%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : RNG125+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 : n012.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 02:37:48 PM UTC 2026
% Result : Theorem 11.28s 1.83s
% Output : Proof 11.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 67 ( 35 unt; 2 def)
% Number of atoms : 155 ( 44 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 159 ( 71 ~; 43 |; 36 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 9 con; 0-4 aty)
% Number of variables : 41 ( 0 sgn 26 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f23,definition,
! [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('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefIdeal) ).
fof(f23_nnf,plain,
! [W0] :
( ( ? [W1] :
( ( ? [W2] :
( ~ aElementOf0(sdtasdt0(W2,W1),W0)
& aElement0(W2) )
| ? [W2] :
( ~ aElementOf0(sdtpldt0(W1,W2),W0)
& aElementOf0(W2,W0) ) )
& aElementOf0(W1,W0) )
| ~ aSet0(W0)
| aIdeal0(W0) )
& ( ( ! [W1] :
( ( ! [W2] :
( aElementOf0(sdtasdt0(W2,W1),W0)
| ~ aElement0(W2) )
& ! [W2] :
( aElementOf0(sdtpldt0(W1,W2),W0)
| ~ aElementOf0(W2,W0) ) )
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aIdeal0(W0) ) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [W0,W1,W2] :
( ( ( ( ( ~ aElementOf0(sdtasdt0(sk10(W0),sk8(W0)),W0)
& aElement0(sk10(W0)) )
| ( ~ aElementOf0(sdtpldt0(sk8(W0),sk9(W0)),W0)
& aElementOf0(sk9(W0),W0) ) )
& aElementOf0(sk8(W0),W0) )
| ~ aSet0(W0)
| aIdeal0(W0) )
& ( ( ( ( ( aElementOf0(sdtasdt0(W2,W1),W0)
| ~ aElement0(W2) )
& ( aElementOf0(sdtpldt0(W1,W2),W0)
| ~ aElementOf0(W2,W0) ) )
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aIdeal0(W0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk8,sk9,sk10])],[f23_nnf]) ).
cnf(c53,plain,
( aSet0(X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(hi46,axiom,
ifeq(aIdeal0(X0),true,aSet0(X0),true) = true,
inference(equality_encoding,[status(esa)],[c53]) ).
fof(f41,hypothesis,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& aIdeal0(xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2174) ).
fof(f41_nnf,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& aIdeal0(xI) ),
inference(nnf_transformation,[status(thm)],[f41]) ).
fof(f41_sk,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& aIdeal0(xI) ),
inference(skolemisation,[status(esa)],[f41_nnf]) ).
cnf(c107,plain,
aIdeal0(xI),
inference(cnf_transformation,[status(esa)],[f41_sk]) ).
cnf(hi96,axiom,
aIdeal0(xI) = true,
inference(equality_encoding,[status(esa)],[c107]) ).
cnf(h397,plain,
aSet0(xI) = true,
inference(hyper_resolution,[status(thm)],[hi46,hi96]) ).
fof(f19,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(f19_nnf,plain,
! [W0] :
( ! [W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [W0,W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0)
| ~ aSet0(W0) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c25,plain,
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi22,axiom,
ifeq(aSet0(X0),true,ifeq(aElementOf0(X1,X0),true,aElement0(X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c25]) ).
fof(f44,hypothesis,
( ! [W0] :
( ( W0 != sz00
& aElementOf0(W0,xI) )
=> ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2273) ).
fof(f44_nnf,plain,
( ! [W0] :
( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| W0 = sz00
| ~ aElementOf0(W0,xI) )
& xu != sz00
& aElementOf0(xu,xI) ),
inference(nnf_transformation,[status(thm)],[f44]) ).
fof(f44_sk,plain,
! [W0] :
( ( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| W0 = sz00
| ~ aElementOf0(W0,xI) )
& xu != sz00
& aElementOf0(xu,xI) ),
inference(skolemisation,[status(esa)],[f44_nnf]) ).
cnf(c115,plain,
aElementOf0(xu,xI),
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(hi103,axiom,
aElementOf0(xu,xI) = true,
inference(equality_encoding,[status(esa)],[c115]) ).
cnf(h1159,plain,
aElement0(xu) = true,
inference(hyper_resolution,[status(thm)],[hi22,h397,hi103]) ).
fof(f33,definition,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( aDivisorOf0(W1,W0)
<=> ( doDivides0(W1,W0)
& aElement0(W1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDvs) ).
fof(f33_nnf,plain,
! [W0] :
( ! [W1] :
( ( ~ doDivides0(W1,W0)
| ~ aElement0(W1)
| aDivisorOf0(W1,W0) )
& ( ( doDivides0(W1,W0)
& aElement0(W1) )
| ~ aDivisorOf0(W1,W0) ) )
| ~ aElement0(W0) ),
inference(nnf_transformation,[status(thm)],[f33]) ).
fof(f33_sk,plain,
! [W0,W1] :
( ( ( ~ doDivides0(W1,W0)
| ~ aElement0(W1)
| aDivisorOf0(W1,W0) )
& ( ( doDivides0(W1,W0)
& aElement0(W1) )
| ~ aDivisorOf0(W1,W0) ) )
| ~ aElement0(W0) ),
inference(skolemisation,[status(esa)],[f33_nnf]) ).
cnf(c83,plain,
( ~ doDivides0(X1,X0)
| ~ aElement0(X1)
| aDivisorOf0(X1,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(esa)],[f33_sk]) ).
cnf(hi74,axiom,
ifeq(aElement0(X0),true,ifeq(aElement0(X1),true,ifeq(doDivides0(X1,X0),true,aDivisorOf0(X1,X0),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c83]) ).
fof(f38,hypothesis,
( aElement0(xb)
& aElement0(xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2091) ).
fof(f38_nnf,plain,
( aElement0(xb)
& aElement0(xa) ),
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
( aElement0(xb)
& aElement0(xa) ),
inference(skolemisation,[status(esa)],[f38_nnf]) ).
cnf(c104,plain,
aElement0(xb),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(hi94,axiom,
aElement0(xb) = true,
inference(equality_encoding,[status(esa)],[c104]) ).
fof(f48,hypothesis,
~ ~ doDivides0(xu,xb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2612) ).
fof(f48_nnf,plain,
doDivides0(xu,xb),
inference(nnf_transformation,[status(thm)],[f48]) ).
cnf(c123,plain,
doDivides0(xu,xb),
inference(cnf_transformation,[status(esa)],[f48_nnf]) ).
cnf(hi109,axiom,
doDivides0(xu,xb) = true,
inference(equality_encoding,[status(esa)],[c123]) ).
cnf(h1762,plain,
aDivisorOf0(xu,xb) = true,
inference(hyper_resolution,[status(thm)],[hi74,hi94,h1159,hi109]) ).
cnf(c103,plain,
aElement0(xa),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(hi93,axiom,
aElement0(xa) = true,
inference(equality_encoding,[status(esa)],[c103]) ).
fof(f47,hypothesis,
~ ~ doDivides0(xu,xa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2479) ).
fof(f47_nnf,plain,
doDivides0(xu,xa),
inference(nnf_transformation,[status(thm)],[f47]) ).
cnf(c122,plain,
doDivides0(xu,xa),
inference(cnf_transformation,[status(esa)],[f47_nnf]) ).
cnf(hi108,axiom,
doDivides0(xu,xa) = true,
inference(equality_encoding,[status(esa)],[c122]) ).
cnf(h1759,plain,
aDivisorOf0(xu,xa) = true,
inference(hyper_resolution,[status(thm)],[hi74,hi93,h1159,hi108]) ).
fof(f45,hypothesis,
~ ( aDivisorOf0(xu,xb)
& aDivisorOf0(xu,xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2383) ).
fof(f45_nnf,plain,
( ~ aDivisorOf0(xu,xb)
| ~ aDivisorOf0(xu,xa) ),
inference(nnf_transformation,[status(thm)],[f45]) ).
fof(f45_sk,plain,
( ~ aDivisorOf0(xu,xb)
| ~ aDivisorOf0(xu,xa) ),
inference(skolemisation,[status(esa)],[f45_nnf]) ).
cnf(c118,plain,
( ~ aDivisorOf0(xu,xb)
| ~ aDivisorOf0(xu,xa) ),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(hi114,axiom,
ifeq(aDivisorOf0(xu,xa),true,ifeq(aDivisorOf0(xu,xb),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c118]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi114,h1759,h1762]) ).
cnf(t2691,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
fof(f17,axiom,
sz10 != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mUnNeZr) ).
fof(f17_nnf,plain,
sz10 != sz00,
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
sz10 != sz00,
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c23,plain,
sz10 != sz00,
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
fof(f39,hypothesis,
( xb != sz00
| xa != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2110) ).
fof(f39_nnf,plain,
( xb != sz00
| xa != sz00 ),
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
( xb != sz00
| xa != sz00 ),
inference(skolemisation,[status(esa)],[f39_nnf]) ).
cnf(c105,plain,
( xb != sz00
| xa != sz00 ),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
fof(f43,hypothesis,
? [W0] :
( W0 != sz00
& aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2228) ).
fof(f43_nnf,plain,
? [W0] :
( W0 != sz00
& aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(nnf_transformation,[status(thm)],[f43]) ).
fof(f43_sk,plain,
( sk20 != sz00
& aElementOf0(sk20,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20])],[f43_nnf]) ).
cnf(c114,plain,
sk20 != sz00,
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(c116,plain,
xu != sz00,
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c23,c105,c114,c116,c118]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t2691]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG125+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.05/0.33 % Computer : n012.cluster.edu
% 0.05/0.33 % Model : x86_64 x86_64
% 0.05/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.33 % Memory : 8046.5625MB
% 0.05/0.33 % OS : Linux 6.8.0-71-generic
% 0.05/0.33 % CPULimit : 300
% 0.05/0.33 % WCLimit : 300
% 0.05/0.33 % DateTime : Thu Sep 24 08:21:37 UTC 2026
% 0.05/0.34 % CPUTime :
% 0.05/0.34 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 11.28/1.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.28/1.83 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------