%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COM012+3 : 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 : 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 06:59:38 AM UTC 2026
% Result : Theorem 0.08s 0.39s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 11 unt; 0 def)
% Number of atoms : 109 ( 20 equ)
% Maximal formula atoms : 21 ( 4 avg)
% Number of connectives : 108 ( 26 ~; 49 |; 29 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 20 ( 0 sgn 4 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mTCTrans,axiom,
! [W0,W1,W2,W3] :
( ( aElement0(W3)
& aElement0(W2)
& aRewritingSystem0(W1)
& aElement0(W0) )
=> ( ( sdtmndtplgtdt0(W2,W1,W3)
& sdtmndtplgtdt0(W0,W1,W2) )
=> sdtmndtplgtdt0(W0,W1,W3) ) ),
file('theBenchmark.p',mTCTrans) ).
fof(m__349,axiom,
( aElement0(xz)
& aElement0(xy)
& aRewritingSystem0(xR)
& aElement0(xx) ),
file('theBenchmark.p',m__349) ).
fof(m__,conjecture,
( ( sdtmndtasgtdt0(xy,xR,xz)
& ( ( sdtmndtplgtdt0(xy,xR,xz)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xz)
& aReductOfIn0(W0,xy,xR)
& aElement0(W0) )
| aReductOfIn0(xz,xy,xR) ) )
| xy = xz )
& sdtmndtasgtdt0(xx,xR,xy)
& ( ( sdtmndtplgtdt0(xx,xR,xy)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xy)
& aReductOfIn0(W0,xx,xR)
& aElement0(W0) )
| aReductOfIn0(xy,xx,xR) ) )
| xx = xy ) )
=> ( sdtmndtasgtdt0(xx,xR,xz)
| sdtmndtplgtdt0(xx,xR,xz)
| ? [W0] :
( sdtmndtplgtdt0(W0,xR,xz)
& aReductOfIn0(W0,xx,xR)
& aElement0(W0) )
| aReductOfIn0(xz,xx,xR)
| xx = xz ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( ( sdtmndtasgtdt0(xy,xR,xz)
& ( ( sdtmndtplgtdt0(xy,xR,xz)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xz)
& aReductOfIn0(W0,xy,xR)
& aElement0(W0) )
| aReductOfIn0(xz,xy,xR) ) )
| xy = xz )
& sdtmndtasgtdt0(xx,xR,xy)
& ( ( sdtmndtplgtdt0(xx,xR,xy)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xy)
& aReductOfIn0(W0,xx,xR)
& aElement0(W0) )
| aReductOfIn0(xy,xx,xR) ) )
| xx = xy ) )
=> ( sdtmndtasgtdt0(xx,xR,xz)
| sdtmndtplgtdt0(xx,xR,xz)
| ? [W0] :
( sdtmndtplgtdt0(W0,xR,xz)
& aReductOfIn0(W0,xx,xR)
& aElement0(W0) )
| aReductOfIn0(xz,xx,xR)
| xx = xz ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_11,plain,
aRewritingSystem0(xR),
inference(clausify,[status(thm)],[m__349]) ).
cnf(c_15,plain,
( sdtmndtplgtdt0(A,B,D)
| ~ sdtmndtplgtdt0(C,B,D)
| ~ sdtmndtplgtdt0(A,B,C)
| ~ aElement0(D)
| ~ aElement0(C)
| ~ aRewritingSystem0(B)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mTCTrans]) ).
cnf(c_28,plain,
( sdtmndtplgtdt0(A,xR,C)
| ~ sdtmndtplgtdt0(B,xR,C)
| ~ sdtmndtplgtdt0(A,xR,B)
| ~ aElement0(C)
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_11,c_15]) ).
cnf(c_32,negated_conjecture,
~ sdtmndtasgtdt0(xx,xR,xz),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_33,negated_conjecture,
~ sdtmndtplgtdt0(xx,xR,xz),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_37,negated_conjecture,
sdtmndtasgtdt0(xy,xR,xz),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_38,negated_conjecture,
( sdtmndtplgtdt0(xy,xR,xz)
| xz = xy ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_42,negated_conjecture,
sdtmndtasgtdt0(xx,xR,xy),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_43,negated_conjecture,
( sdtmndtplgtdt0(xx,xR,xy)
| xy = xx ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_44,negated_conjecture,
( sdtmndtplgtdt0(xx,xR,xy)
| xx = xy ),
inference(copy,[status(thm)],[c_43]) ).
cnf(c_51,plain,
aElement0(xz),
inference(clausify,[status(thm)],[m__349]) ).
cnf(c_52,plain,
aElement0(xy),
inference(clausify,[status(thm)],[m__349]) ).
cnf(c_53,plain,
aElement0(xx),
inference(clausify,[status(thm)],[m__349]) ).
cnf(c_104,negated_conjecture,
( sdtmndtplgtdt0(A,xR,xz)
| ~ sdtmndtplgtdt0(A,xR,xy)
| ~ aElement0(xz)
| ~ aElement0(xy)
| ~ aElement0(A)
| xz = xy ),
inference(resolve,[status(thm)],[c_38,c_28]) ).
cnf(c_105,negated_conjecture,
( sdtmndtplgtdt0(A,xR,xz)
| ~ sdtmndtplgtdt0(A,xR,xy)
| ~ aElement0(xz)
| ~ aElement0(A)
| xz = xy ),
inference(resolve,[status(thm)],[c_52,c_104]) ).
cnf(c_61,negated_conjecture,
( sdtmndtplgtdt0(A,xR,xz)
| ~ sdtmndtplgtdt0(A,xR,xy)
| ~ aElement0(A)
| xz = xy ),
inference(resolve,[status(thm)],[c_51,c_105]) ).
cnf(c_106,negated_conjecture,
( xx = xy
| sdtmndtplgtdt0(xx,xR,xz)
| ~ aElement0(xx)
| xz = xy ),
inference(resolve,[status(thm)],[c_61,c_44]) ).
cnf(c_107,negated_conjecture,
( xx = xy
| sdtmndtplgtdt0(xx,xR,xz)
| xz = xy ),
inference(resolve,[status(thm)],[c_53,c_106]) ).
cnf(c_97,negated_conjecture,
( xx = xy
| xz = xy ),
inference(resolve,[status(thm)],[c_33,c_107]) ).
cnf(c_108,plain,
( ~ sdtmndtasgtdt0(xx,xR,xy)
| xx = xy ),
inference(paramod,[status(thm)],[c_97,c_32]) ).
cnf(c_98,negated_conjecture,
xx = xy,
inference(resolve,[status(thm)],[c_42,c_108]) ).
cnf(c_109,negated_conjecture,
~ sdtmndtasgtdt0(xy,xR,xz),
inference(paramod,[status(thm)],[c_98,c_32]) ).
cnf(c_103,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_37,c_109]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM012+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n018.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 23:23:38 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.37 % Process 1705217 was started by sandbox2 on n018,
% 0.08/0.37 % Sat Sep 26 23:23:38 2026
% 0.08/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 0.08/0.39
% 0.08/0.39 % SZS status Theorem for theBenchmark
% 0.08/0.39
% 0.08/0.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.08/0.39 % Length of proof is 20.
% 0.08/0.39 % Level of proof is 6.
% 0.08/0.39 % Maximum clause weight is 18.000.
% 0.08/0.39 % Given clauses 40.
% 0.08/0.39
% 0.08/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------