%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM849+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n016.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 33.12s 9.99s
% Output : Proof 33.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 13 ( 5 unt; 0 def)
% Number of atoms : 21 ( 20 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 8 ~; 3 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 7 ( 0 sgn 5 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [Vd451] :
( vmul(vmul(vd448,vd449),Vd451) = vmul(vd448,vmul(vd449,Vd451))
=> vmul(vmul(vd448,vd449),vsucc(Vd451)) = vplus(vmul(vmul(vd448,vd449),Vd451),vmul(vd448,vd449)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qtd4) ).
fof(f4_nnf,plain,
! [Vd451] :
( vmul(vmul(vd448,vd449),vsucc(Vd451)) = vplus(vmul(vmul(vd448,vd449),Vd451),vmul(vd448,vd449))
| vmul(vmul(vd448,vd449),Vd451) != vmul(vd448,vmul(vd449,Vd451)) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [Vd451] :
( vmul(vmul(vd448,vd449),vsucc(Vd451)) = vplus(vmul(vmul(vd448,vd449),Vd451),vmul(vd448,vd449))
| vmul(vmul(vd448,vd449),Vd451) != vmul(vd448,vmul(vd449,Vd451)) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c5,plain,
( vmul(vmul(vd448,vd449),vsucc(X0)) = vplus(vmul(vmul(vd448,vd449),X0),vmul(vd448,vd449))
| vmul(vmul(vd448,vd449),X0) != vmul(vd448,vmul(vd449,X0)) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
fof(f0,conjecture,
! [Vd454] :
( vmul(vmul(vd448,vd449),Vd454) = vmul(vd448,vmul(vd449,Vd454))
=> vmul(vmul(vd448,vd449),vsucc(Vd454)) = vmul(vd448,vmul(vd449,vsucc(Vd454))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qtd0) ).
fof(f0_neg,negated_conjecture,
~ ! [Vd454] :
( vmul(vmul(vd448,vd449),Vd454) = vmul(vd448,vmul(vd449,Vd454))
=> vmul(vmul(vd448,vd449),vsucc(Vd454)) = vmul(vd448,vmul(vd449,vsucc(Vd454))) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
? [Vd454] :
( vmul(vmul(vd448,vd449),vsucc(Vd454)) != vmul(vd448,vmul(vd449,vsucc(Vd454)))
& vmul(vmul(vd448,vd449),Vd454) = vmul(vd448,vmul(vd449,Vd454)) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
( vmul(vmul(vd448,vd449),vsucc(sk0)) != vmul(vd448,vmul(vd449,vsucc(sk0)))
& vmul(vmul(vd448,vd449),sk0) = vmul(vd448,vmul(vd449,sk0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c0,plain,
vmul(vmul(vd448,vd449),sk0) = vmul(vd448,vmul(vd449,sk0)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p75,plain,
vmul(vmul(vd448,vd449),vsucc(sk0)) = vmul(vd448,vmul(vd449,vsucc(sk0))),
inference(resolution,[status(thm)],[c5,c0]) ).
cnf(c1,plain,
vmul(vmul(vd448,vd449),vsucc(sk0)) != vmul(vd448,vmul(vd449,vsucc(sk0))),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p76,plain,
vmul(vd448,vmul(vd449,vsucc(sk0))) != vmul(vd448,vmul(vd449,vsucc(sk0))),
inference(demodulation,[status(thm)],[p75,c1]) ).
cnf(p81,plain,
$false,
inference(equality_resolution,[status(thm)],[p76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM849+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Thu Sep 24 05:38:47 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 33.12/9.99 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 33.12/9.99 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------