%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : RNG124+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 02:37:47 PM UTC 2026
% Result : Theorem 60.64s 8.05s
% Output : Proof 60.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 12
% Syntax : Number of formulae : 66 ( 47 unt; 0 def)
% Number of atoms : 104 ( 64 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 83 ( 45 ~; 17 |; 20 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 11 con; 0-4 aty)
% Number of variables : 18 ( 2 sgn 3 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f50,hypothesis,
xr != sz00,
file('/export/starexec/sandbox2/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(c128,plain,
xr != sz00,
inference(cnf_transformation,[status(esa)],[f50_sk]) ).
cnf(t48,plain,
eq(xr,sz00) = false,
inference(equality_encoding,[status(esa)],[c128]) ).
cnf(t4476,plain,
eq(xr,sz00) = false,
inference(orient,[status(thm)],[t48]) ).
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(c117,plain,
( ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu))
| X0 = sz00
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(t187,plain,
ifeq(aElementOf0(X1,xI),true,ifeq(iLess0(sbrdtbr0(X1),sbrdtbr0(xu)),true,X1,sz00),sz00) = sz00,
inference(equality_encoding,[status(esa)],[c117]) ).
cnf(t3132,plain,
ifeq(aElementOf0(X1,xI),true,ifeq(iLess0(sbrdtbr0(X1),sbrdtbr0(xu)),true,X1,sz00),sz00) = sz00,
inference(orient,[status(thm)],[t187]) ).
fof(f49,hypothesis,
( ( iLess0(sbrdtbr0(xr),sbrdtbr0(xu))
| xr = sz00 )
& xb = sdtpldt0(sdtasdt0(xq,xu),xr)
& aElement0(xr)
& aElement0(xq) ),
file('/export/starexec/sandbox2/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(c127,plain,
( iLess0(sbrdtbr0(xr),sbrdtbr0(xu))
| xr = sz00 ),
inference(cnf_transformation,[status(esa)],[f49_sk]) ).
cnf(t167,plain,
or(eq(xr,sz00),iLess0(sbrdtbr0(xr),sbrdtbr0(xu))) = true,
inference(equality_encoding,[status(esa)],[c127]) ).
cnf(t2280,plain,
or(eq(xr,sz00),iLess0(sbrdtbr0(xr),sbrdtbr0(xu))) = true,
inference(orient,[status(thm)],[t167]) ).
cnf(t12037,plain,
or(false,iLess0(sbrdtbr0(xr),sbrdtbr0(xu))) = true,
inference(step,[status(thm)],[t2280,t4476]) ).
cnf(t52,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t267,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t52]) ).
cnf(t12038,plain,
iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) = true,
inference(step,[status(thm)],[t12037,t267]) ).
cnf(t4488,plain,
iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) = true,
inference(rw,[status(thm)],[t12038]) ).
cnf(t11854,plain,
iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) = true,
inference(orient,[status(thm)],[t4488]) ).
cnf(t11855,plain,
sz00 = ifeq(aElementOf0(xr,xI),true,ifeq(true,true,xr,sz00),sz00),
inference(cp,[status(thm)],[t3132,t11854]) ).
fof(f54,hypothesis,
aElementOf0(xr,xI),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2729) ).
fof(f54_nnf,plain,
aElementOf0(xr,xI),
inference(nnf_transformation,[status(thm)],[f54]) ).
cnf(c132,plain,
aElementOf0(xr,xI),
inference(cnf_transformation,[status(esa)],[f54_nnf]) ).
cnf(t23,plain,
aElementOf0(xr,xI) = true,
inference(equality_encoding,[status(esa)],[c132]) ).
cnf(t1883,plain,
aElementOf0(xr,xI) = true,
inference(orient,[status(thm)],[t23]) ).
cnf(t12346,plain,
sz00 = ifeq(true,true,ifeq(true,true,xr,sz00),sz00),
inference(step,[status(thm)],[t11855,t1883]) ).
cnf(t117,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t117]) ).
cnf(t12347,plain,
sz00 = ifeq(true,true,xr,sz00),
inference(step,[status(thm)],[t12346,t256]) ).
cnf(t12348,plain,
sz00 = xr,
inference(step,[status(thm)],[t12347,t256]) ).
cnf(t11856,plain,
sz00 = xr,
inference(orient,[status(thm)],[t12348]) ).
cnf(t12416,plain,
eq(xr,xr) = false,
inference(step,[status(thm)],[t4476,t11856]) ).
cnf(t45,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t2285,plain,
eq(X1,X1) = true,
inference(orient,[status(thm)],[t45]) ).
cnf(t12417,plain,
true = false,
inference(step,[status(thm)],[t12416,t2285]) ).
cnf(t11913,plain,
true = false,
inference(rw,[status(thm)],[t12417]) ).
cnf(t12016,plain,
false = true,
inference(orient,[status(thm)],[t11913]) ).
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]) ).
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]) ).
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]) ).
fof(f48_sk,plain,
~ doDivides0(xu,xb),
inference(skolemisation,[status(esa)],[f48_nnf]) ).
cnf(c123,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,c114,c116,c118,c123,c128]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t12016]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG124+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n012.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Thu Sep 24 08:21:52 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 60.64/8.05 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 60.64/8.05 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------