%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM852+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 : n002.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 02:21:12 PM UTC 2026
% Result : Theorem 11.23s 1.98s
% Output : Proof 11.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 35 ( 23 unt; 0 def)
% Number of atoms : 51 ( 19 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 32 ( 16 ~; 11 |; 2 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 55 ( 2 sgn 35 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [Vd418,Vd419] : vmul(Vd418,Vd419) = vmul(Vd419,Vd418),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd10) ).
fof(f10_nnf,plain,
! [Vd418,Vd419] : vmul(Vd418,Vd419) = vmul(Vd419,Vd418),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [Vd418,Vd419] : vmul(Vd418,Vd419) = vmul(Vd419,Vd418),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
vmul(X0,X1) = vmul(X1,X0),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
fof(f7,axiom,
! [Vd470,Vd471] :
( greater(Vd470,Vd471)
=> Vd470 = vplus(Vd471,vskolem9(Vd470,Vd471)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd7) ).
fof(f7_nnf,plain,
! [Vd470,Vd471] :
( Vd470 = vplus(Vd471,vskolem9(Vd470,Vd471))
| ~ greater(Vd470,Vd471) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [Vd470,Vd471] :
( Vd470 = vplus(Vd471,vskolem9(Vd470,Vd471))
| ~ greater(Vd470,Vd471) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( X0 = vplus(X1,vskolem9(X0,X1))
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
fof(f1,axiom,
greater(vd481,vd480),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd1) ).
fof(f1_nnf,plain,
greater(vd481,vd480),
inference(nnf_transformation,[status(thm)],[f1]) ).
cnf(c1,plain,
greater(vd481,vd480),
inference(cnf_transformation,[status(esa)],[f1_nnf]) ).
cnf(p36,plain,
vd481 = vplus(vd480,vskolem9(vd481,vd480)),
inference(resolution,[status(thm)],[c7,c1]) ).
fof(f9,axiom,
! [Vd432,Vd433,Vd434] : vmul(Vd432,vplus(Vd433,Vd434)) = vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd9) ).
fof(f9_nnf,plain,
! [Vd432,Vd433,Vd434] : vmul(Vd432,vplus(Vd433,Vd434)) = vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434)),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [Vd432,Vd433,Vd434] : vmul(Vd432,vplus(Vd433,Vd434)) = vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434)),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
vmul(X0,vplus(X1,X2)) = vplus(vmul(X0,X1),vmul(X0,X2)),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
fof(f18,axiom,
! [Vd198,Vd199] :
( less(Vd199,Vd198)
<=> ? [Vd201] : Vd198 = vplus(Vd199,Vd201) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd18) ).
fof(f18_nnf,plain,
! [Vd198,Vd199] :
( ( ! [Vd201] : Vd198 != vplus(Vd199,Vd201)
| less(Vd199,Vd198) )
& ( ? [Vd201] : Vd198 = vplus(Vd199,Vd201)
| ~ less(Vd199,Vd198) ) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [Vd199,Vd198,Vd201] :
( ( Vd198 != vplus(Vd199,Vd201)
| less(Vd199,Vd198) )
& ( Vd198 = vplus(Vd199,sk0(Vd198,Vd199))
| ~ less(Vd199,Vd198) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f18_nnf]) ).
cnf(c19,plain,
( X0 != vplus(X1,X2)
| less(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p75,plain,
less(vmul(X0,X1),vmul(X0,vplus(X1,X2))),
inference(resolution,[status(thm)],[c9,c19]) ).
cnf(p134,plain,
less(vmul(X0,vd480),vmul(X0,vd481)),
inference(superposition,[status(thm)],[p36,p75]) ).
cnf(p139,plain,
less(vmul(X0,vd480),vmul(vd481,X0)),
inference(superposition,[status(thm)],[c10,p134]) ).
fof(f12,axiom,
! [Vd226,Vd227] :
( less(Vd226,Vd227)
=> greater(Vd227,Vd226) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd12) ).
fof(f12_nnf,plain,
! [Vd226,Vd227] :
( greater(Vd227,Vd226)
| ~ less(Vd226,Vd227) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [Vd226,Vd227] :
( greater(Vd227,Vd226)
| ~ less(Vd226,Vd227) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( greater(X1,X0)
| ~ less(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p147,plain,
greater(vmul(vd481,X0),vmul(X0,vd480)),
inference(resolution,[status(thm)],[p139,c12]) ).
fof(f0,conjecture,
greater(vmul(vd481,vd469),vmul(vd480,vd469)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd0) ).
fof(f0_neg,negated_conjecture,
~ greater(vmul(vd481,vd469),vmul(vd480,vd469)),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
~ greater(vmul(vd481,vd469),vmul(vd480,vd469)),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
~ greater(vmul(vd481,vd469),vmul(vd480,vd469)),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
~ greater(vmul(vd481,vd469),vmul(vd480,vd469)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p22,plain,
~ greater(vmul(vd481,vd469),vmul(vd469,vd480)),
inference(superposition,[status(thm)],[c10,c0]) ).
cnf(p163,plain,
$false,
inference(resolution,[status(thm)],[p147,p22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM852+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 : n002.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 05:37:03 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 11.23/1.98 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.23/1.98 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------