%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG099+1 : 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 : n006.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 08:26:38 AM UTC 2026
% Result : Theorem 170.03s 37.69s
% Output : CNFRefutation 170.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 65 ( 33 unt; 0 def)
% Number of atoms : 126 ( 14 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 100 ( 39 ~; 35 |; 15 &)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 15 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsB,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> aElement0(sdtpldt0(W0,W1)) ),
file('theBenchmark.p',mSortsB) ).
fof(mSortsB_02,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> aElement0(sdtasdt0(W0,W1)) ),
file('theBenchmark.p',mSortsB_02) ).
fof(mMulComm,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ),
file('theBenchmark.p',mMulComm) ).
fof(mEOfElem,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('theBenchmark.p',mEOfElem) ).
fof(mDefIdeal,axiom,
! [W0] :
( aIdeal0(W0)
<=> ( ! [W1] :
( aElementOf0(W1,W0)
=> ( ! [W2] :
( aElement0(W2)
=> aElementOf0(sdtasdt0(W2,W1),W0) )
& ! [W2] :
( aElementOf0(W2,W0)
=> aElementOf0(sdtpldt0(W1,W2),W0) ) ) )
& aSet0(W0) ) ),
file('theBenchmark.p',mDefIdeal) ).
fof(mDefMod,axiom,
! [W0,W1,W2] :
( ( aIdeal0(W2)
& aElement0(W1)
& aElement0(W0) )
=> ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) ) ),
file('theBenchmark.p',mDefMod) ).
fof(m__1205,axiom,
( aIdeal0(xJ)
& aIdeal0(xI) ),
file('theBenchmark.p',m__1205) ).
fof(m__1217,axiom,
( aElement0(xy)
& aElement0(xx) ),
file('theBenchmark.p',m__1217) ).
fof(m__1294,axiom,
( sdtpldt0(xa,xb) = sz10
& aElementOf0(xb,xJ)
& aElementOf0(xa,xI) ),
file('theBenchmark.p',m__1294) ).
fof(m__,conjecture,
? [W0] :
( sdteqdtlpzmzozddtrp0(W0,xy,xJ)
& sdteqdtlpzmzozddtrp0(W0,xx,xI)
& aElement0(W0) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ? [W0] :
( sdteqdtlpzmzozddtrp0(W0,xy,xJ)
& sdteqdtlpzmzozddtrp0(W0,xx,xI)
& aElement0(W0) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_33,plain,
( aElement0(sdtpldt0(A,B))
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mSortsB]) ).
cnf(c_34,plain,
( aElement0(sdtasdt0(A,B))
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mSortsB_02]) ).
cnf(c_41,plain,
( sdtasdt0(B,A) = sdtasdt0(A,B)
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mMulComm]) ).
cnf(c_56,plain,
( aElement0(B)
| ~ aElementOf0(B,A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mEOfElem]) ).
cnf(c_78,plain,
( aSet0(A)
| ~ aIdeal0(A) ),
inference(clausify,[status(thm)],[mDefIdeal]) ).
cnf(c_89,plain,
( ~ aElementOf0(sdtpldt0(A,smndt0(B)),C)
| sdteqdtlpzmzozddtrp0(A,B,C)
| ~ aIdeal0(C)
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mDefMod]) ).
cnf(c_90,plain,
aIdeal0(xI),
inference(clausify,[status(thm)],[m__1205]) ).
cnf(c_91,plain,
aIdeal0(xJ),
inference(clausify,[status(thm)],[m__1205]) ).
cnf(c_93,plain,
aElement0(xx),
inference(clausify,[status(thm)],[m__1217]) ).
cnf(c_94,plain,
aElement0(xy),
inference(clausify,[status(thm)],[m__1217]) ).
cnf(c_95,plain,
aElementOf0(xa,xI),
inference(clausify,[status(thm)],[m__1294]) ).
cnf(c_96,plain,
aElementOf0(xb,xJ),
inference(clausify,[status(thm)],[m__1294]) ).
fof(m__1319,axiom,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
file('theBenchmark.p',m__1319) ).
cnf(c_99,plain,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
inference(clausify,[status(thm)],[m__1319]) ).
cnf(c_100,plain,
sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)) = xw,
inference(copy,[status(thm)],[c_99]) ).
fof(m__1332,axiom,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
file('theBenchmark.p',m__1332) ).
cnf(c_101,plain,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(clausify,[status(thm)],[m__1332]) ).
fof(m__1409,axiom,
aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
file('theBenchmark.p',m__1409) ).
cnf(c_102,plain,
aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
inference(clausify,[status(thm)],[m__1409]) ).
cnf(c_103,negated_conjecture,
( ~ sdteqdtlpzmzozddtrp0(A,xy,xJ)
| ~ sdteqdtlpzmzozddtrp0(A,xx,xI)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_249,plain,
aSet0(xI),
inference(resolve,[status(thm)],[c_90,c_78]) ).
cnf(c_263,plain,
aSet0(xJ),
inference(resolve,[status(thm)],[c_91,c_78]) ).
cnf(c_22862,plain,
( aElement0(xa)
| ~ aSet0(xI) ),
inference(resolve,[status(thm)],[c_95,c_56]) ).
cnf(c_470,plain,
aElement0(xa),
inference(resolve,[status(thm)],[c_249,c_22862]) ).
cnf(c_22863,plain,
( aElement0(xb)
| ~ aSet0(xJ) ),
inference(resolve,[status(thm)],[c_96,c_56]) ).
cnf(c_497,plain,
aElement0(xb),
inference(resolve,[status(thm)],[c_263,c_22863]) ).
cnf(c_22864,plain,
( sdteqdtlpzmzozddtrp0(xw,xx,xI)
| ~ aIdeal0(xI)
| ~ aElement0(xx)
| ~ aElement0(xw) ),
inference(resolve,[status(thm)],[c_101,c_89]) ).
cnf(c_22865,plain,
( sdteqdtlpzmzozddtrp0(xw,xx,xI)
| ~ aIdeal0(xI)
| ~ aElement0(xw) ),
inference(resolve,[status(thm)],[c_93,c_22864]) ).
cnf(c_512,plain,
( sdteqdtlpzmzozddtrp0(xw,xx,xI)
| ~ aElement0(xw) ),
inference(resolve,[status(thm)],[c_90,c_22865]) ).
cnf(c_22866,plain,
( sdteqdtlpzmzozddtrp0(xw,xy,xJ)
| ~ aIdeal0(xJ)
| ~ aElement0(xy)
| ~ aElement0(xw) ),
inference(resolve,[status(thm)],[c_102,c_89]) ).
cnf(c_22867,plain,
( sdteqdtlpzmzozddtrp0(xw,xy,xJ)
| ~ aIdeal0(xJ)
| ~ aElement0(xw) ),
inference(resolve,[status(thm)],[c_94,c_22866]) ).
cnf(c_542,plain,
( sdteqdtlpzmzozddtrp0(xw,xy,xJ)
| ~ aElement0(xw) ),
inference(resolve,[status(thm)],[c_91,c_22867]) ).
cnf(c_22868,plain,
( sdtasdt0(A,xy) = sdtasdt0(xy,A)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_41,c_94]) ).
cnf(c_22869,plain,
sdtasdt0(xa,xy) = sdtasdt0(xy,xa),
inference(resolve,[status(thm)],[c_22868,c_470]) ).
cnf(c_1434,plain,
sdtasdt0(xy,xa) = sdtasdt0(xa,xy),
inference(copy,[status(thm)],[c_22869]) ).
cnf(c_22870,plain,
( aElement0(sdtasdt0(xy,A))
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_34,c_94]) ).
cnf(c_22871,plain,
aElement0(sdtasdt0(xy,xa)),
inference(resolve,[status(thm)],[c_22870,c_470]) ).
cnf(c_1469,plain,
aElement0(sdtasdt0(xa,xy)),
inference(paramod,[status(thm)],[c_1434,c_22871]) ).
cnf(c_1498,plain,
sdtpldt0(sdtasdt0(xa,xy),sdtasdt0(xx,xb)) = xw,
inference(paramod,[status(thm)],[c_1434,c_100]) ).
cnf(c_22872,plain,
( sdtasdt0(A,xx) = sdtasdt0(xx,A)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_41,c_93]) ).
cnf(c_22873,plain,
sdtasdt0(xb,xx) = sdtasdt0(xx,xb),
inference(resolve,[status(thm)],[c_22872,c_497]) ).
cnf(c_1879,plain,
sdtasdt0(xx,xb) = sdtasdt0(xb,xx),
inference(copy,[status(thm)],[c_22873]) ).
cnf(c_22874,plain,
( aElement0(sdtasdt0(xx,A))
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_34,c_93]) ).
cnf(c_22875,plain,
aElement0(sdtasdt0(xx,xb)),
inference(resolve,[status(thm)],[c_22874,c_497]) ).
cnf(c_1937,plain,
aElement0(sdtasdt0(xb,xx)),
inference(paramod,[status(thm)],[c_1879,c_22875]) ).
cnf(c_1994,plain,
sdtpldt0(sdtasdt0(xa,xy),sdtasdt0(xb,xx)) = xw,
inference(paramod,[status(thm)],[c_1879,c_1498]) ).
cnf(c_22876,plain,
( aElement0(sdtpldt0(sdtasdt0(xa,xy),A))
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_33,c_1469]) ).
cnf(c_22877,plain,
aElement0(sdtpldt0(sdtasdt0(xa,xy),sdtasdt0(xb,xx))),
inference(resolve,[status(thm)],[c_22876,c_1937]) ).
cnf(c_22720,plain,
aElement0(xw),
inference(paramod,[status(thm)],[c_1994,c_22877]) ).
cnf(c_22797,plain,
sdteqdtlpzmzozddtrp0(xw,xy,xJ),
inference(resolve,[status(thm)],[c_22720,c_542]) ).
cnf(c_22798,plain,
sdteqdtlpzmzozddtrp0(xw,xx,xI),
inference(resolve,[status(thm)],[c_22720,c_512]) ).
cnf(c_22878,negated_conjecture,
( ~ sdteqdtlpzmzozddtrp0(xw,xy,xJ)
| ~ sdteqdtlpzmzozddtrp0(xw,xx,xI) ),
inference(resolve,[status(thm)],[c_22720,c_103]) ).
cnf(c_22879,negated_conjecture,
~ sdteqdtlpzmzozddtrp0(xw,xy,xJ),
inference(resolve,[status(thm)],[c_22798,c_22878]) ).
cnf(c_22861,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_22797,c_22879]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG099+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/15.38 % Computer : n006.cluster.edu
% 0.11/15.38 % Model : x86_64 x86_64
% 0.11/15.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/15.38 % Memory : 8046.5625MB
% 0.11/15.38 % OS : Linux 6.8.0-71-generic
% 0.11/15.38 % CPULimit : 300
% 0.11/15.38 % WCLimit : 300
% 0.11/15.38 % DateTime : Sat Sep 26 06:04:27 UTC 2026
% 0.11/15.38 % CPUTime :
% 0.11/15.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/15.39 % Process 523202 was started by sandbox2 on n006,
% 0.11/15.39 % Sat Sep 26 06:04:27 2026
% 0.11/15.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/15.40
% 0.11/15.40 % From the command line: assign(max_seconds, 300).
% 170.03/37.69
% 170.03/37.69 % SZS status Theorem for theBenchmark
% 170.03/37.69
% 170.03/37.69 % Proof 1 at 4.62 (+ 1.38) seconds.
% 170.03/37.69 % Length of proof is 43.
% 170.03/37.69 % Level of proof is 9.
% 170.03/37.69 % Maximum clause weight is 31.000.
% 170.03/37.69 % Given clauses 262.
% 170.03/37.69
% 170.03/37.69 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------