%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG083+1 : 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 : 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 08:26:35 AM UTC 2026
% Result : Theorem 0.17s 0.48s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 40 ( 20 unt; 0 def)
% Number of atoms : 73 ( 38 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 55 ( 22 ~; 18 |; 9 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsU,axiom,
! [W0] :
( aElement0(W0)
=> aElement0(smndt0(W0)) ),
file('theBenchmark.p',mSortsU) ).
fof(mAddInvr,axiom,
! [W0] :
( aElement0(W0)
=> ( sz00 = sdtpldt0(smndt0(W0),W0)
& sdtpldt0(W0,smndt0(W0)) = sz00 ) ),
file('theBenchmark.p',mAddInvr) ).
fof(mMulComm,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ),
file('theBenchmark.p',mMulComm) ).
fof(mMulUnit,axiom,
! [W0] :
( aElement0(W0)
=> ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 ) ),
file('theBenchmark.p',mMulUnit) ).
fof(mAMDistr,axiom,
! [W0,W1,W2] :
( ( aElement0(W2)
& aElement0(W1)
& aElement0(W0) )
=> ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) ) ),
file('theBenchmark.p',mAMDistr) ).
fof(mMulMnOne,axiom,
! [W0] :
( aElement0(W0)
=> ( smndt0(W0) = sdtasdt0(W0,smndt0(sz10))
& sdtasdt0(smndt0(sz10),W0) = smndt0(W0) ) ),
file('theBenchmark.p',mMulMnOne) ).
fof(m__,conjecture,
( sz00 = sdtasdt0(sz00,xx)
& sdtasdt0(xx,sz00) = sz00 ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( sz00 = sdtasdt0(sz00,xx)
& sdtasdt0(xx,sz00) = sz00 ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(mSortsC,axiom,
aElement0(sz00),
file('theBenchmark.p',mSortsC) ).
cnf(c_15,plain,
aElement0(sz00),
inference(clausify,[status(thm)],[mSortsC]) ).
fof(mSortsC_01,axiom,
aElement0(sz10),
file('theBenchmark.p',mSortsC_01) ).
cnf(c_16,plain,
aElement0(sz10),
inference(clausify,[status(thm)],[mSortsC_01]) ).
cnf(c_17,plain,
( aElement0(smndt0(A))
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mSortsU]) ).
cnf(c_24,plain,
( sdtpldt0(A,smndt0(A)) = sz00
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mAddInvr]) ).
cnf(c_26,plain,
( sdtasdt0(B,A) = sdtasdt0(A,B)
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mMulComm]) ).
cnf(c_29,plain,
( sdtasdt0(sz10,A) = A
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mMulUnit]) ).
cnf(c_32,plain,
( sdtasdt0(sdtpldt0(B,C),A) = sdtpldt0(sdtasdt0(B,A),sdtasdt0(C,A))
| ~ aElement0(C)
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mAMDistr]) ).
cnf(c_33,plain,
( sdtpldt0(sdtasdt0(B,A),sdtasdt0(C,A)) = sdtasdt0(sdtpldt0(B,C),A)
| ~ aElement0(C)
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(copy,[status(thm)],[c_32]) ).
cnf(c_34,plain,
( sdtasdt0(smndt0(sz10),A) = smndt0(A)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mMulMnOne]) ).
fof(m__468,axiom,
aElement0(xx),
file('theBenchmark.p',m__468) ).
cnf(c_36,plain,
aElement0(xx),
inference(clausify,[status(thm)],[m__468]) ).
cnf(c_37,negated_conjecture,
( sdtasdt0(sz00,xx) != sz00
| sdtasdt0(xx,sz00) != sz00 ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_38,plain,
aElement0(smndt0(sz10)),
inference(resolve,[status(thm)],[c_17,c_16]) ).
cnf(c_65,plain,
sdtpldt0(sz10,smndt0(sz10)) = sz00,
inference(resolve,[status(thm)],[c_24,c_16]) ).
cnf(c_98,plain,
sdtasdt0(smndt0(sz10),xx) = smndt0(xx),
inference(resolve,[status(thm)],[c_34,c_36]) ).
cnf(c_137,plain,
sdtasdt0(sz10,xx) = xx,
inference(resolve,[status(thm)],[c_29,c_36]) ).
cnf(c_224,plain,
( sdtasdt0(A,sz00) = sdtasdt0(sz00,A)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_26,c_15]) ).
cnf(c_152,plain,
sdtasdt0(xx,sz00) = sdtasdt0(sz00,xx),
inference(resolve,[status(thm)],[c_224,c_36]) ).
cnf(c_154,plain,
sdtpldt0(xx,smndt0(xx)) = sz00,
inference(resolve,[status(thm)],[c_24,c_36]) ).
cnf(c_225,negated_conjecture,
( sdtasdt0(sz00,xx) != sz00
| sdtasdt0(sz00,xx) != sz00 ),
inference(paramod,[status(thm)],[c_152,c_37]) ).
cnf(c_192,negated_conjecture,
sdtasdt0(sz00,xx) != sz00,
inference(copy,[status(thm)],[c_225]) ).
cnf(c_226,plain,
( sdtpldt0(sdtasdt0(A,xx),sdtasdt0(B,xx)) = sdtasdt0(sdtpldt0(A,B),xx)
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_33,c_36]) ).
cnf(c_227,plain,
( sdtpldt0(sdtasdt0(sz10,xx),sdtasdt0(A,xx)) = sdtasdt0(sdtpldt0(sz10,A),xx)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_226,c_16]) ).
cnf(c_228,plain,
sdtpldt0(sdtasdt0(sz10,xx),sdtasdt0(smndt0(sz10),xx)) = sdtasdt0(sdtpldt0(sz10,smndt0(sz10)),xx),
inference(resolve,[status(thm)],[c_227,c_38]) ).
cnf(c_229,plain,
sdtpldt0(xx,sdtasdt0(smndt0(sz10),xx)) = sdtasdt0(sdtpldt0(sz10,smndt0(sz10)),xx),
inference(paramod,[status(thm)],[c_137,c_228]) ).
cnf(c_230,plain,
sdtpldt0(xx,smndt0(xx)) = sdtasdt0(sdtpldt0(sz10,smndt0(sz10)),xx),
inference(paramod,[status(thm)],[c_98,c_229]) ).
cnf(c_231,plain,
sz00 = sdtasdt0(sdtpldt0(sz10,smndt0(sz10)),xx),
inference(paramod,[status(thm)],[c_154,c_230]) ).
cnf(c_232,plain,
sz00 = sdtasdt0(sz00,xx),
inference(paramod,[status(thm)],[c_65,c_231]) ).
cnf(c_233,plain,
sdtasdt0(sz00,xx) = sz00,
inference(copy,[status(thm)],[c_232]) ).
cnf(c_223,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_192,c_233]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG083+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n017.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sat Sep 26 05:56:03 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.45 % Process 3860 was started by sandbox on n017,
% 0.17/0.45 % Sat Sep 26 05:56:03 2026
% 0.17/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.46
% 0.17/0.46 % From the command line: assign(max_seconds, 300).
% 0.17/0.48
% 0.17/0.48 % SZS status Theorem for theBenchmark
% 0.17/0.48
% 0.17/0.48 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.17/0.48 % Length of proof is 26.
% 0.17/0.48 % Level of proof is 4.
% 0.17/0.48 % Maximum clause weight is 34.000.
% 0.17/0.48 % Given clauses 21.
% 0.17/0.48
% 0.17/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------