%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM849+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 02:21:11 PM UTC 2026
% Result : Theorem 3.37s 1.50s
% Output : Proof 3.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 57 ( 50 unt; 0 def)
% Number of atoms : 64 ( 63 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 8 ~; 0 |; 5 &)
% ( 0 <=>; 2 =>; 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 : 87 ( 0 sgn 35 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [Vd418,Vd419] : vmul(Vd418,Vd419) = vmul(Vd419,Vd418),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qtd7) ).
fof(f7_nnf,plain,
! [Vd418,Vd419] : vmul(Vd418,Vd419) = vmul(Vd419,Vd418),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [Vd418,Vd419] : vmul(Vd418,Vd419) = vmul(Vd419,Vd418),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c8,plain,
vmul(X0,X1) = vmul(X1,X0),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t3,plain,
vmul(X1,X2) = vmul(X2,X1),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t17,plain,
vmul(X1,X2) = vmul(X2,X1),
inference(orient,[status(thm)],[t3]) ).
fof(f8,axiom,
! [Vd408,Vd409] : vmul(vsucc(Vd408),Vd409) = vplus(vmul(Vd408,Vd409),Vd409),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qtd8) ).
fof(f8_nnf,plain,
! [Vd408,Vd409] : vmul(vsucc(Vd408),Vd409) = vplus(vmul(Vd408,Vd409),Vd409),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [Vd408,Vd409] : vmul(vsucc(Vd408),Vd409) = vplus(vmul(Vd408,Vd409),Vd409),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c9,plain,
vmul(vsucc(X0),X1) = vplus(vmul(X0,X1),X1),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t8,plain,
vplus(vmul(X1,X2),X2) = vmul(vsucc(X1),X2),
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t36,plain,
vplus(vmul(X1,X2),X2) = vmul(vsucc(X1),X2),
inference(orient,[status(thm)],[t8]) ).
cnf(t44,plain,
vplus(vmul(X1,X2),X2) = vmul(vsucc(X1),X2),
inference(rw,[status(thm)],[t36]) ).
fof(f10,axiom,
! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
file('/export/starexec/sandbox2/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(c12,plain,
vplus(X1,X0) = vplus(X0,X1),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t4,plain,
vplus(X1,X2) = vplus(X2,X1),
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t42,plain,
vplus(X1,X2) = vplus(X2,X1),
inference(orient,[status(thm)],[t4]) ).
cnf(t8987,plain,
vplus(X2,vmul(X1,X2)) = vmul(vsucc(X1),X2),
inference(step,[status(thm)],[t44,t42]) ).
cnf(t78,plain,
vplus(X1,vmul(X2,X1)) = vmul(vsucc(X2),X1),
inference(orient,[status(thm)],[t8987]) ).
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(t9,plain,
vmul(vmul(vd448,vd449),sk0) = vmul(vd448,vmul(vd449,sk0)),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t8967,plain,
vmul(sk0,vmul(vd448,vd449)) = vmul(vd448,vmul(vd449,sk0)),
inference(step,[status(thm)],[t9,t17]) ).
cnf(t8968,plain,
vmul(sk0,vmul(vd449,vd448)) = vmul(vd448,vmul(vd449,sk0)),
inference(step,[status(thm)],[t8967,t17]) ).
cnf(t27,plain,
vmul(sk0,vmul(vd449,vd448)) = vmul(vd448,vmul(vd449,sk0)),
inference(orient,[status(thm)],[t8968]) ).
cnf(t82,plain,
vmul(vsucc(sk0),vmul(vd449,vd448)) = vplus(vmul(vd449,vd448),vmul(vd448,vmul(vd449,sk0))),
inference(cp,[status(thm)],[t78,t27]) ).
fof(f6,axiom,
! [Vd432,Vd433,Vd434] : vmul(Vd432,vplus(Vd433,Vd434)) = vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qtd6) ).
fof(f6_nnf,plain,
! [Vd432,Vd433,Vd434] : vmul(Vd432,vplus(Vd433,Vd434)) = vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434)),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [Vd432,Vd433,Vd434] : vmul(Vd432,vplus(Vd433,Vd434)) = vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434)),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c7,plain,
vmul(X0,vplus(X1,X2)) = vplus(vmul(X0,X1),vmul(X0,X2)),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t10,plain,
vplus(vmul(X1,X2),vmul(X1,X3)) = vmul(X1,vplus(X2,X3)),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t19,plain,
vplus(vmul(X1,X2),vmul(X1,X3)) = vmul(X1,vplus(X2,X3)),
inference(orient,[status(thm)],[t10]) ).
cnf(t21,plain,
vmul(X1,vplus(X2,X3)) = vplus(vmul(X2,X1),vmul(X1,X3)),
inference(cp,[status(thm)],[t19,t17]) ).
cnf(t261,plain,
vplus(vmul(X1,X2),vmul(X2,X3)) = vmul(X2,vplus(X1,X3)),
inference(orient,[status(thm)],[t21]) ).
cnf(t9127,plain,
vmul(vsucc(sk0),vmul(vd449,vd448)) = vmul(vd448,vplus(vd449,vmul(vd449,sk0))),
inference(step,[status(thm)],[t82,t261]) ).
fof(f9,axiom,
! [Vd396,Vd397] :
( vmul(Vd396,v1) = Vd396
& vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396) ),
file('/export/starexec/sandbox2/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(c10,plain,
vmul(X0,vsucc(X1)) = vplus(vmul(X0,X1),X0),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t7,plain,
vplus(vmul(X1,X2),X1) = vmul(X1,vsucc(X2)),
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t24,plain,
vplus(vmul(X1,X2),X1) = vmul(X1,vsucc(X2)),
inference(orient,[status(thm)],[t7]) ).
cnf(t45,plain,
vplus(vmul(X1,X2),X1) = vmul(X1,vsucc(X2)),
inference(rw,[status(thm)],[t24]) ).
cnf(t8988,plain,
vplus(X1,vmul(X1,X2)) = vmul(X1,vsucc(X2)),
inference(step,[status(thm)],[t45,t42]) ).
cnf(t88,plain,
vplus(X1,vmul(X1,X2)) = vmul(X1,vsucc(X2)),
inference(orient,[status(thm)],[t8988]) ).
cnf(t9128,plain,
vmul(vsucc(sk0),vmul(vd449,vd448)) = vmul(vd448,vmul(vd449,vsucc(sk0))),
inference(step,[status(thm)],[t9127,t88]) ).
cnf(t8924,plain,
vmul(vsucc(sk0),vmul(vd449,vd448)) = vmul(vd448,vmul(vd449,vsucc(sk0))),
inference(orient,[status(thm)],[t9128]) ).
cnf(c1,plain,
vmul(vmul(vd448,vd449),vsucc(sk0)) != vmul(vd448,vmul(vd449,vsucc(sk0))),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(goal_0,negated_conjecture,
vmul(vmul(vd448,vd449),vsucc(sk0)) != vmul(vd448,vmul(vd449,vsucc(sk0))),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(g0_0,plain,
vmul(vsucc(sk0),vmul(vd448,vd449)) != vmul(vd448,vmul(vd449,vsucc(sk0))),
inference(rw,[status(thm)],[goal_0,t17]) ).
cnf(g0_1,plain,
vmul(vsucc(sk0),vmul(vd449,vd448)) != vmul(vd448,vmul(vd449,vsucc(sk0))),
inference(rw,[status(thm)],[g0_0,t17]) ).
cnf(g0_2,plain,
vmul(vd448,vmul(vd449,vsucc(sk0))) != vmul(vd448,vmul(vd449,vsucc(sk0))),
inference(rw,[status(thm)],[g0_1,t8924]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM849+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n005.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 05:33:47 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.37/1.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.37/1.50 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------