%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM318+1 : TPTP v9.3.1. Released v3.1.0.
% 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 02:19:01 PM UTC 2026
% Result : Theorem 11.28s 1.92s
% Output : Proof 11.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 21 unt; 0 def)
% Number of atoms : 52 ( 15 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 46 ( 24 ~; 14 |; 6 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 25 ( 0 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/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(f5,axiom,
rdn_translate(n5,rdn_pos(rdnn(n5))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn5) ).
fof(f5_nnf,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(nnf_transformation,[status(thm)],[f5]) ).
cnf(c5,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(cnf_transformation,[status(esa)],[f5_nnf]) ).
cnf(hi5,axiom,
rdn_translate(n5,rdn_pos(rdnn(n5))) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
fof(f132,axiom,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdnn5) ).
fof(f132_nnf,plain,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
inference(nnf_transformation,[status(thm)],[f132]) ).
cnf(c132,plain,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
inference(cnf_transformation,[status(esa)],[f132_nnf]) ).
cnf(hi132,axiom,
rdn_translate(nn5,rdn_neg(rdnn(n5))) = true,
inference(equality_encoding,[status(esa)],[c132]) ).
cnf(h463,plain,
sum(n5,nn5,n0) = true,
inference(hyper_resolution,[status(thm)],[hi292,hi5,hi132]) ).
fof(f401,conjecture,
sum(n5,nn5,n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_n5_nn5_n0) ).
fof(f401_neg,negated_conjecture,
~ sum(n5,nn5,n0),
inference(negated_conjecture,[status(cth)],[f401]) ).
fof(f401_nnf,plain,
~ sum(n5,nn5,n0),
inference(nnf_transformation,[status(thm)],[f401_neg]) ).
fof(f401_sk,plain,
~ sum(n5,nn5,n0),
inference(skolemisation,[status(esa)],[f401_nnf]) ).
cnf(c406,plain,
~ sum(n5,nn5,n0),
inference(cnf_transformation,[status(esa)],[f401_sk]) ).
cnf(hi406,negated_conjecture,
ifeq(sum(n5,nn5,n0),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c406]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi406,h463]) ).
cnf(t916,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
fof(f283,axiom,
! [X,Y] :
( less(X,Y)
<=> ( Y != X
& ~ less(Y,X) ) ),
file('/export/starexec/sandbox/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,t916]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM318+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 03:35:18 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 11.28/1.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.28/1.92 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------