%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM458+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 : n020.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 02:20:05 PM UTC 2026
% Result : Theorem 10.18s 1.85s
% Output : Proof 10.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 43 ( 32 unt; 1 def)
% Number of atoms : 75 ( 35 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 62 ( 30 ~; 17 |; 12 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-4 aty)
% Number of variables : 27 ( 2 sgn 11 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(f7_nnf,plain,
! [W0] :
( ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 )
| ~ aNaturalNumber0(W0) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [W0] :
( ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 )
| ~ aNaturalNumber0(W0) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c8,plain,
( sdtpldt0(X0,sz00) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi6,axiom,
ifeq(aNaturalNumber0(X0),true,sdtpldt0(X0,sz00),X0) = X0,
inference(equality_encoding,[status(esa)],[c8]) ).
fof(f2,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox2/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(c2,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi1,axiom,
aNaturalNumber0(sz10) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h9,plain,
sdtpldt0(sz10,sz00) = sz10,
inference(hyper_resolution,[status(thm)],[hi6,hi1]) ).
fof(f17,definition,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2] :
( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefLE) ).
fof(f17_nnf,plain,
! [W0,W1] :
( ( ( ! [W2] :
( sdtpldt0(W0,W2) != W1
| ~ aNaturalNumber0(W2) )
| sdtlseqdt0(W0,W1) )
& ( ? [W2] :
( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) )
| ~ sdtlseqdt0(W0,W1) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [W0,W1,W2] :
( ( ( sdtpldt0(W0,W2) != W1
| ~ aNaturalNumber0(W2)
| sdtlseqdt0(W0,W1) )
& ( ( sdtpldt0(W0,sk0(W0,W1)) = W1
& aNaturalNumber0(sk0(W0,W1)) )
| ~ sdtlseqdt0(W0,W1) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f17_nnf]) ).
cnf(c27,plain,
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(hi25,axiom,
ifeq(aNaturalNumber0(X0),true,ifeq(aNaturalNumber0(X1),true,ifeq(aNaturalNumber0(X2),true,ifeq(sdtpldt0(X0,X2),X1,sdtlseqdt0(X0,X1),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c27]) ).
fof(f1,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(f1_nnf,plain,
aNaturalNumber0(sz00),
inference(nnf_transformation,[status(thm)],[f1]) ).
cnf(c1,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[status(esa)],[f1_nnf]) ).
cnf(hi0,axiom,
aNaturalNumber0(sz00) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t21,plain,
sdtlseqdt0(sz10,sz10) = true,
inference(hyper_resolution,[status(thm)],[hi25,hi1,hi1,hi0,h9]) ).
cnf(t967,plain,
sdtlseqdt0(sz10,sz10) = true,
inference(orient,[status(thm)],[t21]) ).
fof(f19,hypothesis,
aNaturalNumber0(xm),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__718) ).
fof(f19_nnf,plain,
aNaturalNumber0(xm),
inference(nnf_transformation,[status(thm)],[f19]) ).
cnf(c31,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[status(esa)],[f19_nnf]) ).
cnf(hi29,axiom,
aNaturalNumber0(xm) = true,
inference(equality_encoding,[status(esa)],[c31]) ).
cnf(h24,plain,
sdtpldt0(xm,sz00) = xm,
inference(hyper_resolution,[status(thm)],[hi6,hi29]) ).
cnf(t23,plain,
sdtlseqdt0(xm,xm) = true,
inference(hyper_resolution,[status(thm)],[hi25,hi29,hi29,hi0,h24]) ).
cnf(t972,plain,
sdtlseqdt0(xm,xm) = true,
inference(orient,[status(thm)],[t23]) ).
cnf(t55,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t96,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t55]) ).
cnf(c3,plain,
sz10 != sz00,
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f20,conjecture,
sdtlseqdt0(xm,xm),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f20_neg,negated_conjecture,
~ sdtlseqdt0(xm,xm),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f20_nnf,plain,
~ sdtlseqdt0(xm,xm),
inference(nnf_transformation,[status(thm)],[f20_neg]) ).
fof(f20_sk,plain,
~ sdtlseqdt0(xm,xm),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c32,plain,
~ sdtlseqdt0(xm,xm),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c3,c32]) ).
cnf(g0_0,plain,
true != ifeq(sdtlseqdt0(xm,xm),true,false,true),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
true != ifeq(sdtlseqdt0(xm,xm),true,false,sdtlseqdt0(sz10,sz10)),
inference(rw,[status(thm)],[g0_0,t967]) ).
cnf(g0_2,plain,
true != ifeq(sdtlseqdt0(xm,xm),sdtlseqdt0(xm,xm),false,sdtlseqdt0(sz10,sz10)),
inference(rw,[status(thm)],[g0_1,t972]) ).
cnf(g0_3,plain,
true != false,
inference(rw,[status(thm)],[g0_2,t96]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM458+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 04:05:18 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 10.18/1.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.18/1.85 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------