%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM838+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 : n002.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 6.88s 6.38s
% Output : Proof 6.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 45 ( 17 unt; 0 def)
% Number of atoms : 73 ( 40 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 85 ( 57 ~; 27 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 80 ( 4 sgn 53 !; 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(h7,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(hi26,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)],[hi26,h7]) ).
cnf(t1511,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
fof(f17,axiom,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| Vd203 != Vd204 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd17) ).
fof(f17_nnf,plain,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| Vd203 != Vd204 ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| Vd203 != Vd204 ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
( ~ less(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
fof(f18,axiom,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| ~ greater(Vd203,Vd204) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd18) ).
fof(f18_nnf,plain,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| ~ greater(Vd203,Vd204) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| ~ greater(Vd203,Vd204) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( ~ less(X0,X1)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
fof(f19,axiom,
! [Vd203,Vd204] :
( ~ greater(Vd203,Vd204)
| Vd203 != Vd204 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd19) ).
fof(f19_nnf,plain,
! [Vd203,Vd204] :
( ~ greater(Vd203,Vd204)
| Vd203 != Vd204 ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [Vd203,Vd204] :
( ~ greater(Vd203,Vd204)
| Vd203 != Vd204 ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( ~ greater(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
fof(f23,axiom,
! [Vd120,Vd121] :
( ~ ? [Vd125] : Vd121 = vplus(Vd120,Vd125)
| Vd120 != Vd121 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd23) ).
fof(f23_nnf,plain,
! [Vd120,Vd121] :
( ! [Vd125] : Vd121 != vplus(Vd120,Vd125)
| Vd120 != Vd121 ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [Vd120,Vd121,Vd125] :
( Vd121 != vplus(Vd120,Vd125)
| Vd120 != Vd121 ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c25,plain,
( X1 != vplus(X0,X2)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
fof(f24,axiom,
! [Vd120,Vd121] :
( ~ ? [Vd125] : Vd121 = vplus(Vd120,Vd125)
| ~ ? [Vd123] : Vd120 = vplus(Vd121,Vd123) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd24) ).
fof(f24_nnf,plain,
! [Vd120,Vd121] :
( ! [Vd125] : Vd121 != vplus(Vd120,Vd125)
| ! [Vd123] : Vd120 != vplus(Vd121,Vd123) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [Vd120,Vd121,Vd123,Vd125] :
( Vd121 != vplus(Vd120,Vd125)
| Vd120 != vplus(Vd121,Vd123) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c26,plain,
( X1 != vplus(X0,X3)
| X0 != vplus(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
fof(f25,axiom,
! [Vd120,Vd121] :
( ~ ? [Vd123] : Vd120 = vplus(Vd121,Vd123)
| Vd120 != Vd121 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd25) ).
fof(f25_nnf,plain,
! [Vd120,Vd121] :
( ! [Vd123] : Vd120 != vplus(Vd121,Vd123)
| Vd120 != Vd121 ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [Vd120,Vd121,Vd123] :
( Vd120 != vplus(Vd121,Vd123)
| Vd120 != Vd121 ),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c27,plain,
( X0 != vplus(X1,X2)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c17,c18,c19,c25,c26,c27]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1511]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM838+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/5.37 % Computer : n002.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Thu Sep 24 05:35:41 UTC 2026
% 0.11/5.37 % CPUTime :
% 0.11/5.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.88/6.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.88/6.38 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------