TSTP Solution File: SET621+3 by Z3---4.8.9.0

View Problem - 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
%------------------------------------------------------------------------------