%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM835+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/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 2.86s 2.00s
% Output : Proof 2.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 77 ( 40 unt; 0 def)
% Number of atoms : 134 ( 126 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 143 ( 86 ~; 42 |; 14 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-4 aty)
% Number of variables : 160 ( 23 sgn 90 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f19,axiom,
! [Vd151,Vd152] :
( m(Vd152)
<=> ( ? [Vd157] : Vd152 = vplus(Vd151,Vd157)
| ? [Vd155] : Vd151 = vplus(Vd152,Vd155)
| Vd151 = Vd152 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qtd19) ).
fof(f19_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)],[f19]) ).
fof(f19_sk,plain,
! [Vd152,Vd151,Vd155,Vd157] :
( ( ( Vd152 != vplus(Vd151,Vd157)
& Vd151 != vplus(Vd152,Vd155)
& Vd151 != Vd152 )
| m(Vd152) )
& ( Vd152 = vplus(Vd151,sk2(Vd151,Vd152))
| Vd151 = vplus(Vd152,sk1(Vd151,Vd152))
| Vd151 = Vd152
| ~ m(Vd152) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1,sk2])],[f19_nnf]) ).
cnf(c28,plain,
( X0 != vplus(X1,X2)
| m(X1) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi26,axiom,
ifeq(X0,vplus(X1,X2),m(X1),true) = true,
inference(equality_encoding,[status(esa)],[c28]) ).
cnf(hi65,axiom,
or(false,X0) = X0,
introduced(definition) ).
cnf(h12,plain,
m(V0) = true,
inference(hyper_resolution,[status(thm)],[hi26,hi65]) ).
cnf(c26,plain,
( X1 = vplus(X0,sk2(X0,X1))
| X0 = vplus(X1,sk1(X0,X1))
| X0 = X1
| ~ m(X1) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi24,axiom,
ifeq(m(X0),true,or(eq(X1,X0),or(eq(X1,vplus(X0,sk1(X1,X0))),eq(X0,vplus(X1,sk2(X1,X0))))),true) = true,
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(t77,plain,
or(eq(X1,X2),or(eq(X1,vplus(X2,sk1(X1,X2))),eq(X2,vplus(X1,sk2(X1,X2))))) = true,
inference(hyper_resolution,[status(thm)],[hi24,h12]) ).
cnf(t133,plain,
or(eq(X1,X2),or(eq(X1,vplus(X2,sk1(X1,X2))),eq(X2,vplus(X1,sk2(X1,X2))))) = true,
inference(orient,[status(thm)],[t77]) ).
fof(f0,conjecture,
( vd151 = vd165
| ? [Vd170] : vd151 = vplus(vd165,Vd170)
| ? [Vd180] : vd165 = vplus(vd151,Vd180) ),
file('/export/starexec/sandbox2/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(c0,plain,
vd165 != vplus(vd151,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t17,plain,
eq(vd165,vplus(vd151,X1)) = false,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t351,plain,
eq(vd165,vplus(vd151,X1)) = false,
inference(orient,[status(thm)],[t17]) ).
cnf(t357,plain,
true = or(eq(vd151,vd165),or(eq(vd151,vplus(vd165,sk1(vd151,vd165))),false)),
inference(cp,[status(thm)],[t133,t351]) ).
cnf(c2,plain,
vd151 != vd165,
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t6,plain,
eq(vd151,vd165) = false,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t348,plain,
eq(vd151,vd165) = false,
inference(orient,[status(thm)],[t6]) ).
cnf(t443,plain,
true = or(false,or(eq(vd151,vplus(vd165,sk1(vd151,vd165))),false)),
inference(step,[status(thm)],[t357,t348]) ).
cnf(t9,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t88,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t444,plain,
true = or(eq(vd151,vplus(vd165,sk1(vd151,vd165))),false),
inference(step,[status(thm)],[t443,t88]) ).
cnf(t7,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t87,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t445,plain,
true = eq(vd151,vplus(vd165,sk1(vd151,vd165))),
inference(step,[status(thm)],[t444,t87]) ).
cnf(c1,plain,
vd151 != vplus(vd165,X1),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t16,plain,
eq(vd151,vplus(vd165,X1)) = false,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t340,plain,
eq(vd151,vplus(vd165,X1)) = false,
inference(orient,[status(thm)],[t16]) ).
cnf(t446,plain,
true = false,
inference(step,[status(thm)],[t445,t340]) ).
cnf(t382,plain,
false = true,
inference(orient,[status(thm)],[t446]) ).
fof(f20,axiom,
! [Vd144,Vd145] :
( ~ ? [Vd149] : Vd145 = vplus(Vd144,Vd149)
| Vd144 != Vd145 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qtd20) ).
fof(f20_nnf,plain,
! [Vd144,Vd145] :
( ! [Vd149] : Vd145 != vplus(Vd144,Vd149)
| Vd144 != Vd145 ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [Vd144,Vd145,Vd149] :
( Vd145 != vplus(Vd144,Vd149)
| Vd144 != Vd145 ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c30,plain,
( X1 != vplus(X0,X2)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
fof(f21,axiom,
! [Vd144,Vd145] :
( ~ ? [Vd149] : Vd145 = vplus(Vd144,Vd149)
| ~ ? [Vd147] : Vd144 = vplus(Vd145,Vd147) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qtd21) ).
fof(f21_nnf,plain,
! [Vd144,Vd145] :
( ! [Vd149] : Vd145 != vplus(Vd144,Vd149)
| ! [Vd147] : Vd144 != vplus(Vd145,Vd147) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [Vd144,Vd145,Vd147,Vd149] :
( Vd145 != vplus(Vd144,Vd149)
| Vd144 != vplus(Vd145,Vd147) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c31,plain,
( X1 != vplus(X0,X3)
| X0 != vplus(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
fof(f22,axiom,
! [Vd144,Vd145] :
( ~ ? [Vd147] : Vd144 = vplus(Vd145,Vd147)
| Vd144 != Vd145 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qtd22) ).
fof(f22_nnf,plain,
! [Vd144,Vd145] :
( ! [Vd147] : Vd144 != vplus(Vd145,Vd147)
| Vd144 != Vd145 ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [Vd144,Vd145,Vd147] :
( Vd144 != vplus(Vd145,Vd147)
| Vd144 != Vd145 ),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c32,plain,
( X0 != vplus(X1,X2)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
fof(f23,axiom,
! [Vd127,Vd128] :
~ ? [Vd140,Vd142] :
( Vd127 = vplus(Vd128,Vd140)
& Vd128 = vplus(Vd127,Vd142) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qtd23) ).
fof(f23_nnf,plain,
! [Vd127,Vd128,Vd140,Vd142] :
( Vd127 != vplus(Vd128,Vd140)
| Vd128 != vplus(Vd127,Vd142) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [Vd128,Vd127,Vd142,Vd140] :
( Vd127 != vplus(Vd128,Vd140)
| Vd128 != vplus(Vd127,Vd142) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c33,plain,
( X0 != vplus(X1,X2)
| X1 != vplus(X0,X3) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
fof(f24,axiom,
! [Vd127,Vd128,Vd135,Vd137] :
~ ( Vd127 = vplus(Vd128,Vd135)
& Vd128 = vplus(Vd127,Vd137) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qtd24) ).
fof(f24_nnf,plain,
! [Vd127,Vd128,Vd135,Vd137] :
( Vd127 != vplus(Vd128,Vd135)
| Vd128 != vplus(Vd127,Vd137) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [Vd128,Vd127,Vd137,Vd135] :
( Vd127 != vplus(Vd128,Vd135)
| Vd128 != vplus(Vd127,Vd137) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c34,plain,
( X0 != vplus(X1,X2)
| X1 != vplus(X0,X3) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
fof(f25,axiom,
! [Vd127,Vd128] :
~ ? [Vd133] :
( Vd127 = Vd128
& Vd128 = vplus(Vd127,Vd133) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qtd25) ).
fof(f25_nnf,plain,
! [Vd127,Vd128,Vd133] :
( Vd127 != Vd128
| Vd128 != vplus(Vd127,Vd133) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [Vd128,Vd127,Vd133] :
( Vd127 != Vd128
| Vd128 != vplus(Vd127,Vd133) ),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c35,plain,
( X0 != X1
| X1 != vplus(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
fof(f26,axiom,
! [Vd127,Vd128] :
~ ? [Vd130] :
( Vd127 = Vd128
& Vd127 = vplus(Vd128,Vd130) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qtd26) ).
fof(f26_nnf,plain,
! [Vd127,Vd128,Vd130] :
( Vd127 != Vd128
| Vd127 != vplus(Vd128,Vd130) ),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
! [Vd127,Vd128,Vd130] :
( Vd127 != Vd128
| Vd127 != vplus(Vd128,Vd130) ),
inference(skolemisation,[status(esa)],[f26_nnf]) ).
cnf(c36,plain,
( X0 != X1
| X0 != vplus(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
fof(f28,axiom,
! [Vd92,Vd93] : Vd93 != vplus(Vd92,Vd93),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qtd28) ).
fof(f28_nnf,plain,
! [Vd92,Vd93] : Vd93 != vplus(Vd92,Vd93),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [Vd93,Vd92] : Vd93 != vplus(Vd92,Vd93),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c38,plain,
X1 != vplus(X0,X1),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
fof(f35,axiom,
! [Vd16] : vsucc(Vd16) != Vd16,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qtd35) ).
fof(f35_nnf,plain,
! [Vd16] : vsucc(Vd16) != Vd16,
inference(nnf_transformation,[status(thm)],[f35]) ).
fof(f35_sk,plain,
! [Vd16] : vsucc(Vd16) != Vd16,
inference(skolemisation,[status(esa)],[f35_nnf]) ).
cnf(c46,plain,
vsucc(X0) != X0,
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
fof(f38,axiom,
! [Vd1] : vsucc(Vd1) != v1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qtd38) ).
fof(f38_nnf,plain,
! [Vd1] : vsucc(Vd1) != v1,
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
! [Vd1] : vsucc(Vd1) != v1,
inference(skolemisation,[status(esa)],[f38_nnf]) ).
cnf(c49,plain,
vsucc(X0) != v1,
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c1,c2,c30,c31,c32,c33,c34,c35,c36,c38,c46,c49]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t382]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM835+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n019.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Thu Sep 24 05:32:34 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.86/2.00 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.86/2.00 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------