.39 tff(31,axiom,(![A: $i, B: $i] : (finite(A) => finite(set_difference(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc12_finset_1')).
% 0.20/0.39 tff(32,plain,
% 0.20/0.39 (![A: $i, B: $i] : (finite(set_difference(A, B)) | (~finite(A)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.20/0.39 tff(33,plain,
% 0.20/0.39 (![A: $i, B: $i] : (finite(set_difference(A, B)) | (~finite(A)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.20/0.39 tff(34,plain,(
% 0.20/0.39 ![A: $i, B: $i] : (finite(set_difference(A, B)) | (~finite(A)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[33])).
% 0.20/0.39 tff(35,plain,
% 0.20/0.39 (![A: $i, B: $i] : (finite(set_difference(A, B)) | (~finite(A)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.20/0.39 tff(36,plain,
% 0.20/0.39 (((~![A: $i, B: $i] : (finite(set_difference(A, B)) | (~finite(A)))) | (finite(set_difference(A!27, B!26)) | (~finite(A!27)))) <=> ((~![A: $i, B: $i] : (finite(set_difference(A, B)) | (~finite(A)))) | finite(set_difference(A!27, B!26)) | (~finite(A!27)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(37,plain,
% 0.20/0.39 ((~![A: $i, B: $i] : (finite(set_difference(A, B)) | (~finite(A)))) | (finite(set_difference(A!27, B!26)) | (~finite(A!27)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(38,plain,
% 0.20/0.39 ((~![A: $i, B: $i] : (finite(set_difference(A, B)) | (~finite(A)))) | finite(set_difference(A!27, B!26)) | (~finite(A!27))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.20/0.39 tff(39,plain,
% 0.20/0.39 (finite(set_difference(A!27, B!26))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[38, 35, 25])).
% 0.20/0.39 tff(40,plain,
% 0.20/0.39 (finite(B!26)),
% 0.20/0.39 inference(and_elim,[status(thm)],[24])).
% 0.20/0.39 tff(41,plain,
% 0.20/0.39 (((~![A: $i, B: $i] : (finite(set_difference(A, B)) | (~finite(A)))) | (finite(set_difference(B!26, A!27)) | (~finite(B!26)))) <=> ((~![A: $i, B: $i] : (finite(set_difference(A, B)) | (~finite(A)))) | finite(set_difference(B!26, A!27)) | (~finite(B!26)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(42,plain,
% 0.20/0.39 ((~![A: $i, B: $i] : (finite(set_difference(A, B)) | (~finite(A)))) | (finite(set_difference(B!26, A!27)) | (~finite(B!26)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(43,plain,
% 0.20/0.39 ((~![A: $i, B: $i] : (finite(set_difference(A, B)) | (~finite(A)))) | finite(set_difference(B!26, A!27)) | (~finite(B!26))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.39 tff(44,plain,
% 0.20/0.39 (finite(set_difference(B!26, A!27))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[43, 35, 40])).
% 0.20/0.39 tff(45,plain,
% 0.20/0.39 (^[A: $i, B: $i] : refl((finite(set_union2(A, B)) | (~finite(B)) | (~finite(A))) <=> (finite(set_union2(A, B)) | (~finite(B)) | (~finite(A))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(46,plain,
% 0.20/0.39 (![A: $i, B: $i] : (finite(set_union2(A, B)) | (~finite(B)) | (~finite(A))) <=> ![A: $i, B: $i] : (finite(set_union2(A, B)) | (~finite(B)) | (~finite(A)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[45])).
% 0.20/0.39 tff(47,plain,
% 0.20/0.39 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((finite(A) & finite(B)) <=> (~((~finite(B)) | (~finite(A))))), ((~(finite(A) & finite(B))) <=> (~(~((~finite(B)) | (~finite(A))))))), rewrite((~(~((~finite(B)) | (~finite(A))))) <=> ((~finite(B)) | (~finite(A)))), ((~(finite(A) & finite(B))) <=> ((~finite(B)) | (~finite(A))))), ((finite(set_union2(A, B)) | (~(finite(A) & finite(B)))) <=> (finite(set_union2(A, B)) | ((~finite(B)) | (~finite(A)))))), rewrite((finite(set_union2(A, B)) | ((~finite(B)) | (~finite(A)))) <=> (finite(set_union2(A, B)) | (~finite(B)) | (~finite(A)))), ((finite(set_union2(A, B)) | (~(finite(A) & finite(B)))) <=> (finite(set_union2(A, B)) | (~finite(B)) | (~finite(A)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(48,plain,
% 0.20/0.39 (![A: $i, B: $i] : (finite(set_union2(A, B)) | (~(finite(A) & finite(B)))) <=> ![A: $i, B: $i] : (finite(set_union2(A, B)) | (~finite(B)) | (~finite(A)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[47])).
% 0.20/0.39 tff(49,plain,
% 0.20/0.39 (![A: $i, B: $i] : (finite(set_union2(A, B)) | (~(finite(A) & finite(B)))) <=> ![A: $i, B: $i] : (finite(set_union2(A, B)) | (~(finite(A) & finite(B))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(50,plain,
% 0.20/0.39 (^[A: $i, B: $i] : rewrite(((finite(A) & finite(B)) => finite(set_union2(A, B))) <=> (finite(set_union2(A, B)) | (~(finite(A) & finite(B)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(51,plain,
% 0.20/0.39 (![A: $i, B: $i] : ((finite(A) & finite(B)) => finite(set_union2(A, B))) <=> ![A: $i, B: $i] : (finite(set_union2(A, B)) | (~(finite(A) & finite(B))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[50])).
% 0.20/0.39 tff(52,axiom,(![A: $i, B: $i] : ((finite(A) & finite(B)) => finite(set_union2(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc9_finset_1')).
% 0.20/0.39 tff(53,plain,
% 0.20/0.39 (![A: $i, B: $i] : (finite(set_union2(A, B)) | (~(finite(A) & finite(B))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.20/0.39 tff(54,plain,
% 0.20/0.39 (![A: $i, B: $i] : (finite(set_union2(A, B)) | (~(finite(A) & finite(B))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.20/0.39 tff(55,plain,(
% 0.20/0.39 ![A: $i, B: $i] : (finite(set_union2(A, B)) | (~(finite(A) & finite(B))))),
% 0.20/0.39 inference(skolemize,[status(sab)],[54])).
% 0.20/0.39 tff(56,plain,
% 0.20/0.39 (![A: $i, B: $i] : (finite(set_union2(A, B)) | (~finite(B)) | (~finite(A)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.20/0.39 tff(57,plain,
% 0.20/0.39 (![A: $i, B: $i] : (finite(set_union2(A, B)) | (~finite(B)) | (~finite(A)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[56, 46])).
% 0.20/0.39 tff(58,plain,
% 0.20/0.39 (((~![A: $i, B: $i] : (finite(set_union2(A, B)) | (~finite(B)) | (~finite(A)))) | (finite(set_union2(set_difference(A!27, B!26), set_difference(B!26, A!27))) | (~finite(set_difference(B!26, A!27))) | (~finite(set_difference(A!27, B!26))))) <=> ((~![A: $i, B: $i] : (finite(set_union2(A, B)) | (~finite(B)) | (~finite(A)))) | finite(set_union2(set_difference(A!27, B!26), set_difference(B!26, A!27))) | (~finite(set_difference(B!26, A!27))) | (~finite(set_difference(A!27, B!26))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(59,plain,
% 0.20/0.39 ((~![A: $i, B: $i] : (finite(set_union2(A, B)) | (~finite(B)) | (~finite(A)))) | (finite(set_union2(set_difference(A!27, B!26), set_difference(B!26, A!27))) | (~finite(set_difference(B!26, A!27))) | (~finite(set_difference(A!27, B!26))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(60,plain,
% 0.20/0.39 ((~![A: $i, B: $i] : (finite(set_union2(A, B)) | (~finite(B)) | (~finite(A)))) | finite(set_union2(set_difference(A!27, B!26), set_difference(B!26, A!27))) | (~finite(set_difference(B!26, A!27))) | (~finite(set_difference(A!27, B!26)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.20/0.40 tff(61,plain,
% 0.20/0.40 (finite(set_union2(set_difference(A!27, B!26), set_difference(B!26, A!27))) | (~finite(set_difference(B!26, A!27))) | (~finite(set_difference(A!27, B!26)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[60, 57])).
% 0.20/0.40 tff(62,plain,
% 0.20/0.40 (finite(set_union2(set_difference(A!27, B!26), set_difference(B!26, A!27)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[61, 44, 39])).
% 0.20/0.40 tff(63,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[62, 23])).
% 0.20/0.40 % SZS output end Proof
% 0.20/0.40 % E exiting
%------------------------------------------------------------------------------