%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG070+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 : 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 08:26:33 AM UTC 2026
% Result : Theorem 190.24s 24.59s
% Output : CNFRefutation 190.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 12 unt; 0 def)
% Number of atoms : 41 ( 3 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 32 ( 14 ~; 11 |; 5 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 11 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSumSc,axiom,
! [W0,W1] :
( ( aScalar0(W1)
& aScalar0(W0) )
=> aScalar0(sdtpldt0(W0,W1)) ),
file('theBenchmark.p',mSumSc) ).
fof(mLETot,axiom,
! [W0,W1] :
( ( aScalar0(W1)
& aScalar0(W0) )
=> ( sdtlseqdt0(W1,W0)
| sdtlseqdt0(W0,W1) ) ),
file('theBenchmark.p',mLETot) ).
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__,conjecture,
sdtlseqdt0(sdtpldt0(xR,xS),sdtpldt0(xP,xP)),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ sdtlseqdt0(sdtpldt0(xR,xS),sdtpldt0(xP,xP)),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_61,plain,
( aScalar0(sdtpldt0(A,B))
| ~ aScalar0(B)
| ~ aScalar0(A) ),
inference(clausify,[status(thm)],[mSumSc]) ).
cnf(c_90,plain,
( sdtlseqdt0(B,A)
| sdtlseqdt0(A,B)
| ~ aScalar0(B)
| ~ aScalar0(A) ),
inference(clausify,[status(thm)],[mLETot]) ).
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__2590,axiom,
~ sdtlseqdt0(sdtpldt0(xP,xP),sdtpldt0(xR,xS)),
file('theBenchmark.p',m__2590) ).
cnf(c_154,plain,
~ sdtlseqdt0(sdtpldt0(xP,xP),sdtpldt0(xR,xS)),
inference(clausify,[status(thm)],[m__2590]) ).
cnf(c_155,negated_conjecture,
~ sdtlseqdt0(sdtpldt0(xR,xS),sdtpldt0(xP,xP)),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_156,plain,
( aScalar0(sdtpldt0(A,A))
| ~ aScalar0(A) ),
inference(factor,[status(thm)],[c_61]) ).
cnf(c_1310,plain,
aScalar0(sdtpldt0(xP,xP)),
inference(resolve,[status(thm)],[c_156,c_144]) ).
cnf(c_4089,plain,
( sdtlseqdt0(sdtpldt0(xP,xP),A)
| sdtlseqdt0(A,sdtpldt0(xP,xP))
| ~ aScalar0(A) ),
inference(resolve,[status(thm)],[c_90,c_1310]) ).
cnf(c_4090,negated_conjecture,
( sdtlseqdt0(sdtpldt0(xP,xP),sdtpldt0(xR,xS))
| ~ aScalar0(sdtpldt0(xR,xS)) ),
inference(resolve,[status(thm)],[c_4089,c_155]) ).
cnf(c_3759,negated_conjecture,
~ aScalar0(sdtpldt0(xR,xS)),
inference(resolve,[status(thm)],[c_4090,c_154]) ).
cnf(c_4091,plain,
( aScalar0(sdtpldt0(A,xS))
| ~ aScalar0(A) ),
inference(resolve,[status(thm)],[c_61,c_146]) ).
cnf(c_4092,plain,
~ aScalar0(xR),
inference(resolve,[status(thm)],[c_4091,c_3759]) ).
cnf(c_4088,plain,
$false,
inference(resolve,[status(thm)],[c_142,c_4092]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG070+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.40 % Computer : n026.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sat Sep 26 06:00:56 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.41 % Process 250543 was started by sandbox2 on n026,
% 0.13/0.41 % Sat Sep 26 06:00:56 2026
% 0.13/0.41 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.02/0.43
% 0.02/0.43 % From the command line: assign(max_seconds, 300).
% 190.24/24.59
% 190.24/24.59 % SZS status Theorem for theBenchmark
% 190.24/24.59
% 190.24/24.59 % Proof 1 at 23.58 (+ 0.18) seconds.
% 190.24/24.59 % Length of proof is 17.
% 190.24/24.59 % Level of proof is 5.
% 190.24/24.59 % Maximum clause weight is 10.000.
% 190.24/24.59 % Given clauses 218.
% 190.24/24.59
% 190.24/24.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------