%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM848+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 : n001.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 02:21:11 PM UTC 2026
% Result : Theorem 5.24s 1.28s
% Output : Proof 5.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 19 unt; 0 def)
% Number of atoms : 25 ( 24 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 7 ~; 0 |; 3 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd10) ).
fof(f10_nnf,plain,
! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [Vd79,Vd78] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c11,plain,
vplus(X1,X0) = vplus(X0,X1),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t9,plain,
vplus(X1,X2) = vplus(X2,X1),
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t30,plain,
vplus(X1,X2) = vplus(X2,X1),
inference(orient,[status(thm)],[t9]) ).
fof(f8,axiom,
! [Vd396,Vd397] :
( vmul(Vd396,v1) = Vd396
& vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd8) ).
fof(f8_nnf,plain,
! [Vd396,Vd397] :
( vmul(Vd396,v1) = Vd396
& vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [Vd396,Vd397] :
( vmul(Vd396,v1) = Vd396
& vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
vmul(X0,vsucc(X1)) = vplus(vmul(X0,X1),X0),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t13,plain,
vplus(vmul(X1,X2),X1) = vmul(X1,vsucc(X2)),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t53,plain,
vplus(X1,vmul(X1,X2)) = vmul(X1,vsucc(X2)),
inference(step,[status(thm)],[t13,t30]) ).
cnf(t43,plain,
vplus(X1,vmul(X1,X2)) = vmul(X1,vsucc(X2)),
inference(orient,[status(thm)],[t53]) ).
fof(f0,conjecture,
vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) = vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd0) ).
fof(f0_neg,negated_conjecture,
vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(goal_0,negated_conjecture,
vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(g0_0,plain,
vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
inference(rw,[status(thm)],[goal_0,t30]) ).
cnf(g0_1,plain,
vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
inference(rw,[status(thm)],[g0_0,t43]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM848+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.38 % Computer : n001.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 05:39:36 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.24/1.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.24/1.28 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------