%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM835+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 : 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 02:21:07 PM UTC 2026
% Result : Theorem 11.59s 1.95s
% Output : Proof 11.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 39 ( 30 unt; 0 def)
% Number of atoms : 68 ( 60 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 55 ( 26 ~; 18 |; 10 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-4 aty)
% Number of variables : 50 ( 11 sgn 17 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f16,axiom,
! [Vd151,Vd152] :
( m(Vd152)
<=> ( ? [Vd157] : Vd152 = vplus(Vd151,Vd157)
| ? [Vd155] : Vd151 = vplus(Vd152,Vd155)
| Vd151 = Vd152 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd16) ).
fof(f16_nnf,plain,
! [Vd151,Vd152] :
( ( ( ! [Vd157] : Vd152 != vplus(Vd151,Vd157)
& ! [Vd155] : Vd151 != vplus(Vd152,Vd155)
& Vd151 != Vd152 )
| m(Vd152) )
& ( ? [Vd157] : Vd152 = vplus(Vd151,Vd157)
| ? [Vd155] : Vd151 = vplus(Vd152,Vd155)
| Vd151 = Vd152
| ~ m(Vd152) ) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [Vd152,Vd151,Vd155,Vd157] :
( ( ( Vd152 != vplus(Vd151,Vd157)
& Vd151 != vplus(Vd152,Vd155)
& Vd151 != Vd152 )
| m(Vd152) )
& ( Vd152 = vplus(Vd151,sk1(Vd151,Vd152))
| Vd151 = vplus(Vd152,sk0(Vd151,Vd152))
| Vd151 = Vd152
| ~ m(Vd152) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f16_nnf]) ).
cnf(c20,plain,
( X0 != vplus(X1,X2)
| m(X1) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi18,axiom,
ifeq(X0,vplus(X1,X2),m(X1),true) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(hi36,axiom,
or(false,X0) = X0,
introduced(definition) ).
cnf(h8,plain,
m(V0) = true,
inference(hyper_resolution,[status(thm)],[hi18,hi36]) ).
cnf(c18,plain,
( X1 = vplus(X0,sk1(X0,X1))
| X0 = vplus(X1,sk0(X0,X1))
| X0 = X1
| ~ m(X1) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi16,axiom,
ifeq(m(X0),true,or(eq(X1,X0),or(eq(X1,vplus(X0,sk0(X1,X0))),eq(X0,vplus(X1,sk1(X1,X0))))),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t39,plain,
or(eq(X1,X2),or(eq(X1,vplus(X2,sk0(X1,X2))),eq(X2,vplus(X1,sk1(X1,X2))))) = true,
inference(hyper_resolution,[status(thm)],[hi16,h8]) ).
cnf(t134,plain,
or(eq(X1,X2),or(eq(X1,vplus(X2,sk0(X1,X2))),eq(X2,vplus(X1,sk1(X1,X2))))) = true,
inference(orient,[status(thm)],[t39]) ).
fof(f0,conjecture,
( vd151 = vd165
| ? [Vd170] : vd151 = vplus(vd165,Vd170)
| ? [Vd180] : vd165 = vplus(vd151,Vd180) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd0) ).
fof(f0_neg,negated_conjecture,
~ ( vd151 = vd165
| ? [Vd170] : vd151 = vplus(vd165,Vd170)
| ? [Vd180] : vd165 = vplus(vd151,Vd180) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
( vd151 != vd165
& ! [Vd170] : vd151 != vplus(vd165,Vd170)
& ! [Vd180] : vd165 != vplus(vd151,Vd180) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [Vd180,Vd170] :
( vd151 != vd165
& vd151 != vplus(vd165,Vd170)
& vd165 != vplus(vd151,Vd180) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c2,plain,
vd151 != vd165,
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t2,plain,
eq(vd151,vd165) = false,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t174,plain,
eq(vd151,vd165) = false,
inference(orient,[status(thm)],[t2]) ).
cnf(t176,plain,
true = or(false,or(eq(vd151,vplus(vd165,sk0(vd151,vd165))),eq(vd165,vplus(vd151,sk1(vd151,vd165))))),
inference(cp,[status(thm)],[t134,t174]) ).
cnf(t5,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t46,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t230,plain,
true = or(eq(vd151,vplus(vd165,sk0(vd151,vd165))),eq(vd165,vplus(vd151,sk1(vd151,vd165)))),
inference(step,[status(thm)],[t176,t46]) ).
cnf(c1,plain,
vd151 != vplus(vd165,X1),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t10,plain,
eq(vd151,vplus(vd165,X1)) = false,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t166,plain,
eq(vd151,vplus(vd165,X1)) = false,
inference(orient,[status(thm)],[t10]) ).
cnf(t231,plain,
true = or(false,eq(vd165,vplus(vd151,sk1(vd151,vd165)))),
inference(step,[status(thm)],[t230,t166]) ).
cnf(t232,plain,
true = eq(vd165,vplus(vd151,sk1(vd151,vd165))),
inference(step,[status(thm)],[t231,t46]) ).
cnf(c0,plain,
vd165 != vplus(vd151,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t11,plain,
eq(vd165,vplus(vd151,X1)) = false,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t159,plain,
eq(vd165,vplus(vd151,X1)) = false,
inference(orient,[status(thm)],[t11]) ).
cnf(t233,plain,
true = false,
inference(step,[status(thm)],[t232,t159]) ).
cnf(t184,plain,
false = true,
inference(orient,[status(thm)],[t233]) ).
fof(f23,axiom,
! [Vd16] : vsucc(Vd16) != Vd16,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd23) ).
fof(f23_nnf,plain,
! [Vd16] : vsucc(Vd16) != Vd16,
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [Vd16] : vsucc(Vd16) != Vd16,
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c29,plain,
vsucc(X0) != X0,
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c1,c2,c29]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t184]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM835+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.35 % Computer : n019.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Thu Sep 24 05:32:34 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 11.59/1.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.59/1.95 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------