%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG108+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 : n013.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 08:26:40 AM UTC 2026
% Result : Theorem 0.72s 0.54s
% Output : CNFRefutation 0.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 44 ( 20 unt; 0 def)
% Number of atoms : 96 ( 30 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 93 ( 41 ~; 36 |; 11 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 5 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mMulUnit,axiom,
! [W0] :
( aElement0(W0)
=> ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 ) ),
file('theBenchmark.p',mMulUnit) ).
fof(mMulZero,axiom,
! [W0] :
( aElement0(W0)
=> ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 ) ),
file('theBenchmark.p',mMulZero) ).
fof(mDefPrIdeal,axiom,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( W1 = slsdtgt0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
<=> ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) ) )
& aSet0(W1) ) ) ),
file('theBenchmark.p',mDefPrIdeal) ).
fof(m__2091,axiom,
( aElement0(xb)
& aElement0(xa) ),
file('theBenchmark.p',m__2091) ).
fof(m__,conjecture,
( aElementOf0(xb,slsdtgt0(xb))
& aElementOf0(sz00,slsdtgt0(xb))
& aElementOf0(xa,slsdtgt0(xa))
& aElementOf0(sz00,slsdtgt0(xa)) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( aElementOf0(xb,slsdtgt0(xb))
& aElementOf0(sz00,slsdtgt0(xb))
& aElementOf0(xa,slsdtgt0(xa))
& aElementOf0(sz00,slsdtgt0(xa)) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_71,negated_conjecture,
( ~ aElementOf0(xb,slsdtgt0(xb))
| ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElementOf0(xa,slsdtgt0(xa))
| ~ aElementOf0(sz00,slsdtgt0(xa)) ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_75,plain,
aElement0(xb),
inference(clausify,[status(thm)],[m__2091]) ).
cnf(c_76,plain,
aElement0(xa),
inference(clausify,[status(thm)],[m__2091]) ).
cnf(c_82,plain,
( sdtasdt0(A,D) != C
| ~ aElement0(D)
| aElementOf0(C,B)
| slsdtgt0(A) != B
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mDefPrIdeal]) ).
cnf(c_136,plain,
( sdtasdt0(A,sz00) = sz00
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mMulZero]) ).
cnf(c_144,plain,
( sdtasdt0(A,sz10) = A
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mMulUnit]) ).
fof(mSortsC_01,axiom,
aElement0(sz10),
file('theBenchmark.p',mSortsC_01) ).
cnf(c_156,plain,
aElement0(sz10),
inference(clausify,[status(thm)],[mSortsC_01]) ).
fof(mSortsC,axiom,
aElement0(sz00),
file('theBenchmark.p',mSortsC) ).
cnf(c_157,plain,
aElement0(sz00),
inference(clausify,[status(thm)],[mSortsC]) ).
cnf(c_348,plain,
sdtasdt0(xa,sz00) = sz00,
inference(resolve,[status(thm)],[c_136,c_76]) ).
cnf(c_349,plain,
sdtasdt0(xb,sz00) = sz00,
inference(resolve,[status(thm)],[c_136,c_75]) ).
cnf(c_400,plain,
sdtasdt0(xa,sz10) = xa,
inference(resolve,[status(thm)],[c_144,c_76]) ).
cnf(c_401,plain,
sdtasdt0(xb,sz10) = xb,
inference(resolve,[status(thm)],[c_144,c_75]) ).
cnf(c_747,plain,
( sdtasdt0(xa,C) != B
| ~ aElement0(C)
| aElementOf0(B,A)
| slsdtgt0(xa) != A ),
inference(resolve,[status(thm)],[c_82,c_76]) ).
cnf(c_748,plain,
( sdtasdt0(xa,B) != A
| ~ aElement0(B)
| aElementOf0(A,slsdtgt0(xa)) ),
inference(xxres,[status(thm)],[c_747]) ).
cnf(c_749,plain,
( sdtasdt0(xa,sz10) != A
| aElementOf0(A,slsdtgt0(xa)) ),
inference(resolve,[status(thm)],[c_748,c_156]) ).
cnf(c_750,plain,
aElementOf0(sdtasdt0(xa,sz10),slsdtgt0(xa)),
inference(xxres,[status(thm)],[c_749]) ).
cnf(c_617,plain,
aElementOf0(xa,slsdtgt0(xa)),
inference(paramod,[status(thm)],[c_400,c_750]) ).
cnf(c_751,plain,
( sdtasdt0(xb,C) != B
| ~ aElement0(C)
| aElementOf0(B,A)
| slsdtgt0(xb) != A ),
inference(resolve,[status(thm)],[c_82,c_75]) ).
cnf(c_752,plain,
( sdtasdt0(xb,B) != A
| ~ aElement0(B)
| aElementOf0(A,slsdtgt0(xb)) ),
inference(xxres,[status(thm)],[c_751]) ).
cnf(c_753,plain,
( sdtasdt0(xb,sz10) != A
| aElementOf0(A,slsdtgt0(xb)) ),
inference(resolve,[status(thm)],[c_752,c_156]) ).
cnf(c_754,plain,
aElementOf0(sdtasdt0(xb,sz10),slsdtgt0(xb)),
inference(xxres,[status(thm)],[c_753]) ).
cnf(c_618,plain,
aElementOf0(xb,slsdtgt0(xb)),
inference(paramod,[status(thm)],[c_401,c_754]) ).
cnf(c_755,negated_conjecture,
( ~ aElementOf0(xb,slsdtgt0(xb))
| ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElementOf0(sz00,slsdtgt0(xa)) ),
inference(resolve,[status(thm)],[c_617,c_71]) ).
cnf(c_638,negated_conjecture,
( ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElementOf0(sz00,slsdtgt0(xa)) ),
inference(resolve,[status(thm)],[c_618,c_755]) ).
cnf(c_756,plain,
( sdtasdt0(xa,C) != B
| ~ aElement0(C)
| aElementOf0(B,A)
| slsdtgt0(xa) != A ),
inference(resolve,[status(thm)],[c_82,c_76]) ).
cnf(c_757,plain,
( sdtasdt0(xa,B) != A
| ~ aElement0(B)
| aElementOf0(A,slsdtgt0(xa)) ),
inference(xxres,[status(thm)],[c_756]) ).
cnf(c_758,plain,
( sdtasdt0(xa,sz00) != A
| aElementOf0(A,slsdtgt0(xa)) ),
inference(resolve,[status(thm)],[c_757,c_157]) ).
cnf(c_759,plain,
aElementOf0(sdtasdt0(xa,sz00),slsdtgt0(xa)),
inference(xxres,[status(thm)],[c_758]) ).
cnf(c_729,plain,
aElementOf0(sz00,slsdtgt0(xa)),
inference(paramod,[status(thm)],[c_348,c_759]) ).
cnf(c_760,plain,
( sdtasdt0(xb,C) != B
| ~ aElement0(C)
| aElementOf0(B,A)
| slsdtgt0(xb) != A ),
inference(resolve,[status(thm)],[c_82,c_75]) ).
cnf(c_761,plain,
( sdtasdt0(xb,B) != A
| ~ aElement0(B)
| aElementOf0(A,slsdtgt0(xb)) ),
inference(xxres,[status(thm)],[c_760]) ).
cnf(c_762,plain,
( sdtasdt0(xb,sz00) != A
| aElementOf0(A,slsdtgt0(xb)) ),
inference(resolve,[status(thm)],[c_761,c_157]) ).
cnf(c_763,plain,
aElementOf0(sdtasdt0(xb,sz00),slsdtgt0(xb)),
inference(xxres,[status(thm)],[c_762]) ).
cnf(c_730,plain,
aElementOf0(sz00,slsdtgt0(xb)),
inference(paramod,[status(thm)],[c_349,c_763]) ).
cnf(c_764,negated_conjecture,
~ aElementOf0(sz00,slsdtgt0(xb)),
inference(resolve,[status(thm)],[c_729,c_638]) ).
cnf(c_746,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_730,c_764]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG108+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n013.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 06:06:36 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.35 % Process 2086585 was started by sandbox on n013,
% 0.10/0.35 % Sat Sep 26 06:06:36 2026
% 0.10/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.72/0.54
% 0.72/0.54 % SZS status Theorem for theBenchmark
% 0.72/0.54
% 0.72/0.54 % Proof 1 at 0.11 (+ 0.04) seconds.
% 0.72/0.54 % Length of proof is 23.
% 0.72/0.54 % Level of proof is 5.
% 0.72/0.54 % Maximum clause weight is 26.000.
% 0.72/0.54 % Given clauses 86.
% 0.72/0.54
% 0.72/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------