%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG079+2 : 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 : n007.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 08:26:34 AM UTC 2026
% Result : Theorem 19.89s 5.99s
% Output : CNFRefutation 19.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 69 ( 40 unt; 0 def)
% Number of atoms : 124 ( 49 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 95 ( 40 ~; 38 |; 15 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 13 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDistr,axiom,
! [W0,W1,W2] :
( ( aScalar0(W2)
& aScalar0(W1)
& aScalar0(W0) )
=> ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) ) ),
file('theBenchmark.p',mDistr) ).
fof(mDistr2,axiom,
! [W0,W1,W2,W3] :
( ( aScalar0(W3)
& aScalar0(W2)
& aScalar0(W1)
& aScalar0(W0) )
=> sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))) ),
file('theBenchmark.p',mDistr2) ).
fof(m__1783,axiom,
( xC = sdtasasdt0(xp,xp)
& aScalar0(xC) ),
file('theBenchmark.p',m__1783) ).
fof(m__1800,axiom,
( xD = sdtasasdt0(xq,xq)
& aScalar0(xD) ),
file('theBenchmark.p',m__1800) ).
fof(m__1820,axiom,
( xE = sdtasasdt0(xp,xq)
& aScalar0(xE) ),
file('theBenchmark.p',m__1820) ).
fof(m__1837,axiom,
( xF = sdtasdt0(xA,xA)
& aScalar0(xF) ),
file('theBenchmark.p',m__1837) ).
fof(m__1854,axiom,
( xG = sdtasdt0(xB,xB)
& aScalar0(xG) ),
file('theBenchmark.p',m__1854) ).
fof(m__1873,axiom,
( xH = sdtasdt0(xA,xB)
& aScalar0(xH) ),
file('theBenchmark.p',m__1873) ).
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(sdtasdt0(sdtpldt0(xE,xH),sdtpldt0(xE,xH)),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG))),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(sdtpldt0(xE,xH),sdtpldt0(xE,xH)),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG))),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_76,plain,
( sdtasdt0(A,sdtpldt0(B,C)) = sdtpldt0(sdtasdt0(A,B),sdtasdt0(A,C))
| ~ aScalar0(C)
| ~ aScalar0(B)
| ~ aScalar0(A) ),
inference(clausify,[status(thm)],[mDistr]) ).
cnf(c_77,plain,
( sdtpldt0(sdtasdt0(A,B),sdtasdt0(A,C)) = sdtasdt0(A,sdtpldt0(B,C))
| ~ aScalar0(C)
| ~ aScalar0(B)
| ~ aScalar0(A) ),
inference(copy,[status(thm)],[c_76]) ).
cnf(c_80,plain,
( sdtasdt0(sdtpldt0(A,B),sdtpldt0(C,D)) = sdtpldt0(sdtpldt0(sdtasdt0(A,C),sdtasdt0(A,D)),sdtpldt0(sdtasdt0(B,C),sdtasdt0(B,D)))
| ~ aScalar0(D)
| ~ aScalar0(C)
| ~ aScalar0(B)
| ~ aScalar0(A) ),
inference(clausify,[status(thm)],[mDistr2]) ).
cnf(c_81,plain,
( sdtpldt0(sdtpldt0(sdtasdt0(A,C),sdtasdt0(A,D)),sdtpldt0(sdtasdt0(B,C),sdtasdt0(B,D))) = sdtasdt0(sdtpldt0(A,B),sdtpldt0(C,D))
| ~ aScalar0(D)
| ~ aScalar0(C)
| ~ aScalar0(B)
| ~ aScalar0(A) ),
inference(copy,[status(thm)],[c_80]) ).
cnf(c_130,plain,
aScalar0(xC),
inference(clausify,[status(thm)],[m__1783]) ).
cnf(c_132,plain,
aScalar0(xD),
inference(clausify,[status(thm)],[m__1800]) ).
cnf(c_134,plain,
aScalar0(xE),
inference(clausify,[status(thm)],[m__1820]) ).
cnf(c_136,plain,
aScalar0(xF),
inference(clausify,[status(thm)],[m__1837]) ).
cnf(c_138,plain,
aScalar0(xG),
inference(clausify,[status(thm)],[m__1854]) ).
cnf(c_140,plain,
aScalar0(xH),
inference(clausify,[status(thm)],[m__1873]) ).
cnf(c_143,plain,
sdtasdt0(xC,xG) = xR,
inference(clausify,[status(thm)],[m__1892]) ).
cnf(c_145,plain,
sdtasdt0(xE,xH) = xP,
inference(clausify,[status(thm)],[m__1911]) ).
cnf(c_147,plain,
sdtasdt0(xF,xD) = xS,
inference(clausify,[status(thm)],[m__1930]) ).
fof(m__2905,axiom,
sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),sdtpldt0(sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))),
file('theBenchmark.p',m__2905) ).
cnf(c_155,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),sdtpldt0(sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))),
inference(clausify,[status(thm)],[m__2905]) ).
cnf(c_15452,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),xP),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),sdtpldt0(sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))),
inference(paramod,[status(thm)],[c_145,c_155]) ).
cnf(c_15453,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),xP),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),sdtpldt0(sdtpldt0(sdtasdt0(xC,xD),xR),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))),
inference(paramod,[status(thm)],[c_143,c_15452]) ).
cnf(c_156,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),xP),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),sdtpldt0(sdtpldt0(sdtasdt0(xC,xD),xR),sdtpldt0(xS,sdtasdt0(xF,xG)))),
inference(paramod,[status(thm)],[c_147,c_15453]) ).
cnf(c_157,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(sdtpldt0(xE,xH),sdtpldt0(xE,xH)),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG))),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_15454,plain,
( sdtpldt0(sdtpldt0(sdtasdt0(xC,B),sdtasdt0(xC,C)),sdtpldt0(sdtasdt0(A,B),sdtasdt0(A,C))) = sdtasdt0(sdtpldt0(xC,A),sdtpldt0(B,C))
| ~ aScalar0(C)
| ~ aScalar0(B)
| ~ aScalar0(A) ),
inference(resolve,[status(thm)],[c_81,c_130]) ).
cnf(c_15455,plain,
( sdtpldt0(sdtpldt0(sdtasdt0(xC,A),sdtasdt0(xC,B)),sdtpldt0(sdtasdt0(xF,A),sdtasdt0(xF,B))) = sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(A,B))
| ~ aScalar0(B)
| ~ aScalar0(A) ),
inference(resolve,[status(thm)],[c_15454,c_136]) ).
cnf(c_15456,plain,
( sdtpldt0(sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,A)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,A))) = sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,A))
| ~ aScalar0(A) ),
inference(resolve,[status(thm)],[c_15455,c_132]) ).
cnf(c_15457,plain,
sdtpldt0(sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) = sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG)),
inference(resolve,[status(thm)],[c_15456,c_138]) ).
cnf(c_15458,plain,
sdtpldt0(sdtpldt0(sdtasdt0(xC,xD),xR),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) = sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG)),
inference(paramod,[status(thm)],[c_143,c_15457]) ).
cnf(c_6555,plain,
sdtpldt0(sdtpldt0(sdtasdt0(xC,xD),xR),sdtpldt0(xS,sdtasdt0(xF,xG))) = sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG)),
inference(paramod,[status(thm)],[c_147,c_15458]) ).
cnf(c_15459,plain,
( sdtpldt0(sdtasdt0(xF,A),sdtasdt0(xF,B)) = sdtasdt0(xF,sdtpldt0(A,B))
| ~ aScalar0(B)
| ~ aScalar0(A) ),
inference(resolve,[status(thm)],[c_77,c_136]) ).
cnf(c_15460,plain,
( sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,A)) = sdtasdt0(xF,sdtpldt0(xD,A))
| ~ aScalar0(A) ),
inference(resolve,[status(thm)],[c_15459,c_132]) ).
cnf(c_15461,plain,
sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)) = sdtasdt0(xF,sdtpldt0(xD,xG)),
inference(resolve,[status(thm)],[c_15460,c_138]) ).
cnf(c_8133,plain,
sdtpldt0(xS,sdtasdt0(xF,xG)) = sdtasdt0(xF,sdtpldt0(xD,xG)),
inference(paramod,[status(thm)],[c_147,c_15461]) ).
cnf(c_15462,plain,
( sdtpldt0(sdtasdt0(xC,A),sdtasdt0(xC,B)) = sdtasdt0(xC,sdtpldt0(A,B))
| ~ aScalar0(B)
| ~ aScalar0(A) ),
inference(resolve,[status(thm)],[c_77,c_130]) ).
cnf(c_15463,plain,
( sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,A)) = sdtasdt0(xC,sdtpldt0(xD,A))
| ~ aScalar0(A) ),
inference(resolve,[status(thm)],[c_15462,c_132]) ).
cnf(c_15464,plain,
sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)) = sdtasdt0(xC,sdtpldt0(xD,xG)),
inference(resolve,[status(thm)],[c_15463,c_138]) ).
cnf(c_8154,plain,
sdtpldt0(sdtasdt0(xC,xD),xR) = sdtasdt0(xC,sdtpldt0(xD,xG)),
inference(paramod,[status(thm)],[c_143,c_15464]) ).
cnf(c_15465,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),xP),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),sdtpldt0(sdtasdt0(xC,sdtpldt0(xD,xG)),sdtpldt0(xS,sdtasdt0(xF,xG)))),
inference(paramod,[status(thm)],[c_8154,c_156]) ).
cnf(c_8609,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),xP),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),sdtpldt0(sdtasdt0(xC,sdtpldt0(xD,xG)),sdtasdt0(xF,sdtpldt0(xD,xG)))),
inference(paramod,[status(thm)],[c_8133,c_15465]) ).
cnf(c_15466,plain,
sdtpldt0(sdtasdt0(xC,sdtpldt0(xD,xG)),sdtpldt0(xS,sdtasdt0(xF,xG))) = sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG)),
inference(paramod,[status(thm)],[c_8154,c_6555]) ).
cnf(c_8920,plain,
sdtpldt0(sdtasdt0(xC,sdtpldt0(xD,xG)),sdtasdt0(xF,sdtpldt0(xD,xG))) = sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG)),
inference(paramod,[status(thm)],[c_8133,c_15466]) ).
cnf(c_9988,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),xP),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG))),
inference(paramod,[status(thm)],[c_8920,c_8609]) ).
cnf(c_15467,plain,
( sdtpldt0(sdtpldt0(sdtasdt0(xE,B),sdtasdt0(xE,C)),sdtpldt0(sdtasdt0(A,B),sdtasdt0(A,C))) = sdtasdt0(sdtpldt0(xE,A),sdtpldt0(B,C))
| ~ aScalar0(C)
| ~ aScalar0(B)
| ~ aScalar0(A) ),
inference(resolve,[status(thm)],[c_81,c_134]) ).
cnf(c_15468,plain,
( sdtpldt0(sdtpldt0(sdtasdt0(xE,A),sdtasdt0(xE,B)),sdtpldt0(sdtasdt0(xH,A),sdtasdt0(xH,B))) = sdtasdt0(sdtpldt0(xE,xH),sdtpldt0(A,B))
| ~ aScalar0(B)
| ~ aScalar0(A) ),
inference(resolve,[status(thm)],[c_15467,c_140]) ).
cnf(c_15469,plain,
( sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,A)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,A))) = sdtasdt0(sdtpldt0(xE,xH),sdtpldt0(xE,A))
| ~ aScalar0(A) ),
inference(resolve,[status(thm)],[c_15468,c_134]) ).
cnf(c_15470,plain,
sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) = sdtasdt0(sdtpldt0(xE,xH),sdtpldt0(xE,xH)),
inference(resolve,[status(thm)],[c_15469,c_140]) ).
cnf(c_10323,plain,
sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),xP),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) = sdtasdt0(sdtpldt0(xE,xH),sdtpldt0(xE,xH)),
inference(paramod,[status(thm)],[c_145,c_15470]) ).
cnf(c_15471,plain,
( sdtpldt0(sdtasdt0(xH,A),sdtasdt0(xH,B)) = sdtasdt0(xH,sdtpldt0(A,B))
| ~ aScalar0(B)
| ~ aScalar0(A) ),
inference(resolve,[status(thm)],[c_77,c_140]) ).
cnf(c_15472,plain,
( sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,A)) = sdtasdt0(xH,sdtpldt0(xE,A))
| ~ aScalar0(A) ),
inference(resolve,[status(thm)],[c_15471,c_134]) ).
cnf(c_12720,plain,
sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)) = sdtasdt0(xH,sdtpldt0(xE,xH)),
inference(resolve,[status(thm)],[c_15472,c_140]) ).
cnf(c_15473,plain,
( sdtpldt0(sdtasdt0(xE,A),sdtasdt0(xE,B)) = sdtasdt0(xE,sdtpldt0(A,B))
| ~ aScalar0(B)
| ~ aScalar0(A) ),
inference(resolve,[status(thm)],[c_77,c_134]) ).
cnf(c_15474,plain,
( sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,A)) = sdtasdt0(xE,sdtpldt0(xE,A))
| ~ aScalar0(A) ),
inference(resolve,[status(thm)],[c_15473,c_134]) ).
cnf(c_15475,plain,
sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)) = sdtasdt0(xE,sdtpldt0(xE,xH)),
inference(resolve,[status(thm)],[c_15474,c_140]) ).
cnf(c_12744,plain,
sdtpldt0(sdtasdt0(xE,xE),xP) = sdtasdt0(xE,sdtpldt0(xE,xH)),
inference(paramod,[status(thm)],[c_145,c_15475]) ).
cnf(c_15476,plain,
sdtlseqdt0(sdtpldt0(sdtasdt0(xE,sdtpldt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG))),
inference(paramod,[status(thm)],[c_12744,c_9988]) ).
cnf(c_13335,plain,
sdtlseqdt0(sdtpldt0(sdtasdt0(xE,sdtpldt0(xE,xH)),sdtasdt0(xH,sdtpldt0(xE,xH))),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG))),
inference(paramod,[status(thm)],[c_12720,c_15476]) ).
cnf(c_15477,plain,
sdtpldt0(sdtasdt0(xE,sdtpldt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) = sdtasdt0(sdtpldt0(xE,xH),sdtpldt0(xE,xH)),
inference(paramod,[status(thm)],[c_12744,c_10323]) ).
cnf(c_13744,plain,
sdtpldt0(sdtasdt0(xE,sdtpldt0(xE,xH)),sdtasdt0(xH,sdtpldt0(xE,xH))) = sdtasdt0(sdtpldt0(xE,xH),sdtpldt0(xE,xH)),
inference(paramod,[status(thm)],[c_12720,c_15477]) ).
cnf(c_15478,plain,
sdtlseqdt0(sdtasdt0(sdtpldt0(xE,xH),sdtpldt0(xE,xH)),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG))),
inference(paramod,[status(thm)],[c_13744,c_13335]) ).
cnf(c_15451,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_157,c_15478]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG079+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n007.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 05:58:23 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 2952168 was started by sandbox on n007,
% 0.09/0.36 % Sat Sep 26 05:58:23 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.37
% 0.14/0.37 % From the command line: assign(max_seconds, 300).
% 19.89/5.99
% 19.89/5.99 % SZS status Theorem for theBenchmark
% 19.89/5.99
% 19.89/5.99 % Proof 1 at 2.06 (+ 0.48) seconds.
% 19.89/5.99 % Length of proof is 40.
% 19.89/5.99 % Level of proof is 7.
% 19.89/5.99 % Maximum clause weight is 65.000.
% 19.89/5.99 % Given clauses 76.
% 19.89/5.99
% 19.89/5.99 % SZS output start CNFRefutation for theBenchmark
% See solution above
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