%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COM021+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 : n010.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 2.77s 1.10s
% Output : CNFRefutation 2.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 6 unt; 0 def)
% Number of atoms : 111 ( 24 equ)
% Maximal formula atoms : 25 ( 6 avg)
% Number of connectives : 98 ( 5 ~; 42 |; 51 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 9 ( 1 sgn 0 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__818,axiom,
( aNormalFormOfIn0(xd,xw,xR)
& ~ ? [W0] : aReductOfIn0(W0,xd,xR)
& sdtmndtasgtdt0(xw,xR,xd)
& ( ( sdtmndtplgtdt0(xw,xR,xd)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xd)
& aReductOfIn0(W0,xw,xR)
& aElement0(W0) )
| aReductOfIn0(xd,xw,xR) ) )
| xw = xd )
& aElement0(xd) ),
file('theBenchmark.p',m__818) ).
fof(m__850,axiom,
( sdtmndtasgtdt0(xd,xR,xx)
& ( ( sdtmndtplgtdt0(xd,xR,xx)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xx)
& aReductOfIn0(W0,xd,xR)
& aElement0(W0) )
| aReductOfIn0(xx,xd,xR) ) )
| xd = xx )
& sdtmndtasgtdt0(xb,xR,xx)
& ( ( sdtmndtplgtdt0(xb,xR,xx)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xx)
& aReductOfIn0(W0,xb,xR)
& aElement0(W0) )
| aReductOfIn0(xx,xb,xR) ) )
| xb = xx )
& aElement0(xx) ),
file('theBenchmark.p',m__850) ).
fof(m__,conjecture,
( sdtmndtasgtdt0(xb,xR,xd)
| sdtmndtplgtdt0(xb,xR,xd)
| ? [W0] :
( sdtmndtplgtdt0(W0,xR,xd)
& aReductOfIn0(W0,xb,xR)
& aElement0(W0) )
| aReductOfIn0(xd,xb,xR)
| xb = xd ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( sdtmndtasgtdt0(xb,xR,xd)
| sdtmndtplgtdt0(xb,xR,xd)
| ? [W0] :
( sdtmndtplgtdt0(W0,xR,xd)
& aReductOfIn0(W0,xb,xR)
& aElement0(W0) )
| aReductOfIn0(xd,xb,xR)
| xb = xd ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_94,negated_conjecture,
~ sdtmndtplgtdt0(xb,xR,xd),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_97,negated_conjecture,
xd != xb,
inference(clausify,[status(thm)],[m___neg]) ).
fof(nnf_23,plain,
( sdtmndtasgtdt0(xd,xR,xx)
& ( ( sdtmndtplgtdt0(xd,xR,xx)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xx)
& aReductOfIn0(W0,xd,xR)
& aElement0(W0) )
| aReductOfIn0(xx,xd,xR) ) )
| xx = xd )
& sdtmndtasgtdt0(xb,xR,xx)
& ( ( sdtmndtplgtdt0(xb,xR,xx)
& ( ? [X0] :
( sdtmndtplgtdt0(X0,xR,xx)
& aReductOfIn0(X0,xb,xR)
& aElement0(X0) )
| aReductOfIn0(xx,xb,xR) ) )
| xx = xb )
& aElement0(xx) ),
inference(fof_nnf,[status(thm)],[m__850]) ).
fof(sk_m__850_sk,plain,
( sdtmndtasgtdt0(xd,xR,xx)
& ( ( sdtmndtplgtdt0(xd,xR,xx)
& ( ( sdtmndtplgtdt0(sK0,xR,xx)
& aReductOfIn0(sK0,xd,xR)
& aElement0(sK0) )
| aReductOfIn0(xx,xd,xR) ) )
| xx = xd )
& sdtmndtasgtdt0(xb,xR,xx)
& ( ( sdtmndtplgtdt0(xb,xR,xx)
& ( ( sdtmndtplgtdt0(sK1,xR,xx)
& aReductOfIn0(sK1,xb,xR)
& aElement0(sK1) )
| aReductOfIn0(xx,xb,xR) ) )
| xx = xb )
& aElement0(xx) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0]),skolemize(X0,sK1),skolemize(W0,sK0)],[nnf_23]) ).
fof(sk_m__850,plain,
( sdtmndtasgtdt0(xd,xR,xx)
& ( sdtmndtplgtdt0(xd,xR,xx)
| xx = xd )
& ( sdtmndtplgtdt0(sK0,xR,xx)
| aReductOfIn0(xx,xd,xR)
| xx = xd )
& ( aReductOfIn0(sK0,xd,xR)
| aReductOfIn0(xx,xd,xR)
| xx = xd )
& ( aElement0(sK0)
| aReductOfIn0(xx,xd,xR)
| xx = xd )
& sdtmndtasgtdt0(xb,xR,xx)
& ( sdtmndtplgtdt0(xb,xR,xx)
| xx = xb )
& ( sdtmndtplgtdt0(sK1,xR,xx)
| aReductOfIn0(xx,xb,xR)
| xx = xb )
& ( aReductOfIn0(sK1,xb,xR)
| aReductOfIn0(xx,xb,xR)
| xx = xb )
& ( aElement0(sK1)
| aReductOfIn0(xx,xb,xR)
| xx = xb )
& aElement0(xx) ),
inference(cnf_transformation,[status(thm)],[sk_m__850_sk]) ).
cnf(c_101,plain,
( aReductOfIn0(sK0,xd,xR)
| aReductOfIn0(xx,xd,xR)
| xx = xd ),
inference(split_conjunct,[status(thm)],[sk_m__850]) ).
cnf(c_104,plain,
( sdtmndtplgtdt0(xb,xR,xx)
| xx = xb ),
inference(split_conjunct,[status(thm)],[sk_m__850]) ).
cnf(c_110,plain,
~ aReductOfIn0(A,xd,xR),
inference(clausify,[status(thm)],[m__818]) ).
cnf(c_1209,plain,
( aReductOfIn0(sK0,xd,xR)
| xx = xd ),
inference(resolve,[status(thm)],[c_110,c_101]) ).
cnf(c_481,plain,
xx = xd,
inference(resolve,[status(thm)],[c_110,c_1209]) ).
cnf(c_1210,plain,
( sdtmndtplgtdt0(xb,xR,xx)
| xd = xb ),
inference(paramod,[status(thm)],[c_481,c_104]) ).
cnf(c_1211,plain,
( sdtmndtplgtdt0(xb,xR,xd)
| xd = xb ),
inference(paramod,[status(thm)],[c_481,c_1210]) ).
cnf(c_1212,negated_conjecture,
sdtmndtplgtdt0(xb,xR,xd),
inference(resolve,[status(thm)],[c_97,c_1211]) ).
cnf(c_1208,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_94,c_1212]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM021+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.56 % Computer : n010.cluster.edu
% 0.10/0.56 % Model : x86_64 x86_64
% 0.10/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.56 % Memory : 8046.5625MB
% 0.10/0.56 % OS : Linux 6.8.0-71-generic
% 0.10/0.57 % CPULimit : 300
% 0.10/0.57 % WCLimit : 300
% 0.10/0.57 % DateTime : Sat Sep 26 23:22:49 UTC 2026
% 0.10/0.57 % CPUTime :
% 0.10/0.57 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.57 % Process 296930 was started by sandbox on n010,
% 0.10/0.57 % Sat Sep 26 23:22:49 2026
% 0.10/0.57 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.72
% 0.13/0.72 % From the command line: assign(max_seconds, 300).
% 2.77/1.10
% 2.77/1.10 % SZS status Theorem for theBenchmark
% 2.77/1.10
% 2.77/1.10 % Proof 1 at 0.36 (+ 0.01) seconds.
% 2.77/1.10 % Length of proof is 10.
% 2.77/1.10 % Level of proof is 3.
% 2.77/1.10 % Maximum clause weight is 16.000.
% 2.77/1.10 % Given clauses 0.
% 2.77/1.10
% 2.77/1.10 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------