%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COM018+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 06:59:40 AM UTC 2026
% Result : Theorem 43.84s 16.37s
% Output : CNFRefutation 43.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 7 unt; 0 def)
% Number of atoms : 97 ( 6 equ)
% Maximal formula atoms : 30 ( 5 avg)
% Number of connectives : 98 ( 19 ~; 35 |; 39 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 32 ( 1 sgn 13 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mTermNF,axiom,
! [W0] :
( ( isTerminating0(W0)
& aRewritingSystem0(W0) )
=> ! [W1] :
( aElement0(W1)
=> ? [W2] : aNormalFormOfIn0(W2,W1,W0) ) ),
file('theBenchmark.p',mTermNF) ).
fof(m__656_01,axiom,
( isTerminating0(xR)
& ! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> ( ( sdtmndtplgtdt0(W0,xR,W1)
| ? [W2] :
( sdtmndtplgtdt0(W2,xR,W1)
& aReductOfIn0(W2,W0,xR)
& aElement0(W2) )
| aReductOfIn0(W1,W0,xR) )
=> iLess0(W1,W0) ) )
& isLocallyConfluent0(xR)
& ! [W0,W1,W2] :
( ( aReductOfIn0(W2,W0,xR)
& aReductOfIn0(W1,W0,xR)
& aElement0(W2)
& aElement0(W1)
& aElement0(W0) )
=> ? [W3] :
( sdtmndtasgtdt0(W2,xR,W3)
& ( ( sdtmndtplgtdt0(W2,xR,W3)
& ( ? [W4] :
( sdtmndtplgtdt0(W4,xR,W3)
& aReductOfIn0(W4,W2,xR)
& aElement0(W4) )
| aReductOfIn0(W3,W2,xR) ) )
| W2 = W3 )
& sdtmndtasgtdt0(W1,xR,W3)
& ( ( sdtmndtplgtdt0(W1,xR,W3)
& ( ? [W4] :
( sdtmndtplgtdt0(W4,xR,W3)
& aReductOfIn0(W4,W1,xR)
& aElement0(W4) )
| aReductOfIn0(W3,W1,xR) ) )
| W1 = W3 )
& aElement0(W3) ) ) ),
file('theBenchmark.p',m__656_01) ).
fof(m__799,axiom,
( sdtmndtasgtdt0(xv,xR,xw)
& ( ( sdtmndtplgtdt0(xv,xR,xw)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xw)
& aReductOfIn0(W0,xv,xR)
& aElement0(W0) )
| aReductOfIn0(xw,xv,xR) ) )
| xv = xw )
& sdtmndtasgtdt0(xu,xR,xw)
& ( ( sdtmndtplgtdt0(xu,xR,xw)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xw)
& aReductOfIn0(W0,xu,xR)
& aElement0(W0) )
| aReductOfIn0(xw,xu,xR) ) )
| xu = xw )
& aElement0(xw) ),
file('theBenchmark.p',m__799) ).
fof(m__,conjecture,
? [W0] :
( aNormalFormOfIn0(W0,xw,xR)
| ( ~ ? [W1] : aReductOfIn0(W1,W0,xR)
& ( sdtmndtasgtdt0(xw,xR,W0)
| sdtmndtplgtdt0(xw,xR,W0)
| ? [W1] :
( sdtmndtplgtdt0(W1,xR,W0)
& aReductOfIn0(W1,xw,xR)
& aElement0(W1) )
| aReductOfIn0(W0,xw,xR)
| xw = W0 )
& aElement0(W0) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ? [W0] :
( aNormalFormOfIn0(W0,xw,xR)
| ( ~ ? [W1] : aReductOfIn0(W1,W0,xR)
& ( sdtmndtasgtdt0(xw,xR,W0)
| sdtmndtplgtdt0(xw,xR,W0)
| ? [W1] :
( sdtmndtplgtdt0(W1,xR,W0)
& aReductOfIn0(W1,xw,xR)
& aElement0(W1) )
| aReductOfIn0(W0,xw,xR)
| xw = W0 )
& aElement0(W0) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(m__656,axiom,
aRewritingSystem0(xR),
file('theBenchmark.p',m__656) ).
cnf(c_23,plain,
aRewritingSystem0(xR),
inference(clausify,[status(thm)],[m__656]) ).
fof(nnf_14,plain,
! [W0] :
( ! [W1] :
( ? [W2] : aNormalFormOfIn0(W2,W1,W0)
| ~ aElement0(W1) )
| ~ isTerminating0(W0)
| ~ aRewritingSystem0(W0) ),
inference(fof_nnf,[status(thm)],[mTermNF]) ).
fof(sk_mTermNF_sk,plain,
! [W0] :
( ! [W1] :
( aNormalFormOfIn0(sK0(W0,W1),W1,W0)
| ~ aElement0(W1) )
| ~ isTerminating0(W0)
| ~ aRewritingSystem0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(W2,sK0(W0,W1))],[nnf_14]) ).
fof(sk_mTermNF,plain,
! [VAR_0,VAR_1] :
( aNormalFormOfIn0(sK0(VAR_0,VAR_1),VAR_1,VAR_0)
| ~ aElement0(VAR_1)
| ~ isTerminating0(VAR_0)
| ~ aRewritingSystem0(VAR_0) ),
inference(cnf_transformation,[status(thm)],[sk_mTermNF_sk]) ).
cnf(c_24,plain,
( aNormalFormOfIn0(sK0(A,B),B,A)
| ~ aElement0(B)
| ~ isTerminating0(A)
| ~ aRewritingSystem0(A) ),
inference(split_conjunct,[status(thm)],[sk_mTermNF]) ).
cnf(c_90,plain,
( aNormalFormOfIn0(sK0(xR,A),A,xR)
| ~ aElement0(A)
| ~ isTerminating0(xR) ),
inference(resolve,[status(thm)],[c_23,c_24]) ).
cnf(c_91,negated_conjecture,
~ aNormalFormOfIn0(A,xw,xR),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_115,plain,
aElement0(xw),
inference(clausify,[status(thm)],[m__799]) ).
cnf(c_424,plain,
isTerminating0(xR),
inference(clausify,[status(thm)],[m__656_01]) ).
cnf(c_1145,plain,
( aNormalFormOfIn0(sK0(xR,A),A,xR)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_424,c_90]) ).
cnf(c_12367,plain,
aNormalFormOfIn0(sK0(xR,xw),xw,xR),
inference(resolve,[status(thm)],[c_1145,c_115]) ).
cnf(c_12366,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_91,c_12367]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM018+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/10.55 % Computer : n006.cluster.edu
% 0.09/10.55 % Model : x86_64 x86_64
% 0.09/10.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.55 % Memory : 8046.5625MB
% 0.09/10.55 % OS : Linux 6.8.0-71-generic
% 0.09/10.55 % CPULimit : 300
% 0.09/10.55 % WCLimit : 300
% 0.09/10.55 % DateTime : Sat Sep 26 23:22:26 UTC 2026
% 0.09/10.56 % CPUTime :
% 0.09/10.56 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/10.56 % Process 2375038 was started by sandbox2 on n006,
% 0.09/10.56 % Sat Sep 26 23:22:26 2026
% 0.09/10.56 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/10.71
% 0.14/10.71 % From the command line: assign(max_seconds, 300).
% 43.84/16.37
% 43.84/16.37 % given #500 (I,wt=22): 1036 -aElement0(A) | -aElement0(B) | -sdtmndtasgtdt0(A,xR,B) | -iLess0(A,xa) | sdtmndtasgtdt0(A,xR,f17(A,A,B)). [factor(371,a,b),xx(c)].
% 43.84/16.37
% 43.84/16.37 % SZS status Theorem for theBenchmark
% 43.84/16.37
% 43.84/16.37 % Proof 1 at 4.61 (+ 0.97) seconds.
% 43.84/16.37 % Length of proof is 12.
% 43.84/16.37 % Level of proof is 4.
% 43.84/16.37 % Maximum clause weight is 14.000.
% 43.84/16.37 % Given clauses 570.
% 43.84/16.37
% 43.84/16.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------