%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : RNG124+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 : n008.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 02:37:47 PM UTC 2026
% Result : Theorem 100.54s 19.43s
% Output : Proof 100.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 12
% Syntax : Number of formulae : 76 ( 42 unt; 0 def)
% Number of atoms : 219 ( 102 equ)
% Maximal formula atoms : 17 ( 2 avg)
% Number of connectives : 246 ( 103 ~; 60 |; 80 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 27 ( 27 usr; 17 con; 0-4 aty)
% Number of variables : 62 ( 2 sgn 20 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f50,hypothesis,
xr != sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2673) ).
fof(f50_nnf,plain,
xr != sz00,
inference(nnf_transformation,[status(thm)],[f50]) ).
fof(f50_sk,plain,
xr != sz00,
inference(skolemisation,[status(esa)],[f50_nnf]) ).
cnf(c210,plain,
xr != sz00,
inference(cnf_transformation,[status(esa)],[f50_sk]) ).
cnf(t34,plain,
eq(xr,sz00) = false,
inference(equality_encoding,[status(esa)],[c210]) ).
cnf(t4953,plain,
eq(xr,sz00) = false,
inference(orient,[status(thm)],[t34]) ).
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(c188,plain,
( ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu))
| X0 = sz00
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(t150,plain,
ifeq(aElementOf0(X1,xI),true,ifeq(iLess0(sbrdtbr0(X1),sbrdtbr0(xu)),true,X1,sz00),sz00) = sz00,
inference(equality_encoding,[status(esa)],[c188]) ).
cnf(t364,plain,
ifeq(aElementOf0(X1,xI),true,ifeq(iLess0(sbrdtbr0(X1),sbrdtbr0(xu)),true,X1,sz00),sz00) = sz00,
inference(orient,[status(thm)],[t150]) ).
fof(f49,hypothesis,
( ( iLess0(sbrdtbr0(xr),sbrdtbr0(xu))
| xr = sz00 )
& xb = sdtpldt0(sdtasdt0(xq,xu),xr)
& aElement0(xr)
& aElement0(xq) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2666) ).
fof(f49_nnf,plain,
( ( iLess0(sbrdtbr0(xr),sbrdtbr0(xu))
| xr = sz00 )
& xb = sdtpldt0(sdtasdt0(xq,xu),xr)
& aElement0(xr)
& aElement0(xq) ),
inference(nnf_transformation,[status(thm)],[f49]) ).
fof(f49_sk,plain,
( ( iLess0(sbrdtbr0(xr),sbrdtbr0(xu))
| xr = sz00 )
& xb = sdtpldt0(sdtasdt0(xq,xu),xr)
& aElement0(xr)
& aElement0(xq) ),
inference(skolemisation,[status(esa)],[f49_nnf]) ).
cnf(c209,plain,
( iLess0(sbrdtbr0(xr),sbrdtbr0(xu))
| xr = sz00 ),
inference(cnf_transformation,[status(esa)],[f49_sk]) ).
cnf(t103,plain,
or(eq(xr,sz00),iLess0(sbrdtbr0(xr),sbrdtbr0(xu))) = true,
inference(equality_encoding,[status(esa)],[c209]) ).
cnf(t4509,plain,
or(eq(xr,sz00),iLess0(sbrdtbr0(xr),sbrdtbr0(xu))) = true,
inference(orient,[status(thm)],[t103]) ).
cnf(t111431,plain,
or(false,iLess0(sbrdtbr0(xr),sbrdtbr0(xu))) = true,
inference(step,[status(thm)],[t4509,t4953]) ).
cnf(t38,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t272,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t38]) ).
cnf(t111432,plain,
iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) = true,
inference(step,[status(thm)],[t111431,t272]) ).
cnf(t4965,plain,
iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) = true,
inference(rw,[status(thm)],[t111432]) ).
cnf(t110593,plain,
iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) = true,
inference(orient,[status(thm)],[t4965]) ).
cnf(t110594,plain,
sz00 = ifeq(aElementOf0(xr,xI),true,ifeq(true,true,xr,sz00),sz00),
inference(cp,[status(thm)],[t364,t110593]) ).
fof(f54,hypothesis,
( aElementOf0(xr,xI)
& ? [W0,W1] :
( sdtpldt0(W0,W1) = xr
& aElementOf0(W1,slsdtgt0(xb))
& aElementOf0(W0,slsdtgt0(xa)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2729) ).
fof(f54_nnf,plain,
( aElementOf0(xr,xI)
& ? [W0,W1] :
( sdtpldt0(W0,W1) = xr
& aElementOf0(W1,slsdtgt0(xb))
& aElementOf0(W0,slsdtgt0(xa)) ) ),
inference(nnf_transformation,[status(thm)],[f54]) ).
fof(f54_sk,plain,
( aElementOf0(xr,xI)
& sdtpldt0(sk47,sk48) = xr
& aElementOf0(sk48,slsdtgt0(xb))
& aElementOf0(sk47,slsdtgt0(xa)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk47,sk48])],[f54_nnf]) ).
cnf(c226,plain,
aElementOf0(xr,xI),
inference(cnf_transformation,[status(esa)],[f54_sk]) ).
cnf(t25,plain,
aElementOf0(xr,xI) = true,
inference(equality_encoding,[status(esa)],[c226]) ).
cnf(t4290,plain,
aElementOf0(xr,xI) = true,
inference(orient,[status(thm)],[t25]) ).
cnf(t117345,plain,
sz00 = ifeq(true,true,ifeq(true,true,xr,sz00),sz00),
inference(step,[status(thm)],[t110594,t4290]) ).
cnf(t79,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t79]) ).
cnf(t117346,plain,
sz00 = ifeq(true,true,xr,sz00),
inference(step,[status(thm)],[t117345,t256]) ).
cnf(t117347,plain,
sz00 = xr,
inference(step,[status(thm)],[t117346,t256]) ).
cnf(t110596,plain,
sz00 = xr,
inference(orient,[status(thm)],[t117347]) ).
cnf(t117711,plain,
eq(xr,xr) = false,
inference(step,[status(thm)],[t4953,t110596]) ).
cnf(t31,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t4907,plain,
eq(X1,X1) = true,
inference(orient,[status(thm)],[t31]) ).
cnf(t117712,plain,
true = false,
inference(step,[status(thm)],[t117711,t4907]) ).
cnf(t110895,plain,
true = false,
inference(rw,[status(thm)],[t117712]) ).
cnf(t111399,plain,
false = true,
inference(orient,[status(thm)],[t110895]) ).
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]) ).
fof(f48,hypothesis,
~ ( doDivides0(xu,xb)
| ? [W0] :
( sdtasdt0(xu,W0) = xb
& aElement0(W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2612) ).
fof(f48_nnf,plain,
( ~ doDivides0(xu,xb)
& ! [W0] :
( sdtasdt0(xu,W0) != xb
| ~ aElement0(W0) ) ),
inference(nnf_transformation,[status(thm)],[f48]) ).
fof(f48_sk,plain,
! [W0] :
( ~ doDivides0(xu,xb)
& ( sdtasdt0(xu,W0) != xb
| ~ aElement0(W0) ) ),
inference(skolemisation,[status(esa)],[f48_nnf]) ).
cnf(c204,plain,
( sdtasdt0(xu,X0) != xb
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(esa)],[f48_sk]) ).
cnf(c205,plain,
~ doDivides0(xu,xb),
inference(cnf_transformation,[status(esa)],[f48_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,c204,c205,c210]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t111399]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG124+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/5.36 % Computer : n008.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Thu Sep 24 08:22:59 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 100.54/19.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 100.54/19.43 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------