%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COM012+1 : 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 : n026.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 0.10s 0.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 38 ( 11 unt; 0 def)
% Number of atoms : 120 ( 21 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 133 ( 51 ~; 65 |; 11 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 28 ( 0 sgn 7 !; 0 ?)
% 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(mTCRDef,axiom,
! [W0,W1,W2] :
( ( aElement0(W2)
& aRewritingSystem0(W1)
& aElement0(W0) )
=> ( sdtmndtasgtdt0(W0,W1,W2)
<=> ( sdtmndtplgtdt0(W0,W1,W2)
| W0 = W2 ) ) ),
file('theBenchmark.p',mTCRDef) ).
fof(m__349,axiom,
( aElement0(xz)
& aElement0(xy)
& aRewritingSystem0(xR)
& aElement0(xx) ),
file('theBenchmark.p',m__349) ).
fof(m__,conjecture,
( ( sdtmndtasgtdt0(xy,xR,xz)
& sdtmndtasgtdt0(xx,xR,xy) )
=> sdtmndtasgtdt0(xx,xR,xz) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( ( sdtmndtasgtdt0(xy,xR,xz)
& sdtmndtasgtdt0(xx,xR,xy) )
=> sdtmndtasgtdt0(xx,xR,xz) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_11,plain,
aRewritingSystem0(xR),
inference(clausify,[status(thm)],[m__349]) ).
cnf(c_12,plain,
( ~ sdtmndtplgtdt0(A,B,C)
| sdtmndtasgtdt0(A,B,C)
| ~ aElement0(C)
| ~ aRewritingSystem0(B)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mTCRDef]) ).
cnf(c_14,plain,
( sdtmndtplgtdt0(A,B,C)
| C = A
| ~ sdtmndtasgtdt0(A,B,C)
| ~ aElement0(C)
| ~ aRewritingSystem0(B)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mTCRDef]) ).
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_29,plain,
( sdtmndtplgtdt0(A,xR,B)
| B = A
| ~ sdtmndtasgtdt0(A,xR,B)
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_11,c_14]) ).
cnf(c_31,plain,
( ~ sdtmndtplgtdt0(A,xR,B)
| sdtmndtasgtdt0(A,xR,B)
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_11,c_12]) ).
cnf(c_32,negated_conjecture,
~ sdtmndtasgtdt0(xx,xR,xz),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_33,negated_conjecture,
sdtmndtasgtdt0(xy,xR,xz),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_34,negated_conjecture,
sdtmndtasgtdt0(xx,xR,xy),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_35,plain,
aElement0(xz),
inference(clausify,[status(thm)],[m__349]) ).
cnf(c_36,plain,
aElement0(xy),
inference(clausify,[status(thm)],[m__349]) ).
cnf(c_37,plain,
aElement0(xx),
inference(clausify,[status(thm)],[m__349]) ).
cnf(c_82,negated_conjecture,
( sdtmndtplgtdt0(xy,xR,xz)
| xz = xy
| ~ aElement0(xz)
| ~ aElement0(xy) ),
inference(resolve,[status(thm)],[c_33,c_29]) ).
cnf(c_83,negated_conjecture,
( sdtmndtplgtdt0(xy,xR,xz)
| xz = xy
| ~ aElement0(xz) ),
inference(resolve,[status(thm)],[c_36,c_82]) ).
cnf(c_45,negated_conjecture,
( sdtmndtplgtdt0(xy,xR,xz)
| xz = xy ),
inference(resolve,[status(thm)],[c_35,c_83]) ).
cnf(c_84,negated_conjecture,
( sdtmndtplgtdt0(xx,xR,xy)
| xy = xx
| ~ aElement0(xy)
| ~ aElement0(xx) ),
inference(resolve,[status(thm)],[c_34,c_29]) ).
cnf(c_85,negated_conjecture,
( sdtmndtplgtdt0(xx,xR,xy)
| xx = xy
| ~ aElement0(xy)
| ~ aElement0(xx) ),
inference(copy,[status(thm)],[c_84]) ).
cnf(c_86,negated_conjecture,
( sdtmndtplgtdt0(xx,xR,xy)
| xx = xy
| ~ aElement0(xy) ),
inference(resolve,[status(thm)],[c_37,c_85]) ).
cnf(c_46,negated_conjecture,
( sdtmndtplgtdt0(xx,xR,xy)
| xx = xy ),
inference(resolve,[status(thm)],[c_36,c_86]) ).
cnf(c_87,plain,
( ~ sdtmndtplgtdt0(xx,xR,A)
| sdtmndtasgtdt0(xx,xR,A)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_31,c_37]) ).
cnf(c_88,plain,
( ~ sdtmndtplgtdt0(xx,xR,xz)
| sdtmndtasgtdt0(xx,xR,xz) ),
inference(resolve,[status(thm)],[c_87,c_35]) ).
cnf(c_53,negated_conjecture,
~ sdtmndtplgtdt0(xx,xR,xz),
inference(resolve,[status(thm)],[c_88,c_32]) ).
cnf(c_89,plain,
( sdtmndtplgtdt0(A,xR,xz)
| ~ sdtmndtplgtdt0(A,xR,xy)
| ~ aElement0(xz)
| ~ aElement0(xy)
| ~ aElement0(A)
| xz = xy ),
inference(resolve,[status(thm)],[c_45,c_28]) ).
cnf(c_90,plain,
( sdtmndtplgtdt0(A,xR,xz)
| ~ sdtmndtplgtdt0(A,xR,xy)
| ~ aElement0(xz)
| ~ aElement0(A)
| xz = xy ),
inference(resolve,[status(thm)],[c_36,c_89]) ).
cnf(c_60,plain,
( sdtmndtplgtdt0(A,xR,xz)
| ~ sdtmndtplgtdt0(A,xR,xy)
| ~ aElement0(A)
| xz = xy ),
inference(resolve,[status(thm)],[c_35,c_90]) ).
cnf(c_91,plain,
( xx = xy
| sdtmndtplgtdt0(xx,xR,xz)
| ~ aElement0(xx)
| xz = xy ),
inference(resolve,[status(thm)],[c_60,c_46]) ).
cnf(c_92,plain,
( xx = xy
| sdtmndtplgtdt0(xx,xR,xz)
| xz = xy ),
inference(resolve,[status(thm)],[c_37,c_91]) ).
cnf(c_75,plain,
( xx = xy
| xz = xy ),
inference(resolve,[status(thm)],[c_53,c_92]) ).
cnf(c_93,plain,
( ~ sdtmndtasgtdt0(xx,xR,xy)
| xx = xy ),
inference(paramod,[status(thm)],[c_75,c_32]) ).
cnf(c_77,negated_conjecture,
xx = xy,
inference(resolve,[status(thm)],[c_34,c_93]) ).
cnf(c_94,negated_conjecture,
~ sdtmndtasgtdt0(xy,xR,xz),
inference(paramod,[status(thm)],[c_77,c_32]) ).
cnf(c_81,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_33,c_94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM012+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n026.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sat Sep 26 23:23:42 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 2211055 was started by sandbox on n026,
% 0.10/0.38 % Sat Sep 26 23:23:42 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.10/0.40
% 0.10/0.40 % SZS status Theorem for theBenchmark
% 0.10/0.40
% 0.10/0.40 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.10/0.40 % Length of proof is 24.
% 0.10/0.40 % Level of proof is 7.
% 0.10/0.40 % Maximum clause weight is 18.000.
% 0.10/0.40 % Given clauses 43.
% 0.10/0.40
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------