%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG109+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 : 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 08:26:40 AM UTC 2026
% Result : Theorem 6.21s 1.30s
% Output : CNFRefutation 6.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 42 ( 18 unt; 0 def)
% Number of atoms : 286 ( 98 equ)
% Maximal formula atoms : 127 ( 6 avg)
% Number of connectives : 380 ( 136 ~; 124 |; 110 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 41 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 91 ( 0 sgn 57 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mAddZero,axiom,
! [W0] :
( aElement0(W0)
=> ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 ) ),
file('theBenchmark.p',mAddZero) ).
fof(m__2091,axiom,
( aElement0(xb)
& aElement0(xa) ),
file('theBenchmark.p',m__2091) ).
fof(m__2129,axiom,
( aGcdOfAnd0(xc,xa,xb)
& ! [W0] :
( ( ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ? [W1] :
( sdtasdt0(W0,W1) = xb
& aElement0(W1) ) )
& ( aDivisorOf0(W0,xa)
| ( ( doDivides0(W0,xa)
| ? [W1] :
( sdtasdt0(W0,W1) = xa
& aElement0(W1) ) )
& aElement0(W0) ) ) )
=> ( doDivides0(W0,xc)
& ? [W1] :
( sdtasdt0(W0,W1) = xc
& aElement0(W1) ) ) )
& aDivisorOf0(xc,xb)
& doDivides0(xc,xb)
& ? [W0] :
( sdtasdt0(xc,W0) = xb
& aElement0(W0) )
& aElement0(xc)
& aDivisorOf0(xc,xa)
& doDivides0(xc,xa)
& ? [W0] :
( sdtasdt0(xc,W0) = xa
& aElement0(W0) )
& aElement0(xc) ),
file('theBenchmark.p',m__2129) ).
fof(m__2203,axiom,
( aElementOf0(xb,slsdtgt0(xb))
& ? [W0] :
( sdtasdt0(xb,W0) = xb
& aElement0(W0) )
& aElementOf0(sz00,slsdtgt0(xb))
& ? [W0] :
( sdtasdt0(xb,W0) = sz00
& aElement0(W0) )
& aElementOf0(xa,slsdtgt0(xa))
& ? [W0] :
( sdtasdt0(xa,W0) = xa
& aElement0(W0) )
& aElementOf0(sz00,slsdtgt0(xa))
& ? [W0] :
( sdtasdt0(xa,W0) = sz00
& aElement0(W0) ) ),
file('theBenchmark.p',m__2203) ).
fof(m__,conjecture,
? [W0] :
( W0 != sz00
& ( ! [W1] :
( aElementOf0(W1,slsdtgt0(xa))
<=> ? [W2] :
( sdtasdt0(xa,W2) = W1
& aElement0(W2) ) )
=> ( ! [W1] :
( aElementOf0(W1,slsdtgt0(xb))
<=> ? [W2] :
( sdtasdt0(xb,W2) = W1
& aElement0(W2) ) )
=> ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) ) ) ) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ? [W0] :
( W0 != sz00
& ( ! [W1] :
( aElementOf0(W1,slsdtgt0(xa))
<=> ? [W2] :
( sdtasdt0(xa,W2) = W1
& aElement0(W2) ) )
=> ( ! [W1] :
( aElementOf0(W1,slsdtgt0(xb))
<=> ? [W2] :
( sdtasdt0(xb,W2) = W1
& aElement0(W2) ) )
=> ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) ) ) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_74,negated_conjecture,
( sz00 = C
| sdtpldt0(A,B) != C
| ~ aElementOf0(B,slsdtgt0(xb))
| ~ aElementOf0(A,slsdtgt0(xa)) ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_81,plain,
aElementOf0(xb,slsdtgt0(xb)),
inference(clausify,[status(thm)],[m__2203]) ).
cnf(c_87,plain,
aElementOf0(xa,slsdtgt0(xa)),
inference(clausify,[status(thm)],[m__2203]) ).
cnf(c_90,plain,
aElementOf0(sz00,slsdtgt0(xa)),
inference(clausify,[status(thm)],[m__2203]) ).
fof(nnf_37,plain,
( aGcdOfAnd0(xc,xa,xb)
& ! [W0] :
( ( doDivides0(W0,xc)
& ? [W1] :
( sdtasdt0(W0,W1) = xc
& aElement0(W1) ) )
| ( ~ aDivisorOf0(W0,xb)
& ~ doDivides0(W0,xb)
& ! [X3] :
( sdtasdt0(W0,X3) != xb
| ~ aElement0(X3) ) )
| ( ~ aDivisorOf0(W0,xa)
& ( ( ~ doDivides0(W0,xa)
& ! [X5] :
( sdtasdt0(W0,X5) != xa
| ~ aElement0(X5) ) )
| ~ aElement0(W0) ) ) )
& aDivisorOf0(xc,xb)
& doDivides0(xc,xb)
& ? [X4] :
( sdtasdt0(xc,X4) = xb
& aElement0(X4) )
& aElement0(xc)
& aDivisorOf0(xc,xa)
& doDivides0(xc,xa)
& ? [X0] :
( sdtasdt0(xc,X0) = xa
& aElement0(X0) )
& aElement0(xc) ),
inference(fof_nnf,[status(thm)],[m__2129]) ).
fof(sk_m__2129_sk,plain,
( aGcdOfAnd0(xc,xa,xb)
& ! [W0] :
( ( doDivides0(W0,xc)
& sdtasdt0(W0,sK8(W0)) = xc
& aElement0(sK8(W0)) )
| ( ~ aDivisorOf0(W0,xb)
& ~ doDivides0(W0,xb)
& ! [X3] :
( sdtasdt0(W0,X3) != xb
| ~ aElement0(X3) ) )
| ( ~ aDivisorOf0(W0,xa)
& ( ( ~ doDivides0(W0,xa)
& ! [X5] :
( sdtasdt0(W0,X5) != xa
| ~ aElement0(X5) ) )
| ~ aElement0(W0) ) ) )
& aDivisorOf0(xc,xb)
& doDivides0(xc,xb)
& sdtasdt0(xc,sK0) = xb
& aElement0(sK0)
& aElement0(xc)
& aDivisorOf0(xc,xa)
& doDivides0(xc,xa)
& sdtasdt0(xc,sK1) = xa
& aElement0(sK1)
& aElement0(xc) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0,sK8]),skolemize(X0,sK1),skolemize(X4,sK0),skolemize(W1,sK8(W0))],[nnf_37]) ).
fof(sk_m__2129,plain,
( aGcdOfAnd0(xc,xa,xb)
& ! [VAR_0] :
( doDivides0(VAR_0,xc)
| ~ aDivisorOf0(VAR_0,xb)
| ~ aDivisorOf0(VAR_0,xa) )
& ! [VAR_0] :
( sdtasdt0(VAR_0,sK8(VAR_0)) = xc
| ~ aDivisorOf0(VAR_0,xb)
| ~ aDivisorOf0(VAR_0,xa) )
& ! [VAR_0] :
( aElement0(sK8(VAR_0))
| ~ aDivisorOf0(VAR_0,xb)
| ~ aDivisorOf0(VAR_0,xa) )
& ! [VAR_0] :
( doDivides0(VAR_0,xc)
| ~ doDivides0(VAR_0,xb)
| ~ aDivisorOf0(VAR_0,xa) )
& ! [VAR_0] :
( sdtasdt0(VAR_0,sK8(VAR_0)) = xc
| ~ doDivides0(VAR_0,xb)
| ~ aDivisorOf0(VAR_0,xa) )
& ! [VAR_0] :
( aElement0(sK8(VAR_0))
| ~ doDivides0(VAR_0,xb)
| ~ aDivisorOf0(VAR_0,xa) )
& ! [VAR_0,VAR_1] :
( doDivides0(VAR_0,xc)
| sdtasdt0(VAR_0,VAR_1) != xb
| ~ aElement0(VAR_1)
| ~ aDivisorOf0(VAR_0,xa) )
& ! [VAR_0,VAR_1] :
( sdtasdt0(VAR_0,sK8(VAR_0)) = xc
| sdtasdt0(VAR_0,VAR_1) != xb
| ~ aElement0(VAR_1)
| ~ aDivisorOf0(VAR_0,xa) )
& ! [VAR_0,VAR_1] :
( aElement0(sK8(VAR_0))
| sdtasdt0(VAR_0,VAR_1) != xb
| ~ aElement0(VAR_1)
| ~ aDivisorOf0(VAR_0,xa) )
& ! [VAR_0] :
( doDivides0(VAR_0,xc)
| ~ aDivisorOf0(VAR_0,xb)
| ~ doDivides0(VAR_0,xa)
| ~ aElement0(VAR_0) )
& ! [VAR_0] :
( sdtasdt0(VAR_0,sK8(VAR_0)) = xc
| ~ aDivisorOf0(VAR_0,xb)
| ~ doDivides0(VAR_0,xa)
| ~ aElement0(VAR_0) )
& ! [VAR_0] :
( aElement0(sK8(VAR_0))
| ~ aDivisorOf0(VAR_0,xb)
| ~ doDivides0(VAR_0,xa)
| ~ aElement0(VAR_0) )
& ! [VAR_0] :
( doDivides0(VAR_0,xc)
| ~ doDivides0(VAR_0,xb)
| ~ doDivides0(VAR_0,xa)
| ~ aElement0(VAR_0) )
& ! [VAR_0] :
( sdtasdt0(VAR_0,sK8(VAR_0)) = xc
| ~ doDivides0(VAR_0,xb)
| ~ doDivides0(VAR_0,xa)
| ~ aElement0(VAR_0) )
& ! [VAR_0] :
( aElement0(sK8(VAR_0))
| ~ doDivides0(VAR_0,xb)
| ~ doDivides0(VAR_0,xa)
| ~ aElement0(VAR_0) )
& ! [VAR_0,VAR_1] :
( doDivides0(VAR_0,xc)
| sdtasdt0(VAR_0,VAR_1) != xb
| ~ aElement0(VAR_1)
| ~ doDivides0(VAR_0,xa)
| ~ aElement0(VAR_0) )
& ! [VAR_0,VAR_1] :
( sdtasdt0(VAR_0,sK8(VAR_0)) = xc
| sdtasdt0(VAR_0,VAR_1) != xb
| ~ aElement0(VAR_1)
| ~ doDivides0(VAR_0,xa)
| ~ aElement0(VAR_0) )
& ! [VAR_0,VAR_1] :
( aElement0(sK8(VAR_0))
| sdtasdt0(VAR_0,VAR_1) != xb
| ~ aElement0(VAR_1)
| ~ doDivides0(VAR_0,xa)
| ~ aElement0(VAR_0) )
& ! [VAR_0,VAR_1] :
( doDivides0(VAR_0,xc)
| ~ aDivisorOf0(VAR_0,xb)
| sdtasdt0(VAR_0,VAR_1) != xa
| ~ aElement0(VAR_1)
| ~ aElement0(VAR_0) )
& ! [VAR_0,VAR_1] :
( sdtasdt0(VAR_0,sK8(VAR_0)) = xc
| ~ aDivisorOf0(VAR_0,xb)
| sdtasdt0(VAR_0,VAR_1) != xa
| ~ aElement0(VAR_1)
| ~ aElement0(VAR_0) )
& ! [VAR_0,VAR_1] :
( aElement0(sK8(VAR_0))
| ~ aDivisorOf0(VAR_0,xb)
| sdtasdt0(VAR_0,VAR_1) != xa
| ~ aElement0(VAR_1)
| ~ aElement0(VAR_0) )
& ! [VAR_0,VAR_1] :
( doDivides0(VAR_0,xc)
| ~ doDivides0(VAR_0,xb)
| sdtasdt0(VAR_0,VAR_1) != xa
| ~ aElement0(VAR_1)
| ~ aElement0(VAR_0) )
& ! [VAR_0,VAR_1] :
( sdtasdt0(VAR_0,sK8(VAR_0)) = xc
| ~ doDivides0(VAR_0,xb)
| sdtasdt0(VAR_0,VAR_1) != xa
| ~ aElement0(VAR_1)
| ~ aElement0(VAR_0) )
& ! [VAR_0,VAR_1] :
( aElement0(sK8(VAR_0))
| ~ doDivides0(VAR_0,xb)
| sdtasdt0(VAR_0,VAR_1) != xa
| ~ aElement0(VAR_1)
| ~ aElement0(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( doDivides0(VAR_0,xc)
| sdtasdt0(VAR_0,VAR_2) != xb
| ~ aElement0(VAR_2)
| sdtasdt0(VAR_0,VAR_1) != xa
| ~ aElement0(VAR_1)
| ~ aElement0(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( sdtasdt0(VAR_0,sK8(VAR_0)) = xc
| sdtasdt0(VAR_0,VAR_2) != xb
| ~ aElement0(VAR_2)
| sdtasdt0(VAR_0,VAR_1) != xa
| ~ aElement0(VAR_1)
| ~ aElement0(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( aElement0(sK8(VAR_0))
| sdtasdt0(VAR_0,VAR_2) != xb
| ~ aElement0(VAR_2)
| sdtasdt0(VAR_0,VAR_1) != xa
| ~ aElement0(VAR_1)
| ~ aElement0(VAR_0) )
& aDivisorOf0(xc,xb)
& doDivides0(xc,xb)
& sdtasdt0(xc,sK0) = xb
& aElement0(sK0)
& aDivisorOf0(xc,xa)
& doDivides0(xc,xa)
& sdtasdt0(xc,sK1) = xa
& aElement0(sK1)
& aElement0(xc) ),
inference(cnf_transformation,[status(thm)],[sk_m__2129_sk]) ).
cnf(c_137,plain,
sdtasdt0(xc,sK0) = xb,
inference(split_conjunct,[status(thm)],[sk_m__2129]) ).
cnf(c_141,plain,
sdtasdt0(xc,sK1) = xa,
inference(split_conjunct,[status(thm)],[sk_m__2129]) ).
fof(m__2110,axiom,
( xb != sz00
| xa != sz00 ),
file('theBenchmark.p',m__2110) ).
cnf(c_144,plain,
( xb != sz00
| xa != sz00 ),
inference(clausify,[status(thm)],[m__2110]) ).
cnf(c_4134,plain,
( xb != sz00
| sz00 != xa ),
inference(copy,[status(thm)],[c_144]) ).
cnf(c_145,plain,
( sz00 != xb
| sz00 != xa ),
inference(copy,[status(thm)],[c_4134]) ).
cnf(c_146,plain,
aElement0(xb),
inference(clausify,[status(thm)],[m__2091]) ).
cnf(c_147,plain,
aElement0(xa),
inference(clausify,[status(thm)],[m__2091]) ).
cnf(c_220,plain,
( sdtpldt0(sz00,A) = A
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mAddZero]) ).
cnf(c_221,plain,
( sdtpldt0(A,sz00) = A
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mAddZero]) ).
cnf(c_353,plain,
( sz00 = B
| sdtpldt0(A,xb) != B
| ~ aElementOf0(A,slsdtgt0(xa)) ),
inference(resolve,[status(thm)],[c_81,c_74]) ).
cnf(c_2014,plain,
sdtpldt0(sz00,xb) = xb,
inference(resolve,[status(thm)],[c_220,c_146]) ).
cnf(c_2022,plain,
sdtpldt0(xa,sz00) = xa,
inference(resolve,[status(thm)],[c_221,c_147]) ).
cnf(c_4135,plain,
( sz00 = A
| sdtpldt0(sz00,xb) != A ),
inference(resolve,[status(thm)],[c_353,c_90]) ).
cnf(c_3443,plain,
( sz00 = A
| xb != A ),
inference(paramod,[status(thm)],[c_2014,c_4135]) ).
cnf(c_3444,plain,
( sz00 = A
| sdtpldt0(xa,xb) != A ),
inference(resolve,[status(thm)],[c_353,c_87]) ).
cnf(c_4136,plain,
xb = sdtasdt0(xc,sK0),
inference(copy,[status(thm)],[c_137]) ).
cnf(c_4137,plain,
sz00 = sdtasdt0(xc,sK0),
inference(resolve,[status(thm)],[c_3443,c_4136]) ).
cnf(c_3566,plain,
sz00 = xb,
inference(paramod,[status(thm)],[c_137,c_4137]) ).
cnf(c_3578,plain,
( xb = A
| sdtpldt0(xa,xb) != A ),
inference(paramod,[status(thm)],[c_3566,c_3444]) ).
cnf(c_3899,plain,
sdtpldt0(xa,xb) = xa,
inference(paramod,[status(thm)],[c_3566,c_2022]) ).
cnf(c_4138,plain,
( sz00 != xb
| xb != xa ),
inference(paramod,[status(thm)],[c_3566,c_145]) ).
cnf(c_4139,plain,
( xb != xb
| xb != xa ),
inference(paramod,[status(thm)],[c_3566,c_4138]) ).
cnf(c_4073,plain,
xb != xa,
inference(copy,[status(thm)],[c_4139]) ).
cnf(c_4085,plain,
( xb = A
| xa != A ),
inference(paramod,[status(thm)],[c_3899,c_3578]) ).
cnf(c_4140,plain,
xa = sdtasdt0(xc,sK1),
inference(copy,[status(thm)],[c_141]) ).
cnf(c_4141,plain,
xb = sdtasdt0(xc,sK1),
inference(resolve,[status(thm)],[c_4085,c_4140]) ).
cnf(c_4142,plain,
xb = xa,
inference(paramod,[status(thm)],[c_141,c_4141]) ).
cnf(c_4133,plain,
$false,
inference(resolve,[status(thm)],[c_4073,c_4142]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG109+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 06:10:25 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 268588 was started by sandbox on n026,
% 0.10/0.37 % Sat Sep 26 06:10:25 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 6.21/1.30
% 6.21/1.30 % SZS status Theorem for theBenchmark
% 6.21/1.30
% 6.21/1.30 % Proof 1 at 0.66 (+ 0.18) seconds.
% 6.21/1.30 % Length of proof is 28.
% 6.21/1.30 % Level of proof is 7.
% 6.21/1.30 % Maximum clause weight is 26.000.
% 6.21/1.30 % Given clauses 344.
% 6.21/1.30
% 6.21/1.30 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------