%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM844+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n019.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 35.07s 10.84s
% Output : Proof 35.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 24 unt; 0 def)
% Number of atoms : 30 ( 29 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 8 ~; 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [Vd396,Vd397] :
( vmul(Vd396,v1) = Vd396
& vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd9) ).
fof(f9_nnf,plain,
! [Vd396,Vd397] :
( vmul(Vd396,v1) = Vd396
& vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [Vd396,Vd397] :
( vmul(Vd396,v1) = Vd396
& vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
vmul(X0,vsucc(X1)) = vplus(vmul(X0,X1),X0),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
fof(f44,axiom,
! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd44) ).
fof(f44_nnf,plain,
! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
inference(nnf_transformation,[status(thm)],[f44]) ).
fof(f44_sk,plain,
! [Vd79,Vd78] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
inference(skolemisation,[status(esa)],[f44_nnf]) ).
cnf(c53,plain,
vplus(X1,X0) = vplus(X0,X1),
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(p282,plain,
vplus(X0,vmul(X0,X1)) = vmul(X0,vsucc(X1)),
inference(superposition,[status(thm)],[c9,c53]) ).
fof(f4,axiom,
vmul(vsucc(vd411),vd413) = vplus(vmul(vd411,vd413),vd413),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd4) ).
fof(f4_nnf,plain,
vmul(vsucc(vd411),vd413) = vplus(vmul(vd411,vd413),vd413),
inference(nnf_transformation,[status(thm)],[f4]) ).
cnf(c4,plain,
vmul(vsucc(vd411),vd413) = vplus(vmul(vd411,vd413),vd413),
inference(cnf_transformation,[status(esa)],[f4_nnf]) ).
cnf(p261,plain,
vplus(vd413,vmul(vd411,vd413)) = vmul(vsucc(vd411),vd413),
inference(superposition,[status(thm)],[c4,c53]) ).
fof(f1,axiom,
vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)) = vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd1) ).
fof(f1_nnf,plain,
vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)) = vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))),
inference(nnf_transformation,[status(thm)],[f1]) ).
cnf(c1,plain,
vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)) = vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))),
inference(cnf_transformation,[status(esa)],[f1_nnf]) ).
cnf(p238,plain,
vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vplus(vsucc(vd411),vplus(vd413,vmul(vd411,vd413))),
inference(superposition,[status(thm)],[c1,c53]) ).
fof(f0,conjecture,
vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd0) ).
fof(f0_neg,negated_conjecture,
vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) != vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) != vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) != vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) != vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p236,plain,
vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) != vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))),
inference(superposition,[status(thm)],[c53,c0]) ).
cnf(p256,plain,
vplus(vsucc(vd411),vplus(vd413,vmul(vd411,vd413))) != vplus(vsucc(vd411),vplus(vd413,vmul(vd411,vd413))),
inference(demodulation,[status(thm)],[p238,p236]) ).
cnf(p279,plain,
vplus(vsucc(vd411),vmul(vsucc(vd411),vd413)) != vplus(vsucc(vd411),vmul(vsucc(vd411),vd413)),
inference(demodulation,[status(thm)],[p261,p256]) ).
cnf(p299,plain,
vmul(vsucc(vd411),vsucc(vd413)) != vmul(vsucc(vd411),vsucc(vd413)),
inference(demodulation,[status(thm)],[p282,p279]) ).
cnf(p2173,plain,
$false,
inference(equality_resolution,[status(thm)],[p299]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM844+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/5.59 % Computer : n019.cluster.edu
% 0.13/5.59 % Model : x86_64 x86_64
% 0.13/5.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.59 % Memory : 8046.5625MB
% 0.13/5.59 % OS : Linux 6.8.0-71-generic
% 0.13/5.59 % CPULimit : 300
% 0.13/5.59 % WCLimit : 300
% 0.13/5.59 % DateTime : Thu Sep 24 05:33:26 UTC 2026
% 0.13/5.59 % CPUTime :
% 0.13/5.59 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 35.07/10.84 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 35.07/10.84 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------