%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : RNG111+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n004.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 : Fri Sep 25 02:37:45 PM UTC 2026
% Result : Theorem 25.92s 4.01s
% Output : Proof 25.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 1
% Syntax : Number of formulae : 45 ( 5 unt; 0 def)
% Number of atoms : 214 ( 143 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 234 ( 65 ~; 127 |; 30 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-1 aty)
% Number of variables : 30 ( 0 sgn 13 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f44,conjecture,
! [W0] :
( ( W0 != sz00
& aElementOf0(W0,xI) )
=> ( ! [W1] :
( ( W1 != sz00
& aElementOf0(W1,xI) )
=> ( iLess0(sbrdtbr0(W1),sbrdtbr0(W0))
=> ? [W2] :
( ! [W3] :
( ( W3 != sz00
& aElementOf0(W3,xI) )
=> ~ iLess0(sbrdtbr0(W3),sbrdtbr0(W2)) )
& W2 != sz00
& aElementOf0(W2,xI) ) ) )
=> ? [W1] :
( ! [W2] :
( ( W2 != sz00
& aElementOf0(W2,xI) )
=> ~ iLess0(sbrdtbr0(W2),sbrdtbr0(W1)) )
& W1 != sz00
& aElementOf0(W1,xI) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f44_neg,negated_conjecture,
~ ! [W0] :
( ( W0 != sz00
& aElementOf0(W0,xI) )
=> ( ! [W1] :
( ( W1 != sz00
& aElementOf0(W1,xI) )
=> ( iLess0(sbrdtbr0(W1),sbrdtbr0(W0))
=> ? [W2] :
( ! [W3] :
( ( W3 != sz00
& aElementOf0(W3,xI) )
=> ~ iLess0(sbrdtbr0(W3),sbrdtbr0(W2)) )
& W2 != sz00
& aElementOf0(W2,xI) ) ) )
=> ? [W1] :
( ! [W2] :
( ( W2 != sz00
& aElementOf0(W2,xI) )
=> ~ iLess0(sbrdtbr0(W2),sbrdtbr0(W1)) )
& W1 != sz00
& aElementOf0(W1,xI) ) ) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f44_nnf,plain,
? [W0] :
( ! [W1] :
( ? [W2] :
( iLess0(sbrdtbr0(W2),sbrdtbr0(W1))
& W2 != sz00
& aElementOf0(W2,xI) )
| W1 = sz00
| ~ aElementOf0(W1,xI) )
& ! [W1] :
( ? [W2] :
( ! [W3] :
( ~ iLess0(sbrdtbr0(W3),sbrdtbr0(W2))
| W3 = sz00
| ~ aElementOf0(W3,xI) )
& W2 != sz00
& aElementOf0(W2,xI) )
| ~ iLess0(sbrdtbr0(W1),sbrdtbr0(W0))
| W1 = sz00
| ~ aElementOf0(W1,xI) )
& W0 != sz00
& aElementOf0(W0,xI) ),
inference(nnf_transformation,[status(thm)],[f44_neg]) ).
fof(f44_sk,plain,
! [W1,W3] :
( ( ( iLess0(sbrdtbr0(sk23(W1)),sbrdtbr0(W1))
& sk23(W1) != sz00
& aElementOf0(sk23(W1),xI) )
| W1 = sz00
| ~ aElementOf0(W1,xI) )
& ( ( ( ~ iLess0(sbrdtbr0(W3),sbrdtbr0(sk22(W1)))
| W3 = sz00
| ~ aElementOf0(W3,xI) )
& sk22(W1) != sz00
& aElementOf0(sk22(W1),xI) )
| ~ iLess0(sbrdtbr0(W1),sbrdtbr0(sk21))
| W1 = sz00
| ~ aElementOf0(W1,xI) )
& sk21 != sz00
& aElementOf0(sk21,xI) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk21,sk22,sk23])],[f44_nnf]) ).
cnf(c117,plain,
( aElementOf0(sk22(X1),xI)
| ~ iLess0(sbrdtbr0(X1),sbrdtbr0(sk21))
| X1 = sz00
| ~ aElementOf0(X1,xI) ),
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(c120,plain,
( aElementOf0(sk23(X1),xI)
| X1 = sz00
| ~ aElementOf0(X1,xI) ),
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(c115,plain,
aElementOf0(sk21,xI),
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(p128,plain,
( aElementOf0(sk23(sk21),xI)
| sk21 = sz00 ),
inference(resolution,[status(thm)],[c120,c115]) ).
cnf(p147,plain,
( sk21 = sz00
| aElementOf0(sk22(sk23(sk21)),xI)
| ~ iLess0(sbrdtbr0(sk23(sk21)),sbrdtbr0(sk21))
| sk23(sk21) = sz00 ),
inference(resolution,[status(thm)],[c117,p128]) ).
cnf(c122,plain,
( iLess0(sbrdtbr0(sk23(X1)),sbrdtbr0(X1))
| X1 = sz00
| ~ aElementOf0(X1,xI) ),
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(p127,plain,
( iLess0(sbrdtbr0(sk23(sk21)),sbrdtbr0(sk21))
| sk21 = sz00 ),
inference(resolution,[status(thm)],[c115,c122]) ).
cnf(p149,plain,
( sk21 = sz00
| sk21 = sz00
| aElementOf0(sk22(sk23(sk21)),xI)
| sk23(sk21) = sz00 ),
inference(resolution,[status(thm)],[p147,p127]) ).
cnf(p150,plain,
( sk21 = sz00
| aElementOf0(sk22(sk23(sk21)),xI)
| sk23(sk21) = sz00 ),
inference(factoring,[status(thm)],[p149]) ).
cnf(p153,plain,
( aElementOf0(sk23(sk22(sk23(sk21))),xI)
| sk22(sk23(sk21)) = sz00
| sk21 = sz00
| sk23(sk21) = sz00 ),
inference(resolution,[status(thm)],[p150,c120]) ).
cnf(c119,plain,
( ~ iLess0(sbrdtbr0(X3),sbrdtbr0(sk22(X1)))
| X3 = sz00
| ~ aElementOf0(X3,xI)
| ~ iLess0(sbrdtbr0(X1),sbrdtbr0(sk21))
| X1 = sz00
| ~ aElementOf0(X1,xI) ),
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(p129,plain,
( ~ iLess0(sbrdtbr0(X0),sbrdtbr0(sk22(sk23(sk21))))
| X0 = sz00
| ~ aElementOf0(X0,xI)
| ~ iLess0(sbrdtbr0(sk23(sk21)),sbrdtbr0(sk21))
| sk23(sk21) = sz00
| sk21 = sz00 ),
inference(resolution,[status(thm)],[p128,c119]) ).
cnf(p137,plain,
( sk21 = sz00
| ~ iLess0(sbrdtbr0(X0),sbrdtbr0(sk22(sk23(sk21))))
| X0 = sz00
| ~ aElementOf0(X0,xI)
| sk23(sk21) = sz00
| sk21 = sz00 ),
inference(resolution,[status(thm)],[p129,p127]) ).
cnf(p139,plain,
( ~ iLess0(sbrdtbr0(X0),sbrdtbr0(sk22(sk23(sk21))))
| X0 = sz00
| ~ aElementOf0(X0,xI)
| sk23(sk21) = sz00
| sk21 = sz00 ),
inference(factoring,[status(thm)],[p137]) ).
cnf(p162,plain,
( ~ iLess0(sbrdtbr0(sk23(sk22(sk23(sk21)))),sbrdtbr0(sk22(sk23(sk21))))
| sk23(sk22(sk23(sk21))) = sz00
| sk23(sk21) = sz00
| sk21 = sz00
| sk22(sk23(sk21)) = sz00
| sk21 = sz00
| sk23(sk21) = sz00 ),
inference(resolution,[status(thm)],[p153,p139]) ).
cnf(p184,plain,
( ~ iLess0(sbrdtbr0(sk23(sk22(sk23(sk21)))),sbrdtbr0(sk22(sk23(sk21))))
| sk23(sk22(sk23(sk21))) = sz00
| sk21 = sz00
| sk22(sk23(sk21)) = sz00
| sk21 = sz00
| sk23(sk21) = sz00 ),
inference(factoring,[status(thm)],[p162]) ).
cnf(p186,plain,
( ~ iLess0(sbrdtbr0(sk23(sk22(sk23(sk21)))),sbrdtbr0(sk22(sk23(sk21))))
| sk23(sk22(sk23(sk21))) = sz00
| sk22(sk23(sk21)) = sz00
| sk21 = sz00
| sk23(sk21) = sz00 ),
inference(factoring,[status(thm)],[p184]) ).
cnf(p152,plain,
( iLess0(sbrdtbr0(sk23(sk22(sk23(sk21)))),sbrdtbr0(sk22(sk23(sk21))))
| sk22(sk23(sk21)) = sz00
| sk21 = sz00
| sk23(sk21) = sz00 ),
inference(resolution,[status(thm)],[p150,c122]) ).
cnf(p298,plain,
( sk22(sk23(sk21)) = sz00
| sk21 = sz00
| sk23(sk21) = sz00
| sk23(sk22(sk23(sk21))) = sz00
| sk22(sk23(sk21)) = sz00
| sk21 = sz00
| sk23(sk21) = sz00 ),
inference(resolution,[status(thm)],[p186,p152]) ).
cnf(p304,plain,
( sk21 = sz00
| sk23(sk21) = sz00
| sk23(sk22(sk23(sk21))) = sz00
| sk22(sk23(sk21)) = sz00
| sk21 = sz00
| sk23(sk21) = sz00 ),
inference(factoring,[status(thm)],[p298]) ).
cnf(p305,plain,
( sk21 = sz00
| sk23(sk22(sk23(sk21))) = sz00
| sk22(sk23(sk21)) = sz00
| sk21 = sz00
| sk23(sk21) = sz00 ),
inference(factoring,[status(thm)],[p304]) ).
cnf(p307,plain,
( sk23(sk22(sk23(sk21))) = sz00
| sk22(sk23(sk21)) = sz00
| sk21 = sz00
| sk23(sk21) = sz00 ),
inference(factoring,[status(thm)],[p305]) ).
cnf(c121,plain,
( sk23(X1) != sz00
| X1 = sz00
| ~ aElementOf0(X1,xI) ),
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(p265,plain,
( sk21 = sz00
| sk23(sk21) = sz00
| sk23(sk22(sk23(sk21))) != sz00
| sk22(sk23(sk21)) = sz00 ),
inference(resolution,[status(thm)],[c121,p150]) ).
cnf(p310,plain,
( sk21 = sz00
| sk23(sk21) = sz00
| sk22(sk23(sk21)) = sz00
| sk22(sk23(sk21)) = sz00
| sk21 = sz00
| sk23(sk21) = sz00 ),
inference(resolution,[status(thm)],[p307,p265]) ).
cnf(p313,plain,
( sk21 = sz00
| sk23(sk21) = sz00
| sk22(sk23(sk21)) = sz00
| sk21 = sz00
| sk23(sk21) = sz00 ),
inference(factoring,[status(thm)],[p310]) ).
cnf(p314,plain,
( sk21 = sz00
| sk22(sk23(sk21)) = sz00
| sk21 = sz00
| sk23(sk21) = sz00 ),
inference(factoring,[status(thm)],[p313]) ).
cnf(p316,plain,
( sk22(sk23(sk21)) = sz00
| sk21 = sz00
| sk23(sk21) = sz00 ),
inference(factoring,[status(thm)],[p314]) ).
cnf(c118,plain,
( sk22(X1) != sz00
| ~ iLess0(sbrdtbr0(X1),sbrdtbr0(sk21))
| X1 = sz00
| ~ aElementOf0(X1,xI) ),
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(p144,plain,
( sk21 = sz00
| sk22(sk23(sk21)) != sz00
| ~ iLess0(sbrdtbr0(sk23(sk21)),sbrdtbr0(sk21))
| sk23(sk21) = sz00 ),
inference(resolution,[status(thm)],[c118,p128]) ).
cnf(p145,plain,
( sk21 = sz00
| sk21 = sz00
| sk22(sk23(sk21)) != sz00
| sk23(sk21) = sz00 ),
inference(resolution,[status(thm)],[p144,p127]) ).
cnf(p148,plain,
( sk21 = sz00
| sk22(sk23(sk21)) != sz00
| sk23(sk21) = sz00 ),
inference(factoring,[status(thm)],[p145]) ).
cnf(p319,plain,
( sk21 = sz00
| sk23(sk21) = sz00
| sk21 = sz00
| sk23(sk21) = sz00 ),
inference(resolution,[status(thm)],[p316,p148]) ).
cnf(p320,plain,
( sk21 = sz00
| sk21 = sz00
| sk23(sk21) = sz00 ),
inference(factoring,[status(thm)],[p319]) ).
cnf(p322,plain,
( sk21 = sz00
| sk23(sk21) = sz00 ),
inference(factoring,[status(thm)],[p320]) ).
cnf(p263,plain,
( sk23(sk21) != sz00
| sk21 = sz00 ),
inference(resolution,[status(thm)],[c121,c115]) ).
cnf(p325,plain,
( sk21 = sz00
| sk21 = sz00 ),
inference(resolution,[status(thm)],[p322,p263]) ).
cnf(p326,plain,
sk21 = sz00,
inference(factoring,[status(thm)],[p325]) ).
cnf(c116,plain,
sk21 != sz00,
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(p328,plain,
sz00 != sz00,
inference(demodulation,[status(thm)],[p326,c116]) ).
cnf(p333,plain,
$false,
inference(equality_resolution,[status(thm)],[p328]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG111+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n004.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 08:17:20 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 25.92/4.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.92/4.01 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------