%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COM018+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 06:57:53 AM UTC 2026
% Result : Theorem 44.52s 13.66s
% Output : Refutation 44.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 23 ( 10 unt; 0 typ; 1 def)
% Number of atoms : 57 ( 3 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 141 ( 21 ~; 14 |; 11 &; 91 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 21 ( 2 ^; 13 !; 5 ?; 21 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(aElement0_decl,type,
aElement0: $i > $o ).
thf(aRewritingSystem0_decl,type,
aRewritingSystem0: $i > $o ).
thf(sdtmndtasgtdt0_decl,type,
sdtmndtasgtdt0: $i > $i > $i > $o ).
thf(isLocallyConfluent0_decl,type,
isLocallyConfluent0: $i > $o ).
thf(isTerminating0_decl,type,
isTerminating0: $i > $o ).
thf(aNormalFormOfIn0_decl,type,
aNormalFormOfIn0: $i > $i > $i > $o ).
thf(xw_decl,type,
xw: $i ).
thf(xR_decl,type,
xR: $i ).
thf(xv_decl,type,
xv: $i ).
thf(xu_decl,type,
xu: $i ).
thf(sk13_decl,type,
sk13: $i > $i > $i ).
thf(sk13_def,definition,
( sk13
= ( ^ [A: $i,B: $i] :
@+[C: $i] : ( B @ ( A @ ( C @ aNormalFormOfIn0 ) ) ) ) ) ).
thf(21,axiom,
! [A: $i] :
( ( ( A @ isTerminating0 )
& ( A @ aRewritingSystem0 ) )
=> ! [B: $i] :
( ( B @ aElement0 )
=> ? [C: $i] : ( A @ ( B @ ( C @ aNormalFormOfIn0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mTermNF) ).
thf(111,plain,
! [A: $i] :
( ( ( A @ isTerminating0 )
& ( A @ aRewritingSystem0 ) )
=> ! [B: $i] :
( ( B @ aElement0 )
=> ? [C: $i] : ( A @ ( B @ ( C @ aNormalFormOfIn0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(112,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ ( B @ sk13 ) @ aNormalFormOfIn0 ) ) )
| ~ ( B @ aElement0 )
| ~ ( A @ isTerminating0 )
| ~ ( A @ aRewritingSystem0 ) ),
inference(cnf,[status(esa)],[111]) ).
thf(1,conjecture,
? [A: $i] : ( xR @ ( xw @ ( A @ aNormalFormOfIn0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ? [A: $i] : ( xR @ ( xw @ ( A @ aNormalFormOfIn0 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(25,plain,
~ ? [A: $i] : ( xR @ ( xw @ ( A @ aNormalFormOfIn0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(26,plain,
! [A: $i] :
~ ( xR @ ( xw @ ( A @ aNormalFormOfIn0 ) ) ),
inference(cnf,[status(esa)],[25]) ).
thf(15943,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ sk13 ) @ aNormalFormOfIn0 ) ) )
!= ( xR @ ( xw @ ( C @ aNormalFormOfIn0 ) ) ) )
| ~ $true
| ~ ( B @ aElement0 )
| ~ ( A @ isTerminating0 )
| ~ ( A @ aRewritingSystem0 ) ),
inference(paramod_ordered,[status(thm)],[112,26]) ).
thf(15944,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ sk13 ) @ aNormalFormOfIn0 ) ) )
!= ( xR @ ( xw @ ( C @ aNormalFormOfIn0 ) ) ) )
| ~ ( B @ aElement0 )
| ~ ( A @ isTerminating0 )
| ~ ( A @ aRewritingSystem0 ) ),
inference(simp,[status(thm)],[15943]) ).
thf(15945,plain,
( ~ ( xw @ aElement0 )
| ~ ( xR @ isTerminating0 )
| ~ ( xR @ aRewritingSystem0 ) ),
inference(pattern_uni,[status(thm)],[15944:[bind(A,$thf( xR )),bind(B,$thf( xw )),bind(C,$thf( xR @ ( xw @ sk13 ) ))]]) ).
thf(22,axiom,
xR @ aRewritingSystem0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__656) ).
thf(113,plain,
xR @ aRewritingSystem0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(19,axiom,
( ( xw @ ( xR @ ( xv @ sdtmndtasgtdt0 ) ) )
& ( xw @ ( xR @ ( xu @ sdtmndtasgtdt0 ) ) )
& ( xw @ aElement0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__799) ).
thf(101,plain,
( ( xw @ ( xR @ ( xv @ sdtmndtasgtdt0 ) ) )
& ( xw @ ( xR @ ( xu @ sdtmndtasgtdt0 ) ) )
& ( xw @ aElement0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(102,plain,
( ( xw @ ( xR @ ( xv @ sdtmndtasgtdt0 ) ) )
& ( xw @ ( xR @ ( xu @ sdtmndtasgtdt0 ) ) )
& ( xw @ aElement0 ) ),
inference(cnf,[status(esa)],[101]) ).
thf(103,plain,
xw @ aElement0,
inference(cnfConj,[status(thm)],[102]) ).
thf(16,axiom,
( ( xR @ isTerminating0 )
& ( xR @ isLocallyConfluent0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__656_01) ).
thf(88,plain,
( ( xR @ isTerminating0 )
& ( xR @ isLocallyConfluent0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(89,plain,
( ( xR @ isTerminating0 )
& ( xR @ isLocallyConfluent0 ) ),
inference(cnf,[status(esa)],[88]) ).
thf(91,plain,
xR @ isTerminating0,
inference(cnfConj,[status(thm)],[89]) ).
thf(16167,plain,
( ~ $true
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[15945,113,103,91]) ).
thf(16168,plain,
$false,
inference(simp,[status(thm)],[16167]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM018+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.16/0.41 % Computer : n018.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sat Sep 26 23:24:38 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.88/1.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.40/1.22 % [INFO] Parsing done (213ms).
% 1.40/1.23 % [INFO] Running in sequential loop mode.
% 2.12/1.65 % [INFO] eprover registered as external prover.
% 2.12/1.66 % [INFO] Scanning for conjecture ...
% 2.33/1.73 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.33/1.75 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.33/1.76 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.33/1.76 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.33/1.77 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.33/1.77 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.56/1.80 % [INFO] Found a conjecture (or negated_conjecture) and 22 axioms. Running axiom selection ...
% 2.56/1.88 % [INFO] Axiom selection finished. Selected 22 axioms (removed 0 axioms).
% 2.56/1.89 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.56/1.89 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.56/1.90 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.75/1.90 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.75/1.90 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.75/1.91 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.75/1.92 % [INFO] Problem is first-order (TPTP FOF).
% 2.75/1.92 % [INFO] Type checking passed.
% 2.75/1.93 % [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 ...
% 44.52/13.65 % [INFO] Killing All external provers ...
% 44.52/13.66 % Time passed: 13101ms (effective reasoning time: 12417ms)
% 44.52/13.66 % 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)>
% 44.52/13.66 % Axioms used in derivation (4): mTermNF, m__656, m__799, m__656_01
% 44.52/13.66 % No. of inferences in proof: 22
% 44.52/13.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 13101 ms resp. 12417 ms w/o parsing
% 44.84/13.70 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 44.84/13.70 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------