%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM838+1 : 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 02:21:08 PM UTC 2026
% Result : Theorem 8.04s 1.59s
% Output : Proof 8.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 57 ( 29 unt; 0 def)
% Number of atoms : 85 ( 52 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 97 ( 69 ~; 27 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-4 aty)
% Number of variables : 96 ( 6 sgn 65 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [Vd310,Vd311,Vd312] :
( greater(Vd311,Vd312)
=> greater(vplus(Vd311,Vd310),vplus(Vd312,Vd310)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd6) ).
fof(f6_nnf,plain,
! [Vd310,Vd311,Vd312] :
( greater(vplus(Vd311,Vd310),vplus(Vd312,Vd310))
| ~ greater(Vd311,Vd312) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [Vd311,Vd312,Vd310] :
( greater(vplus(Vd311,Vd310),vplus(Vd312,Vd310))
| ~ greater(Vd311,Vd312) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( greater(vplus(X1,X0),vplus(X2,X0))
| ~ greater(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi5,axiom,
ifeq(greater(X0,X1),true,greater(vplus(X0,X2),vplus(X1,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
fof(f1,axiom,
greater(vd301,vd302),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd1) ).
fof(f1_nnf,plain,
greater(vd301,vd302),
inference(nnf_transformation,[status(thm)],[f1]) ).
cnf(c1,plain,
greater(vd301,vd302),
inference(cnf_transformation,[status(esa)],[f1_nnf]) ).
cnf(hi0,axiom,
greater(vd301,vd302) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h16,plain,
greater(vplus(vd301,V0),vplus(vd302,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi5,hi0]) ).
fof(f0,conjecture,
greater(vplus(vd301,vd303),vplus(vd302,vd303)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd0) ).
fof(f0_neg,negated_conjecture,
~ greater(vplus(vd301,vd303),vplus(vd302,vd303)),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
~ greater(vplus(vd301,vd303),vplus(vd302,vd303)),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
~ greater(vplus(vd301,vd303),vplus(vd302,vd303)),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
~ greater(vplus(vd301,vd303),vplus(vd302,vd303)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi42,negated_conjecture,
ifeq(greater(vplus(vd301,vd303),vplus(vd302,vd303)),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi42,h16]) ).
cnf(t262,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
fof(f23,axiom,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| Vd203 != Vd204 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd23) ).
fof(f23_nnf,plain,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| Vd203 != Vd204 ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| Vd203 != Vd204 ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c28,plain,
( ~ less(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
fof(f24,axiom,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| ~ greater(Vd203,Vd204) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd24) ).
fof(f24_nnf,plain,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| ~ greater(Vd203,Vd204) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| ~ greater(Vd203,Vd204) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c29,plain,
( ~ less(X0,X1)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
fof(f25,axiom,
! [Vd203,Vd204] :
( ~ greater(Vd203,Vd204)
| Vd203 != Vd204 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd25) ).
fof(f25_nnf,plain,
! [Vd203,Vd204] :
( ~ greater(Vd203,Vd204)
| Vd203 != Vd204 ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [Vd203,Vd204] :
( ~ greater(Vd203,Vd204)
| Vd203 != Vd204 ),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c30,plain,
( ~ greater(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
fof(f29,axiom,
! [Vd120,Vd121] :
( ~ ? [Vd125] : Vd121 = vplus(Vd120,Vd125)
| Vd120 != Vd121 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd29) ).
fof(f29_nnf,plain,
! [Vd120,Vd121] :
( ! [Vd125] : Vd121 != vplus(Vd120,Vd125)
| Vd120 != Vd121 ),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [Vd120,Vd121,Vd125] :
( Vd121 != vplus(Vd120,Vd125)
| Vd120 != Vd121 ),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c36,plain,
( X1 != vplus(X0,X2)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
fof(f30,axiom,
! [Vd120,Vd121] :
( ~ ? [Vd125] : Vd121 = vplus(Vd120,Vd125)
| ~ ? [Vd123] : Vd120 = vplus(Vd121,Vd123) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd30) ).
fof(f30_nnf,plain,
! [Vd120,Vd121] :
( ! [Vd125] : Vd121 != vplus(Vd120,Vd125)
| ! [Vd123] : Vd120 != vplus(Vd121,Vd123) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [Vd120,Vd121,Vd123,Vd125] :
( Vd121 != vplus(Vd120,Vd125)
| Vd120 != vplus(Vd121,Vd123) ),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c37,plain,
( X1 != vplus(X0,X3)
| X0 != vplus(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
fof(f31,axiom,
! [Vd120,Vd121] :
( ~ ? [Vd123] : Vd120 = vplus(Vd121,Vd123)
| Vd120 != Vd121 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd31) ).
fof(f31_nnf,plain,
! [Vd120,Vd121] :
( ! [Vd123] : Vd120 != vplus(Vd121,Vd123)
| Vd120 != Vd121 ),
inference(nnf_transformation,[status(thm)],[f31]) ).
fof(f31_sk,plain,
! [Vd120,Vd121,Vd123] :
( Vd120 != vplus(Vd121,Vd123)
| Vd120 != Vd121 ),
inference(skolemisation,[status(esa)],[f31_nnf]) ).
cnf(c38,plain,
( X0 != vplus(X1,X2)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
fof(f33,axiom,
! [Vd92,Vd93] : Vd93 != vplus(Vd92,Vd93),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd33) ).
fof(f33_nnf,plain,
! [Vd92,Vd93] : Vd93 != vplus(Vd92,Vd93),
inference(nnf_transformation,[status(thm)],[f33]) ).
fof(f33_sk,plain,
! [Vd93,Vd92] : Vd93 != vplus(Vd92,Vd93),
inference(skolemisation,[status(esa)],[f33_nnf]) ).
cnf(c40,plain,
X1 != vplus(X0,X1),
inference(cnf_transformation,[status(esa)],[f33_sk]) ).
fof(f40,axiom,
! [Vd16] : vsucc(Vd16) != Vd16,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd40) ).
fof(f40_nnf,plain,
! [Vd16] : vsucc(Vd16) != Vd16,
inference(nnf_transformation,[status(thm)],[f40]) ).
fof(f40_sk,plain,
! [Vd16] : vsucc(Vd16) != Vd16,
inference(skolemisation,[status(esa)],[f40_nnf]) ).
cnf(c48,plain,
vsucc(X0) != X0,
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
fof(f43,axiom,
! [Vd1] : vsucc(Vd1) != v1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd43) ).
fof(f43_nnf,plain,
! [Vd1] : vsucc(Vd1) != v1,
inference(nnf_transformation,[status(thm)],[f43]) ).
fof(f43_sk,plain,
! [Vd1] : vsucc(Vd1) != v1,
inference(skolemisation,[status(esa)],[f43_nnf]) ).
cnf(c51,plain,
vsucc(X0) != v1,
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c28,c29,c30,c36,c37,c38,c40,c48,c51]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t262]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM838+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n019.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 05:32:49 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 8.04/1.59 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.04/1.59 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------