%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM504+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n007.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 02:20:12 PM UTC 2026
% Result : Theorem 67.78s 19.03s
% Output : Proof 67.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 16
% Syntax : Number of formulae : 111 ( 63 unt; 1 def)
% Number of atoms : 320 ( 170 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 340 ( 131 ~; 68 |; 133 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 15 con; 0-4 aty)
% Number of variables : 71 ( 2 sgn 32 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f50,hypothesis,
( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
& ? [W0] :
( sdtpldt0(sdtasdt0(xp,xm),W0) = sdtasdt0(xp,xk)
& aNaturalNumber0(W0) )
& sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
& sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
& ? [W0] :
( sdtpldt0(sdtasdt0(xn,xm),W0) = sdtasdt0(xp,xm)
& aNaturalNumber0(W0) )
& sdtasdt0(xn,xm) != sdtasdt0(xp,xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2414) ).
fof(f50_nnf,plain,
( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
& ? [W0] :
( sdtpldt0(sdtasdt0(xp,xm),W0) = sdtasdt0(xp,xk)
& aNaturalNumber0(W0) )
& sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
& sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
& ? [W0] :
( sdtpldt0(sdtasdt0(xn,xm),W0) = sdtasdt0(xp,xm)
& aNaturalNumber0(W0) )
& sdtasdt0(xn,xm) != sdtasdt0(xp,xm) ),
inference(nnf_transformation,[status(thm)],[f50]) ).
fof(f50_sk,plain,
( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
& sdtpldt0(sdtasdt0(xp,xm),sk16) = sdtasdt0(xp,xk)
& aNaturalNumber0(sk16)
& sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
& sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
& sdtpldt0(sdtasdt0(xn,xm),sk15) = sdtasdt0(xp,xm)
& aNaturalNumber0(sk15)
& sdtasdt0(xn,xm) != sdtasdt0(xp,xm) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk15,sk16])],[f50_nnf]) ).
cnf(c243,plain,
sdtasdt0(xn,xm) != sdtasdt0(xp,xm),
inference(cnf_transformation,[status(esa)],[f50_sk]) ).
cnf(t152,plain,
eq(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) = false,
inference(equality_encoding,[status(esa)],[c243]) ).
fof(f44,hypothesis,
( xk = sdtsldt0(sdtasdt0(xn,xm),xp)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& aNaturalNumber0(xk) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).
fof(f44_nnf,plain,
( xk = sdtsldt0(sdtasdt0(xn,xm),xp)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& aNaturalNumber0(xk) ),
inference(nnf_transformation,[status(thm)],[f44]) ).
fof(f44_sk,plain,
( xk = sdtsldt0(sdtasdt0(xn,xm),xp)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& aNaturalNumber0(xk) ),
inference(skolemisation,[status(esa)],[f44_nnf]) ).
cnf(c220,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(t130,plain,
sdtasdt0(xp,xk) = sdtasdt0(xn,xm),
inference(equality_encoding,[status(esa)],[c220]) ).
cnf(t4324,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(orient,[status(thm)],[t130]) ).
cnf(t14310,plain,
eq(sdtasdt0(xp,xk),sdtasdt0(xp,xm)) = false,
inference(step,[status(thm)],[t152,t4324]) ).
cnf(t5924,plain,
eq(sdtasdt0(xp,xk),sdtasdt0(xp,xm)) = false,
inference(orient,[status(thm)],[t14310]) ).
fof(f20,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W1,W0)
& sdtlseqdt0(W0,W1) )
=> W0 = W1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEAsym) ).
fof(f20_nnf,plain,
! [W0,W1] :
( W0 = W1
| ~ sdtlseqdt0(W1,W0)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [W0,W1] :
( W0 = W1
| ~ sdtlseqdt0(W1,W0)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c32,plain,
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(t217,plain,
ifeq(aNaturalNumber0(X1),true,ifeq(aNaturalNumber0(X2),true,ifeq(sdtlseqdt0(X1,X2),true,ifeq(sdtlseqdt0(X2,X1),true,X1,X2),X2),X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c32]) ).
cnf(t247,plain,
ifeq(aNaturalNumber0(X1),true,ifeq(aNaturalNumber0(X2),true,ifeq(sdtlseqdt0(X1,X2),true,ifeq(sdtlseqdt0(X2,X1),true,X1,X2),X2),X2),X2) = X2,
inference(orient,[status(thm)],[t217]) ).
cnf(c246,plain,
sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(cnf_transformation,[status(esa)],[f50_sk]) ).
cnf(t157,plain,
sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) = true,
inference(equality_encoding,[status(esa)],[c246]) ).
cnf(t3469,plain,
sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) = true,
inference(orient,[status(thm)],[t157]) ).
cnf(t14296,plain,
sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xm)) = true,
inference(step,[status(thm)],[t3469,t4324]) ).
cnf(t4348,plain,
sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xm)) = true,
inference(rw,[status(thm)],[t14296]) ).
cnf(t14178,plain,
sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xm)) = true,
inference(orient,[status(thm)],[t4348]) ).
cnf(t14181,plain,
sdtasdt0(xp,xm) = ifeq(aNaturalNumber0(sdtasdt0(xp,xk)),true,ifeq(aNaturalNumber0(sdtasdt0(xp,xm)),true,ifeq(true,true,ifeq(sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)),true,sdtasdt0(xp,xk),sdtasdt0(xp,xm)),sdtasdt0(xp,xm)),sdtasdt0(xp,xm)),sdtasdt0(xp,xm)),
inference(cp,[status(thm)],[t247,t14178]) ).
fof(f4,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f4_nnf,plain,
! [W0,W1] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [W0,W1] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c5,plain,
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi3,axiom,
ifeq(aNaturalNumber0(X0),true,ifeq(aNaturalNumber0(X1),true,aNaturalNumber0(sdtasdt0(X0,X1)),true),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
fof(f38,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(f38_nnf,plain,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
inference(skolemisation,[status(esa)],[f38_nnf]) ).
cnf(c72,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(hi67,axiom,
aNaturalNumber0(xp) = true,
inference(equality_encoding,[status(esa)],[c72]) ).
cnf(c219,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(hi206,axiom,
aNaturalNumber0(xk) = true,
inference(equality_encoding,[status(esa)],[c219]) ).
cnf(t90,plain,
aNaturalNumber0(sdtasdt0(xp,xk)) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi67,hi206]) ).
cnf(t304,plain,
aNaturalNumber0(sdtasdt0(xp,xk)) = true,
inference(orient,[status(thm)],[t90]) ).
cnf(t14871,plain,
sdtasdt0(xp,xm) = ifeq(true,true,ifeq(aNaturalNumber0(sdtasdt0(xp,xm)),true,ifeq(true,true,ifeq(sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)),true,sdtasdt0(xp,xk),sdtasdt0(xp,xm)),sdtasdt0(xp,xm)),sdtasdt0(xp,xm)),sdtasdt0(xp,xm)),
inference(step,[status(thm)],[t14181,t304]) ).
cnf(t114,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t238,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t114]) ).
cnf(t14872,plain,
sdtasdt0(xp,xm) = ifeq(aNaturalNumber0(sdtasdt0(xp,xm)),true,ifeq(true,true,ifeq(sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)),true,sdtasdt0(xp,xk),sdtasdt0(xp,xm)),sdtasdt0(xp,xm)),sdtasdt0(xp,xm)),
inference(step,[status(thm)],[t14871,t238]) ).
cnf(c71,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(hi66,axiom,
aNaturalNumber0(xm) = true,
inference(equality_encoding,[status(esa)],[c71]) ).
cnf(t91,plain,
aNaturalNumber0(sdtasdt0(xp,xm)) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi67,hi66]) ).
cnf(t270,plain,
aNaturalNumber0(sdtasdt0(xp,xm)) = true,
inference(orient,[status(thm)],[t91]) ).
cnf(t14873,plain,
sdtasdt0(xp,xm) = ifeq(true,true,ifeq(true,true,ifeq(sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)),true,sdtasdt0(xp,xk),sdtasdt0(xp,xm)),sdtasdt0(xp,xm)),sdtasdt0(xp,xm)),
inference(step,[status(thm)],[t14872,t270]) ).
cnf(t14874,plain,
sdtasdt0(xp,xm) = ifeq(true,true,ifeq(sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)),true,sdtasdt0(xp,xk),sdtasdt0(xp,xm)),sdtasdt0(xp,xm)),
inference(step,[status(thm)],[t14873,t238]) ).
cnf(t14875,plain,
sdtasdt0(xp,xm) = ifeq(sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)),true,sdtasdt0(xp,xk),sdtasdt0(xp,xm)),
inference(step,[status(thm)],[t14874,t238]) ).
cnf(c250,plain,
sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)),
inference(cnf_transformation,[status(esa)],[f50_sk]) ).
cnf(t158,plain,
sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) = true,
inference(equality_encoding,[status(esa)],[c250]) ).
cnf(t3450,plain,
sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) = true,
inference(orient,[status(thm)],[t158]) ).
cnf(t14876,plain,
sdtasdt0(xp,xm) = ifeq(true,true,sdtasdt0(xp,xk),sdtasdt0(xp,xm)),
inference(step,[status(thm)],[t14875,t3450]) ).
cnf(t14877,plain,
sdtasdt0(xp,xm) = sdtasdt0(xp,xk),
inference(step,[status(thm)],[t14876,t238]) ).
cnf(t14195,plain,
sdtasdt0(xp,xk) = sdtasdt0(xp,xm),
inference(orient,[status(thm)],[t14877]) ).
cnf(t14884,plain,
eq(sdtasdt0(xp,xm),sdtasdt0(xp,xm)) = false,
inference(step,[status(thm)],[t5924,t14195]) ).
cnf(t7,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t3424,plain,
eq(X1,X1) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(t14885,plain,
true = false,
inference(step,[status(thm)],[t14884,t3424]) ).
cnf(t14234,plain,
true = false,
inference(rw,[status(thm)],[t14885]) ).
cnf(t14237,plain,
false = true,
inference(orient,[status(thm)],[t14234]) ).
fof(f2,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f2_nnf,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c3,plain,
sz10 != sz00,
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f36,definition,
! [W0] :
( aNaturalNumber0(W0)
=> ( isPrime0(W0)
<=> ( ! [W1] :
( ( doDivides0(W1,W0)
& aNaturalNumber0(W1) )
=> ( W1 = W0
| W1 = sz10 ) )
& W0 != sz10
& W0 != sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPrime) ).
fof(f36_nnf,plain,
! [W0] :
( ( ( ? [W1] :
( W1 != W0
& W1 != sz10
& doDivides0(W1,W0)
& aNaturalNumber0(W1) )
| W0 = sz10
| W0 = sz00
| isPrime0(W0) )
& ( ( ! [W1] :
( W1 = W0
| W1 = sz10
| ~ doDivides0(W1,W0)
| ~ aNaturalNumber0(W1) )
& W0 != sz10
& W0 != sz00 )
| ~ isPrime0(W0) ) )
| ~ aNaturalNumber0(W0) ),
inference(nnf_transformation,[status(thm)],[f36]) ).
fof(f36_sk,plain,
! [W0,W1] :
( ( ( ( sk2(W0) != W0
& sk2(W0) != sz10
& doDivides0(sk2(W0),W0)
& aNaturalNumber0(sk2(W0)) )
| W0 = sz10
| W0 = sz00
| isPrime0(W0) )
& ( ( ( W1 = W0
| W1 = sz10
| ~ doDivides0(W1,W0)
| ~ aNaturalNumber0(W1) )
& W0 != sz10
& W0 != sz00 )
| ~ isPrime0(W0) ) )
| ~ aNaturalNumber0(W0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f36_nnf]) ).
cnf(c60,plain,
( X0 != sz00
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(c61,plain,
( X0 != sz10
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
fof(f40,hypothesis,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [W0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,W0)
& aNaturalNumber0(W0) )
& isPrime0(xp)
& ! [W0] :
( ( ( doDivides0(W0,xp)
| ? [W1] :
( xp = sdtasdt0(W0,W1)
& aNaturalNumber0(W1) ) )
& aNaturalNumber0(W0) )
=> ( W0 = xp
| W0 = sz10 ) )
& xp != sz10
& xp != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).
fof(f40_nnf,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [W0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,W0)
& aNaturalNumber0(W0) )
& isPrime0(xp)
& ! [W0] :
( W0 = xp
| W0 = sz10
| ( ~ doDivides0(W0,xp)
& ! [W1] :
( xp != sdtasdt0(W0,W1)
| ~ aNaturalNumber0(W1) ) )
| ~ aNaturalNumber0(W0) )
& xp != sz10
& xp != sz00 ),
inference(nnf_transformation,[status(thm)],[f40]) ).
fof(f40_sk,plain,
! [W0,W1] :
( doDivides0(xp,sdtasdt0(xn,xm))
& sdtasdt0(xn,xm) = sdtasdt0(xp,sk8)
& aNaturalNumber0(sk8)
& isPrime0(xp)
& ( W0 = xp
| W0 = sz10
| ( ~ doDivides0(W0,xp)
& ( xp != sdtasdt0(W0,W1)
| ~ aNaturalNumber0(W1) ) )
| ~ aNaturalNumber0(W0) )
& xp != sz10
& xp != sz00 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk8])],[f40_nnf]) ).
cnf(c199,plain,
xp != sz00,
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(c200,plain,
xp != sz10,
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
fof(f41,hypothesis,
~ ( sdtlseqdt0(xp,xn)
| ? [W0] :
( sdtpldt0(xp,W0) = xn
& aNaturalNumber0(W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1870) ).
fof(f41_nnf,plain,
( ~ sdtlseqdt0(xp,xn)
& ! [W0] :
( sdtpldt0(xp,W0) != xn
| ~ aNaturalNumber0(W0) ) ),
inference(nnf_transformation,[status(thm)],[f41]) ).
fof(f41_sk,plain,
! [W0] :
( ~ sdtlseqdt0(xp,xn)
& ( sdtpldt0(xp,W0) != xn
| ~ aNaturalNumber0(W0) ) ),
inference(skolemisation,[status(esa)],[f41_nnf]) ).
cnf(c207,plain,
( sdtpldt0(xp,X0) != xn
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(esa)],[f41_sk]) ).
cnf(c208,plain,
~ sdtlseqdt0(xp,xn),
inference(cnf_transformation,[status(esa)],[f41_sk]) ).
fof(f42,hypothesis,
~ ( sdtlseqdt0(xp,xm)
| ? [W0] :
( sdtpldt0(xp,W0) = xm
& aNaturalNumber0(W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2075) ).
fof(f42_nnf,plain,
( ~ sdtlseqdt0(xp,xm)
& ! [W0] :
( sdtpldt0(xp,W0) != xm
| ~ aNaturalNumber0(W0) ) ),
inference(nnf_transformation,[status(thm)],[f42]) ).
fof(f42_sk,plain,
! [W0] :
( ~ sdtlseqdt0(xp,xm)
& ( sdtpldt0(xp,W0) != xm
| ~ aNaturalNumber0(W0) ) ),
inference(skolemisation,[status(esa)],[f42_nnf]) ).
cnf(c209,plain,
( sdtpldt0(xp,X0) != xm
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(c210,plain,
~ sdtlseqdt0(xp,xm),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
fof(f43,hypothesis,
( sdtlseqdt0(xm,xp)
& ? [W0] :
( sdtpldt0(xm,W0) = xp
& aNaturalNumber0(W0) )
& xm != xp
& sdtlseqdt0(xn,xp)
& ? [W0] :
( sdtpldt0(xn,W0) = xp
& aNaturalNumber0(W0) )
& xn != xp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2287) ).
fof(f43_nnf,plain,
( sdtlseqdt0(xm,xp)
& ? [W0] :
( sdtpldt0(xm,W0) = xp
& aNaturalNumber0(W0) )
& xm != xp
& sdtlseqdt0(xn,xp)
& ? [W0] :
( sdtpldt0(xn,W0) = xp
& aNaturalNumber0(W0) )
& xn != xp ),
inference(nnf_transformation,[status(thm)],[f43]) ).
fof(f43_sk,plain,
( sdtlseqdt0(xm,xp)
& sdtpldt0(xm,sk10) = xp
& aNaturalNumber0(sk10)
& xm != xp
& sdtlseqdt0(xn,xp)
& sdtpldt0(xn,sk9) = xp
& aNaturalNumber0(sk9)
& xn != xp ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk9,sk10])],[f43_nnf]) ).
cnf(c211,plain,
xn != xp,
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(c215,plain,
xm != xp,
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
fof(f45,hypothesis,
~ ( xk = sz10
| xk = sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2315) ).
fof(f45_nnf,plain,
( xk != sz10
& xk != sz00 ),
inference(nnf_transformation,[status(thm)],[f45]) ).
fof(f45_sk,plain,
( xk != sz10
& xk != sz00 ),
inference(skolemisation,[status(esa)],[f45_nnf]) ).
cnf(c222,plain,
xk != sz00,
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(c223,plain,
xk != sz10,
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
fof(f46,hypothesis,
( xk != sz10
& xk != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2327) ).
fof(f46_nnf,plain,
( xk != sz10
& xk != sz00 ),
inference(nnf_transformation,[status(thm)],[f46]) ).
fof(f46_sk,plain,
( xk != sz10
& xk != sz00 ),
inference(skolemisation,[status(esa)],[f46_nnf]) ).
cnf(c224,plain,
xk != sz00,
inference(cnf_transformation,[status(esa)],[f46_sk]) ).
cnf(c225,plain,
xk != sz10,
inference(cnf_transformation,[status(esa)],[f46_sk]) ).
fof(f47,hypothesis,
( isPrime0(xr)
& ! [W0] :
( ( ( doDivides0(W0,xr)
| ? [W1] :
( xr = sdtasdt0(W0,W1)
& aNaturalNumber0(W1) ) )
& aNaturalNumber0(W0) )
=> ( W0 = xr
| W0 = sz10 ) )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& ? [W0] :
( xk = sdtasdt0(xr,W0)
& aNaturalNumber0(W0) )
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2342) ).
fof(f47_nnf,plain,
( isPrime0(xr)
& ! [W0] :
( W0 = xr
| W0 = sz10
| ( ~ doDivides0(W0,xr)
& ! [W1] :
( xr != sdtasdt0(W0,W1)
| ~ aNaturalNumber0(W1) ) )
| ~ aNaturalNumber0(W0) )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& ? [W0] :
( xk = sdtasdt0(xr,W0)
& aNaturalNumber0(W0) )
& aNaturalNumber0(xr) ),
inference(nnf_transformation,[status(thm)],[f47]) ).
fof(f47_sk,plain,
! [W0,W1] :
( isPrime0(xr)
& ( W0 = xr
| W0 = sz10
| ( ~ doDivides0(W0,xr)
& ( xr != sdtasdt0(W0,W1)
| ~ aNaturalNumber0(W1) ) )
| ~ aNaturalNumber0(W0) )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& xk = sdtasdt0(xr,sk11)
& aNaturalNumber0(sk11)
& aNaturalNumber0(xr) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk11])],[f47_nnf]) ).
cnf(c230,plain,
xr != sz00,
inference(cnf_transformation,[status(esa)],[f47_sk]) ).
cnf(c231,plain,
xr != sz10,
inference(cnf_transformation,[status(esa)],[f47_sk]) ).
cnf(c247,plain,
sdtasdt0(xp,xm) != sdtasdt0(xp,xk),
inference(cnf_transformation,[status(esa)],[f50_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c3,c60,c61,c199,c200,c207,c208,c209,c210,c211,c215,c222,c223,c224,c225,c230,c231,c243,c247]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t14237]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM504+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/10.36 % Computer : n007.cluster.edu
% 0.08/10.36 % Model : x86_64 x86_64
% 0.08/10.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/10.36 % Memory : 8046.5625MB
% 0.08/10.36 % OS : Linux 6.8.0-71-generic
% 0.08/10.36 % CPULimit : 300
% 0.08/10.36 % WCLimit : 300
% 0.08/10.36 % DateTime : Thu Sep 24 04:18:19 UTC 2026
% 0.08/10.37 % CPUTime :
% 0.08/10.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 67.78/19.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 67.78/19.03 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------