TSTP Solution File: SET618+3 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SET618+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n024.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 05:07:21 EDT 2022

% Result   : Theorem 0.20s 0.39s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET618+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33  % Computer : n024.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Sat Sep  3 07:00:48 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34  Usage: tptp [options] [-file:]file
% 0.13/0.34    -h, -?       prints this message.
% 0.13/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.34    -m, -model   generate model.
% 0.13/0.34    -p, -proof   generate proof.
% 0.13/0.34    -c, -core    generate unsat core of named formulas.
% 0.13/0.34    -st, -statistics display statistics.
% 0.13/0.34    -t:timeout   set timeout (in second).
% 0.13/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34    -<param>:<value> configuration parameter and value.
% 0.13/0.34    -o:<output-file> file to place output in.
% 0.20/0.39  % SZS status Theorem
% 0.20/0.39  % SZS output start Proof
% 0.20/0.39  tff(empty_set_type, type, (
% 0.20/0.39     empty_set: $i)).
% 0.20/0.39  tff(symmetric_difference_type, type, (
% 0.20/0.39     symmetric_difference: ( $i * $i ) > $i)).
% 0.20/0.39  tff(tptp_fun_B_3_type, type, (
% 0.20/0.39     tptp_fun_B_3: $i)).
% 0.20/0.39  tff(difference_type, type, (
% 0.20/0.39     difference: ( $i * $i ) > $i)).
% 0.20/0.39  tff(union_type, type, (
% 0.20/0.39     union: ( $i * $i ) > $i)).
% 0.20/0.39  tff(1,plain,
% 0.20/0.39      (^[B: $i] : refl((difference(B, B) = empty_set) <=> (difference(B, B) = empty_set))),
% 0.20/0.39      inference(bind,[status(th)],[])).
% 0.20/0.39  tff(2,plain,
% 0.20/0.39      (![B: $i] : (difference(B, B) = empty_set) <=> ![B: $i] : (difference(B, B) = empty_set)),
% 0.20/0.39      inference(quant_intro,[status(thm)],[1])).
% 0.20/0.39  tff(3,plain,
% 0.20/0.39      (![B: $i] : (difference(B, B) = empty_set) <=> ![B: $i] : (difference(B, B) = empty_set)),
% 0.20/0.39      inference(rewrite,[status(thm)],[])).
% 0.20/0.39  tff(4,axiom,(![B: $i] : (difference(B, B) = empty_set)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','self_difference_is_empty_set')).
% 0.20/0.39  tff(5,plain,
% 0.20/0.39      (![B: $i] : (difference(B, B) = empty_set)),
% 0.20/0.39      inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.39  tff(6,plain,(
% 0.20/0.39      ![B: $i] : (difference(B, B) = empty_set)),
% 0.20/0.39      inference(skolemize,[status(sab)],[5])).
% 0.20/0.39  tff(7,plain,
% 0.20/0.39      (![B: $i] : (difference(B, B) = empty_set)),
% 0.20/0.39      inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.39  tff(8,plain,
% 0.20/0.39      ((~![B: $i] : (difference(B, B) = empty_set)) | (difference(B!3, B!3) = empty_set)),
% 0.20/0.39      inference(quant_inst,[status(thm)],[])).
% 0.20/0.39  tff(9,plain,
% 0.20/0.39      (difference(B!3, B!3) = empty_set),
% 0.20/0.39      inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.39  tff(10,plain,
% 0.20/0.39      (^[B: $i] : refl((union(B, B) = B) <=> (union(B, B) = B))),
% 0.20/0.39      inference(bind,[status(th)],[])).
% 0.20/0.39  tff(11,plain,
% 0.20/0.39      (![B: $i] : (union(B, B) = B) <=> ![B: $i] : (union(B, B) = B)),
% 0.20/0.39      inference(quant_intro,[status(thm)],[10])).
% 0.20/0.39  tff(12,plain,
% 0.20/0.39      (![B: $i] : (union(B, B) = B) <=> ![B: $i] : (union(B, B) = B)),
% 0.20/0.39      inference(rewrite,[status(thm)],[])).
% 0.20/0.39  tff(13,axiom,(![B: $i] : (union(B, B) = B)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','idempotency_of_union')).
% 0.20/0.39  tff(14,plain,
% 0.20/0.39      (![B: $i] : (union(B, B) = B)),
% 0.20/0.39      inference(modus_ponens,[status(thm)],[13, 12])).
% 0.20/0.39  tff(15,plain,(
% 0.20/0.39      ![B: $i] : (union(B, B) = B)),
% 0.20/0.39      inference(skolemize,[status(sab)],[14])).
% 0.20/0.39  tff(16,plain,
% 0.20/0.39      (![B: $i] : (union(B, B) = B)),
% 0.20/0.39      inference(modus_ponens,[status(thm)],[15, 11])).
% 0.20/0.39  tff(17,plain,
% 0.20/0.39      ((~![B: $i] : (union(B, B) = B)) | (union(difference(B!3, B!3), difference(B!3, B!3)) = difference(B!3, B!3))),
% 0.20/0.39      inference(quant_inst,[status(thm)],[])).
% 0.20/0.39  tff(18,plain,
% 0.20/0.39      (union(difference(B!3, B!3), difference(B!3, B!3)) = difference(B!3, B!3)),
% 0.20/0.39      inference(unit_resolution,[status(thm)],[17, 16])).
% 0.20/0.39  tff(19,plain,
% 0.20/0.39      (^[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))))),
% 0.20/0.39      inference(bind,[status(th)],[])).
% 0.20/0.39  tff(20,plain,
% 0.20/0.39      (![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)))),
% 0.20/0.39      inference(quant_intro,[status(thm)],[19])).
% 0.20/0.39  tff(21,plain,
% 0.20/0.39      (![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)))),
% 0.20/0.39      inference(rewrite,[status(thm)],[])).
% 0.20/0.39  tff(22,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')).
% 0.20/0.39  tff(23,plain,
% 0.20/0.39      (![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.20/0.39      inference(modus_ponens,[status(thm)],[22, 21])).
% 0.20/0.39  tff(24,plain,(
% 0.20/0.39      ![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.20/0.39      inference(skolemize,[status(sab)],[23])).
% 0.20/0.39  tff(25,plain,
% 0.20/0.39      (![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.20/0.39      inference(modus_ponens,[status(thm)],[24, 20])).
% 0.20/0.39  tff(26,plain,
% 0.20/0.39      ((~![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))) | (symmetric_difference(B!3, B!3) = union(difference(B!3, B!3), difference(B!3, B!3)))),
% 0.20/0.39      inference(quant_inst,[status(thm)],[])).
% 0.20/0.39  tff(27,plain,
% 0.20/0.39      (symmetric_difference(B!3, B!3) = union(difference(B!3, B!3), difference(B!3, B!3))),
% 0.20/0.39      inference(unit_resolution,[status(thm)],[26, 25])).
% 0.20/0.39  tff(28,plain,
% 0.20/0.39      (symmetric_difference(B!3, B!3) = empty_set),
% 0.20/0.39      inference(transitivity,[status(thm)],[27, 18, 9])).
% 0.20/0.39  tff(29,plain,
% 0.20/0.39      ((~![B: $i] : (symmetric_difference(B, B) = empty_set)) <=> (~![B: $i] : (symmetric_difference(B, B) = empty_set))),
% 0.20/0.39      inference(rewrite,[status(thm)],[])).
% 0.20/0.39  tff(30,axiom,(~![B: $i] : (symmetric_difference(B, B) = empty_set)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_th93')).
% 0.20/0.39  tff(31,plain,
% 0.20/0.39      (~![B: $i] : (symmetric_difference(B, B) = empty_set)),
% 0.20/0.39      inference(modus_ponens,[status(thm)],[30, 29])).
% 0.20/0.39  tff(32,plain,
% 0.20/0.39      (~![B: $i] : (symmetric_difference(B, B) = empty_set)),
% 0.20/0.39      inference(modus_ponens,[status(thm)],[31, 29])).
% 0.20/0.39  tff(33,plain,
% 0.20/0.39      (~![B: $i] : (symmetric_difference(B, B) = empty_set)),
% 0.20/0.39      inference(modus_ponens,[status(thm)],[32, 29])).
% 0.20/0.39  tff(34,plain,
% 0.20/0.39      (~![B: $i] : (symmetric_difference(B, B) = empty_set)),
% 0.20/0.39      inference(modus_ponens,[status(thm)],[33, 29])).
% 0.20/0.39  tff(35,plain,
% 0.20/0.39      (~![B: $i] : (symmetric_difference(B, B) = empty_set)),
% 0.20/0.39      inference(modus_ponens,[status(thm)],[34, 29])).
% 0.20/0.39  tff(36,plain,
% 0.20/0.39      (~![B: $i] : (symmetric_difference(B, B) = empty_set)),
% 0.20/0.39      inference(modus_ponens,[status(thm)],[35, 29])).
% 0.20/0.39  tff(37,plain,
% 0.20/0.39      (~![B: $i] : (symmetric_difference(B, B) = empty_set)),
% 0.20/0.39      inference(modus_ponens,[status(thm)],[36, 29])).
% 0.20/0.39  tff(38,plain,(
% 0.20/0.39      ~(symmetric_difference(B!3, B!3) = empty_set)),
% 0.20/0.39      inference(skolemize,[status(sab)],[37])).
% 0.20/0.39  tff(39,plain,
% 0.20/0.39      ($false),
% 0.20/0.39      inference(unit_resolution,[status(thm)],[38, 28])).
% 0.20/0.39  % SZS output end Proof
%------------------------------------------------------------------------------