%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM844+2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n005.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 02:21:10 PM UTC 2026
% Result : Theorem 5.38s 1.21s
% Output : Proof 5.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 26 unt; 0 def)
% Number of atoms : 26 ( 25 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 8 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
vmul(vsucc(vd411),vsucc(vd413)) = vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qtd3) ).
fof(f3_nnf,plain,
vmul(vsucc(vd411),vsucc(vd413)) = vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)),
inference(nnf_transformation,[status(thm)],[f3]) ).
cnf(c3,plain,
vmul(vsucc(vd411),vsucc(vd413)) = vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)),
inference(cnf_transformation,[status(esa)],[f3_nnf]) ).
fof(f12,axiom,
! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qtd12) ).
fof(f12_nnf,plain,
! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [Vd79,Vd78] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c13,plain,
vplus(X1,X0) = vplus(X0,X1),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p47,plain,
vplus(vsucc(vd411),vmul(vsucc(vd411),vd413)) = vmul(vsucc(vd411),vsucc(vd413)),
inference(superposition,[status(thm)],[c3,c13]) ).
fof(f2,axiom,
vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)) = vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qtd2) ).
fof(f2_nnf,plain,
vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)) = vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)),
inference(nnf_transformation,[status(thm)],[f2]) ).
cnf(c2,plain,
vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)) = vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)),
inference(cnf_transformation,[status(esa)],[f2_nnf]) ).
cnf(p40,plain,
vplus(vsucc(vd411),vplus(vd413,vmul(vd411,vd413))) = vplus(vsucc(vd411),vmul(vsucc(vd411),vd413)),
inference(superposition,[status(thm)],[c2,c13]) ).
fof(f1,axiom,
vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)) = vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))),
file('/export/starexec/sandbox2/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(p32,plain,
vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vplus(vsucc(vd411),vplus(vd413,vmul(vd411,vd413))),
inference(superposition,[status(thm)],[c1,c13]) ).
fof(f0,conjecture,
vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)),
file('/export/starexec/sandbox2/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(p30,plain,
vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) != vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))),
inference(superposition,[status(thm)],[c13,c0]) ).
cnf(p37,plain,
vplus(vsucc(vd411),vplus(vd413,vmul(vd411,vd413))) != vplus(vsucc(vd411),vplus(vd413,vmul(vd411,vd413))),
inference(demodulation,[status(thm)],[p32,p30]) ).
cnf(p45,plain,
vplus(vsucc(vd411),vmul(vsucc(vd411),vd413)) != vplus(vsucc(vd411),vmul(vsucc(vd411),vd413)),
inference(demodulation,[status(thm)],[p40,p37]) ).
cnf(p52,plain,
vmul(vsucc(vd411),vsucc(vd413)) != vmul(vsucc(vd411),vsucc(vd413)),
inference(demodulation,[status(thm)],[p47,p45]) ).
cnf(p120,plain,
$false,
inference(equality_resolution,[status(thm)],[p52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM844+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.13/0.38 % Computer : n005.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Thu Sep 24 05:33:03 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.38/1.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.38/1.21 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------