%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG072+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 : n017.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 08:26:33 AM UTC 2026
% Result : Theorem 8.86s 1.59s
% Output : CNFRefutation 8.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 29 ( 13 unt; 0 def)
% Number of atoms : 74 ( 3 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 82 ( 37 ~; 32 |; 10 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 19 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSumSc,axiom,
! [W0,W1] :
( ( aScalar0(W1)
& aScalar0(W0) )
=> aScalar0(sdtpldt0(W0,W1)) ),
file('theBenchmark.p',mSumSc) ).
fof(mLEMonM,axiom,
! [W0,W1,W2,W3] :
( ( aScalar0(W3)
& aScalar0(W2)
& aScalar0(W1)
& aScalar0(W0) )
=> ( ( sdtlseqdt0(W2,W3)
& sdtlseqdt0(sz0z00,W2)
& sdtlseqdt0(W0,W1) )
=> sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3)) ) ),
file('theBenchmark.p',mLEMonM) ).
fof(m__1892,axiom,
( xR = sdtasdt0(xC,xG)
& aScalar0(xR) ),
file('theBenchmark.p',m__1892) ).
fof(m__1911,axiom,
( xP = sdtasdt0(xE,xH)
& aScalar0(xP) ),
file('theBenchmark.p',m__1911) ).
fof(m__1930,axiom,
( xS = sdtasdt0(xF,xD)
& aScalar0(xS) ),
file('theBenchmark.p',m__1930) ).
fof(m__2628,axiom,
( sdtlseqdt0(sz0z00,sdtpldt0(xP,xP))
& sdtlseqdt0(sz0z00,sdtpldt0(xR,xS)) ),
file('theBenchmark.p',m__2628) ).
fof(m__,conjecture,
sdtlseqdt0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)),sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)),sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_62,plain,
( aScalar0(sdtpldt0(A,B))
| ~ aScalar0(B)
| ~ aScalar0(A) ),
inference(clausify,[status(thm)],[mSumSc]) ).
cnf(c_90,plain,
( sdtlseqdt0(sdtasdt0(A,C),sdtasdt0(B,D))
| ~ sdtlseqdt0(C,D)
| ~ sdtlseqdt0(sz0z00,C)
| ~ sdtlseqdt0(A,B)
| ~ aScalar0(D)
| ~ aScalar0(C)
| ~ aScalar0(B)
| ~ aScalar0(A) ),
inference(clausify,[status(thm)],[mLEMonM]) ).
cnf(c_142,plain,
aScalar0(xR),
inference(clausify,[status(thm)],[m__1892]) ).
cnf(c_144,plain,
aScalar0(xP),
inference(clausify,[status(thm)],[m__1911]) ).
cnf(c_146,plain,
aScalar0(xS),
inference(clausify,[status(thm)],[m__1930]) ).
fof(m__2610,axiom,
sdtlseqdt0(sdtpldt0(xR,xS),sdtpldt0(xP,xP)),
file('theBenchmark.p',m__2610) ).
cnf(c_155,plain,
sdtlseqdt0(sdtpldt0(xR,xS),sdtpldt0(xP,xP)),
inference(clausify,[status(thm)],[m__2610]) ).
cnf(c_156,plain,
sdtlseqdt0(sz0z00,sdtpldt0(xR,xS)),
inference(clausify,[status(thm)],[m__2628]) ).
cnf(c_158,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)),sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_159,plain,
( aScalar0(sdtpldt0(A,A))
| ~ aScalar0(A) ),
inference(factor,[status(thm)],[c_62]) ).
cnf(c_2127,plain,
( sdtlseqdt0(sdtasdt0(A,sdtpldt0(xR,xS)),sdtasdt0(B,sdtpldt0(xP,xP)))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(xR,xS))
| ~ sdtlseqdt0(A,B)
| ~ aScalar0(sdtpldt0(xP,xP))
| ~ aScalar0(sdtpldt0(xR,xS))
| ~ aScalar0(B)
| ~ aScalar0(A) ),
inference(resolve,[status(thm)],[c_155,c_90]) ).
cnf(c_1310,plain,
( sdtlseqdt0(sdtasdt0(A,sdtpldt0(xR,xS)),sdtasdt0(B,sdtpldt0(xP,xP)))
| ~ sdtlseqdt0(A,B)
| ~ aScalar0(sdtpldt0(xP,xP))
| ~ aScalar0(sdtpldt0(xR,xS))
| ~ aScalar0(B)
| ~ aScalar0(A) ),
inference(resolve,[status(thm)],[c_156,c_2127]) ).
cnf(c_1317,plain,
( sdtlseqdt0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)),sdtasdt0(A,sdtpldt0(xP,xP)))
| ~ sdtlseqdt0(sdtpldt0(xR,xS),A)
| ~ aScalar0(sdtpldt0(xP,xP))
| ~ aScalar0(A)
| ~ aScalar0(sdtpldt0(xR,xS)) ),
inference(factor,[status(thm)],[c_1310]) ).
cnf(c_2128,plain,
( sdtlseqdt0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)),sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)))
| ~ sdtlseqdt0(sdtpldt0(xR,xS),sdtpldt0(xP,xP))
| ~ aScalar0(sdtpldt0(xP,xP))
| ~ aScalar0(sdtpldt0(xR,xS)) ),
inference(factor,[status(thm)],[c_1317]) ).
cnf(c_2129,plain,
( sdtlseqdt0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)),sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)))
| ~ aScalar0(sdtpldt0(xP,xP))
| ~ aScalar0(sdtpldt0(xR,xS)) ),
inference(resolve,[status(thm)],[c_155,c_2128]) ).
cnf(c_1339,negated_conjecture,
( ~ aScalar0(sdtpldt0(xP,xP))
| ~ aScalar0(sdtpldt0(xR,xS)) ),
inference(resolve,[status(thm)],[c_158,c_2129]) ).
cnf(c_1432,plain,
aScalar0(sdtpldt0(xP,xP)),
inference(resolve,[status(thm)],[c_159,c_144]) ).
cnf(c_1488,negated_conjecture,
~ aScalar0(sdtpldt0(xR,xS)),
inference(resolve,[status(thm)],[c_1432,c_1339]) ).
cnf(c_2130,plain,
( aScalar0(sdtpldt0(A,xS))
| ~ aScalar0(A) ),
inference(resolve,[status(thm)],[c_62,c_146]) ).
cnf(c_2131,plain,
~ aScalar0(xR),
inference(resolve,[status(thm)],[c_2130,c_1488]) ).
cnf(c_2126,plain,
$false,
inference(resolve,[status(thm)],[c_142,c_2131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG072+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 05:53:47 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 1546 was started by sandbox2 on n017,
% 0.09/0.36 % Sat Sep 26 05:53:47 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.38
% 0.13/0.38 % From the command line: assign(max_seconds, 300).
% 8.86/1.59
% 8.86/1.59 % SZS status Theorem for theBenchmark
% 8.86/1.59
% 8.86/1.59 % Proof 1 at 1.11 (+ 0.07) seconds.
% 8.86/1.59 % Length of proof is 22.
% 8.86/1.59 % Level of proof is 6.
% 8.86/1.59 % Maximum clause weight is 43.000.
% 8.86/1.59 % Given clauses 172.
% 8.86/1.59
% 8.86/1.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------