%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM318+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n011.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 02:23:41 PM UTC 2026
% Result : Theorem 3.74s 1.28s
% Output : CNFRefutation 3.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 12 unt; 0 def)
% Number of atoms : 33 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 16 ~; 12 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-1 aty)
% Number of variables : 16 ( 0 sgn 16 !; 0 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
rdn_translate(n5,rdn_pos(rdnn(n5))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdn5) ).
fof(f133,axiom,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdnn5) ).
fof(f291,axiom,
! [X0,X1,X2] :
( ( rdn_translate(X1,rdn_neg(X2))
& rdn_translate(X0,rdn_pos(X2)) )
=> sum(X0,X1,n0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+2.ax',sum_entry_point_posx_negx) ).
fof(f402,conjecture,
sum(n5,nn5,n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_n5_nn5_n0) ).
fof(f403,negated_conjecture,
~ sum(n5,nn5,n0),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f404,plain,
~ sum(n5,nn5,n0),
inference(flattening,[],[f403]) ).
fof(f407,plain,
! [X0,X1,X2] :
( ~ rdn_translate(X1,rdn_neg(X2))
| ~ rdn_translate(X0,rdn_pos(X2))
| sum(X0,X1,n0) ),
inference(ennf_transformation,[],[f291]) ).
fof(f408,plain,
! [X0,X1,X2] :
( ~ rdn_translate(X1,rdn_neg(X2))
| ~ rdn_translate(X0,rdn_pos(X2))
| sum(X0,X1,n0) ),
inference(flattening,[],[f407]) ).
fof(f434,plain,
~ sum(n5,nn5,n0),
inference(cnf_transformation,[],[f404]) ).
fof(f443,plain,
! [X2,X0,X1] :
( ~ rdn_translate(X1,rdn_neg(X2))
| ~ rdn_translate(X0,rdn_pos(X2))
| sum(X0,X1,n0) ),
inference(cnf_transformation,[],[f408]) ).
fof(f475,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(cnf_transformation,[],[f6]) ).
fof(f476,plain,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
inference(cnf_transformation,[],[f133]) ).
tcf(c_49,negated_conjecture,
~ sum(n5,nn5,n0),
inference(cnf_transformation,[],[f434]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X0,X2,n0)
| ~ rdn_translate(X2,rdn_neg(X1))
| ~ rdn_translate(X0,rdn_pos(X1)) ),
inference(cnf_transformation,[],[f443]) ).
tcf(c_90,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(cnf_transformation,[],[f475]) ).
tcf(c_91,plain,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
inference(cnf_transformation,[],[f476]) ).
tcf(c_1040,plain,
! [X0: $i] :
( sum(n5,X0,n0)
| ~ rdn_translate(n5,rdn_pos(rdnn(n5)))
| ~ rdn_translate(X0,rdn_neg(rdnn(n5))) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_1275,plain,
( sum(n5,nn5,n0)
| ~ rdn_translate(nn5,rdn_neg(rdnn(n5)))
| ~ rdn_translate(n5,rdn_pos(rdnn(n5))) ),
inference(instantiation,[status(thm)],[c_1040]) ).
tcf(c_1276,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1275,c_90,c_91,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM318+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.37 % Computer : n011.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Thu Sep 24 03:35:29 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.40 Running first-order theorem proving
% 0.08/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.41
% 0.08/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.41
% 0.08/0.42 % Detected problem language: tptp
% 0.08/0.43 % Proving...
% 3.74/1.28 % SZS status Started for theBenchmark.p
% 3.74/1.28 % SZS status Theorem for theBenchmark.p
% 3.74/1.28
% 3.74/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.74/1.28
% 3.74/1.28 % ------ iProver source info
% 3.74/1.28
% 3.74/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 3.74/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.74/1.28 % git: non_committed_changes: false
% 3.74/1.28
% 3.74/1.28 % ------ Parsing...
% 3.74/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.74/1.28
% 3.74/1.28 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.74/1.28
% 3.74/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.74/1.28 % ------ Proving...
% 3.74/1.28 % ------ Problem Properties
% 3.74/1.28
% 3.74/1.28 %
% 3.74/1.28 % clauses 146
% 3.74/1.28 % conjectures 1
% 3.74/1.28 % EPR 1
% 3.74/1.28 % Horn 146
% 3.74/1.28 % unary 130
% 3.74/1.28 % binary 4
% 3.74/1.28 % lits 195
% 3.74/1.28 % lits eq 0
% 3.74/1.28 % fd_pure 0
% 3.74/1.28 % fd_pseudo 0
% 3.74/1.28 % fd_cond 0
% 3.74/1.28 % fd_pseudo_cond 0
% 3.74/1.28 % AC symbols 0
% 3.74/1.28
% 3.74/1.28 % ------ Schedule dynamic 5 is on
% 3.74/1.28
% 3.74/1.28 % ------ no equalities: superposition off
% 3.74/1.28
% 3.74/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.74/1.28
% 3.74/1.28
% 3.74/1.28 % ------
% 3.74/1.28 % Current options:
% 3.74/1.28 % ------
% 3.74/1.28
% 3.74/1.28
% 3.74/1.28 %
% 3.74/1.28
% 3.74/1.28 % ------ Proving...
% 3.74/1.28 %
% 3.74/1.28
% 3.74/1.28 % SZS status Theorem for theBenchmark.p
% 3.74/1.28
% 3.74/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.74/1.28
% 3.74/1.28
%------------------------------------------------------------------------------