%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM458+2 : 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 02:20:05 PM UTC 2026
% Result : Theorem 4.16s 0.98s
% Output : Proof 4.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 18 unt; 0 def)
% Number of atoms : 49 ( 25 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 38 ( 19 ~; 8 |; 10 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 11 ( 0 sgn 5 !; 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(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(h113,plain,
sdtpldt0(xm,sz00) = xm,
inference(hyper_resolution,[status(thm)],[hi6,hi29]) ).
fof(f20,conjecture,
( sdtlseqdt0(xm,xm)
| ? [W0] :
( sdtpldt0(xm,W0) = xm
& aNaturalNumber0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f20_neg,negated_conjecture,
~ ( sdtlseqdt0(xm,xm)
| ? [W0] :
( sdtpldt0(xm,W0) = xm
& aNaturalNumber0(W0) ) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f20_nnf,plain,
( ~ sdtlseqdt0(xm,xm)
& ! [W0] :
( sdtpldt0(xm,W0) != xm
| ~ aNaturalNumber0(W0) ) ),
inference(nnf_transformation,[status(thm)],[f20_neg]) ).
fof(f20_sk,plain,
! [W0] :
( ~ sdtlseqdt0(xm,xm)
& ( sdtpldt0(xm,W0) != xm
| ~ aNaturalNumber0(W0) ) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c32,plain,
( sdtpldt0(xm,X0) != xm
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(hi31,negated_conjecture,
ifeq(aNaturalNumber0(X0),true,ifeq(sdtpldt0(xm,X0),xm,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c32]) ).
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(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi31,hi0,h113]) ).
cnf(t2532,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
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(c3,plain,
sz10 != sz00,
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(c33,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,c33]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t2532]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM458+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Thu Sep 24 04:04:35 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.16/0.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.16/0.98 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------