TSTP Solution File: SEU097+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU097+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 07:27:29 EDT 2022
% Result : Theorem 0.21s 0.42s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU097+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n007.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 : Sat Sep 3 09:10:04 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.21/0.42 % SZS status Theorem
% 0.21/0.42 % SZS output start Proof
% 0.21/0.42 tff(finite_type, type, (
% 0.21/0.42 finite: $i > $o)).
% 0.21/0.42 tff(set_union2_type, type, (
% 0.21/0.42 set_union2: ( $i * $i ) > $i)).
% 0.21/0.42 tff(set_difference_type, type, (
% 0.21/0.42 set_difference: ( $i * $i ) > $i)).
% 0.21/0.42 tff(tptp_fun_A_27_type, type, (
% 0.21/0.42 tptp_fun_A_27: $i)).
% 0.21/0.42 tff(tptp_fun_B_26_type, type, (
% 0.21/0.42 tptp_fun_B_26: $i)).
% 0.21/0.42 tff(symmetric_difference_type, type, (
% 0.21/0.42 symmetric_difference: ( $i * $i ) > $i)).
% 0.21/0.42 tff(1,plain,
% 0.21/0.42 (^[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))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(2,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.42 tff(3,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(4,axiom,(![A: $i, B: $i] : (symmetric_difference(A, B) = set_union2(set_difference(A, B), set_difference(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d6_xboole_0')).
% 0.21/0.42 tff(5,plain,
% 0.21/0.42 (![A: $i, B: $i] : (symmetric_difference(A, B) = set_union2(set_difference(A, B), set_difference(B, A)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.42 tff(6,plain,(
% 0.21/0.42 ![A: $i, B: $i] : (symmetric_difference(A, B) = set_union2(set_difference(A, B), set_difference(B, A)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[5])).
% 0.21/0.42 tff(7,plain,
% 0.21/0.42 (![A: $i, B: $i] : (symmetric_difference(A, B) = set_union2(set_difference(A, B), set_difference(B, A)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.42 tff(8,plain,
% 0.21/0.42 ((~![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)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(9,plain,
% 0.21/0.42 (symmetric_difference(A!27, B!26) = set_union2(set_difference(A!27, B!26), set_difference(B!26, A!27))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.42 tff(10,plain,
% 0.21/0.42 (set_union2(set_difference(A!27, B!26), set_difference(B!26, A!27)) = symmetric_difference(A!27, B!26)),
% 0.21/0.42 inference(symmetry,[status(thm)],[9])).
% 0.21/0.42 tff(11,plain,
% 0.21/0.42 (finite(set_union2(set_difference(A!27, B!26), set_difference(B!26, A!27))) <=> finite(symmetric_difference(A!27, B!26))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[10])).
% 0.21/0.42 tff(12,plain,
% 0.21/0.42 (finite(symmetric_difference(A!27, B!26)) <=> finite(set_union2(set_difference(A!27, B!26), set_difference(B!26, A!27)))),
% 0.21/0.42 inference(symmetry,[status(thm)],[11])).
% 0.21/0.42 tff(13,plain,
% 0.21/0.42 ((~finite(symmetric_difference(A!27, B!26))) <=> (~finite(set_union2(set_difference(A!27, B!26), set_difference(B!26, A!27))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[12])).
% 0.21/0.42 tff(14,plain,
% 0.21/0.42 ((~![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)))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(15,plain,
% 0.21/0.42 ((~![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)))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(16,axiom,(~![A: $i, B: $i] : ((finite(A) & finite(B)) => finite(symmetric_difference(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t28_finset_1')).
% 0.21/0.42 tff(17,plain,
% 0.21/0.42 (~![A: $i, B: $i] : (finite(symmetric_difference(A, B)) | (~(finite(A) & finite(B))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.21/0.42 tff(18,plain,
% 0.21/0.42 (~![A: $i, B: $i] : (finite(symmetric_difference(A, B)) | (~(finite(A) & finite(B))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.21/0.43 tff(19,plain,
% 0.21/0.43 (~![A: $i, B: $i] : (finite(symmetric_difference(A, B)) | (~(finite(A) & finite(B))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.21/0.43 tff(20,plain,
% 0.21/0.43 (~![A: $i, B: $i] : (finite(symmetric_difference(A, B)) | (~(finite(A) & finite(B))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.21/0.43 tff(21,plain,
% 0.21/0.43 (~![A: $i, B: $i] : (finite(symmetric_difference(A, B)) | (~(finite(A) & finite(B))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[20, 14])).
% 0.21/0.43 tff(22,plain,
% 0.21/0.43 (~![A: $i, B: $i] : (finite(symmetric_difference(A, B)) | (~(finite(A) & finite(B))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.21/0.43 tff(23,plain,
% 0.21/0.43 (~![A: $i, B: $i] : (finite(symmetric_difference(A, B)) | (~(finite(A) & finite(B))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[22, 14])).
% 0.21/0.43 tff(24,plain,(
% 0.21/0.43 ~(finite(symmetric_difference(A!27, B!26)) | (~(finite(A!27) & finite(B!26))))),
% 0.21/0.43 inference(skolemize,[status(sab)],[23])).
% 0.21/0.43 tff(25,plain,
% 0.21/0.43 (~finite(symmetric_difference(A!27, B!26))),
% 0.21/0.43 inference(or_elim,[status(thm)],[24])).
% 0.21/0.43 tff(26,plain,
% 0.21/0.43 (~finite(set_union2(set_difference(A!27, B!26), set_difference(B!26, A!27)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[25, 13])).
% 0.21/0.43 tff(27,plain,
% 0.21/0.43 (finite(A!27) & finite(B!26)),
% 0.21/0.43 inference(or_elim,[status(thm)],[24])).
% 0.21/0.43 tff(28,plain,
% 0.21/0.43 (finite(A!27)),
% 0.21/0.43 inference(and_elim,[status(thm)],[27])).
% 0.21/0.43 tff(29,plain,
% 0.21/0.43 (^[A: $i, B: $i] : refl((finite(set_difference(A, B)) | (~finite(A))) <=> (finite(set_difference(A, B)) | (~finite(A))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(30,plain,
% 0.21/0.43 (![A: $i, B: $i] : (finite(set_difference(A, B)) | (~finite(A))) <=> ![A: $i, B: $i] : (finite(set_difference(A, B)) | (~finite(A)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[29])).
% 0.21/0.43 tff(31,plain,
% 0.21/0.43 (![A: $i, B: $i] : (finite(set_difference(A, B)) | (~finite(A))) <=> ![A: $i, B: $i] : (finite(set_difference(A, B)) | (~finite(A)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(32,plain,
% 0.21/0.43 (^[A: $i, B: $i] : rewrite((finite(A) => finite(set_difference(A, B))) <=> (finite(set_difference(A, B)) | (~finite(A))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(33,plain,
% 0.21/0.43 (![A: $i, B: $i] : (finite(A) => finite(set_difference(A, B))) <=> ![A: $i, B: $i] : (finite(set_difference(A, B)) | (~finite(A)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[32])).
% 0.21/0.43 tff(34,axiom,(![A: $i, B: $i] : (finite(A) => finite(set_difference(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc12_finset_1')).
% 0.21/0.43 tff(35,plain,
% 0.21/0.43 (![A: $i, B: $i] : (finite(set_difference(A, B)) | (~finite(A)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.21/0.43 tff(36,plain,
% 0.21/0.43 (![A: $i, B: $i] : (finite(set_difference(A, B)) | (~finite(A)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.21/0.43 tff(37,plain,(
% 0.21/0.43 ![A: $i, B: $i] : (finite(set_difference(A, B)) | (~finite(A)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[36])).
% 0.21/0.43 tff(38,plain,
% 0.21/0.43 (![A: $i, B: $i] : (finite(set_difference(A, B)) | (~finite(A)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.21/0.43 tff(39,plain,
% 0.21/0.43 (((~![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)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(40,plain,
% 0.21/0.43 ((~![A: $i, B: $i] : (finite(set_difference(A, B)) | (~finite(A)))) | (finite(set_difference(A!27, B!26)) | (~finite(A!27)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(41,plain,
% 0.21/0.43 ((~![A: $i, B: $i] : (finite(set_difference(A, B)) | (~finite(A)))) | finite(set_difference(A!27, B!26)) | (~finite(A!27))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.21/0.43 tff(42,plain,
% 0.21/0.43 (finite(set_difference(A!27, B!26))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[41, 38, 28])).
% 0.21/0.43 tff(43,plain,
% 0.21/0.43 (finite(B!26)),
% 0.21/0.43 inference(and_elim,[status(thm)],[27])).
% 0.21/0.43 tff(44,plain,
% 0.21/0.43 (((~![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)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(45,plain,
% 0.21/0.43 ((~![A: $i, B: $i] : (finite(set_difference(A, B)) | (~finite(A)))) | (finite(set_difference(B!26, A!27)) | (~finite(B!26)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(46,plain,
% 0.21/0.43 ((~![A: $i, B: $i] : (finite(set_difference(A, B)) | (~finite(A)))) | finite(set_difference(B!26, A!27)) | (~finite(B!26))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.21/0.43 tff(47,plain,
% 0.21/0.43 (finite(set_difference(B!26, A!27))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[46, 38, 43])).
% 0.21/0.43 tff(48,plain,
% 0.21/0.43 (^[A: $i, B: $i] : refl((finite(set_union2(A, B)) | (~finite(B)) | (~finite(A))) <=> (finite(set_union2(A, B)) | (~finite(B)) | (~finite(A))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(49,plain,
% 0.21/0.43 (![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)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[48])).
% 0.21/0.43 tff(50,plain,
% 0.21/0.43 (^[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)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(51,plain,
% 0.21/0.43 (![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)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[50])).
% 0.21/0.43 tff(52,plain,
% 0.21/0.43 (![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))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(53,plain,
% 0.21/0.43 (^[A: $i, B: $i] : rewrite(((finite(A) & finite(B)) => finite(set_union2(A, B))) <=> (finite(set_union2(A, B)) | (~(finite(A) & finite(B)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(54,plain,
% 0.21/0.43 (![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))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[53])).
% 0.21/0.43 tff(55,axiom,(![A: $i, B: $i] : ((finite(A) & finite(B)) => finite(set_union2(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc9_finset_1')).
% 0.21/0.43 tff(56,plain,
% 0.21/0.43 (![A: $i, B: $i] : (finite(set_union2(A, B)) | (~(finite(A) & finite(B))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.21/0.43 tff(57,plain,
% 0.21/0.43 (![A: $i, B: $i] : (finite(set_union2(A, B)) | (~(finite(A) & finite(B))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.21/0.43 tff(58,plain,(
% 0.21/0.43 ![A: $i, B: $i] : (finite(set_union2(A, B)) | (~(finite(A) & finite(B))))),
% 0.21/0.43 inference(skolemize,[status(sab)],[57])).
% 0.21/0.43 tff(59,plain,
% 0.21/0.43 (![A: $i, B: $i] : (finite(set_union2(A, B)) | (~finite(B)) | (~finite(A)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.21/0.43 tff(60,plain,
% 0.21/0.43 (![A: $i, B: $i] : (finite(set_union2(A, B)) | (~finite(B)) | (~finite(A)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[59, 49])).
% 0.21/0.43 tff(61,plain,
% 0.21/0.43 (((~![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))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(62,plain,
% 0.21/0.43 ((~![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))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(63,plain,
% 0.21/0.43 ((~![A: $i, B: $i] : (finite(set_union2(A, B)) | (~finite(B)) | (~finite(A)))) | finite(set_union2(set_difference(A!27, B!26), set_difference(B!26, A!27))) | (~finite(set_difference(B!26, A!27))) | (~finite(set_difference(A!27, B!26)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.21/0.43 tff(64,plain,
% 0.21/0.43 (finite(set_union2(set_difference(A!27, B!26), set_difference(B!26, A!27))) | (~finite(set_difference(B!26, A!27))) | (~finite(set_difference(A!27, B!26)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[63, 60])).
% 0.21/0.43 tff(65,plain,
% 0.21/0.43 (finite(set_union2(set_difference(A!27, B!26), set_difference(B!26, A!27)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[64, 47, 42])).
% 0.21/0.43 tff(66,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[65, 26])).
% 0.21/0.43 % SZS output end Proof
%------------------------------------------------------------------------------