%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG059+2 : 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 : n006.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 08:26:31 AM UTC 2026
% Result : Theorem 41.72s 21.60s
% Output : CNFRefutation 41.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 18 unt; 0 def)
% Number of atoms : 54 ( 31 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 40 ( 16 ~; 12 |; 10 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 17 ( 1 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mArith,axiom,
! [W0,W1,W2] :
( ( aScalar0(W2)
& aScalar0(W1)
& aScalar0(W0) )
=> ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0)
& sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2))
& sdtpldt0(W0,W1) = sdtpldt0(W1,W0)
& sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ),
file('theBenchmark.p',mArith) ).
fof(mMNeg,axiom,
! [W0,W1] :
( ( aScalar0(W1)
& aScalar0(W0) )
=> ( sdtasdt0(smndt0(W0),W1) = smndt0(sdtasdt0(W0,W1))
& sdtasdt0(W0,smndt0(W1)) = smndt0(sdtasdt0(W0,W1)) ) ),
file('theBenchmark.p',mMNeg) ).
fof(m__1892,axiom,
( xR = sdtasdt0(xC,xG)
& aScalar0(xR) ),
file('theBenchmark.p',m__1892) ).
fof(m__1930,axiom,
( xS = sdtasdt0(xF,xD)
& aScalar0(xS) ),
file('theBenchmark.p',m__1930) ).
fof(m__1949,axiom,
( xN = sdtasdt0(xR,xS)
& aScalar0(xN) ),
file('theBenchmark.p',m__1949) ).
fof(m__,conjecture,
sdtasdt0(smndt0(xS),xR) = smndt0(xN),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
sdtasdt0(smndt0(xS),xR) != smndt0(xN),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_75,plain,
( sdtasdt0(B,A) = sdtasdt0(A,B)
| ~ aScalar0(C)
| ~ aScalar0(B)
| ~ aScalar0(A) ),
inference(clausify,[status(thm)],[mArith]) ).
cnf(c_82,plain,
( smndt0(sdtasdt0(A,B)) = sdtasdt0(A,smndt0(B))
| ~ aScalar0(B)
| ~ aScalar0(A) ),
inference(clausify,[status(thm)],[mMNeg]) ).
cnf(c_83,plain,
( smndt0(sdtasdt0(A,B)) = sdtasdt0(smndt0(A),B)
| ~ aScalar0(B)
| ~ aScalar0(A) ),
inference(clausify,[status(thm)],[mMNeg]) ).
cnf(c_142,plain,
aScalar0(xR),
inference(clausify,[status(thm)],[m__1892]) ).
cnf(c_146,plain,
aScalar0(xS),
inference(clausify,[status(thm)],[m__1930]) ).
cnf(c_149,plain,
sdtasdt0(xR,xS) = xN,
inference(clausify,[status(thm)],[m__1949]) ).
cnf(c_152,negated_conjecture,
smndt0(xN) != sdtasdt0(smndt0(xS),xR),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_153,negated_conjecture,
sdtasdt0(smndt0(xS),xR) != smndt0(xN),
inference(copy,[status(thm)],[c_152]) ).
cnf(c_163,plain,
( sdtasdt0(B,A) = sdtasdt0(A,B)
| ~ aScalar0(B)
| ~ aScalar0(A) ),
inference(factor,[status(thm)],[c_75]) ).
cnf(c_23740,plain,
( smndt0(sdtasdt0(xS,A)) = sdtasdt0(smndt0(xS),A)
| ~ aScalar0(A) ),
inference(resolve,[status(thm)],[c_83,c_146]) ).
cnf(c_18345,plain,
smndt0(sdtasdt0(xS,xR)) = sdtasdt0(smndt0(xS),xR),
inference(resolve,[status(thm)],[c_23740,c_142]) ).
cnf(c_23741,plain,
( smndt0(sdtasdt0(xS,A)) = sdtasdt0(xS,smndt0(A))
| ~ aScalar0(A) ),
inference(resolve,[status(thm)],[c_82,c_146]) ).
cnf(c_23742,plain,
smndt0(sdtasdt0(xS,xR)) = sdtasdt0(xS,smndt0(xR)),
inference(resolve,[status(thm)],[c_23741,c_142]) ).
cnf(c_18366,plain,
sdtasdt0(smndt0(xS),xR) = sdtasdt0(xS,smndt0(xR)),
inference(paramod,[status(thm)],[c_18345,c_23742]) ).
cnf(c_20099,plain,
smndt0(sdtasdt0(xS,xR)) = sdtasdt0(xS,smndt0(xR)),
inference(paramod,[status(thm)],[c_18366,c_18345]) ).
cnf(c_20100,negated_conjecture,
sdtasdt0(xS,smndt0(xR)) != smndt0(xN),
inference(paramod,[status(thm)],[c_18366,c_153]) ).
cnf(c_23743,plain,
( sdtasdt0(A,xS) = sdtasdt0(xS,A)
| ~ aScalar0(A) ),
inference(resolve,[status(thm)],[c_163,c_146]) ).
cnf(c_23744,plain,
sdtasdt0(xR,xS) = sdtasdt0(xS,xR),
inference(resolve,[status(thm)],[c_23743,c_142]) ).
cnf(c_23745,plain,
xN = sdtasdt0(xS,xR),
inference(paramod,[status(thm)],[c_149,c_23744]) ).
cnf(c_23326,plain,
sdtasdt0(xS,xR) = xN,
inference(copy,[status(thm)],[c_23745]) ).
cnf(c_23746,plain,
smndt0(xN) = sdtasdt0(xS,smndt0(xR)),
inference(paramod,[status(thm)],[c_23326,c_20099]) ).
cnf(c_23747,plain,
sdtasdt0(xS,smndt0(xR)) = smndt0(xN),
inference(copy,[status(thm)],[c_23746]) ).
cnf(c_23739,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_20100,c_23747]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG059+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/15.60 % Computer : n006.cluster.edu
% 0.10/15.60 % Model : x86_64 x86_64
% 0.10/15.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/15.60 % Memory : 8046.5625MB
% 0.10/15.60 % OS : Linux 6.8.0-71-generic
% 0.10/15.60 % CPULimit : 300
% 0.10/15.60 % WCLimit : 300
% 0.10/15.60 % DateTime : Sat Sep 26 05:54:59 UTC 2026
% 0.10/15.60 % CPUTime :
% 0.10/15.60 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/15.60 % Process 510960 was started by sandbox2 on n006,
% 0.10/15.60 % Sat Sep 26 05:54:59 2026
% 0.10/15.60 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/15.62
% 0.10/15.62 % From the command line: assign(max_seconds, 300).
% 41.72/21.60
% 41.72/21.60 % SZS status Theorem for theBenchmark
% 41.72/21.60
% 41.72/21.60 % Proof 1 at 4.75 (+ 1.21) seconds.
% 41.72/21.60 % Length of proof is 21.
% 41.72/21.60 % Level of proof is 5.
% 41.72/21.60 % Maximum clause weight is 28.000.
% 41.72/21.60 % Given clauses 97.
% 41.72/21.60
% 41.72/21.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------