%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM850+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 02:21:11 PM UTC 2026
% Result : Theorem 6.72s 1.34s
% Output : Proof 6.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 57 ( 29 unt; 0 def)
% Number of atoms : 89 ( 63 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 103 ( 71 ~; 29 |; 2 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 100 ( 8 sgn 66 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f34,axiom,
! [Vd193,Vd194] :
( greater(Vd194,Vd193)
<=> ? [Vd196] : Vd194 = vplus(Vd193,Vd196) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd34) ).
fof(f34_nnf,plain,
! [Vd193,Vd194] :
( ( ! [Vd196] : Vd194 != vplus(Vd193,Vd196)
| greater(Vd194,Vd193) )
& ( ? [Vd196] : Vd194 = vplus(Vd193,Vd196)
| ~ greater(Vd194,Vd193) ) ),
inference(nnf_transformation,[status(thm)],[f34]) ).
fof(f34_sk,plain,
! [Vd194,Vd193,Vd196] :
( ( Vd194 != vplus(Vd193,Vd196)
| greater(Vd194,Vd193) )
& ( Vd194 = vplus(Vd193,sk1(Vd193,Vd194))
| ~ greater(Vd194,Vd193) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f34_nnf]) ).
cnf(c42,plain,
( X1 = vplus(X0,sk1(X0,X1))
| ~ greater(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(hi39,axiom,
ifeq(greater(X0,X1),true,X0,vplus(X1,sk1(X1,X0))) = vplus(X1,sk1(X1,X0)),
inference(equality_encoding,[status(esa)],[c42]) ).
fof(f1,axiom,
greater(vd470,vd471),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd1) ).
fof(f1_nnf,plain,
greater(vd470,vd471),
inference(nnf_transformation,[status(thm)],[f1]) ).
cnf(c1,plain,
greater(vd470,vd471),
inference(cnf_transformation,[status(esa)],[f1_nnf]) ).
cnf(hi0,axiom,
greater(vd470,vd471) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h10,plain,
vd470 = vplus(vd471,sk1(vd471,vd470)),
inference(hyper_resolution,[status(thm)],[hi39,hi0]) ).
fof(f0,conjecture,
? [Vd473] : vd470 = vplus(vd471,Vd473),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd0) ).
fof(f0_neg,negated_conjecture,
~ ? [Vd473] : vd470 = vplus(vd471,Vd473),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
! [Vd473] : vd470 != vplus(vd471,Vd473),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [Vd473] : vd470 != vplus(vd471,Vd473),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
vd470 != vplus(vd471,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi51,negated_conjecture,
ifeq(vd470,vplus(vd471,X0),false,true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi51,h10]) ).
cnf(t265,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
fof(f30,axiom,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| Vd203 != Vd204 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd30) ).
fof(f30_nnf,plain,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| Vd203 != Vd204 ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| Vd203 != Vd204 ),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c37,plain,
( ~ less(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
fof(f31,axiom,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| ~ greater(Vd203,Vd204) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd31) ).
fof(f31_nnf,plain,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| ~ greater(Vd203,Vd204) ),
inference(nnf_transformation,[status(thm)],[f31]) ).
fof(f31_sk,plain,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| ~ greater(Vd203,Vd204) ),
inference(skolemisation,[status(esa)],[f31_nnf]) ).
cnf(c38,plain,
( ~ less(X0,X1)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
fof(f32,axiom,
! [Vd203,Vd204] :
( ~ greater(Vd203,Vd204)
| Vd203 != Vd204 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd32) ).
fof(f32_nnf,plain,
! [Vd203,Vd204] :
( ~ greater(Vd203,Vd204)
| Vd203 != Vd204 ),
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
! [Vd203,Vd204] :
( ~ greater(Vd203,Vd204)
| Vd203 != Vd204 ),
inference(skolemisation,[status(esa)],[f32_nnf]) ).
cnf(c39,plain,
( ~ greater(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
fof(f36,axiom,
! [Vd120,Vd121] :
( ~ ? [Vd125] : Vd121 = vplus(Vd120,Vd125)
| Vd120 != Vd121 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd36) ).
fof(f36_nnf,plain,
! [Vd120,Vd121] :
( ! [Vd125] : Vd121 != vplus(Vd120,Vd125)
| Vd120 != Vd121 ),
inference(nnf_transformation,[status(thm)],[f36]) ).
fof(f36_sk,plain,
! [Vd120,Vd121,Vd125] :
( Vd121 != vplus(Vd120,Vd125)
| Vd120 != Vd121 ),
inference(skolemisation,[status(esa)],[f36_nnf]) ).
cnf(c45,plain,
( X1 != vplus(X0,X2)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
fof(f37,axiom,
! [Vd120,Vd121] :
( ~ ? [Vd125] : Vd121 = vplus(Vd120,Vd125)
| ~ ? [Vd123] : Vd120 = vplus(Vd121,Vd123) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd37) ).
fof(f37_nnf,plain,
! [Vd120,Vd121] :
( ! [Vd125] : Vd121 != vplus(Vd120,Vd125)
| ! [Vd123] : Vd120 != vplus(Vd121,Vd123) ),
inference(nnf_transformation,[status(thm)],[f37]) ).
fof(f37_sk,plain,
! [Vd120,Vd121,Vd123,Vd125] :
( Vd121 != vplus(Vd120,Vd125)
| Vd120 != vplus(Vd121,Vd123) ),
inference(skolemisation,[status(esa)],[f37_nnf]) ).
cnf(c46,plain,
( X1 != vplus(X0,X3)
| X0 != vplus(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f37_sk]) ).
fof(f38,axiom,
! [Vd120,Vd121] :
( ~ ? [Vd123] : Vd120 = vplus(Vd121,Vd123)
| Vd120 != Vd121 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd38) ).
fof(f38_nnf,plain,
! [Vd120,Vd121] :
( ! [Vd123] : Vd120 != vplus(Vd121,Vd123)
| Vd120 != Vd121 ),
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
! [Vd120,Vd121,Vd123] :
( Vd120 != vplus(Vd121,Vd123)
| Vd120 != Vd121 ),
inference(skolemisation,[status(esa)],[f38_nnf]) ).
cnf(c47,plain,
( X0 != vplus(X1,X2)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
fof(f40,axiom,
! [Vd92,Vd93] : Vd93 != vplus(Vd92,Vd93),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd40) ).
fof(f40_nnf,plain,
! [Vd92,Vd93] : Vd93 != vplus(Vd92,Vd93),
inference(nnf_transformation,[status(thm)],[f40]) ).
fof(f40_sk,plain,
! [Vd93,Vd92] : Vd93 != vplus(Vd92,Vd93),
inference(skolemisation,[status(esa)],[f40_nnf]) ).
cnf(c49,plain,
X1 != vplus(X0,X1),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
fof(f47,axiom,
! [Vd16] : vsucc(Vd16) != Vd16,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd47) ).
fof(f47_nnf,plain,
! [Vd16] : vsucc(Vd16) != Vd16,
inference(nnf_transformation,[status(thm)],[f47]) ).
fof(f47_sk,plain,
! [Vd16] : vsucc(Vd16) != Vd16,
inference(skolemisation,[status(esa)],[f47_nnf]) ).
cnf(c57,plain,
vsucc(X0) != X0,
inference(cnf_transformation,[status(esa)],[f47_sk]) ).
fof(f50,axiom,
! [Vd1] : vsucc(Vd1) != v1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd50) ).
fof(f50_nnf,plain,
! [Vd1] : vsucc(Vd1) != v1,
inference(nnf_transformation,[status(thm)],[f50]) ).
fof(f50_sk,plain,
! [Vd1] : vsucc(Vd1) != v1,
inference(skolemisation,[status(esa)],[f50_nnf]) ).
cnf(c60,plain,
vsucc(X0) != v1,
inference(cnf_transformation,[status(esa)],[f50_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c37,c38,c39,c45,c46,c47,c49,c57,c60]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t265]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM850+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % 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 05:34:49 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.72/1.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.72/1.34 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------