%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM330+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 : n008.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 02:23:43 PM UTC 2026
% Result : Theorem 7.26s 16.98s
% Output : CNFRefutation 7.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 17 unt; 0 def)
% Number of atoms : 82 ( 9 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 88 ( 42 ~; 36 |; 8 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 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 : 6 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 72 ( 0 sgn 68 !; 4 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
rdn_translate(n4,rdn_pos(rdnn(n4))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdn4) ).
fof(f9,axiom,
rdn_translate(n8,rdn_pos(rdnn(n8))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdn8) ).
fof(f287,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( rdn_translate(X2,rdn_pos(X5))
& rdn_add_with_carry(rdnn(n0),X3,X4,X5)
& rdn_translate(X1,rdn_pos(X4))
& rdn_translate(X0,rdn_pos(X3)) )
=> sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+2.ax',sum_entry_point_pos_pos) ).
fof(f297,axiom,
! [X0,X1,X2,X3,X4] :
( ( rdn_digit_add(rdnn(X4),rdnn(X0),rdnn(X3),rdnn(n0))
& rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X4),rdnn(n0)) )
=> rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+2.ax',add_digit_digit_digit) ).
fof(f346,axiom,
rdn_digit_add(rdnn(n4),rdnn(n4),rdnn(n8),rdnn(n0)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n4_n4_n8_n0) ).
fof(f382,axiom,
rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(n8),rdnn(n0)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n8_n0_n8_n0) ).
fof(f402,conjecture,
? [X0,X1] :
( X1 = n4
& X0 = n4
& sum(X0,X1,n8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_n4_n4_n8) ).
fof(f403,negated_conjecture,
~ ? [X0,X1] :
( X1 = n4
& X0 = n4
& sum(X0,X1,n8) ),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f404,plain,
! [X0,X1] :
( n4 != X1
| n4 != X0
| ~ sum(X0,X1,n8) ),
inference(ennf_transformation,[],[f403]) ).
fof(f421,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ rdn_translate(X2,rdn_pos(X5))
| ~ rdn_add_with_carry(rdnn(n0),X3,X4,X5)
| ~ rdn_translate(X1,rdn_pos(X4))
| ~ rdn_translate(X0,rdn_pos(X3))
| sum(X0,X1,X2) ),
inference(ennf_transformation,[],[f287]) ).
fof(f422,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ rdn_translate(X2,rdn_pos(X5))
| ~ rdn_add_with_carry(rdnn(n0),X3,X4,X5)
| ~ rdn_translate(X1,rdn_pos(X4))
| ~ rdn_translate(X0,rdn_pos(X3))
| sum(X0,X1,X2) ),
inference(flattening,[],[f421]) ).
fof(f439,plain,
! [X0,X1,X2,X3,X4] :
( ~ rdn_digit_add(rdnn(X4),rdnn(X0),rdnn(X3),rdnn(n0))
| ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X4),rdnn(n0))
| rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(X3)) ),
inference(ennf_transformation,[],[f297]) ).
fof(f440,plain,
! [X0,X1,X2,X3,X4] :
( ~ rdn_digit_add(rdnn(X4),rdnn(X0),rdnn(X3),rdnn(n0))
| ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X4),rdnn(n0))
| rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(X3)) ),
inference(flattening,[],[f439]) ).
fof(f448,plain,
! [X0,X1] :
( n4 != X1
| n4 != X0
| ~ sum(X0,X1,n8) ),
inference(cnf_transformation,[],[f404]) ).
fof(f470,plain,
rdn_digit_add(rdnn(n4),rdnn(n4),rdnn(n8),rdnn(n0)),
inference(cnf_transformation,[],[f346]) ).
fof(f482,plain,
rdn_translate(n4,rdn_pos(rdnn(n4))),
inference(cnf_transformation,[],[f5]) ).
fof(f488,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ rdn_translate(X2,rdn_pos(X5))
| ~ rdn_add_with_carry(rdnn(n0),X3,X4,X5)
| ~ rdn_translate(X1,rdn_pos(X4))
| ~ rdn_translate(X0,rdn_pos(X3))
| sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f422]) ).
fof(f498,plain,
rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(n8),rdnn(n0)),
inference(cnf_transformation,[],[f382]) ).
fof(f511,plain,
rdn_translate(n8,rdn_pos(rdnn(n8))),
inference(cnf_transformation,[],[f9]) ).
fof(f589,plain,
! [X2,X3,X0,X1,X4] :
( ~ rdn_digit_add(rdnn(X4),rdnn(X0),rdnn(X3),rdnn(n0))
| ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X4),rdnn(n0))
| rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(X3)) ),
inference(cnf_transformation,[],[f440]) ).
fof(f603,plain,
! [X1] :
( n4 != X1
| ~ sum(n4,X1,n8) ),
inference(equality_resolution,[],[f448]) ).
fof(f604,plain,
~ sum(n4,n4,n8),
inference(equality_resolution,[],[f603]) ).
tcf(c_49,negated_conjecture,
~ sum(n4,n4,n8),
inference(cnf_transformation,[],[f604]) ).
tcf(c_71,plain,
rdn_digit_add(rdnn(n4),rdnn(n4),rdnn(n8),rdnn(n0)),
inference(cnf_transformation,[],[f470]) ).
tcf(c_83,plain,
rdn_translate(n4,rdn_pos(rdnn(n4))),
inference(cnf_transformation,[],[f482]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sum(X5,X3,X4)
| ~ rdn_translate(X5,rdn_pos(X0))
| ~ rdn_translate(X4,rdn_pos(X2))
| ~ rdn_translate(X3,rdn_pos(X1))
| ~ rdn_add_with_carry(rdnn(n0),X0,X1,X2) ),
inference(cnf_transformation,[],[f488]) ).
tcf(c_99,plain,
rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(n8),rdnn(n0)),
inference(cnf_transformation,[],[f498]) ).
tcf(c_112,plain,
rdn_translate(n8,rdn_pos(rdnn(n8))),
inference(cnf_transformation,[],[f511]) ).
tcf(c_190,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( rdn_add_with_carry(rdnn(X3),rdnn(X0),rdnn(X1),rdnn(X4))
| ~ rdn_digit_add(rdnn(X2),rdnn(X3),rdnn(X4),rdnn(n0))
| ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(n0)) ),
inference(cnf_transformation,[],[f589]) ).
tcf(c_3551,plain,
! [X0: $i,X1: $i] :
( rdn_add_with_carry(rdnn(X0),rdnn(n4),rdnn(n4),rdnn(X1))
| ~ rdn_digit_add(rdnn(n8),rdnn(X0),rdnn(X1),rdnn(n0)) ),
inference(superposition,[status(thm)],[c_71,c_190]) ).
tcf(c_8598,plain,
rdn_add_with_carry(rdnn(n0),rdnn(n4),rdnn(n4),rdnn(n8)),
inference(superposition,[status(thm)],[c_99,c_3551]) ).
tcf(c_8610,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X2,X0,X1)
| ~ rdn_translate(X2,rdn_pos(rdnn(n4)))
| ~ rdn_translate(X1,rdn_pos(rdnn(n8)))
| ~ rdn_translate(X0,rdn_pos(rdnn(n4))) ),
inference(superposition,[status(thm)],[c_8598,c_89]) ).
tcf(c_13858,plain,
! [X0: $i,X1: $i] :
( sum(n4,X0,X1)
| ~ rdn_translate(X1,rdn_pos(rdnn(n8)))
| ~ rdn_translate(X0,rdn_pos(rdnn(n4))) ),
inference(superposition,[status(thm)],[c_83,c_8610]) ).
tcf(c_13869,plain,
! [X0: $i] :
( sum(n4,X0,n8)
| ~ rdn_translate(X0,rdn_pos(rdnn(n4))) ),
inference(superposition,[status(thm)],[c_112,c_13858]) ).
tcf(c_13877,plain,
sum(n4,n4,n8),
inference(superposition,[status(thm)],[c_83,c_13869]) ).
tcf(c_13878,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_13877,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM330+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/15.59 % Computer : n008.cluster.edu
% 0.09/15.59 % Model : x86_64 x86_64
% 0.09/15.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/15.59 % Memory : 8046.5625MB
% 0.09/15.59 % OS : Linux 6.8.0-71-generic
% 0.09/15.59 % CPULimit : 300
% 0.09/15.59 % WCLimit : 300
% 0.09/15.59 % DateTime : Thu Sep 24 03:37:40 UTC 2026
% 0.14/15.60 % CPUTime :
% 0.14/15.60 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/15.64 Running first-order theorem proving
% 0.14/15.64 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
% 0.14/15.65
% 0.14/15.65 % ======== iProver multi-core TPTP/SMT =========
% 0.14/15.65
% 0.14/15.65 % Detected problem language: tptp
% 0.14/15.66 % Proving...
% 7.26/16.98 % SZS status Started for theBenchmark.p
% 7.26/16.98 % SZS status Theorem for theBenchmark.p
% 7.26/16.98
% 7.26/16.98 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.26/16.98
% 7.26/16.98 % ------ iProver source info
% 7.26/16.98
% 7.26/16.98 % git: date: 2026-07-19 20:42:38 +0200
% 7.26/16.98 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.26/16.98 % git: non_committed_changes: false
% 7.26/16.98
% 7.26/16.98 % ------ Parsing...
% 7.26/16.98 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.26/16.98
% 7.26/16.98 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 7.26/16.98
% 7.26/16.98 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.26/16.98
% 7.26/16.98 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.26/16.98 % ------ Proving...
% 7.26/16.98 % ------ Problem Properties
% 7.26/16.98
% 7.26/16.98 %
% 7.26/16.98 % clauses 155
% 7.26/16.98 % conjectures 1
% 7.26/16.98 % EPR 7
% 7.26/16.98 % Horn 154
% 7.26/16.98 % unary 130
% 7.26/16.98 % binary 6
% 7.26/16.98 % lits 222
% 7.26/16.98 % lits eq 4
% 7.26/16.98 % fd_pure 0
% 7.26/16.98 % fd_pseudo 0
% 7.26/16.98 % fd_cond 0
% 7.26/16.98 % fd_pseudo_cond 4
% 7.26/16.98 % AC symbols 0
% 7.26/16.98
% 7.26/16.98 % ------ Schedule dynamic 5 is on
% 7.26/16.98
% 7.26/16.98 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.26/16.98
% 7.26/16.98
% 7.26/16.98 % ------
% 7.26/16.98 % Current options:
% 7.26/16.98 % ------
% 7.26/16.98
% 7.26/16.98
% 7.26/16.98 %
% 7.26/16.98
% 7.26/16.98 % ------ Proving...
% 7.26/16.98 %
% 7.26/16.98
% 7.26/16.98 % SZS status Theorem for theBenchmark.p
% 7.26/16.98
% 7.26/16.98 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.26/16.98
% 7.26/16.98
%------------------------------------------------------------------------------