TSTP Solution File: COM012+3 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : COM012+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n008.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 : Fri May 19 10:13:53 EDT 2023
% Result : Theorem 3.19s 1.73s
% Output : Refutation 3.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 20
% Syntax : Number of formulae : 32 ( 5 unt; 10 typ; 0 def)
% Number of atoms : 147 ( 12 equ; 0 cnn)
% Maximal formula atoms : 21 ( 6 avg)
% Number of connectives : 398 ( 2 ~; 30 |; 68 &; 271 @)
% ( 2 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 45 ( 0 ^; 33 !; 12 ?; 45 :)
% Comments :
%------------------------------------------------------------------------------
thf(aElement0_type,type,
aElement0: $i > $o ).
thf(aRewritingSystem0_type,type,
aRewritingSystem0: $i > $o ).
thf(sdtmndtplgtdt0_type,type,
sdtmndtplgtdt0: $i > $i > $i > $o ).
thf(aReductOfIn0_type,type,
aReductOfIn0: $i > $i > $i > $o ).
thf(sdtmndtasgtdt0_type,type,
sdtmndtasgtdt0: $i > $i > $i > $o ).
thf(xx_type,type,
xx: $i ).
thf(xy_type,type,
xy: $i ).
thf(xR_type,type,
xR: $i ).
thf(xz_type,type,
xz: $i ).
thf(iLess0_type,type,
iLess0: $i > $i > $o ).
thf(10,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( aElement0 @ A )
& ( aRewritingSystem0 @ B )
& ( aElement0 @ C )
& ( aElement0 @ D ) )
=> ( ( ( sdtmndtplgtdt0 @ A @ B @ C )
& ( sdtmndtplgtdt0 @ C @ B @ D ) )
=> ( sdtmndtplgtdt0 @ A @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mTCTrans) ).
thf(56,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( aElement0 @ A )
& ( aRewritingSystem0 @ B )
& ( aElement0 @ C )
& ( aElement0 @ D ) )
=> ( ( ( sdtmndtplgtdt0 @ A @ B @ C )
& ( sdtmndtplgtdt0 @ C @ B @ D ) )
=> ( sdtmndtplgtdt0 @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aElement0 @ A )
& ( aRewritingSystem0 @ B )
& ( aElement0 @ C ) )
=> ( ( sdtmndtasgtdt0 @ A @ B @ C )
<=> ( ( A = C )
| ( sdtmndtplgtdt0 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mTCRDef) ).
thf(37,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aElement0 @ A )
& ( aRewritingSystem0 @ B )
& ( aElement0 @ C ) )
=> ( ( ( sdtmndtasgtdt0 @ A @ B @ C )
=> ( ( A = C )
| ( sdtmndtplgtdt0 @ A @ B @ C ) ) )
& ( ( ( A = C )
| ( sdtmndtplgtdt0 @ A @ B @ C ) )
=> ( sdtmndtasgtdt0 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aRewritingSystem0 @ B ) )
=> ! [C: $i] :
( ( aReductOfIn0 @ C @ A @ B )
=> ( aElement0 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mReduct) ).
thf(52,plain,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aRewritingSystem0 @ B ) )
=> ! [C: $i] :
( ( aReductOfIn0 @ C @ A @ B )
=> ( aElement0 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aElement0 @ A )
& ( aRewritingSystem0 @ B )
& ( aElement0 @ C ) )
=> ( ( sdtmndtplgtdt0 @ A @ B @ C )
<=> ( ( aReductOfIn0 @ C @ A @ B )
| ? [D: $i] :
( ( aElement0 @ D )
& ( aReductOfIn0 @ D @ A @ B )
& ( sdtmndtplgtdt0 @ D @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mTCDef) ).
thf(44,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aElement0 @ A )
& ( aRewritingSystem0 @ B )
& ( aElement0 @ C ) )
=> ( ( ( sdtmndtplgtdt0 @ A @ B @ C )
=> ( ( aReductOfIn0 @ C @ A @ B )
| ? [D: $i] :
( ( aElement0 @ D )
& ( aReductOfIn0 @ D @ A @ B )
& ( sdtmndtplgtdt0 @ D @ B @ C ) ) ) )
& ( ( ( aReductOfIn0 @ C @ A @ B )
| ? [D: $i] :
( ( aElement0 @ D )
& ( aReductOfIn0 @ D @ A @ B )
& ( sdtmndtplgtdt0 @ D @ B @ C ) ) )
=> ( sdtmndtplgtdt0 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mElmSort) ).
thf(50,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aElement0 @ A )
& ( aRewritingSystem0 @ B )
& ( aElement0 @ C ) )
=> ( ( sdtmndtplgtdt0 @ A @ B @ C )
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mTCbr) ).
thf(55,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(11,axiom,
( ( aElement0 @ xx )
& ( aRewritingSystem0 @ xR )
& ( aElement0 @ xy )
& ( aElement0 @ xz ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__349) ).
thf(58,plain,
( ( aElement0 @ xx )
& ( aRewritingSystem0 @ xR )
& ( aElement0 @ xy )
& ( aElement0 @ xz ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(6,axiom,
! [A: $i] :
( ( aRewritingSystem0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mRelSort) ).
thf(51,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,conjecture,
( ( ( ( xx = xy )
| ( ( ( aReductOfIn0 @ xy @ xx @ xR )
| ? [A: $i] :
( ( aElement0 @ A )
& ( aReductOfIn0 @ A @ xx @ xR )
& ( sdtmndtplgtdt0 @ A @ xR @ xy ) ) )
& ( sdtmndtplgtdt0 @ xx @ xR @ xy ) ) )
& ( sdtmndtasgtdt0 @ xx @ xR @ xy )
& ( ( xy = xz )
| ( ( ( aReductOfIn0 @ xz @ xy @ xR )
| ? [A: $i] :
( ( aElement0 @ A )
& ( aReductOfIn0 @ A @ xy @ xR )
& ( sdtmndtplgtdt0 @ A @ xR @ xz ) ) )
& ( sdtmndtplgtdt0 @ xy @ xR @ xz ) ) )
& ( sdtmndtasgtdt0 @ xy @ xR @ xz ) )
=> ( ( xx = xz )
| ( aReductOfIn0 @ xz @ xx @ xR )
| ? [A: $i] :
( ( aElement0 @ A )
& ( aReductOfIn0 @ A @ xx @ xR )
& ( sdtmndtplgtdt0 @ A @ xR @ xz ) )
| ( sdtmndtplgtdt0 @ xx @ xR @ xz )
| ( sdtmndtasgtdt0 @ xx @ xR @ xz ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( ( ( xx = xy )
| ( ( ( aReductOfIn0 @ xy @ xx @ xR )
| ? [A: $i] :
( ( aElement0 @ A )
& ( aReductOfIn0 @ A @ xx @ xR )
& ( sdtmndtplgtdt0 @ A @ xR @ xy ) ) )
& ( sdtmndtplgtdt0 @ xx @ xR @ xy ) ) )
& ( sdtmndtasgtdt0 @ xx @ xR @ xy )
& ( ( xy = xz )
| ( ( ( aReductOfIn0 @ xz @ xy @ xR )
| ? [A: $i] :
( ( aElement0 @ A )
& ( aReductOfIn0 @ A @ xy @ xR )
& ( sdtmndtplgtdt0 @ A @ xR @ xz ) ) )
& ( sdtmndtplgtdt0 @ xy @ xR @ xz ) ) )
& ( sdtmndtasgtdt0 @ xy @ xR @ xz ) )
=> ( ( xx = xz )
| ( aReductOfIn0 @ xz @ xx @ xR )
| ? [A: $i] :
( ( aElement0 @ A )
& ( aReductOfIn0 @ A @ xx @ xR )
& ( sdtmndtplgtdt0 @ A @ xR @ xz ) )
| ( sdtmndtplgtdt0 @ xx @ xR @ xz )
| ( sdtmndtasgtdt0 @ xx @ xR @ xz ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(12,plain,
~ ( ( ( ( xx = xy )
| ( ( ( aReductOfIn0 @ xy @ xx @ xR )
| ? [A: $i] :
( ( aElement0 @ A )
& ( aReductOfIn0 @ A @ xx @ xR )
& ( sdtmndtplgtdt0 @ A @ xR @ xy ) ) )
& ( sdtmndtplgtdt0 @ xx @ xR @ xy ) ) )
& ( sdtmndtasgtdt0 @ xx @ xR @ xy )
& ( ( xy = xz )
| ( ( ( aReductOfIn0 @ xz @ xy @ xR )
| ? [A: $i] :
( ( aElement0 @ A )
& ( aReductOfIn0 @ A @ xy @ xR )
& ( sdtmndtplgtdt0 @ A @ xR @ xz ) ) )
& ( sdtmndtplgtdt0 @ xy @ xR @ xz ) ) )
& ( sdtmndtasgtdt0 @ xy @ xR @ xz ) )
=> ( ( xx = xz )
| ( aReductOfIn0 @ xz @ xx @ xR )
| ? [A: $i] :
( ( aElement0 @ A )
& ( aReductOfIn0 @ A @ xx @ xR )
& ( sdtmndtplgtdt0 @ A @ xR @ xz ) )
| ( sdtmndtplgtdt0 @ xx @ xR @ xz )
| ( sdtmndtasgtdt0 @ xx @ xR @ xz ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( ( iLess0 @ A @ B )
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mWFOrd) ).
thf(54,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(63,plain,
$false,
inference(cvc4,[status(thm)],[56,37,52,44,50,55,58,51,12,54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : COM012+3 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n008.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 19 03:25:10 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.83/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.25/0.97 % [INFO] Parsing done (131ms).
% 1.25/0.98 % [INFO] Running in sequential loop mode.
% 1.69/1.17 % [INFO] eprover registered as external prover.
% 1.69/1.17 % [INFO] cvc4 registered as external prover.
% 1.69/1.18 % [INFO] Scanning for conjecture ...
% 1.78/1.22 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.78/1.23 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.88/1.25 % [INFO] Found a conjecture and 9 axioms. Running axiom selection ...
% 1.88/1.28 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 1.88/1.28 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.88/1.29 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.88/1.29 % [INFO] Problem is first-order (TPTP FOF).
% 1.88/1.30 % [INFO] Type checking passed.
% 2.12/1.30 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 3.19/1.73 % External prover 'cvc4' found a proof!
% 3.19/1.73 % [INFO] Killing All external provers ...
% 3.19/1.73 % Time passed: 1210ms (effective reasoning time: 745ms)
% 3.19/1.73 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 3.19/1.73 % Axioms used in derivation (9): mWFOrd, m__349, mTCTrans, mReduct, mTCbr, mTCDef, mElmSort, mRelSort, mTCRDef
% 3.19/1.73 % No. of inferences in proof: 22
% 3.19/1.73 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1210 ms resp. 745 ms w/o parsing
% 3.19/1.77 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.19/1.77 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------