TSTP Solution File: SET583+3 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SET583+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n019.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 05:07:07 EDT 2022

% Result   : Theorem 0.21s 0.39s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET583+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n019.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % 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 06:51:05 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.
% 0.21/0.39  % SZS status Theorem
% 0.21/0.39  % SZS output start Proof
% 0.21/0.39  tff(subset_type, type, (
% 0.21/0.39     subset: ( $i * $i ) > $o)).
% 0.21/0.39  tff(tptp_fun_B_2_type, type, (
% 0.21/0.39     tptp_fun_B_2: $i)).
% 0.21/0.39  tff(tptp_fun_C_1_type, type, (
% 0.21/0.39     tptp_fun_C_1: $i)).
% 0.21/0.39  tff(1,plain,
% 0.21/0.39      ((~![B: $i, C: $i] : ((~(subset(B, C) & subset(C, B))) | (B = C))) <=> (~![B: $i, C: $i] : ((~(subset(B, C) & subset(C, B))) | (B = C)))),
% 0.21/0.39      inference(rewrite,[status(thm)],[])).
% 0.21/0.39  tff(2,plain,
% 0.21/0.39      ((~![B: $i, C: $i] : ((subset(B, C) & subset(C, B)) => (B = C))) <=> (~![B: $i, C: $i] : ((~(subset(B, C) & subset(C, B))) | (B = C)))),
% 0.21/0.39      inference(rewrite,[status(thm)],[])).
% 0.21/0.39  tff(3,axiom,(~![B: $i, C: $i] : ((subset(B, C) & subset(C, B)) => (B = C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_extensionality')).
% 0.21/0.39  tff(4,plain,
% 0.21/0.39      (~![B: $i, C: $i] : ((~(subset(B, C) & subset(C, B))) | (B = C))),
% 0.21/0.39      inference(modus_ponens,[status(thm)],[3, 2])).
% 0.21/0.39  tff(5,plain,
% 0.21/0.39      (~![B: $i, C: $i] : ((~(subset(B, C) & subset(C, B))) | (B = C))),
% 0.21/0.39      inference(modus_ponens,[status(thm)],[4, 1])).
% 0.21/0.39  tff(6,plain,
% 0.21/0.39      (~![B: $i, C: $i] : ((~(subset(B, C) & subset(C, B))) | (B = C))),
% 0.21/0.39      inference(modus_ponens,[status(thm)],[5, 1])).
% 0.21/0.39  tff(7,plain,
% 0.21/0.39      (~![B: $i, C: $i] : ((~(subset(B, C) & subset(C, B))) | (B = C))),
% 0.21/0.39      inference(modus_ponens,[status(thm)],[6, 1])).
% 0.21/0.39  tff(8,plain,
% 0.21/0.39      (~![B: $i, C: $i] : ((~(subset(B, C) & subset(C, B))) | (B = C))),
% 0.21/0.39      inference(modus_ponens,[status(thm)],[7, 1])).
% 0.21/0.39  tff(9,plain,
% 0.21/0.39      (~![B: $i, C: $i] : ((~(subset(B, C) & subset(C, B))) | (B = C))),
% 0.21/0.39      inference(modus_ponens,[status(thm)],[8, 1])).
% 0.21/0.39  tff(10,plain,
% 0.21/0.39      (~![B: $i, C: $i] : ((~(subset(B, C) & subset(C, B))) | (B = C))),
% 0.21/0.39      inference(modus_ponens,[status(thm)],[9, 1])).
% 0.21/0.39  tff(11,plain,(
% 0.21/0.39      ~((~(subset(B!2, C!1) & subset(C!1, B!2))) | (B!2 = C!1))),
% 0.21/0.39      inference(skolemize,[status(sab)],[10])).
% 0.21/0.39  tff(12,plain,
% 0.21/0.39      (subset(B!2, C!1) & subset(C!1, B!2)),
% 0.21/0.39      inference(or_elim,[status(thm)],[11])).
% 0.21/0.39  tff(13,plain,
% 0.21/0.39      (subset(C!1, B!2)),
% 0.21/0.39      inference(and_elim,[status(thm)],[12])).
% 0.21/0.39  tff(14,plain,
% 0.21/0.39      (subset(B!2, C!1)),
% 0.21/0.39      inference(and_elim,[status(thm)],[12])).
% 0.21/0.39  tff(15,plain,
% 0.21/0.39      ((~((~subset(B!2, C!1)) | (~subset(C!1, B!2)))) | (~subset(B!2, C!1)) | (~subset(C!1, B!2))),
% 0.21/0.39      inference(tautology,[status(thm)],[])).
% 0.21/0.39  tff(16,plain,
% 0.21/0.39      (~((~subset(B!2, C!1)) | (~subset(C!1, B!2)))),
% 0.21/0.39      inference(unit_resolution,[status(thm)],[15, 14, 13])).
% 0.21/0.39  tff(17,plain,
% 0.21/0.39      (~(B!2 = C!1)),
% 0.21/0.39      inference(or_elim,[status(thm)],[11])).
% 0.21/0.39  tff(18,plain,
% 0.21/0.39      ((~((B!2 = C!1) <=> (~((~subset(B!2, C!1)) | (~subset(C!1, B!2)))))) | (B!2 = C!1) | ((~subset(B!2, C!1)) | (~subset(C!1, B!2)))),
% 0.21/0.39      inference(tautology,[status(thm)],[])).
% 0.21/0.39  tff(19,plain,
% 0.21/0.39      (~((B!2 = C!1) <=> (~((~subset(B!2, C!1)) | (~subset(C!1, B!2)))))),
% 0.21/0.39      inference(unit_resolution,[status(thm)],[18, 17, 16])).
% 0.21/0.39  tff(20,plain,
% 0.21/0.39      (^[B: $i, C: $i] : refl(((B = C) <=> (~((~subset(B, C)) | (~subset(C, B))))) <=> ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B))))))),
% 0.21/0.39      inference(bind,[status(th)],[])).
% 0.21/0.39  tff(21,plain,
% 0.21/0.39      (![B: $i, C: $i] : ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B))))) <=> ![B: $i, C: $i] : ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B)))))),
% 0.21/0.39      inference(quant_intro,[status(thm)],[20])).
% 0.21/0.39  tff(22,plain,
% 0.21/0.39      (^[B: $i, C: $i] : rewrite(((B = C) <=> (subset(B, C) & subset(C, B))) <=> ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B))))))),
% 0.21/0.39      inference(bind,[status(th)],[])).
% 0.21/0.39  tff(23,plain,
% 0.21/0.39      (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B))) <=> ![B: $i, C: $i] : ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B)))))),
% 0.21/0.39      inference(quant_intro,[status(thm)],[22])).
% 0.21/0.39  tff(24,plain,
% 0.21/0.39      (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B))) <=> ![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 0.21/0.39      inference(rewrite,[status(thm)],[])).
% 0.21/0.39  tff(25,axiom,(![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','equal_defn')).
% 0.21/0.39  tff(26,plain,
% 0.21/0.39      (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 0.21/0.39      inference(modus_ponens,[status(thm)],[25, 24])).
% 0.21/0.39  tff(27,plain,(
% 0.21/0.40      ![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 0.21/0.40      inference(skolemize,[status(sab)],[26])).
% 0.21/0.40  tff(28,plain,
% 0.21/0.40      (![B: $i, C: $i] : ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B)))))),
% 0.21/0.40      inference(modus_ponens,[status(thm)],[27, 23])).
% 0.21/0.40  tff(29,plain,
% 0.21/0.40      (![B: $i, C: $i] : ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B)))))),
% 0.21/0.40      inference(modus_ponens,[status(thm)],[28, 21])).
% 0.21/0.40  tff(30,plain,
% 0.21/0.40      ((~![B: $i, C: $i] : ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B)))))) | ((B!2 = C!1) <=> (~((~subset(B!2, C!1)) | (~subset(C!1, B!2)))))),
% 0.21/0.40      inference(quant_inst,[status(thm)],[])).
% 0.21/0.40  tff(31,plain,
% 0.21/0.40      ($false),
% 0.21/0.40      inference(unit_resolution,[status(thm)],[30, 29, 19])).
% 0.21/0.40  % SZS output end Proof
%------------------------------------------------------------------------------