%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COM013+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 06:59:39 AM UTC 2026
% Result : Theorem 0.13s 10.65s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 3
% Syntax : Number of formulae : 41 ( 12 unt; 0 def)
% Number of atoms : 232 ( 20 equ)
% Maximal formula atoms : 50 ( 5 avg)
% Number of connectives : 295 ( 104 ~; 109 |; 70 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-1 aty)
% Number of variables : 69 ( 3 sgn 33 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mReduct,axiom,
! [W0,W1] :
( ( aRewritingSystem0(W1)
& aElement0(W0) )
=> ! [W2] :
( aReductOfIn0(W2,W0,W1)
=> aElement0(W2) ) ),
file('theBenchmark.p',mReduct) ).
fof(m__587,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) ) )
& aRewritingSystem0(xR) ),
file('theBenchmark.p',m__587) ).
fof(m__,conjecture,
! [W0] :
( aElement0(W0)
=> ( ! [W1] :
( aElement0(W1)
=> ( iLess0(W1,W0)
=> ? [W2] :
( aNormalFormOfIn0(W2,W1,xR)
& ~ ? [W3] : aReductOfIn0(W3,W2,xR)
& sdtmndtasgtdt0(W1,xR,W2)
& ( ( sdtmndtplgtdt0(W1,xR,W2)
& ( ? [W3] :
( sdtmndtplgtdt0(W3,xR,W2)
& aReductOfIn0(W3,W1,xR)
& aElement0(W3) )
| aReductOfIn0(W2,W1,xR) ) )
| W1 = W2 )
& aElement0(W2) ) ) )
=> ? [W1] :
( aNormalFormOfIn0(W1,W0,xR)
| ( ~ ? [W2] : aReductOfIn0(W2,W1,xR)
& ( sdtmndtasgtdt0(W0,xR,W1)
| sdtmndtplgtdt0(W0,xR,W1)
| ? [W2] :
( sdtmndtplgtdt0(W2,xR,W1)
& aReductOfIn0(W2,W0,xR)
& aElement0(W2) )
| aReductOfIn0(W1,W0,xR)
| W0 = W1 )
& aElement0(W1) ) ) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ! [W0] :
( aElement0(W0)
=> ( ! [W1] :
( aElement0(W1)
=> ( iLess0(W1,W0)
=> ? [W2] :
( aNormalFormOfIn0(W2,W1,xR)
& ~ ? [W3] : aReductOfIn0(W3,W2,xR)
& sdtmndtasgtdt0(W1,xR,W2)
& ( ( sdtmndtplgtdt0(W1,xR,W2)
& ( ? [W3] :
( sdtmndtplgtdt0(W3,xR,W2)
& aReductOfIn0(W3,W1,xR)
& aElement0(W3) )
| aReductOfIn0(W2,W1,xR) ) )
| W1 = W2 )
& aElement0(W2) ) ) )
=> ? [W1] :
( aNormalFormOfIn0(W1,W0,xR)
| ( ~ ? [W2] : aReductOfIn0(W2,W1,xR)
& ( sdtmndtasgtdt0(W0,xR,W1)
| sdtmndtplgtdt0(W0,xR,W1)
| ? [W2] :
( sdtmndtplgtdt0(W2,xR,W1)
& aReductOfIn0(W2,W0,xR)
& aElement0(W2) )
| aReductOfIn0(W1,W0,xR)
| W0 = W1 )
& aElement0(W1) ) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_16,plain,
aRewritingSystem0(xR),
inference(clausify,[status(thm)],[m__587]) ).
cnf(c_54,plain,
( aElement0(C)
| ~ aReductOfIn0(C,A,B)
| ~ aRewritingSystem0(B)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mReduct]) ).
cnf(c_55,plain,
( iLess0(B,A)
| ~ aReductOfIn0(B,A,xR)
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[m__587]) ).
fof(nnf_15,plain,
? [W0] :
( ! [W1] :
( ~ aNormalFormOfIn0(W1,W0,xR)
& ( ? [W2] : aReductOfIn0(W2,W1,xR)
| ( ~ sdtmndtasgtdt0(W0,xR,W1)
& ~ sdtmndtplgtdt0(W0,xR,W1)
& ! [X3] :
( ~ sdtmndtplgtdt0(X3,xR,W1)
| ~ aReductOfIn0(X3,W0,xR)
| ~ aElement0(X3) )
& ~ aReductOfIn0(W1,W0,xR)
& W1 != W0 )
| ~ aElement0(W1) ) )
& ! [X0] :
( ? [X1] :
( aNormalFormOfIn0(X1,X0,xR)
& ! [W3] : ~ aReductOfIn0(W3,X1,xR)
& sdtmndtasgtdt0(X0,xR,X1)
& ( ( sdtmndtplgtdt0(X0,xR,X1)
& ( ? [X2] :
( sdtmndtplgtdt0(X2,xR,X1)
& aReductOfIn0(X2,X0,xR)
& aElement0(X2) )
| aReductOfIn0(X1,X0,xR) ) )
| X1 = X0 )
& aElement0(X1) )
| ~ iLess0(X0,W0)
| ~ aElement0(X0) )
& aElement0(W0) ),
inference(fof_nnf,[status(thm)],[m___neg]) ).
fof(sk_m___neg_sk,plain,
( ! [W1] :
( ~ aNormalFormOfIn0(W1,sK0,xR)
& ( aReductOfIn0(sK2(W1),W1,xR)
| ( ~ sdtmndtasgtdt0(sK0,xR,W1)
& ~ sdtmndtplgtdt0(sK0,xR,W1)
& ! [X3] :
( ~ sdtmndtplgtdt0(X3,xR,W1)
| ~ aReductOfIn0(X3,sK0,xR)
| ~ aElement0(X3) )
& ~ aReductOfIn0(W1,sK0,xR)
& W1 != sK0 )
| ~ aElement0(W1) ) )
& ! [X0] :
( ( aNormalFormOfIn0(sK1(X0),X0,xR)
& ! [W3] : ~ aReductOfIn0(W3,sK1(X0),xR)
& sdtmndtasgtdt0(X0,xR,sK1(X0))
& ( ( sdtmndtplgtdt0(X0,xR,sK1(X0))
& ( ( sdtmndtplgtdt0(sK3(X0),xR,sK1(X0))
& aReductOfIn0(sK3(X0),X0,xR)
& aElement0(sK3(X0)) )
| aReductOfIn0(sK1(X0),X0,xR) ) )
| sK1(X0) = X0 )
& aElement0(sK1(X0)) )
| ~ iLess0(X0,sK0)
| ~ aElement0(X0) )
& aElement0(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK3,sK2]),skolemize(W0,sK0),skolemize(X1,sK1(X0)),skolemize(X2,sK3(X0)),skolemize(W2,sK2(W1))],[nnf_15]) ).
fof(sk_m___neg,plain,
( ! [VAR_0] : ~ aNormalFormOfIn0(VAR_0,sK0,xR)
& ! [VAR_0] :
( aReductOfIn0(sK2(VAR_0),VAR_0,xR)
| ~ sdtmndtasgtdt0(sK0,xR,VAR_0)
| ~ aElement0(VAR_0) )
& ! [VAR_0] :
( aReductOfIn0(sK2(VAR_0),VAR_0,xR)
| ~ sdtmndtplgtdt0(sK0,xR,VAR_0)
| ~ aElement0(VAR_0) )
& ! [VAR_0,VAR_1] :
( aReductOfIn0(sK2(VAR_0),VAR_0,xR)
| ~ sdtmndtplgtdt0(VAR_1,xR,VAR_0)
| ~ aReductOfIn0(VAR_1,sK0,xR)
| ~ aElement0(VAR_1)
| ~ aElement0(VAR_0) )
& ! [VAR_0] :
( aReductOfIn0(sK2(VAR_0),VAR_0,xR)
| ~ aReductOfIn0(VAR_0,sK0,xR)
| ~ aElement0(VAR_0) )
& ! [VAR_0] :
( aReductOfIn0(sK2(VAR_0),VAR_0,xR)
| VAR_0 != sK0
| ~ aElement0(VAR_0) )
& ! [VAR_0] :
( aNormalFormOfIn0(sK1(VAR_0),VAR_0,xR)
| ~ iLess0(VAR_0,sK0)
| ~ aElement0(VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ aReductOfIn0(VAR_1,sK1(VAR_0),xR)
| ~ iLess0(VAR_0,sK0)
| ~ aElement0(VAR_0) )
& ! [VAR_0] :
( sdtmndtasgtdt0(VAR_0,xR,sK1(VAR_0))
| ~ iLess0(VAR_0,sK0)
| ~ aElement0(VAR_0) )
& ! [VAR_0] :
( sdtmndtplgtdt0(VAR_0,xR,sK1(VAR_0))
| sK1(VAR_0) = VAR_0
| ~ iLess0(VAR_0,sK0)
| ~ aElement0(VAR_0) )
& ! [VAR_0] :
( sdtmndtplgtdt0(sK3(VAR_0),xR,sK1(VAR_0))
| aReductOfIn0(sK1(VAR_0),VAR_0,xR)
| sK1(VAR_0) = VAR_0
| ~ iLess0(VAR_0,sK0)
| ~ aElement0(VAR_0) )
& ! [VAR_0] :
( aReductOfIn0(sK3(VAR_0),VAR_0,xR)
| aReductOfIn0(sK1(VAR_0),VAR_0,xR)
| sK1(VAR_0) = VAR_0
| ~ iLess0(VAR_0,sK0)
| ~ aElement0(VAR_0) )
& ! [VAR_0] :
( aElement0(sK3(VAR_0))
| aReductOfIn0(sK1(VAR_0),VAR_0,xR)
| sK1(VAR_0) = VAR_0
| ~ iLess0(VAR_0,sK0)
| ~ aElement0(VAR_0) )
& ! [VAR_0] :
( aElement0(sK1(VAR_0))
| ~ iLess0(VAR_0,sK0)
| ~ aElement0(VAR_0) )
& aElement0(sK0) ),
inference(cnf_transformation,[status(thm)],[sk_m___neg_sk]) ).
cnf(c_58,negated_conjecture,
aElement0(sK0),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_59,negated_conjecture,
( aElement0(sK1(A))
| ~ iLess0(A,sK0)
| ~ aElement0(A) ),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_63,negated_conjecture,
( sdtmndtplgtdt0(A,xR,sK1(A))
| sK1(A) = A
| ~ iLess0(A,sK0)
| ~ aElement0(A) ),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_65,negated_conjecture,
( ~ aReductOfIn0(B,sK1(A),xR)
| ~ iLess0(A,sK0)
| ~ aElement0(A) ),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_67,negated_conjecture,
( aReductOfIn0(sK2(A),A,xR)
| A != sK0
| ~ aElement0(A) ),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_68,negated_conjecture,
( aReductOfIn0(sK2(A),A,xR)
| sK0 != A
| ~ aElement0(A) ),
inference(copy,[status(thm)],[c_67]) ).
cnf(c_69,negated_conjecture,
( aReductOfIn0(sK2(A),A,xR)
| ~ aReductOfIn0(A,sK0,xR)
| ~ aElement0(A) ),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_70,negated_conjecture,
( aReductOfIn0(sK2(A),A,xR)
| ~ sdtmndtplgtdt0(B,xR,A)
| ~ aReductOfIn0(B,sK0,xR)
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_106,plain,
( aElement0(B)
| ~ aReductOfIn0(B,A,xR)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_16,c_54]) ).
cnf(c_281,negated_conjecture,
( aReductOfIn0(sK2(sK0),sK0,xR)
| sK0 != sK0 ),
inference(resolve,[status(thm)],[c_68,c_58]) ).
cnf(c_140,negated_conjecture,
aReductOfIn0(sK2(sK0),sK0,xR),
inference(copy,[status(thm)],[c_281]) ).
cnf(c_282,plain,
( aElement0(sK2(sK0))
| ~ aElement0(sK0) ),
inference(resolve,[status(thm)],[c_140,c_106]) ).
cnf(c_165,negated_conjecture,
aElement0(sK2(sK0)),
inference(resolve,[status(thm)],[c_58,c_282]) ).
cnf(c_283,plain,
( iLess0(sK2(sK0),sK0)
| ~ aElement0(sK2(sK0))
| ~ aElement0(sK0) ),
inference(resolve,[status(thm)],[c_140,c_55]) ).
cnf(c_284,negated_conjecture,
( iLess0(sK2(sK0),sK0)
| ~ aElement0(sK2(sK0)) ),
inference(resolve,[status(thm)],[c_58,c_283]) ).
cnf(c_174,negated_conjecture,
iLess0(sK2(sK0),sK0),
inference(resolve,[status(thm)],[c_165,c_284]) ).
cnf(c_285,negated_conjecture,
( sdtmndtplgtdt0(sK2(sK0),xR,sK1(sK2(sK0)))
| sK1(sK2(sK0)) = sK2(sK0)
| ~ aElement0(sK2(sK0)) ),
inference(resolve,[status(thm)],[c_174,c_63]) ).
cnf(c_201,negated_conjecture,
( sdtmndtplgtdt0(sK2(sK0),xR,sK1(sK2(sK0)))
| sK1(sK2(sK0)) = sK2(sK0) ),
inference(resolve,[status(thm)],[c_165,c_285]) ).
cnf(c_286,negated_conjecture,
( aElement0(sK1(sK2(sK0)))
| ~ aElement0(sK2(sK0)) ),
inference(resolve,[status(thm)],[c_174,c_59]) ).
cnf(c_205,negated_conjecture,
aElement0(sK1(sK2(sK0))),
inference(resolve,[status(thm)],[c_165,c_286]) ).
cnf(c_287,negated_conjecture,
( ~ aReductOfIn0(A,sK1(sK2(sK0)),xR)
| ~ iLess0(sK2(sK0),sK0) ),
inference(resolve,[status(thm)],[c_65,c_165]) ).
cnf(c_206,negated_conjecture,
~ aReductOfIn0(A,sK1(sK2(sK0)),xR),
inference(resolve,[status(thm)],[c_287,c_174]) ).
cnf(c_288,negated_conjecture,
( aReductOfIn0(sK2(sK1(sK2(sK0))),sK1(sK2(sK0)),xR)
| ~ sdtmndtplgtdt0(A,xR,sK1(sK2(sK0)))
| ~ aReductOfIn0(A,sK0,xR)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_70,c_205]) ).
cnf(c_289,negated_conjecture,
( aReductOfIn0(sK2(sK1(sK2(sK0))),sK1(sK2(sK0)),xR)
| ~ sdtmndtplgtdt0(sK2(sK0),xR,sK1(sK2(sK0)))
| ~ aReductOfIn0(sK2(sK0),sK0,xR) ),
inference(resolve,[status(thm)],[c_288,c_165]) ).
cnf(c_290,negated_conjecture,
( aReductOfIn0(sK2(sK1(sK2(sK0))),sK1(sK2(sK0)),xR)
| ~ sdtmndtplgtdt0(sK2(sK0),xR,sK1(sK2(sK0))) ),
inference(resolve,[status(thm)],[c_289,c_140]) ).
cnf(c_277,negated_conjecture,
~ sdtmndtplgtdt0(sK2(sK0),xR,sK1(sK2(sK0))),
inference(resolve,[status(thm)],[c_290,c_206]) ).
cnf(c_291,negated_conjecture,
( aReductOfIn0(sK2(sK1(sK2(sK0))),sK1(sK2(sK0)),xR)
| ~ aReductOfIn0(sK1(sK2(sK0)),sK0,xR) ),
inference(resolve,[status(thm)],[c_69,c_205]) ).
cnf(c_278,negated_conjecture,
~ aReductOfIn0(sK1(sK2(sK0)),sK0,xR),
inference(resolve,[status(thm)],[c_291,c_206]) ).
cnf(c_279,negated_conjecture,
sK1(sK2(sK0)) = sK2(sK0),
inference(resolve,[status(thm)],[c_277,c_201]) ).
cnf(c_292,negated_conjecture,
~ aReductOfIn0(sK2(sK0),sK0,xR),
inference(paramod,[status(thm)],[c_279,c_278]) ).
cnf(c_280,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_140,c_292]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM013+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/10.58 % Computer : n008.cluster.edu
% 0.08/10.58 % Model : x86_64 x86_64
% 0.08/10.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/10.58 % Memory : 8046.5625MB
% 0.08/10.58 % OS : Linux 6.8.0-71-generic
% 0.08/10.58 % CPULimit : 300
% 0.08/10.58 % WCLimit : 300
% 0.08/10.58 % DateTime : Sat Sep 26 23:22:06 UTC 2026
% 0.08/10.58 % CPUTime :
% 0.08/10.59 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/10.59 % Process 622842 was started by sandbox on n008,
% 0.08/10.59 % Sat Sep 26 23:22:06 2026
% 0.08/10.59 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/10.59
% 0.08/10.59 % From the command line: assign(max_seconds, 300).
% 0.13/10.65
% 0.13/10.65 % SZS status Theorem for theBenchmark
% 0.13/10.65
% 0.13/10.65 % Proof 1 at 0.04 (+ 0.01) seconds.
% 0.13/10.65 % Length of proof is 25.
% 0.13/10.65 % Level of proof is 9.
% 0.13/10.65 % Maximum clause weight is 17.000.
% 0.13/10.65 % Given clauses 101.
% 0.13/10.65
% 0.13/10.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------