%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM845+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 : n003.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 6.08s 1.22s
% Output : Proof 6.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of formulae : 64 ( 54 unt; 0 def)
% Number of atoms : 74 ( 73 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 7 ~; 0 |; 8 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 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 : 95 ( 0 sgn 32 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [Vd42,Vd43] :
( vplus(Vd42,v1) = vsucc(Vd42)
& vplus(Vd42,vsucc(Vd43)) = vsucc(vplus(Vd42,Vd43)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd14) ).
fof(f14_nnf,plain,
! [Vd42,Vd43] :
( vplus(Vd42,v1) = vsucc(Vd42)
& vplus(Vd42,vsucc(Vd43)) = vsucc(vplus(Vd42,Vd43)) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [Vd42,Vd43] :
( vplus(Vd42,v1) = vsucc(Vd42)
& vplus(Vd42,vsucc(Vd43)) = vsucc(vplus(Vd42,Vd43)) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c16,plain,
vplus(X0,vsucc(X1)) = vsucc(vplus(X0,X1)),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t5,plain,
vsucc(vplus(X1,X2)) = vplus(X1,vsucc(X2)),
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t29,plain,
vsucc(vplus(X1,X2)) = vplus(X1,vsucc(X2)),
inference(orient,[status(thm)],[t5]) ).
fof(f11,axiom,
! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd11) ).
fof(f11_nnf,plain,
! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [Vd79,Vd78] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c13,plain,
vplus(X1,X0) = vplus(X0,X1),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t4,plain,
vplus(X1,X2) = vplus(X2,X1),
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t25,plain,
vplus(X1,X2) = vplus(X2,X1),
inference(orient,[status(thm)],[t4]) ).
cnf(t30,plain,
vplus(X1,vsucc(X2)) = vsucc(vplus(X2,X1)),
inference(cp,[status(thm)],[t29,t25]) ).
cnf(t539,plain,
vplus(X1,vsucc(X2)) = vplus(X2,vsucc(X1)),
inference(step,[status(thm)],[t30,t29]) ).
cnf(t218,plain,
vplus(X1,vsucc(X2)) = vplus(X2,vsucc(X1)),
inference(orient,[status(thm)],[t539]) ).
fof(f13,axiom,
! [Vd46,Vd47,Vd48] : vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd13) ).
fof(f13_nnf,plain,
! [Vd46,Vd47,Vd48] : vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [Vd46,Vd47,Vd48] : vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c15,plain,
vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t9,plain,
vplus(vplus(X1,X2),X3) = vplus(X1,vplus(X2,X3)),
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t26,plain,
vplus(vplus(X1,X2),X3) = vplus(X1,vplus(X2,X3)),
inference(orient,[status(thm)],[t9]) ).
fof(f10,axiom,
! [Vd396,Vd397] :
( vmul(Vd396,v1) = Vd396
& vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd10) ).
fof(f10_nnf,plain,
! [Vd396,Vd397] :
( vmul(Vd396,v1) = Vd396
& vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [Vd396,Vd397] :
( vmul(Vd396,v1) = Vd396
& vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c11,plain,
vmul(X0,vsucc(X1)) = vplus(vmul(X0,X1),X0),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t6,plain,
vplus(vmul(X1,X2),X1) = vmul(X1,vsucc(X2)),
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t491,plain,
vplus(X1,vmul(X1,X2)) = vmul(X1,vsucc(X2)),
inference(step,[status(thm)],[t6,t25]) ).
cnf(t58,plain,
vplus(X1,vmul(X1,X2)) = vmul(X1,vsucc(X2)),
inference(orient,[status(thm)],[t491]) ).
cnf(t61,plain,
vplus(X1,vplus(vmul(X1,X2),X3)) = vplus(vmul(X1,vsucc(X2)),X3),
inference(cp,[status(thm)],[t26,t58]) ).
cnf(t331,plain,
vplus(X1,vplus(vmul(X1,X2),X3)) = vplus(vmul(X1,vsucc(X2)),X3),
inference(orient,[status(thm)],[t61]) ).
cnf(t341,plain,
vplus(vmul(X1,vsucc(X2)),X3) = vplus(X1,vplus(X3,vmul(X1,X2))),
inference(cp,[status(thm)],[t331,t25]) ).
cnf(t442,plain,
vplus(X1,vplus(X2,vmul(X1,X3))) = vplus(vmul(X1,vsucc(X3)),X2),
inference(orient,[status(thm)],[t341]) ).
fof(f0,conjecture,
! [Vd416] :
( vmul(vsucc(vd411),Vd416) = vplus(vmul(vd411,Vd416),Vd416)
=> vmul(vsucc(vd411),vsucc(Vd416)) = vplus(vmul(vd411,vsucc(Vd416)),vsucc(Vd416)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd0) ).
fof(f0_neg,negated_conjecture,
~ ! [Vd416] :
( vmul(vsucc(vd411),Vd416) = vplus(vmul(vd411,Vd416),Vd416)
=> vmul(vsucc(vd411),vsucc(Vd416)) = vplus(vmul(vd411,vsucc(Vd416)),vsucc(Vd416)) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
? [Vd416] :
( vmul(vsucc(vd411),vsucc(Vd416)) != vplus(vmul(vd411,vsucc(Vd416)),vsucc(Vd416))
& vmul(vsucc(vd411),Vd416) = vplus(vmul(vd411,Vd416),Vd416) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
( vmul(vsucc(vd411),vsucc(sk0)) != vplus(vmul(vd411,vsucc(sk0)),vsucc(sk0))
& vmul(vsucc(vd411),sk0) = vplus(vmul(vd411,sk0),sk0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c0,plain,
vmul(vsucc(vd411),sk0) = vplus(vmul(vd411,sk0),sk0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t7,plain,
vplus(vmul(vd411,sk0),sk0) = vmul(vsucc(vd411),sk0),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t511,plain,
vplus(sk0,vmul(vd411,sk0)) = vmul(vsucc(vd411),sk0),
inference(step,[status(thm)],[t7,t25]) ).
cnf(t119,plain,
vplus(sk0,vmul(vd411,sk0)) = vmul(vsucc(vd411),sk0),
inference(orient,[status(thm)],[t511]) ).
cnf(t452,plain,
vplus(vmul(vd411,vsucc(sk0)),sk0) = vplus(vd411,vmul(vsucc(vd411),sk0)),
inference(cp,[status(thm)],[t442,t119]) ).
cnf(t547,plain,
vplus(sk0,vmul(vd411,vsucc(sk0))) = vplus(vd411,vmul(vsucc(vd411),sk0)),
inference(step,[status(thm)],[t452,t25]) ).
cnf(t465,plain,
vplus(sk0,vmul(vd411,vsucc(sk0))) = vplus(vd411,vmul(vsucc(vd411),sk0)),
inference(orient,[status(thm)],[t547]) ).
cnf(t467,plain,
vplus(sk0,vsucc(vmul(vd411,vsucc(sk0)))) = vsucc(vplus(vd411,vmul(vsucc(vd411),sk0))),
inference(cp,[status(thm)],[t29,t465]) ).
cnf(t548,plain,
vplus(sk0,vsucc(vmul(vd411,vsucc(sk0)))) = vplus(vd411,vsucc(vmul(vsucc(vd411),sk0))),
inference(step,[status(thm)],[t467,t29]) ).
fof(f12,axiom,
! [Vd59] : vplus(v1,Vd59) = vsucc(Vd59),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd12) ).
fof(f12_nnf,plain,
! [Vd59] : vplus(v1,Vd59) = vsucc(Vd59),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [Vd59] : vplus(v1,Vd59) = vsucc(Vd59),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c14,plain,
vplus(v1,X0) = vsucc(X0),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(t2,plain,
vplus(v1,X1) = vsucc(X1),
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t132,plain,
vplus(v1,X1) = vsucc(X1),
inference(orient,[status(thm)],[t2]) ).
cnf(t136,plain,
vplus(v1,vplus(X1,X2)) = vplus(vsucc(X1),X2),
inference(cp,[status(thm)],[t26,t132]) ).
cnf(t533,plain,
vsucc(vplus(X1,X2)) = vplus(vsucc(X1),X2),
inference(step,[status(thm)],[t136,t132]) ).
cnf(t534,plain,
vplus(X1,vsucc(X2)) = vplus(vsucc(X1),X2),
inference(step,[status(thm)],[t533,t29]) ).
cnf(t175,plain,
vplus(vsucc(X1),X2) = vplus(X1,vsucc(X2)),
inference(orient,[status(thm)],[t534]) ).
cnf(t177,plain,
vplus(X1,vsucc(vmul(vsucc(X1),X2))) = vmul(vsucc(X1),vsucc(X2)),
inference(cp,[status(thm)],[t175,t58]) ).
cnf(t292,plain,
vplus(X1,vsucc(vmul(vsucc(X1),X2))) = vmul(vsucc(X1),vsucc(X2)),
inference(orient,[status(thm)],[t177]) ).
cnf(t549,plain,
vplus(sk0,vsucc(vmul(vd411,vsucc(sk0)))) = vmul(vsucc(vd411),vsucc(sk0)),
inference(step,[status(thm)],[t548,t292]) ).
cnf(t470,plain,
vplus(sk0,vsucc(vmul(vd411,vsucc(sk0)))) = vmul(vsucc(vd411),vsucc(sk0)),
inference(orient,[status(thm)],[t549]) ).
cnf(c1,plain,
vmul(vsucc(vd411),vsucc(sk0)) != vplus(vmul(vd411,vsucc(sk0)),vsucc(sk0)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(goal_0,negated_conjecture,
vplus(vmul(vd411,vsucc(sk0)),vsucc(sk0)) != vmul(vsucc(vd411),vsucc(sk0)),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(g0_0,plain,
vplus(sk0,vsucc(vmul(vd411,vsucc(sk0)))) != vmul(vsucc(vd411),vsucc(sk0)),
inference(rw,[status(thm)],[goal_0,t218]) ).
cnf(g0_1,plain,
vmul(vsucc(vd411),vsucc(sk0)) != vmul(vsucc(vd411),vsucc(sk0)),
inference(rw,[status(thm)],[g0_0,t470]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM845+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 : n003.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 05:34:36 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.08/1.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.08/1.22 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------