TSTP Solution File: SET148+3 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SET148+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n020.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 05:05:54 EDT 2022

% Result   : Theorem 0.21s 0.41s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : SET148+3 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.14  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.36  % Computer : n020.cluster.edu
% 0.13/0.36  % Model    : x86_64 x86_64
% 0.13/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36  % Memory   : 8042.1875MB
% 0.13/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36  % CPULimit : 300
% 0.13/0.36  % WCLimit  : 300
% 0.13/0.36  % DateTime : Sat Sep  3 02:56:44 EDT 2022
% 0.13/0.36  % CPUTime  : 
% 0.13/0.36  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.36  Usage: tptp [options] [-file:]file
% 0.13/0.36    -h, -?       prints this message.
% 0.13/0.36    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.36    -m, -model   generate model.
% 0.13/0.36    -p, -proof   generate proof.
% 0.13/0.36    -c, -core    generate unsat core of named formulas.
% 0.13/0.36    -st, -statistics display statistics.
% 0.13/0.36    -t:timeout   set timeout (in second).
% 0.13/0.36    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.36    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.36    -<param>:<value> configuration parameter and value.
% 0.13/0.36    -o:<output-file> file to place output in.
% 0.21/0.41  % SZS status Theorem
% 0.21/0.41  % SZS output start Proof
% 0.21/0.41  tff(subset_type, type, (
% 0.21/0.41     subset: ( $i * $i ) > $o)).
% 0.21/0.41  tff(tptp_fun_B_2_type, type, (
% 0.21/0.41     tptp_fun_B_2: $i)).
% 0.21/0.41  tff(intersection_type, type, (
% 0.21/0.41     intersection: ( $i * $i ) > $i)).
% 0.21/0.41  tff(1,plain,
% 0.21/0.41      ((~![B: $i] : (intersection(B, B) = B)) <=> (~![B: $i] : (intersection(B, B) = B))),
% 0.21/0.41      inference(rewrite,[status(thm)],[])).
% 0.21/0.41  tff(2,axiom,(~![B: $i] : (intersection(B, B) = B)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_idempotency_of_intersection')).
% 0.21/0.41  tff(3,plain,
% 0.21/0.41      (~![B: $i] : (intersection(B, B) = B)),
% 0.21/0.41      inference(modus_ponens,[status(thm)],[2, 1])).
% 0.21/0.41  tff(4,plain,
% 0.21/0.41      (~![B: $i] : (intersection(B, B) = B)),
% 0.21/0.41      inference(modus_ponens,[status(thm)],[3, 1])).
% 0.21/0.41  tff(5,plain,
% 0.21/0.41      (~![B: $i] : (intersection(B, B) = B)),
% 0.21/0.41      inference(modus_ponens,[status(thm)],[4, 1])).
% 0.21/0.41  tff(6,plain,
% 0.21/0.41      (~![B: $i] : (intersection(B, B) = B)),
% 0.21/0.41      inference(modus_ponens,[status(thm)],[5, 1])).
% 0.21/0.41  tff(7,plain,
% 0.21/0.41      (~![B: $i] : (intersection(B, B) = B)),
% 0.21/0.41      inference(modus_ponens,[status(thm)],[6, 1])).
% 0.21/0.41  tff(8,plain,
% 0.21/0.41      (~![B: $i] : (intersection(B, B) = B)),
% 0.21/0.41      inference(modus_ponens,[status(thm)],[7, 1])).
% 0.21/0.41  tff(9,plain,
% 0.21/0.41      (~![B: $i] : (intersection(B, B) = B)),
% 0.21/0.41      inference(modus_ponens,[status(thm)],[8, 1])).
% 0.21/0.41  tff(10,plain,(
% 0.21/0.41      ~(intersection(B!2, B!2) = B!2)),
% 0.21/0.41      inference(skolemize,[status(sab)],[9])).
% 0.21/0.41  tff(11,plain,
% 0.21/0.41      (^[B: $i, C: $i] : refl(((~subset(B, C)) | (intersection(B, C) = B)) <=> ((~subset(B, C)) | (intersection(B, C) = B)))),
% 0.21/0.41      inference(bind,[status(th)],[])).
% 0.21/0.41  tff(12,plain,
% 0.21/0.41      (![B: $i, C: $i] : ((~subset(B, C)) | (intersection(B, C) = B)) <=> ![B: $i, C: $i] : ((~subset(B, C)) | (intersection(B, C) = B))),
% 0.21/0.41      inference(quant_intro,[status(thm)],[11])).
% 0.21/0.41  tff(13,plain,
% 0.21/0.41      (![B: $i, C: $i] : ((~subset(B, C)) | (intersection(B, C) = B)) <=> ![B: $i, C: $i] : ((~subset(B, C)) | (intersection(B, C) = B))),
% 0.21/0.41      inference(rewrite,[status(thm)],[])).
% 0.21/0.41  tff(14,plain,
% 0.21/0.41      (^[B: $i, C: $i] : rewrite((subset(B, C) => (intersection(B, C) = B)) <=> ((~subset(B, C)) | (intersection(B, C) = B)))),
% 0.21/0.41      inference(bind,[status(th)],[])).
% 0.21/0.41  tff(15,plain,
% 0.21/0.41      (![B: $i, C: $i] : (subset(B, C) => (intersection(B, C) = B)) <=> ![B: $i, C: $i] : ((~subset(B, C)) | (intersection(B, C) = B))),
% 0.21/0.41      inference(quant_intro,[status(thm)],[14])).
% 0.21/0.41  tff(16,axiom,(![B: $i, C: $i] : (subset(B, C) => (intersection(B, C) = B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','subset_intersection')).
% 0.21/0.41  tff(17,plain,
% 0.21/0.41      (![B: $i, C: $i] : ((~subset(B, C)) | (intersection(B, C) = B))),
% 0.21/0.41      inference(modus_ponens,[status(thm)],[16, 15])).
% 0.21/0.41  tff(18,plain,
% 0.21/0.41      (![B: $i, C: $i] : ((~subset(B, C)) | (intersection(B, C) = B))),
% 0.21/0.41      inference(modus_ponens,[status(thm)],[17, 13])).
% 0.21/0.41  tff(19,plain,(
% 0.21/0.41      ![B: $i, C: $i] : ((~subset(B, C)) | (intersection(B, C) = B))),
% 0.21/0.41      inference(skolemize,[status(sab)],[18])).
% 0.21/0.41  tff(20,plain,
% 0.21/0.41      (![B: $i, C: $i] : ((~subset(B, C)) | (intersection(B, C) = B))),
% 0.21/0.41      inference(modus_ponens,[status(thm)],[19, 12])).
% 0.21/0.41  tff(21,plain,
% 0.21/0.41      (((~![B: $i, C: $i] : ((~subset(B, C)) | (intersection(B, C) = B))) | ((~subset(B!2, B!2)) | (intersection(B!2, B!2) = B!2))) <=> ((~![B: $i, C: $i] : ((~subset(B, C)) | (intersection(B, C) = B))) | (~subset(B!2, B!2)) | (intersection(B!2, B!2) = B!2))),
% 0.21/0.41      inference(rewrite,[status(thm)],[])).
% 0.21/0.41  tff(22,plain,
% 0.21/0.41      ((~![B: $i, C: $i] : ((~subset(B, C)) | (intersection(B, C) = B))) | ((~subset(B!2, B!2)) | (intersection(B!2, B!2) = B!2))),
% 0.21/0.41      inference(quant_inst,[status(thm)],[])).
% 0.21/0.41  tff(23,plain,
% 0.21/0.41      ((~![B: $i, C: $i] : ((~subset(B, C)) | (intersection(B, C) = B))) | (~subset(B!2, B!2)) | (intersection(B!2, B!2) = B!2)),
% 0.21/0.41      inference(modus_ponens,[status(thm)],[22, 21])).
% 0.21/0.41  tff(24,plain,
% 0.21/0.41      (~subset(B!2, B!2)),
% 0.21/0.41      inference(unit_resolution,[status(thm)],[23, 20, 10])).
% 0.21/0.41  tff(25,plain,
% 0.21/0.41      (^[B: $i] : refl(subset(B, B) <=> subset(B, B))),
% 0.21/0.41      inference(bind,[status(th)],[])).
% 0.21/0.41  tff(26,plain,
% 0.21/0.41      (![B: $i] : subset(B, B) <=> ![B: $i] : subset(B, B)),
% 0.21/0.41      inference(quant_intro,[status(thm)],[25])).
% 0.21/0.41  tff(27,plain,
% 0.21/0.41      (![B: $i] : subset(B, B) <=> ![B: $i] : subset(B, B)),
% 0.21/0.41      inference(rewrite,[status(thm)],[])).
% 0.21/0.41  tff(28,axiom,(![B: $i] : subset(B, B)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','reflexivity_of_subset')).
% 0.21/0.41  tff(29,plain,
% 0.21/0.41      (![B: $i] : subset(B, B)),
% 0.21/0.41      inference(modus_ponens,[status(thm)],[28, 27])).
% 0.21/0.41  tff(30,plain,(
% 0.21/0.41      ![B: $i] : subset(B, B)),
% 0.21/0.41      inference(skolemize,[status(sab)],[29])).
% 0.21/0.41  tff(31,plain,
% 0.21/0.41      (![B: $i] : subset(B, B)),
% 0.21/0.41      inference(modus_ponens,[status(thm)],[30, 26])).
% 0.21/0.41  tff(32,plain,
% 0.21/0.41      ((~![B: $i] : subset(B, B)) | subset(B!2, B!2)),
% 0.21/0.41      inference(quant_inst,[status(thm)],[])).
% 0.21/0.41  tff(33,plain,
% 0.21/0.41      ($false),
% 0.21/0.41      inference(unit_resolution,[status(thm)],[32, 31, 24])).
% 0.21/0.41  % SZS output end Proof
%------------------------------------------------------------------------------