%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM840+2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n003.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 02:21:09 PM UTC 2026
% Result : Theorem 24.64s 3.54s
% Output : Proof 24.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 41 ( 14 unt; 0 def)
% Number of atoms : 73 ( 12 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 63 ( 31 ~; 29 |; 0 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 56 ( 0 sgn 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [Vd203,Vd204] :
( less(Vd203,Vd204)
| greater(Vd203,Vd204)
| Vd203 = Vd204 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd9) ).
fof(f9_nnf,plain,
! [Vd203,Vd204] :
( less(Vd203,Vd204)
| greater(Vd203,Vd204)
| Vd203 = Vd204 ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [Vd203,Vd204] :
( less(Vd203,Vd204)
| greater(Vd203,Vd204)
| Vd203 = Vd204 ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( less(X0,X1)
| greater(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
fof(f8,axiom,
! [Vd208,Vd209] :
( greater(Vd208,Vd209)
=> less(Vd209,Vd208) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd8) ).
fof(f8_nnf,plain,
! [Vd208,Vd209] :
( less(Vd209,Vd208)
| ~ greater(Vd208,Vd209) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [Vd208,Vd209] :
( less(Vd209,Vd208)
| ~ greater(Vd208,Vd209) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( less(X1,X0)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p60,plain,
( less(X1,X0)
| less(X0,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[c9,c8]) ).
fof(f0,conjecture,
less(vd328,vd329),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd0) ).
fof(f0_neg,negated_conjecture,
~ less(vd328,vd329),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
~ less(vd328,vd329),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
~ less(vd328,vd329),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
~ less(vd328,vd329),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p503,plain,
( less(vd329,vd328)
| vd328 = vd329 ),
inference(resolution,[status(thm)],[p60,c0]) ).
fof(f4,axiom,
! [Vd301,Vd302,Vd303] :
( less(Vd301,Vd302)
=> less(vplus(Vd301,Vd303),vplus(Vd302,Vd303)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd4) ).
fof(f4_nnf,plain,
! [Vd301,Vd302,Vd303] :
( less(vplus(Vd301,Vd303),vplus(Vd302,Vd303))
| ~ less(Vd301,Vd302) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [Vd301,Vd302,Vd303] :
( less(vplus(Vd301,Vd303),vplus(Vd302,Vd303))
| ~ less(Vd301,Vd302) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( less(vplus(X0,X2),vplus(X1,X2))
| ~ less(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p511,plain,
( less(vplus(vd329,X0),vplus(vd328,X0))
| vd328 = vd329 ),
inference(resolution,[status(thm)],[p503,c4]) ).
fof(f7,axiom,
! [Vd226,Vd227] :
( less(Vd226,Vd227)
=> greater(Vd227,Vd226) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd7) ).
fof(f7_nnf,plain,
! [Vd226,Vd227] :
( greater(Vd227,Vd226)
| ~ less(Vd226,Vd227) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [Vd226,Vd227] :
( greater(Vd227,Vd226)
| ~ less(Vd226,Vd227) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( greater(X1,X0)
| ~ less(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
fof(f1,axiom,
less(vplus(vd328,vd330),vplus(vd329,vd330)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd1) ).
fof(f1_nnf,plain,
less(vplus(vd328,vd330),vplus(vd329,vd330)),
inference(nnf_transformation,[status(thm)],[f1]) ).
cnf(c1,plain,
less(vplus(vd328,vd330),vplus(vd329,vd330)),
inference(cnf_transformation,[status(esa)],[f1_nnf]) ).
cnf(p31,plain,
greater(vplus(vd329,vd330),vplus(vd328,vd330)),
inference(resolution,[status(thm)],[c7,c1]) ).
fof(f11,axiom,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| ~ greater(Vd203,Vd204) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd11) ).
fof(f11_nnf,plain,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| ~ greater(Vd203,Vd204) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| ~ greater(Vd203,Vd204) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( ~ less(X0,X1)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p37,plain,
~ less(vplus(vd329,vd330),vplus(vd328,vd330)),
inference(resolution,[status(thm)],[p31,c11]) ).
cnf(p538,plain,
vd328 = vd329,
inference(resolution,[status(thm)],[p511,p37]) ).
cnf(p539,plain,
less(vplus(vd328,vd330),vplus(vd328,vd330)),
inference(superposition,[status(thm)],[p538,c1]) ).
fof(f10,axiom,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| Vd203 != Vd204 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd10) ).
fof(f10_nnf,plain,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| Vd203 != Vd204 ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| Vd203 != Vd204 ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( ~ less(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p32,plain,
~ less(X0,X0),
inference(equality_resolution,[status(thm)],[c10]) ).
cnf(p584,plain,
$false,
inference(resolution,[status(thm)],[p539,p32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM840+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.35 % Computer : n003.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Thu Sep 24 05:35:21 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 24.64/3.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.64/3.54 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------