%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM837+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 : n014.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 11.55s 2.07s
% Output : Proof 11.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 45 ( 17 unt; 0 def)
% Number of atoms : 77 ( 51 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 91 ( 59 ~; 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 : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 84 ( 6 sgn 54 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13,axiom,
! [Vd198,Vd199] :
( less(Vd199,Vd198)
<=> ? [Vd201] : Vd198 = vplus(Vd199,Vd201) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd13) ).
fof(f13_nnf,plain,
! [Vd198,Vd199] :
( ( ! [Vd201] : Vd198 != vplus(Vd199,Vd201)
| less(Vd199,Vd198) )
& ( ? [Vd201] : Vd198 = vplus(Vd199,Vd201)
| ~ less(Vd199,Vd198) ) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [Vd199,Vd198,Vd201] :
( ( Vd198 != vplus(Vd199,Vd201)
| less(Vd199,Vd198) )
& ( Vd198 = vplus(Vd199,sk0(Vd198,Vd199))
| ~ less(Vd199,Vd198) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f13_nnf]) ).
cnf(c17,plain,
( X0 = vplus(X1,sk0(X0,X1))
| ~ less(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi13,axiom,
ifeq(less(X0,X1),true,X1,vplus(X0,sk0(X1,X0))) = vplus(X0,sk0(X1,X0)),
inference(equality_encoding,[status(esa)],[c17]) ).
fof(f2,axiom,
less(vd268,vd269),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd2) ).
fof(f2_nnf,plain,
less(vd268,vd269),
inference(nnf_transformation,[status(thm)],[f2]) ).
cnf(c2,plain,
less(vd268,vd269),
inference(cnf_transformation,[status(esa)],[f2_nnf]) ).
cnf(hi1,axiom,
less(vd268,vd269) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h15,plain,
vd269 = vplus(vd268,sk0(vd269,vd268)),
inference(hyper_resolution,[status(thm)],[hi13,hi1]) ).
fof(f0,conjecture,
? [Vd273] : vd269 = vplus(vd268,Vd273),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd0) ).
fof(f0_neg,negated_conjecture,
~ ? [Vd273] : vd269 = vplus(vd268,Vd273),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
! [Vd273] : vd269 != vplus(vd268,Vd273),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [Vd273] : vd269 != vplus(vd268,Vd273),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
vd269 != vplus(vd268,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi22,negated_conjecture,
ifeq(vd269,vplus(vd268,X0),false,true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi22,h15]) ).
cnf(t292,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
fof(f10,axiom,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| Vd203 != Vd204 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd10) ).
fof(f10_nnf,plain,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| Vd203 != Vd204 ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| Vd203 != Vd204 ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c14,plain,
( ~ less(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
fof(f11,axiom,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| ~ greater(Vd203,Vd204) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd11) ).
fof(f11_nnf,plain,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| ~ greater(Vd203,Vd204) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| ~ greater(Vd203,Vd204) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c15,plain,
( ~ less(X0,X1)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
fof(f12,axiom,
! [Vd203,Vd204] :
( ~ greater(Vd203,Vd204)
| Vd203 != Vd204 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd12) ).
fof(f12_nnf,plain,
! [Vd203,Vd204] :
( ~ greater(Vd203,Vd204)
| Vd203 != Vd204 ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [Vd203,Vd204] :
( ~ greater(Vd203,Vd204)
| Vd203 != Vd204 ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c16,plain,
( ~ greater(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
fof(f16,axiom,
! [Vd120,Vd121] :
( ~ ? [Vd125] : Vd121 = vplus(Vd120,Vd125)
| Vd120 != Vd121 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd16) ).
fof(f16_nnf,plain,
! [Vd120,Vd121] :
( ! [Vd125] : Vd121 != vplus(Vd120,Vd125)
| Vd120 != Vd121 ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [Vd120,Vd121,Vd125] :
( Vd121 != vplus(Vd120,Vd125)
| Vd120 != Vd121 ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c22,plain,
( X1 != vplus(X0,X2)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
fof(f17,axiom,
! [Vd120,Vd121] :
( ~ ? [Vd125] : Vd121 = vplus(Vd120,Vd125)
| ~ ? [Vd123] : Vd120 = vplus(Vd121,Vd123) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd17) ).
fof(f17_nnf,plain,
! [Vd120,Vd121] :
( ! [Vd125] : Vd121 != vplus(Vd120,Vd125)
| ! [Vd123] : Vd120 != vplus(Vd121,Vd123) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [Vd120,Vd121,Vd123,Vd125] :
( Vd121 != vplus(Vd120,Vd125)
| Vd120 != vplus(Vd121,Vd123) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c23,plain,
( X1 != vplus(X0,X3)
| X0 != vplus(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
fof(f18,axiom,
! [Vd120,Vd121] :
( ~ ? [Vd123] : Vd120 = vplus(Vd121,Vd123)
| Vd120 != Vd121 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd18) ).
fof(f18_nnf,plain,
! [Vd120,Vd121] :
( ! [Vd123] : Vd120 != vplus(Vd121,Vd123)
| Vd120 != Vd121 ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [Vd120,Vd121,Vd123] :
( Vd120 != vplus(Vd121,Vd123)
| Vd120 != Vd121 ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c24,plain,
( X0 != vplus(X1,X2)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c14,c15,c16,c22,c23,c24]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t292]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM837+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n014.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 05:32:33 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 11.55/2.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.55/2.07 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------