%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM344+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n006.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 02:19:03 PM UTC 2026
% Result : Theorem 10.64s 1.84s
% Output : Proof 10.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 46 ( 24 unt; 0 def)
% Number of atoms : 93 ( 20 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 89 ( 42 ~; 32 |; 11 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 82 ( 8 sgn 46 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f281,axiom,
! [X,Y,RDN_X,RDN_Y] :
( ( rdn_translate(Y,rdn_pos(RDN_Y))
& rdn_translate(X,rdn_neg(RDN_X)) )
=> less(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_entry_point_neg_pos) ).
fof(f281_nnf,plain,
! [X,Y,RDN_X,RDN_Y] :
( less(X,Y)
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(X,rdn_neg(RDN_X)) ),
inference(nnf_transformation,[status(thm)],[f281]) ).
fof(f281_sk,plain,
! [X,RDN_X,Y,RDN_Y] :
( less(X,Y)
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(X,rdn_neg(RDN_X)) ),
inference(skolemisation,[status(esa)],[f281_nnf]) ).
cnf(c281,plain,
( less(X0,X1)
| ~ rdn_translate(X1,rdn_pos(X3))
| ~ rdn_translate(X0,rdn_neg(X2)) ),
inference(cnf_transformation,[status(esa)],[f281_sk]) ).
cnf(hi281,axiom,
ifeq(rdn_translate(X0,rdn_neg(X1)),true,ifeq(rdn_translate(X2,rdn_pos(X3)),true,less(X0,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c281]) ).
fof(f128,axiom,
rdn_translate(nn1,rdn_neg(rdnn(n1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdnn1) ).
fof(f128_nnf,plain,
rdn_translate(nn1,rdn_neg(rdnn(n1))),
inference(nnf_transformation,[status(thm)],[f128]) ).
cnf(c128,plain,
rdn_translate(nn1,rdn_neg(rdnn(n1))),
inference(cnf_transformation,[status(esa)],[f128_nnf]) ).
cnf(hi128,axiom,
rdn_translate(nn1,rdn_neg(rdnn(n1))) = true,
inference(equality_encoding,[status(esa)],[c128]) ).
fof(f0,axiom,
rdn_translate(n0,rdn_pos(rdnn(n0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn0) ).
fof(f0_nnf,plain,
rdn_translate(n0,rdn_pos(rdnn(n0))),
inference(nnf_transformation,[status(thm)],[f0]) ).
cnf(c0,plain,
rdn_translate(n0,rdn_pos(rdnn(n0))),
inference(cnf_transformation,[status(esa)],[f0_nnf]) ).
cnf(hi0,axiom,
rdn_translate(n0,rdn_pos(rdnn(n0))) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h119,plain,
less(nn1,n0) = true,
inference(hyper_resolution,[status(thm)],[hi281,hi128,hi0]) ).
fof(f290,axiom,
! [POS_X,NEG_X,RDN_X] :
( ( rdn_translate(NEG_X,rdn_neg(RDN_X))
& rdn_translate(POS_X,rdn_pos(RDN_X)) )
=> sum(POS_X,NEG_X,n0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_entry_point_posx_negx) ).
fof(f290_nnf,plain,
! [POS_X,NEG_X,RDN_X] :
( sum(POS_X,NEG_X,n0)
| ~ rdn_translate(NEG_X,rdn_neg(RDN_X))
| ~ rdn_translate(POS_X,rdn_pos(RDN_X)) ),
inference(nnf_transformation,[status(thm)],[f290]) ).
fof(f290_sk,plain,
! [POS_X,RDN_X,NEG_X] :
( sum(POS_X,NEG_X,n0)
| ~ rdn_translate(NEG_X,rdn_neg(RDN_X))
| ~ rdn_translate(POS_X,rdn_pos(RDN_X)) ),
inference(skolemisation,[status(esa)],[f290_nnf]) ).
cnf(c294,plain,
( sum(X0,X1,n0)
| ~ rdn_translate(X1,rdn_neg(X2))
| ~ rdn_translate(X0,rdn_pos(X2)) ),
inference(cnf_transformation,[status(esa)],[f290_sk]) ).
cnf(hi292,axiom,
ifeq(rdn_translate(X0,rdn_pos(X1)),true,ifeq(rdn_translate(X2,rdn_neg(X1)),true,sum(X0,X2,n0),true),true) = true,
inference(equality_encoding,[status(esa)],[c294]) ).
fof(f1,axiom,
rdn_translate(n1,rdn_pos(rdnn(n1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn1) ).
fof(f1_nnf,plain,
rdn_translate(n1,rdn_pos(rdnn(n1))),
inference(nnf_transformation,[status(thm)],[f1]) ).
cnf(c1,plain,
rdn_translate(n1,rdn_pos(rdnn(n1))),
inference(cnf_transformation,[status(esa)],[f1_nnf]) ).
cnf(hi1,axiom,
rdn_translate(n1,rdn_pos(rdnn(n1))) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h109,plain,
sum(n1,nn1,n0) = true,
inference(hyper_resolution,[status(thm)],[hi292,hi1,hi128]) ).
fof(f291,axiom,
! [X,Y,Z,RDN_X,RDN_Y] :
( ( sum(Y,X,Z)
& rdn_translate(Y,rdn_pos(RDN_Y))
& rdn_translate(X,rdn_neg(RDN_X)) )
=> sum(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_entry_point_neg_pos) ).
fof(f291_nnf,plain,
! [X,Y,Z,RDN_X,RDN_Y] :
( sum(X,Y,Z)
| ~ sum(Y,X,Z)
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(X,rdn_neg(RDN_X)) ),
inference(nnf_transformation,[status(thm)],[f291]) ).
fof(f291_sk,plain,
! [X,RDN_X,Y,RDN_Y,Z] :
( sum(X,Y,Z)
| ~ sum(Y,X,Z)
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(X,rdn_neg(RDN_X)) ),
inference(skolemisation,[status(esa)],[f291_nnf]) ).
cnf(c295,plain,
( sum(X0,X1,X2)
| ~ sum(X1,X0,X2)
| ~ rdn_translate(X1,rdn_pos(X4))
| ~ rdn_translate(X0,rdn_neg(X3)) ),
inference(cnf_transformation,[status(esa)],[f291_sk]) ).
cnf(hi293,axiom,
ifeq(rdn_translate(X0,rdn_neg(X1)),true,ifeq(rdn_translate(X2,rdn_pos(X3)),true,ifeq(sum(X2,X0,X4),true,sum(X0,X2,X4),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c295]) ).
cnf(h183,plain,
sum(nn1,n1,n0) = true,
inference(hyper_resolution,[status(thm)],[hi293,hi128,hi1,h109]) ).
fof(f401,conjecture,
? [X,Y] :
( less(X,Y)
& sum(X,n1,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exist_bigger_plus_one) ).
fof(f401_neg,negated_conjecture,
~ ? [X,Y] :
( less(X,Y)
& sum(X,n1,Y) ),
inference(negated_conjecture,[status(cth)],[f401]) ).
fof(f401_nnf,plain,
! [X,Y] :
( ~ less(X,Y)
| ~ sum(X,n1,Y) ),
inference(nnf_transformation,[status(thm)],[f401_neg]) ).
fof(f401_sk,plain,
! [X,Y] :
( ~ less(X,Y)
| ~ sum(X,n1,Y) ),
inference(skolemisation,[status(esa)],[f401_nnf]) ).
cnf(c406,plain,
( ~ less(X0,X1)
| ~ sum(X0,n1,X1) ),
inference(cnf_transformation,[status(esa)],[f401_sk]) ).
cnf(hi406,negated_conjecture,
ifeq(sum(X0,n1,X1),true,ifeq(less(X0,X1),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c406]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi406,h183,h119]) ).
cnf(t384,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
fof(f283,axiom,
! [X,Y] :
( less(X,Y)
<=> ( Y != X
& ~ less(Y,X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_property) ).
fof(f283_nnf,plain,
! [X,Y] :
( ( Y = X
| less(Y,X)
| less(X,Y) )
& ( ( Y != X
& ~ less(Y,X) )
| ~ less(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f283]) ).
fof(f283_sk,plain,
! [X,Y] :
( ( Y = X
| less(Y,X)
| less(X,Y) )
& ( ( Y != X
& ~ less(Y,X) )
| ~ less(X,Y) ) ),
inference(skolemisation,[status(esa)],[f283_nnf]) ).
cnf(c283,plain,
( ~ less(X1,X0)
| ~ less(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f283_sk]) ).
cnf(c284,plain,
( X1 != X0
| ~ less(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f283_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c283,c284,c406]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t384]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM344+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.36 % Computer : n006.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Thu Sep 24 03:39:11 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 10.64/1.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.64/1.84 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------