TSTP Solution File: SET621+3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET621+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 05:07:22 EDT 2022
% Result : Theorem 0.15s 0.35s
% Output : Proof 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SET621+3 : TPTP v8.1.0. Released v2.2.0.
% 0.00/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.30 % Computer : n026.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Sat Sep 3 07:14:08 EDT 2022
% 0.09/0.30 % CPUTime :
% 0.09/0.30 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.09/0.30 Usage: tptp [options] [-file:]file
% 0.09/0.30 -h, -? prints this message.
% 0.09/0.30 -smt2 print SMT-LIB2 benchmark.
% 0.09/0.30 -m, -model generate model.
% 0.09/0.30 -p, -proof generate proof.
% 0.09/0.30 -c, -core generate unsat core of named formulas.
% 0.09/0.30 -st, -statistics display statistics.
% 0.09/0.30 -t:timeout set timeout (in second).
% 0.09/0.30 -smt2status display status in smt2 format instead of SZS.
% 0.09/0.30 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.09/0.30 -<param>:<value> configuration parameter and value.
% 0.09/0.30 -o:<output-file> file to place output in.
% 0.15/0.35 % SZS status Theorem
% 0.15/0.35 % SZS output start Proof
% 0.15/0.35 tff(union_type, type, (
% 0.15/0.35 union: ( $i * $i ) > $i)).
% 0.15/0.35 tff(difference_type, type, (
% 0.15/0.35 difference: ( $i * $i ) > $i)).
% 0.15/0.35 tff(tptp_fun_D_2_type, type, (
% 0.15/0.35 tptp_fun_D_2: $i)).
% 0.15/0.35 tff(tptp_fun_B_4_type, type, (
% 0.15/0.35 tptp_fun_B_4: $i)).
% 0.15/0.35 tff(tptp_fun_C_3_type, type, (
% 0.15/0.35 tptp_fun_C_3: $i)).
% 0.15/0.35 tff(symmetric_difference_type, type, (
% 0.15/0.35 symmetric_difference: ( $i * $i ) > $i)).
% 0.15/0.35 tff(1,plain,
% 0.15/0.35 (^[B: $i, C: $i, D: $i] : refl((difference(difference(B, C), D) = difference(B, union(C, D))) <=> (difference(difference(B, C), D) = difference(B, union(C, D))))),
% 0.15/0.35 inference(bind,[status(th)],[])).
% 0.15/0.35 tff(2,plain,
% 0.15/0.35 (![B: $i, C: $i, D: $i] : (difference(difference(B, C), D) = difference(B, union(C, D))) <=> ![B: $i, C: $i, D: $i] : (difference(difference(B, C), D) = difference(B, union(C, D)))),
% 0.15/0.35 inference(quant_intro,[status(thm)],[1])).
% 0.15/0.35 tff(3,plain,
% 0.15/0.35 (![B: $i, C: $i, D: $i] : (difference(difference(B, C), D) = difference(B, union(C, D))) <=> ![B: $i, C: $i, D: $i] : (difference(difference(B, C), D) = difference(B, union(C, D)))),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(4,axiom,(![B: $i, C: $i, D: $i] : (difference(difference(B, C), D) = difference(B, union(C, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','difference_difference_union')).
% 0.15/0.35 tff(5,plain,
% 0.15/0.35 (![B: $i, C: $i, D: $i] : (difference(difference(B, C), D) = difference(B, union(C, D)))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.15/0.35 tff(6,plain,(
% 0.15/0.35 ![B: $i, C: $i, D: $i] : (difference(difference(B, C), D) = difference(B, union(C, D)))),
% 0.15/0.35 inference(skolemize,[status(sab)],[5])).
% 0.15/0.35 tff(7,plain,
% 0.15/0.35 (![B: $i, C: $i, D: $i] : (difference(difference(B, C), D) = difference(B, union(C, D)))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.15/0.35 tff(8,plain,
% 0.15/0.35 ((~![B: $i, C: $i, D: $i] : (difference(difference(B, C), D) = difference(B, union(C, D)))) | (difference(difference(C!3, B!4), D!2) = difference(C!3, union(B!4, D!2)))),
% 0.15/0.35 inference(quant_inst,[status(thm)],[])).
% 0.15/0.35 tff(9,plain,
% 0.15/0.35 (difference(difference(C!3, B!4), D!2) = difference(C!3, union(B!4, D!2))),
% 0.15/0.35 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.15/0.35 tff(10,plain,
% 0.15/0.35 ((~![B: $i, C: $i, D: $i] : (difference(difference(B, C), D) = difference(B, union(C, D)))) | (difference(difference(B!4, C!3), D!2) = difference(B!4, union(C!3, D!2)))),
% 0.15/0.35 inference(quant_inst,[status(thm)],[])).
% 0.15/0.35 tff(11,plain,
% 0.15/0.35 (difference(difference(B!4, C!3), D!2) = difference(B!4, union(C!3, D!2))),
% 0.15/0.35 inference(unit_resolution,[status(thm)],[10, 7])).
% 0.15/0.35 tff(12,plain,
% 0.15/0.35 (union(difference(difference(B!4, C!3), D!2), difference(difference(C!3, B!4), D!2)) = union(difference(B!4, union(C!3, D!2)), difference(C!3, union(B!4, D!2)))),
% 0.15/0.35 inference(monotonicity,[status(thm)],[11, 9])).
% 0.15/0.35 tff(13,plain,
% 0.15/0.35 (^[B: $i, C: $i, D: $i] : refl((difference(union(B, C), D) = union(difference(B, D), difference(C, D))) <=> (difference(union(B, C), D) = union(difference(B, D), difference(C, D))))),
% 0.15/0.35 inference(bind,[status(th)],[])).
% 0.15/0.35 tff(14,plain,
% 0.15/0.35 (![B: $i, C: $i, D: $i] : (difference(union(B, C), D) = union(difference(B, D), difference(C, D))) <=> ![B: $i, C: $i, D: $i] : (difference(union(B, C), D) = union(difference(B, D), difference(C, D)))),
% 0.15/0.35 inference(quant_intro,[status(thm)],[13])).
% 0.15/0.35 tff(15,plain,
% 0.15/0.35 (![B: $i, C: $i, D: $i] : (difference(union(B, C), D) = union(difference(B, D), difference(C, D))) <=> ![B: $i, C: $i, D: $i] : (difference(union(B, C), D) = union(difference(B, D), difference(C, D)))),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(16,axiom,(![B: $i, C: $i, D: $i] : (difference(union(B, C), D) = union(difference(B, D), difference(C, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','difference_distributes_over_union')).
% 0.15/0.35 tff(17,plain,
% 0.15/0.35 (![B: $i, C: $i, D: $i] : (difference(union(B, C), D) = union(difference(B, D), difference(C, D)))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.15/0.35 tff(18,plain,(
% 0.15/0.35 ![B: $i, C: $i, D: $i] : (difference(union(B, C), D) = union(difference(B, D), difference(C, D)))),
% 0.15/0.35 inference(skolemize,[status(sab)],[17])).
% 0.15/0.35 tff(19,plain,
% 0.15/0.35 (![B: $i, C: $i, D: $i] : (difference(union(B, C), D) = union(difference(B, D), difference(C, D)))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.15/0.35 tff(20,plain,
% 0.15/0.35 ((~![B: $i, C: $i, D: $i] : (difference(union(B, C), D) = union(difference(B, D), difference(C, D)))) | (difference(union(difference(B!4, C!3), difference(C!3, B!4)), D!2) = union(difference(difference(B!4, C!3), D!2), difference(difference(C!3, B!4), D!2)))),
% 0.15/0.35 inference(quant_inst,[status(thm)],[])).
% 0.15/0.35 tff(21,plain,
% 0.15/0.35 (difference(union(difference(B!4, C!3), difference(C!3, B!4)), D!2) = union(difference(difference(B!4, C!3), D!2), difference(difference(C!3, B!4), D!2))),
% 0.15/0.35 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.15/0.35 tff(22,plain,
% 0.15/0.35 (^[B: $i, C: $i] : refl((symmetric_difference(B, C) = union(difference(B, C), difference(C, B))) <=> (symmetric_difference(B, C) = union(difference(B, C), difference(C, B))))),
% 0.15/0.35 inference(bind,[status(th)],[])).
% 0.15/0.35 tff(23,plain,
% 0.15/0.35 (![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B))) <=> ![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.15/0.35 inference(quant_intro,[status(thm)],[22])).
% 0.15/0.35 tff(24,plain,
% 0.15/0.35 (![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B))) <=> ![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(25,axiom,(![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','symmetric_difference_defn')).
% 0.15/0.35 tff(26,plain,
% 0.15/0.35 (![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.15/0.35 tff(27,plain,(
% 0.15/0.35 ![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.15/0.35 inference(skolemize,[status(sab)],[26])).
% 0.15/0.35 tff(28,plain,
% 0.15/0.35 (![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.15/0.35 tff(29,plain,
% 0.15/0.35 ((~![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))) | (symmetric_difference(B!4, C!3) = union(difference(B!4, C!3), difference(C!3, B!4)))),
% 0.15/0.35 inference(quant_inst,[status(thm)],[])).
% 0.15/0.35 tff(30,plain,
% 0.15/0.35 (symmetric_difference(B!4, C!3) = union(difference(B!4, C!3), difference(C!3, B!4))),
% 0.15/0.35 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.15/0.35 tff(31,plain,
% 0.15/0.35 (difference(symmetric_difference(B!4, C!3), D!2) = difference(union(difference(B!4, C!3), difference(C!3, B!4)), D!2)),
% 0.15/0.35 inference(monotonicity,[status(thm)],[30])).
% 0.15/0.35 tff(32,plain,
% 0.15/0.35 (difference(symmetric_difference(B!4, C!3), D!2) = union(difference(B!4, union(C!3, D!2)), difference(C!3, union(B!4, D!2)))),
% 0.15/0.35 inference(transitivity,[status(thm)],[31, 21, 12])).
% 0.15/0.35 tff(33,plain,
% 0.15/0.35 ((~![B: $i, C: $i, D: $i] : (difference(symmetric_difference(B, C), D) = union(difference(B, union(C, D)), difference(C, union(B, D))))) <=> (~![B: $i, C: $i, D: $i] : (difference(symmetric_difference(B, C), D) = union(difference(B, union(C, D)), difference(C, union(B, D)))))),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(34,axiom,(~![B: $i, C: $i, D: $i] : (difference(symmetric_difference(B, C), D) = union(difference(B, union(C, D)), difference(C, union(B, D))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_th97')).
% 0.15/0.35 tff(35,plain,
% 0.15/0.35 (~![B: $i, C: $i, D: $i] : (difference(symmetric_difference(B, C), D) = union(difference(B, union(C, D)), difference(C, union(B, D))))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.15/0.35 tff(36,plain,
% 0.15/0.35 (~![B: $i, C: $i, D: $i] : (difference(symmetric_difference(B, C), D) = union(difference(B, union(C, D)), difference(C, union(B, D))))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[35, 33])).
% 0.15/0.35 tff(37,plain,
% 0.15/0.35 (~![B: $i, C: $i, D: $i] : (difference(symmetric_difference(B, C), D) = union(difference(B, union(C, D)), difference(C, union(B, D))))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[36, 33])).
% 0.15/0.35 tff(38,plain,
% 0.15/0.35 (~![B: $i, C: $i, D: $i] : (difference(symmetric_difference(B, C), D) = union(difference(B, union(C, D)), difference(C, union(B, D))))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.15/0.35 tff(39,plain,
% 0.15/0.35 (~![B: $i, C: $i, D: $i] : (difference(symmetric_difference(B, C), D) = union(difference(B, union(C, D)), difference(C, union(B, D))))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[38, 33])).
% 0.15/0.35 tff(40,plain,
% 0.15/0.35 (~![B: $i, C: $i, D: $i] : (difference(symmetric_difference(B, C), D) = union(difference(B, union(C, D)), difference(C, union(B, D))))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[39, 33])).
% 0.15/0.35 tff(41,plain,
% 0.15/0.35 (~![B: $i, C: $i, D: $i] : (difference(symmetric_difference(B, C), D) = union(difference(B, union(C, D)), difference(C, union(B, D))))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.15/0.35 tff(42,plain,(
% 0.15/0.35 ~(difference(symmetric_difference(B!4, C!3), D!2) = union(difference(B!4, union(C!3, D!2)), difference(C!3, union(B!4, D!2))))),
% 0.15/0.35 inference(skolemize,[status(sab)],[41])).
% 0.15/0.35 tff(43,plain,
% 0.15/0.35 ($false),
% 0.15/0.35 inference(unit_resolution,[status(thm)],[42, 32])).
% 0.15/0.35 % SZS output end Proof
%------------------------------------------------------------------------------