%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG119+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 : n005.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 08:26:42 AM UTC 2026
% Result : Theorem 111.48s 15.73s
% Output : CNFRefutation 111.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of formulae : 54 ( 27 unt; 0 def)
% Number of atoms : 111 ( 34 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 96 ( 39 ~; 30 |; 15 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 14 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mAddComm,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ),
file('theBenchmark.p',mAddComm) ).
fof(mAddZero,axiom,
! [W0] :
( aElement0(W0)
=> ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 ) ),
file('theBenchmark.p',mAddZero) ).
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(mDefDiv,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> ( doDivides0(W0,W1)
<=> ? [W2] :
( sdtasdt0(W0,W2) = W1
& aElement0(W2) ) ) ),
file('theBenchmark.p',mDefDiv) ).
fof(m__2091,axiom,
( aElement0(xb)
& aElement0(xa) ),
file('theBenchmark.p',m__2091) ).
fof(m__2174,axiom,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& aIdeal0(xI) ),
file('theBenchmark.p',m__2174) ).
fof(m__2273,axiom,
( ! [W0] :
( ( W0 != sz00
& aElementOf0(W0,xI) )
=> ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI) ),
file('theBenchmark.p',m__2273) ).
fof(m__2666,axiom,
( ( iLess0(sbrdtbr0(xr),sbrdtbr0(xu))
| xr = sz00 )
& xb = sdtpldt0(sdtasdt0(xq,xu),xr)
& aElement0(xr)
& aElement0(xq) ),
file('theBenchmark.p',m__2666) ).
fof(m__,conjecture,
xr != sz00,
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( xr != sz00 ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(mSortsC,axiom,
aElement0(sz00),
file('theBenchmark.p',mSortsC) ).
cnf(c_70,plain,
aElement0(sz00),
inference(clausify,[status(thm)],[mSortsC]) ).
cnf(c_75,plain,
( sdtpldt0(B,A) = sdtpldt0(A,B)
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mAddComm]) ).
cnf(c_78,plain,
( sdtpldt0(sz00,A) = A
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mAddZero]) ).
cnf(c_81,plain,
( sdtasdt0(B,A) = sdtasdt0(A,B)
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mMulComm]) ).
cnf(c_96,plain,
( aElement0(B)
| ~ aElementOf0(B,A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mEOfElem]) ).
cnf(c_118,plain,
( aSet0(A)
| ~ aIdeal0(A) ),
inference(clausify,[status(thm)],[mDefIdeal]) ).
cnf(c_120,plain,
( aElementOf0(sdtasdt0(C,B),A)
| ~ aElement0(C)
| ~ aElementOf0(B,A)
| ~ aIdeal0(A) ),
inference(clausify,[status(thm)],[mDefIdeal]) ).
cnf(c_140,plain,
( sdtasdt0(A,C) != B
| ~ aElement0(C)
| doDivides0(A,B)
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mDefDiv]) ).
cnf(c_154,plain,
aElement0(xb),
inference(clausify,[status(thm)],[m__2091]) ).
cnf(c_156,plain,
aIdeal0(xI),
inference(clausify,[status(thm)],[m__2174]) ).
cnf(c_166,plain,
aElementOf0(xu,xI),
inference(clausify,[status(thm)],[m__2273]) ).
fof(m__2612,axiom,
~ doDivides0(xu,xb),
file('theBenchmark.p',m__2612) ).
cnf(c_174,plain,
~ doDivides0(xu,xb),
inference(clausify,[status(thm)],[m__2612]) ).
cnf(c_175,plain,
aElement0(xq),
inference(clausify,[status(thm)],[m__2666]) ).
cnf(c_177,plain,
sdtpldt0(sdtasdt0(xq,xu),xr) = xb,
inference(clausify,[status(thm)],[m__2666]) ).
cnf(c_179,negated_conjecture,
xr = sz00,
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_263,plain,
sdtpldt0(sdtasdt0(xq,xu),sz00) = xb,
inference(paramod,[status(thm)],[c_179,c_177]) ).
cnf(c_41646,plain,
( sdtpldt0(A,sz00) = sdtpldt0(sz00,A)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_75,c_70]) ).
cnf(c_302,plain,
( sdtpldt0(sz00,A) = sdtpldt0(A,sz00)
| ~ aElement0(A) ),
inference(copy,[status(thm)],[c_41646]) ).
cnf(c_468,plain,
( sdtasdt0(A,B) != xb
| ~ aElement0(B)
| doDivides0(A,xb)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_154,c_140]) ).
cnf(c_530,plain,
aSet0(xI),
inference(resolve,[status(thm)],[c_156,c_118]) ).
cnf(c_41647,plain,
( aElementOf0(sdtasdt0(A,xu),xI)
| ~ aElement0(A)
| ~ aIdeal0(xI) ),
inference(resolve,[status(thm)],[c_166,c_120]) ).
cnf(c_700,plain,
( aElementOf0(sdtasdt0(A,xu),xI)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_156,c_41647]) ).
cnf(c_41648,plain,
( aElement0(xu)
| ~ aSet0(xI) ),
inference(resolve,[status(thm)],[c_166,c_96]) ).
cnf(c_714,plain,
aElement0(xu),
inference(resolve,[status(thm)],[c_530,c_41648]) ).
cnf(c_881,plain,
( sdtasdt0(xq,A) = sdtasdt0(A,xq)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_175,c_81]) ).
cnf(c_41649,plain,
( sdtasdt0(xu,A) != xb
| ~ aElement0(A)
| doDivides0(xu,xb) ),
inference(resolve,[status(thm)],[c_468,c_714]) ).
cnf(c_19563,plain,
( sdtasdt0(xu,A) != xb
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_174,c_41649]) ).
cnf(c_19864,plain,
sdtasdt0(xu,xq) != xb,
inference(resolve,[status(thm)],[c_19563,c_175]) ).
cnf(c_25415,plain,
aElementOf0(sdtasdt0(xq,xu),xI),
inference(resolve,[status(thm)],[c_700,c_175]) ).
cnf(c_41650,plain,
( aElement0(sdtasdt0(xq,xu))
| ~ aSet0(xI) ),
inference(resolve,[status(thm)],[c_25415,c_96]) ).
cnf(c_26157,plain,
aElement0(sdtasdt0(xq,xu)),
inference(resolve,[status(thm)],[c_530,c_41650]) ).
cnf(c_41651,plain,
sdtpldt0(sz00,sdtasdt0(xq,xu)) = sdtpldt0(sdtasdt0(xq,xu),sz00),
inference(resolve,[status(thm)],[c_26157,c_302]) ).
cnf(c_26198,plain,
sdtpldt0(sz00,sdtasdt0(xq,xu)) = xb,
inference(paramod,[status(thm)],[c_263,c_41651]) ).
cnf(c_41652,plain,
sdtpldt0(sz00,sdtasdt0(xq,xu)) = sdtasdt0(xq,xu),
inference(resolve,[status(thm)],[c_26157,c_78]) ).
cnf(c_41653,plain,
xb = sdtasdt0(xq,xu),
inference(paramod,[status(thm)],[c_26198,c_41652]) ).
cnf(c_26208,plain,
sdtasdt0(xq,xu) = xb,
inference(copy,[status(thm)],[c_41653]) ).
cnf(c_41654,plain,
sdtasdt0(xq,xu) = sdtasdt0(xu,xq),
inference(resolve,[status(thm)],[c_881,c_714]) ).
cnf(c_41655,plain,
xb = sdtasdt0(xu,xq),
inference(paramod,[status(thm)],[c_26208,c_41654]) ).
cnf(c_41656,plain,
sdtasdt0(xu,xq) = xb,
inference(copy,[status(thm)],[c_41655]) ).
cnf(c_41645,plain,
$false,
inference(resolve,[status(thm)],[c_19864,c_41656]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG119+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n005.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 26 06:09:47 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 1385156 was started by sandbox2 on n005,
% 0.11/0.37 % Sat Sep 26 06:09:47 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 111.48/15.73
% 111.48/15.73 % given #500 (A,wt=16): 394 slsdtgt0(sz10) != A | aSet0(A). [resolve(144,a,71,a)].
% 111.48/15.73
% 111.48/15.73 % given #1000 (T,wt=15): 15585 doDivides0(sz10,f14(sz00,sz10)). [resolve(388,a,11450,a),rewrite([12274(10)]),xx(b)].
% 111.48/15.73
% 111.48/15.73 % given #1500 (A,wt=28): 782 -aElement0(A) | sdtpldt0(sdtpldt0(A,c2),A) = sdtpldt0(A,sdtpldt0(c2,A)). [factor(761,a,b)].
% 111.48/15.73
% 111.48/15.73 % SZS status Theorem for theBenchmark
% 111.48/15.73
% 111.48/15.73 % Proof 1 at 4.88 (+ 2.11) seconds.
% 111.48/15.73 % Length of proof is 40.
% 111.48/15.73 % Level of proof is 7.
% 111.48/15.73 % Maximum clause weight is 24.000.
% 111.48/15.73 % Given clauses 1756.
% 111.48/15.73
% 111.48/15.73 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------