%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COM016+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 : n004.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 0.15s 5.51s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 48 ( 13 unt; 0 def)
% Number of atoms : 189 ( 4 equ)
% Maximal formula atoms : 30 ( 3 avg)
% Number of connectives : 239 ( 98 ~; 112 |; 25 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-3 aty)
% Number of variables : 63 ( 0 sgn 30 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mTCDef,axiom,
! [W0,W1,W2] :
( ( aElement0(W2)
& aRewritingSystem0(W1)
& aElement0(W0) )
=> ( sdtmndtplgtdt0(W0,W1,W2)
<=> ( ? [W3] :
( sdtmndtplgtdt0(W3,W1,W2)
& aReductOfIn0(W3,W0,W1)
& aElement0(W3) )
| aReductOfIn0(W2,W0,W1) ) ) ),
file('theBenchmark.p',mTCDef) ).
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__731,axiom,
( aElement0(xc)
& aElement0(xb)
& aElement0(xa) ),
file('theBenchmark.p',m__731) ).
fof(m__731_02,axiom,
( sdtmndtplgtdt0(xa,xR,xc)
& sdtmndtplgtdt0(xa,xR,xb) ),
file('theBenchmark.p',m__731_02) ).
fof(m__,conjecture,
? [W0] :
( sdtmndtasgtdt0(W0,xR,xb)
& aReductOfIn0(W0,xa,xR)
& aElement0(W0) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ? [W0] :
( sdtmndtasgtdt0(W0,xR,xb)
& aReductOfIn0(W0,xa,xR)
& aElement0(W0) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(m__656,axiom,
aRewritingSystem0(xR),
file('theBenchmark.p',m__656) ).
cnf(c_20,plain,
aRewritingSystem0(xR),
inference(clausify,[status(thm)],[m__656]) ).
cnf(c_50,plain,
( ~ sdtmndtplgtdt0(A,B,C)
| sdtmndtasgtdt0(A,B,C)
| ~ aElement0(C)
| ~ aRewritingSystem0(B)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mTCRDef]) ).
cnf(c_51,plain,
( C != A
| sdtmndtasgtdt0(A,B,C)
| ~ aElement0(C)
| ~ aRewritingSystem0(B)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mTCRDef]) ).
fof(nnf_6,plain,
! [W0,W1,W2] :
( ( ( ( ! [W3] :
( ~ sdtmndtplgtdt0(W3,W1,W2)
| ~ aReductOfIn0(W3,W0,W1)
| ~ aElement0(W3) )
& ~ aReductOfIn0(W2,W0,W1) )
| sdtmndtplgtdt0(W0,W1,W2) )
& ( ? [X0] :
( sdtmndtplgtdt0(X0,W1,W2)
& aReductOfIn0(X0,W0,W1)
& aElement0(X0) )
| aReductOfIn0(W2,W0,W1)
| ~ sdtmndtplgtdt0(W0,W1,W2) ) )
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mTCDef]) ).
fof(sk_mTCDef_sk,plain,
! [W0,W1,W2] :
( ( ( ( ! [W3] :
( ~ sdtmndtplgtdt0(W3,W1,W2)
| ~ aReductOfIn0(W3,W0,W1)
| ~ aElement0(W3) )
& ~ aReductOfIn0(W2,W0,W1) )
| sdtmndtplgtdt0(W0,W1,W2) )
& ( ( sdtmndtplgtdt0(sK0(W0,W1,W2),W1,W2)
& aReductOfIn0(sK0(W0,W1,W2),W0,W1)
& aElement0(sK0(W0,W1,W2)) )
| aReductOfIn0(W2,W0,W1)
| ~ sdtmndtplgtdt0(W0,W1,W2) ) )
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ aElement0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0(W0,W1,W2))],[nnf_6]) ).
fof(sk_mTCDef,plain,
( ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ sdtmndtplgtdt0(VAR_3,VAR_1,VAR_2)
| ~ aReductOfIn0(VAR_3,VAR_0,VAR_1)
| ~ aElement0(VAR_3)
| sdtmndtplgtdt0(VAR_0,VAR_1,VAR_2)
| ~ aElement0(VAR_2)
| ~ aRewritingSystem0(VAR_1)
| ~ aElement0(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ aReductOfIn0(VAR_2,VAR_0,VAR_1)
| sdtmndtplgtdt0(VAR_0,VAR_1,VAR_2)
| ~ aElement0(VAR_2)
| ~ aRewritingSystem0(VAR_1)
| ~ aElement0(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( sdtmndtplgtdt0(sK0(VAR_0,VAR_1,VAR_2),VAR_1,VAR_2)
| aReductOfIn0(VAR_2,VAR_0,VAR_1)
| ~ sdtmndtplgtdt0(VAR_0,VAR_1,VAR_2)
| ~ aElement0(VAR_2)
| ~ aRewritingSystem0(VAR_1)
| ~ aElement0(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( aReductOfIn0(sK0(VAR_0,VAR_1,VAR_2),VAR_0,VAR_1)
| aReductOfIn0(VAR_2,VAR_0,VAR_1)
| ~ sdtmndtplgtdt0(VAR_0,VAR_1,VAR_2)
| ~ aElement0(VAR_2)
| ~ aRewritingSystem0(VAR_1)
| ~ aElement0(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( aElement0(sK0(VAR_0,VAR_1,VAR_2))
| aReductOfIn0(VAR_2,VAR_0,VAR_1)
| ~ sdtmndtplgtdt0(VAR_0,VAR_1,VAR_2)
| ~ aElement0(VAR_2)
| ~ aRewritingSystem0(VAR_1)
| ~ aElement0(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_mTCDef_sk]) ).
cnf(c_56,plain,
( sdtmndtplgtdt0(sK0(A,B,C),B,C)
| aReductOfIn0(C,A,B)
| ~ sdtmndtplgtdt0(A,B,C)
| ~ aElement0(C)
| ~ aRewritingSystem0(B)
| ~ aElement0(A) ),
inference(split_conjunct,[status(thm)],[sk_mTCDef]) ).
cnf(c_57,plain,
( aReductOfIn0(sK0(A,B,C),A,B)
| aReductOfIn0(C,A,B)
| ~ sdtmndtplgtdt0(A,B,C)
| ~ aElement0(C)
| ~ aRewritingSystem0(B)
| ~ aElement0(A) ),
inference(split_conjunct,[status(thm)],[sk_mTCDef]) ).
cnf(c_58,plain,
( aElement0(sK0(A,B,C))
| aReductOfIn0(C,A,B)
| ~ sdtmndtplgtdt0(A,B,C)
| ~ aElement0(C)
| ~ aRewritingSystem0(B)
| ~ aElement0(A) ),
inference(split_conjunct,[status(thm)],[sk_mTCDef]) ).
cnf(c_61,plain,
( aElement0(sK0(A,xR,B))
| aReductOfIn0(B,A,xR)
| ~ sdtmndtplgtdt0(A,xR,B)
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_20,c_58]) ).
cnf(c_62,plain,
( aReductOfIn0(sK0(A,xR,B),A,xR)
| aReductOfIn0(B,A,xR)
| ~ sdtmndtplgtdt0(A,xR,B)
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_20,c_57]) ).
cnf(c_63,plain,
( sdtmndtplgtdt0(sK0(A,xR,B),xR,B)
| aReductOfIn0(B,A,xR)
| ~ sdtmndtplgtdt0(A,xR,B)
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_20,c_56]) ).
cnf(c_68,plain,
( B != A
| sdtmndtasgtdt0(A,xR,B)
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_20,c_51]) ).
cnf(c_69,plain,
( ~ sdtmndtplgtdt0(A,xR,B)
| sdtmndtasgtdt0(A,xR,B)
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_20,c_50]) ).
cnf(c_89,negated_conjecture,
( ~ sdtmndtasgtdt0(A,xR,xb)
| ~ aReductOfIn0(A,xa,xR)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_91,plain,
sdtmndtplgtdt0(xa,xR,xb),
inference(clausify,[status(thm)],[m__731_02]) ).
cnf(c_96,plain,
aElement0(xb),
inference(clausify,[status(thm)],[m__731]) ).
cnf(c_97,plain,
aElement0(xa),
inference(clausify,[status(thm)],[m__731]) ).
cnf(c_1254,plain,
( A != A
| sdtmndtasgtdt0(A,xR,A)
| ~ aElement0(A) ),
inference(factor,[status(thm)],[c_68]) ).
cnf(c_106,plain,
( sdtmndtasgtdt0(A,xR,A)
| ~ aElement0(A) ),
inference(copy,[status(thm)],[c_1254]) ).
cnf(c_1255,plain,
( sdtmndtplgtdt0(sK0(xa,xR,xb),xR,xb)
| aReductOfIn0(xb,xa,xR)
| ~ aElement0(xb)
| ~ aElement0(xa) ),
inference(resolve,[status(thm)],[c_91,c_63]) ).
cnf(c_1256,plain,
( sdtmndtplgtdt0(sK0(xa,xR,xb),xR,xb)
| aReductOfIn0(xb,xa,xR)
| ~ aElement0(xb) ),
inference(resolve,[status(thm)],[c_97,c_1255]) ).
cnf(c_202,plain,
( sdtmndtplgtdt0(sK0(xa,xR,xb),xR,xb)
| aReductOfIn0(xb,xa,xR) ),
inference(resolve,[status(thm)],[c_96,c_1256]) ).
cnf(c_1257,plain,
( aReductOfIn0(sK0(xa,xR,xb),xa,xR)
| aReductOfIn0(xb,xa,xR)
| ~ aElement0(xb)
| ~ aElement0(xa) ),
inference(resolve,[status(thm)],[c_91,c_62]) ).
cnf(c_1258,plain,
( aReductOfIn0(sK0(xa,xR,xb),xa,xR)
| aReductOfIn0(xb,xa,xR)
| ~ aElement0(xb) ),
inference(resolve,[status(thm)],[c_97,c_1257]) ).
cnf(c_203,plain,
( aReductOfIn0(sK0(xa,xR,xb),xa,xR)
| aReductOfIn0(xb,xa,xR) ),
inference(resolve,[status(thm)],[c_96,c_1258]) ).
cnf(c_1259,plain,
( aElement0(sK0(xa,xR,xb))
| aReductOfIn0(xb,xa,xR)
| ~ aElement0(xb)
| ~ aElement0(xa) ),
inference(resolve,[status(thm)],[c_91,c_61]) ).
cnf(c_1260,plain,
( aElement0(sK0(xa,xR,xb))
| aReductOfIn0(xb,xa,xR)
| ~ aElement0(xb) ),
inference(resolve,[status(thm)],[c_97,c_1259]) ).
cnf(c_204,plain,
( aElement0(sK0(xa,xR,xb))
| aReductOfIn0(xb,xa,xR) ),
inference(resolve,[status(thm)],[c_96,c_1260]) ).
cnf(c_313,plain,
( ~ sdtmndtasgtdt0(xb,xR,xb)
| ~ aReductOfIn0(xb,xa,xR) ),
inference(resolve,[status(thm)],[c_96,c_89]) ).
cnf(c_332,plain,
( ~ sdtmndtplgtdt0(A,xR,xb)
| sdtmndtasgtdt0(A,xR,xb)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_96,c_69]) ).
cnf(c_478,plain,
sdtmndtasgtdt0(xb,xR,xb),
inference(resolve,[status(thm)],[c_106,c_96]) ).
cnf(c_488,plain,
~ aReductOfIn0(xb,xa,xR),
inference(resolve,[status(thm)],[c_478,c_313]) ).
cnf(c_493,plain,
aElement0(sK0(xa,xR,xb)),
inference(resolve,[status(thm)],[c_488,c_204]) ).
cnf(c_494,plain,
aReductOfIn0(sK0(xa,xR,xb),xa,xR),
inference(resolve,[status(thm)],[c_488,c_203]) ).
cnf(c_495,plain,
sdtmndtplgtdt0(sK0(xa,xR,xb),xR,xb),
inference(resolve,[status(thm)],[c_488,c_202]) ).
cnf(c_1261,plain,
( ~ sdtmndtplgtdt0(sK0(xa,xR,xb),xR,xb)
| sdtmndtasgtdt0(sK0(xa,xR,xb),xR,xb) ),
inference(resolve,[status(thm)],[c_493,c_332]) ).
cnf(c_1077,plain,
sdtmndtasgtdt0(sK0(xa,xR,xb),xR,xb),
inference(resolve,[status(thm)],[c_495,c_1261]) ).
cnf(c_1262,negated_conjecture,
( ~ sdtmndtasgtdt0(sK0(xa,xR,xb),xR,xb)
| ~ aReductOfIn0(sK0(xa,xR,xb),xa,xR) ),
inference(resolve,[status(thm)],[c_493,c_89]) ).
cnf(c_1263,negated_conjecture,
~ sdtmndtasgtdt0(sK0(xa,xR,xb),xR,xb),
inference(resolve,[status(thm)],[c_494,c_1262]) ).
cnf(c_1253,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_1077,c_1263]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM016+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.38 % Computer : n004.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Sat Sep 26 23:21:44 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.38 % Process 2884020 was started by sandbox on n004,
% 0.11/5.38 % Sat Sep 26 23:21:44 2026
% 0.11/5.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/5.39
% 0.11/5.39 % From the command line: assign(max_seconds, 300).
% 0.15/5.51
% 0.15/5.51 % SZS status Theorem for theBenchmark
% 0.15/5.51
% 0.15/5.51 % Proof 1 at 0.09 (+ 0.02) seconds.
% 0.15/5.51 % Length of proof is 33.
% 0.15/5.51 % Level of proof is 8.
% 0.15/5.51 % Maximum clause weight is 29.000.
% 0.15/5.51 % Given clauses 202.
% 0.15/5.51
% 0.15/5.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------