%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COM021+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 : n012.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 0.25s 0.40s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 57 ( 20 unt; 0 def)
% Number of atoms : 215 ( 11 equ)
% Maximal formula atoms : 30 ( 3 avg)
% Number of connectives : 272 ( 114 ~; 119 |; 31 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 9 con; 0-3 aty)
% Number of variables : 82 ( 4 sgn 37 !; 3 ?)
% 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(mTCRTrans,axiom,
! [W0,W1,W2,W3] :
( ( aElement0(W3)
& aElement0(W2)
& aRewritingSystem0(W1)
& aElement0(W0) )
=> ( ( sdtmndtasgtdt0(W2,W1,W3)
& sdtmndtasgtdt0(W0,W1,W2) )
=> sdtmndtasgtdt0(W0,W1,W3) ) ),
file('theBenchmark.p',mTCRTrans) ).
fof(mNFRDef,axiom,
! [W0,W1] :
( ( aRewritingSystem0(W1)
& aElement0(W0) )
=> ! [W2] :
( aNormalFormOfIn0(W2,W0,W1)
<=> ( ~ ? [W3] : aReductOfIn0(W3,W2,W1)
& sdtmndtasgtdt0(W0,W1,W2)
& aElement0(W2) ) ) ),
file('theBenchmark.p',mNFRDef) ).
fof(m__731,axiom,
( aElement0(xc)
& aElement0(xb)
& aElement0(xa) ),
file('theBenchmark.p',m__731) ).
fof(m__799,axiom,
( sdtmndtasgtdt0(xv,xR,xw)
& sdtmndtasgtdt0(xu,xR,xw)
& aElement0(xw) ),
file('theBenchmark.p',m__799) ).
fof(m__850,axiom,
( sdtmndtasgtdt0(xd,xR,xx)
& sdtmndtasgtdt0(xb,xR,xx)
& aElement0(xx) ),
file('theBenchmark.p',m__850) ).
fof(m__,conjecture,
sdtmndtasgtdt0(xb,xR,xd),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ sdtmndtasgtdt0(xb,xR,xd),
inference(assume_negation,[status(cth)],[m__]) ).
fof(m__656,axiom,
aRewritingSystem0(xR),
file('theBenchmark.p',m__656) ).
cnf(c_24,plain,
aRewritingSystem0(xR),
inference(clausify,[status(thm)],[m__656]) ).
cnf(c_27,plain,
( ~ aReductOfIn0(D,C,B)
| ~ aNormalFormOfIn0(C,A,B)
| ~ aRewritingSystem0(B)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mNFRDef]) ).
cnf(c_29,plain,
( aElement0(C)
| ~ aNormalFormOfIn0(C,A,B)
| ~ aRewritingSystem0(B)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mNFRDef]) ).
cnf(c_53,plain,
( sdtmndtasgtdt0(A,B,D)
| ~ sdtmndtasgtdt0(C,B,D)
| ~ sdtmndtasgtdt0(A,B,C)
| ~ aElement0(D)
| ~ aElement0(C)
| ~ aRewritingSystem0(B)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mTCRTrans]) ).
cnf(c_55,plain,
( C != A
| sdtmndtasgtdt0(A,B,C)
| ~ aElement0(C)
| ~ aRewritingSystem0(B)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mTCRDef]) ).
cnf(c_56,plain,
( sdtmndtplgtdt0(A,B,C)
| 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_61,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_66,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_24,c_61]) ).
cnf(c_71,plain,
( sdtmndtplgtdt0(A,xR,B)
| B = A
| ~ sdtmndtasgtdt0(A,xR,B)
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_24,c_56]) ).
cnf(c_72,plain,
( B != A
| sdtmndtasgtdt0(A,xR,B)
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_24,c_55]) ).
cnf(c_74,plain,
( sdtmndtasgtdt0(A,xR,C)
| ~ sdtmndtasgtdt0(B,xR,C)
| ~ sdtmndtasgtdt0(A,xR,B)
| ~ aElement0(C)
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_24,c_53]) ).
cnf(c_88,plain,
( aElement0(B)
| ~ aNormalFormOfIn0(B,A,xR)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_24,c_29]) ).
cnf(c_90,plain,
( ~ aReductOfIn0(C,B,xR)
| ~ aNormalFormOfIn0(B,A,xR)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_24,c_27]) ).
cnf(c_93,negated_conjecture,
~ sdtmndtasgtdt0(xb,xR,xd),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_94,plain,
sdtmndtasgtdt0(xd,xR,xx),
inference(clausify,[status(thm)],[m__850]) ).
cnf(c_95,plain,
sdtmndtasgtdt0(xb,xR,xx),
inference(clausify,[status(thm)],[m__850]) ).
cnf(c_96,plain,
aElement0(xx),
inference(clausify,[status(thm)],[m__850]) ).
fof(m__818,axiom,
aNormalFormOfIn0(xd,xw,xR),
file('theBenchmark.p',m__818) ).
cnf(c_97,plain,
aNormalFormOfIn0(xd,xw,xR),
inference(clausify,[status(thm)],[m__818]) ).
cnf(c_100,plain,
aElement0(xw),
inference(clausify,[status(thm)],[m__799]) ).
cnf(c_113,plain,
aElement0(xb),
inference(clausify,[status(thm)],[m__731]) ).
cnf(c_553,plain,
( A != A
| sdtmndtasgtdt0(A,xR,A)
| ~ aElement0(A) ),
inference(factor,[status(thm)],[c_72]) ).
cnf(c_123,plain,
( sdtmndtasgtdt0(A,xR,A)
| ~ aElement0(A) ),
inference(copy,[status(thm)],[c_553]) ).
cnf(c_554,plain,
( sdtmndtplgtdt0(xd,xR,xx)
| xx = xd
| ~ aElement0(xx)
| ~ aElement0(xd) ),
inference(resolve,[status(thm)],[c_94,c_71]) ).
cnf(c_555,plain,
( sdtmndtplgtdt0(xd,xR,xx)
| xd = xx
| ~ aElement0(xx)
| ~ aElement0(xd) ),
inference(copy,[status(thm)],[c_554]) ).
cnf(c_178,plain,
( sdtmndtplgtdt0(xd,xR,xx)
| xd = xx
| ~ aElement0(xd) ),
inference(resolve,[status(thm)],[c_96,c_555]) ).
cnf(c_556,plain,
( ~ aReductOfIn0(A,xd,xR)
| ~ aElement0(xw) ),
inference(resolve,[status(thm)],[c_97,c_90]) ).
cnf(c_197,plain,
~ aReductOfIn0(A,xd,xR),
inference(resolve,[status(thm)],[c_100,c_556]) ).
cnf(c_557,plain,
( aElement0(xd)
| ~ aElement0(xw) ),
inference(resolve,[status(thm)],[c_97,c_88]) ).
cnf(c_199,plain,
aElement0(xd),
inference(resolve,[status(thm)],[c_100,c_557]) ).
cnf(c_206,plain,
( sdtmndtplgtdt0(xd,xR,xx)
| xd = xx ),
inference(resolve,[status(thm)],[c_199,c_178]) ).
cnf(c_364,plain,
sdtmndtasgtdt0(xx,xR,xx),
inference(resolve,[status(thm)],[c_123,c_96]) ).
cnf(c_558,plain,
( sdtmndtasgtdt0(xb,xR,B)
| ~ sdtmndtasgtdt0(A,xR,B)
| ~ sdtmndtasgtdt0(xb,xR,A)
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_74,c_113]) ).
cnf(c_559,plain,
( sdtmndtasgtdt0(xb,xR,A)
| ~ sdtmndtasgtdt0(xx,xR,A)
| ~ sdtmndtasgtdt0(xb,xR,xx)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_558,c_96]) ).
cnf(c_560,plain,
( sdtmndtasgtdt0(xb,xR,xd)
| ~ sdtmndtasgtdt0(xx,xR,xd)
| ~ sdtmndtasgtdt0(xb,xR,xx) ),
inference(resolve,[status(thm)],[c_559,c_199]) ).
cnf(c_561,plain,
( sdtmndtasgtdt0(xb,xR,xd)
| ~ sdtmndtasgtdt0(xx,xR,xd) ),
inference(resolve,[status(thm)],[c_560,c_95]) ).
cnf(c_516,negated_conjecture,
~ sdtmndtasgtdt0(xx,xR,xd),
inference(resolve,[status(thm)],[c_561,c_93]) ).
cnf(c_562,plain,
( aReductOfIn0(sK0(xd,xR,A),xd,xR)
| aReductOfIn0(A,xd,xR)
| ~ sdtmndtplgtdt0(xd,xR,A)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_66,c_199]) ).
cnf(c_563,plain,
( aReductOfIn0(sK0(xd,xR,xx),xd,xR)
| aReductOfIn0(xx,xd,xR)
| ~ sdtmndtplgtdt0(xd,xR,xx) ),
inference(resolve,[status(thm)],[c_562,c_96]) ).
cnf(c_564,plain,
( aReductOfIn0(sK0(xd,xR,xx),xd,xR)
| ~ sdtmndtplgtdt0(xd,xR,xx) ),
inference(resolve,[status(thm)],[c_563,c_197]) ).
cnf(c_525,plain,
~ sdtmndtplgtdt0(xd,xR,xx),
inference(resolve,[status(thm)],[c_564,c_197]) ).
cnf(c_538,plain,
xd = xx,
inference(resolve,[status(thm)],[c_525,c_206]) ).
cnf(c_565,negated_conjecture,
~ sdtmndtasgtdt0(xx,xR,xx),
inference(paramod,[status(thm)],[c_538,c_516]) ).
cnf(c_552,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_364,c_565]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : COM021+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sat Sep 26 23:22:37 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.30 % Process 1750013 was started by sandbox on n012,
% 0.03/0.30 % Sat Sep 26 23:22:37 2026
% 0.03/0.30 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.03/0.30
% 0.03/0.30 % From the command line: assign(max_seconds, 300).
% 0.25/0.40
% 0.25/0.40 % SZS status Theorem for theBenchmark
% 0.25/0.40
% 0.25/0.40 % Proof 1 at 0.08 (+ 0.00) seconds.
% 0.25/0.40 % Length of proof is 38.
% 0.25/0.40 % Level of proof is 6.
% 0.25/0.40 % Maximum clause weight is 19.000.
% 0.25/0.40 % Given clauses 98.
% 0.25/0.40
% 0.25/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------