%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : RNG115+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n017.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 02:37:46 PM UTC 2026
% Result : Theorem 25.30s 3.61s
% Output : Proof 25.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 48 ( 18 unt; 0 def)
% Number of atoms : 196 ( 83 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 266 ( 118 ~; 74 |; 71 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 13 con; 0-4 aty)
% Number of variables : 69 ( 0 sgn 25 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f46,conjecture,
? [W0,W1] :
( xu = sdtpldt0(W0,W1)
& ( aElementOf0(W1,slsdtgt0(xb))
| ? [W2] :
( sdtasdt0(xb,W2) = W1
& aElement0(W2) ) )
& ( aElementOf0(W0,slsdtgt0(xa))
| ? [W2] :
( sdtasdt0(xa,W2) = W0
& aElement0(W2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f46_neg,negated_conjecture,
~ ? [W0,W1] :
( xu = sdtpldt0(W0,W1)
& ( aElementOf0(W1,slsdtgt0(xb))
| ? [W2] :
( sdtasdt0(xb,W2) = W1
& aElement0(W2) ) )
& ( aElementOf0(W0,slsdtgt0(xa))
| ? [W2] :
( sdtasdt0(xa,W2) = W0
& aElement0(W2) ) ) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f46_nnf,plain,
! [W0,W1] :
( xu != sdtpldt0(W0,W1)
| ( ~ aElementOf0(W1,slsdtgt0(xb))
& ! [W2] :
( sdtasdt0(xb,W2) != W1
| ~ aElement0(W2) ) )
| ( ~ aElementOf0(W0,slsdtgt0(xa))
& ! [W2] :
( sdtasdt0(xa,W2) != W0
| ~ aElement0(W2) ) ) ),
inference(nnf_transformation,[status(thm)],[f46_neg]) ).
fof(f46_sk,plain,
! [W2,W0,W1] :
( xu != sdtpldt0(W0,W1)
| ( ~ aElementOf0(W1,slsdtgt0(xb))
& ( sdtasdt0(xb,W2) != W1
| ~ aElement0(W2) ) )
| ( ~ aElementOf0(W0,slsdtgt0(xa))
& ( sdtasdt0(xa,W2) != W0
| ~ aElement0(W2) ) ) ),
inference(skolemisation,[status(esa)],[f46_nnf]) ).
cnf(c201,plain,
( xu != sdtpldt0(X0,X1)
| ~ aElementOf0(X1,slsdtgt0(xb))
| ~ aElementOf0(X0,slsdtgt0(xa)) ),
inference(cnf_transformation,[status(esa)],[f46_sk]) ).
cnf(hi192,negated_conjecture,
ifeq(aElementOf0(X0,slsdtgt0(xa)),true,ifeq(aElementOf0(X1,slsdtgt0(xb)),true,ifeq(xu,sdtpldt0(X0,X1),false,true),true),true) = true,
inference(equality_encoding,[status(esa)],[c201]) ).
fof(f44,hypothesis,
( ! [W0] :
( ( W0 != sz00
& ( aElementOf0(W0,xI)
| ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) ) ) )
=> ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI)
& ? [W0,W1] :
( sdtpldt0(W0,W1) = xu
& aElementOf0(W1,slsdtgt0(xb))
& aElementOf0(W0,slsdtgt0(xa)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2273) ).
fof(f44_nnf,plain,
( ! [W0] :
( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| W0 = sz00
| ( ~ aElementOf0(W0,xI)
& ! [W1,W2] :
( sdtpldt0(W1,W2) != W0
| ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
& xu != sz00
& aElementOf0(xu,xI)
& ? [W0,W1] :
( sdtpldt0(W0,W1) = xu
& aElementOf0(W1,slsdtgt0(xb))
& aElementOf0(W0,slsdtgt0(xa)) ) ),
inference(nnf_transformation,[status(thm)],[f44]) ).
fof(f44_sk,plain,
! [W1,W2,W0] :
( ( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| W0 = sz00
| ( ~ aElementOf0(W0,xI)
& ( sdtpldt0(W1,W2) != W0
| ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
& xu != sz00
& aElementOf0(xu,xI)
& sdtpldt0(sk36,sk37) = xu
& aElementOf0(sk37,slsdtgt0(xb))
& aElementOf0(sk36,slsdtgt0(xa)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk36,sk37])],[f44_nnf]) ).
cnf(c182,plain,
aElementOf0(sk36,slsdtgt0(xa)),
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(hi170,axiom,
aElementOf0(sk36,slsdtgt0(xa)) = true,
inference(equality_encoding,[status(esa)],[c182]) ).
cnf(c183,plain,
aElementOf0(sk37,slsdtgt0(xb)),
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(hi171,axiom,
aElementOf0(sk37,slsdtgt0(xb)) = true,
inference(equality_encoding,[status(esa)],[c183]) ).
cnf(c184,plain,
sdtpldt0(sk36,sk37) = xu,
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(hi172,axiom,
sdtpldt0(sk36,sk37) = xu,
inference(equality_encoding,[status(esa)],[c184]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi192,hi170,hi171,hi172]) ).
cnf(t4676,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
fof(f17,axiom,
sz10 != sz00,
file('/export/starexec/sandbox/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/sandbox/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)))
& ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) )
& ! [W1] :
( aElementOf0(W1,slsdtgt0(xb))
<=> ? [W2] :
( sdtasdt0(xb,W2) = W1
& aElement0(W2) ) )
& ! [W1] :
( aElementOf0(W1,slsdtgt0(xa))
<=> ? [W2] :
( sdtasdt0(xa,W2) = W1
& aElement0(W2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2228) ).
fof(f43_nnf,plain,
? [W0] :
( W0 != sz00
& aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) )
& ! [W1] :
( ( ! [W2] :
( sdtasdt0(xb,W2) != W1
| ~ aElement0(W2) )
| aElementOf0(W1,slsdtgt0(xb)) )
& ( ? [W2] :
( sdtasdt0(xb,W2) = W1
& aElement0(W2) )
| ~ aElementOf0(W1,slsdtgt0(xb)) ) )
& ! [W1] :
( ( ! [W2] :
( sdtasdt0(xa,W2) != W1
| ~ aElement0(W2) )
| aElementOf0(W1,slsdtgt0(xa)) )
& ( ? [W2] :
( sdtasdt0(xa,W2) = W1
& aElement0(W2) )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) ),
inference(nnf_transformation,[status(thm)],[f43]) ).
fof(f43_sk,plain,
! [W1,W2] :
( sk31 != sz00
& aElementOf0(sk31,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& sdtpldt0(sk34,sk35) = sk31
& aElementOf0(sk35,slsdtgt0(xb))
& aElementOf0(sk34,slsdtgt0(xa))
& ( sdtasdt0(xb,W2) != W1
| ~ aElement0(W2)
| aElementOf0(W1,slsdtgt0(xb)) )
& ( ( sdtasdt0(xb,sk33(W1)) = W1
& aElement0(sk33(W1)) )
| ~ aElementOf0(W1,slsdtgt0(xb)) )
& ( sdtasdt0(xa,W2) != W1
| ~ aElement0(W2)
| aElementOf0(W1,slsdtgt0(xa)) )
& ( ( sdtasdt0(xa,sk32(W1)) = W1
& aElement0(sk32(W1)) )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk31,sk32,sk33,sk34,sk35])],[f43_nnf]) ).
cnf(c181,plain,
sk31 != sz00,
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(c186,plain,
xu != sz00,
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
fof(f45,hypothesis,
~ ( ( aDivisorOf0(xu,xb)
| doDivides0(xu,xb)
| ? [W0] :
( sdtasdt0(xu,W0) = xb
& aElement0(W0) ) )
& ( aDivisorOf0(xu,xa)
| doDivides0(xu,xa)
| ? [W0] :
( sdtasdt0(xu,W0) = xa
& aElement0(W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2383) ).
fof(f45_nnf,plain,
( ( ~ aDivisorOf0(xu,xb)
& ~ doDivides0(xu,xb)
& ! [W0] :
( sdtasdt0(xu,W0) != xb
| ~ aElement0(W0) ) )
| ( ~ aDivisorOf0(xu,xa)
& ~ doDivides0(xu,xa)
& ! [W0] :
( sdtasdt0(xu,W0) != xa
| ~ aElement0(W0) ) ) ),
inference(nnf_transformation,[status(thm)],[f45]) ).
fof(f45_sk,plain,
! [W0] :
( ( ~ aDivisorOf0(xu,xb)
& ~ doDivides0(xu,xb)
& ( sdtasdt0(xu,W0) != xb
| ~ aElement0(W0) ) )
| ( ~ aDivisorOf0(xu,xa)
& ~ doDivides0(xu,xa)
& ( sdtasdt0(xu,W0) != xa
| ~ aElement0(W0) ) ) ),
inference(skolemisation,[status(esa)],[f45_nnf]) ).
cnf(c189,plain,
( sdtasdt0(xu,X0) != xb
| ~ aElement0(X0)
| sdtasdt0(xu,X0) != xa
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(c190,plain,
( ~ doDivides0(xu,xb)
| sdtasdt0(xu,X0) != xa
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(c191,plain,
( ~ aDivisorOf0(xu,xb)
| sdtasdt0(xu,X0) != xa
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(c192,plain,
( sdtasdt0(xu,X0) != xb
| ~ aElement0(X0)
| ~ doDivides0(xu,xa) ),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(c193,plain,
( ~ doDivides0(xu,xb)
| ~ doDivides0(xu,xa) ),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(c194,plain,
( ~ aDivisorOf0(xu,xb)
| ~ doDivides0(xu,xa) ),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(c195,plain,
( sdtasdt0(xu,X0) != xb
| ~ aElement0(X0)
| ~ aDivisorOf0(xu,xa) ),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(c196,plain,
( ~ doDivides0(xu,xb)
| ~ aDivisorOf0(xu,xa) ),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(c197,plain,
( ~ aDivisorOf0(xu,xb)
| ~ aDivisorOf0(xu,xa) ),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(c198,plain,
( xu != sdtpldt0(X0,X1)
| sdtasdt0(xb,X2) != X1
| ~ aElement0(X2)
| sdtasdt0(xa,X2) != X0
| ~ aElement0(X2) ),
inference(cnf_transformation,[status(esa)],[f46_sk]) ).
cnf(c199,plain,
( xu != sdtpldt0(X0,X1)
| ~ aElementOf0(X1,slsdtgt0(xb))
| sdtasdt0(xa,X2) != X0
| ~ aElement0(X2) ),
inference(cnf_transformation,[status(esa)],[f46_sk]) ).
cnf(c200,plain,
( xu != sdtpldt0(X0,X1)
| sdtasdt0(xb,X2) != X1
| ~ aElement0(X2)
| ~ aElementOf0(X0,slsdtgt0(xa)) ),
inference(cnf_transformation,[status(esa)],[f46_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c23,c105,c181,c186,c189,c190,c191,c192,c193,c194,c195,c196,c197,c198,c199,c200,c201]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t4676]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG115+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.35 % Computer : n017.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Thu Sep 24 08:14:15 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.07/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 25.30/3.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.30/3.61 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------