%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM329+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 : n003.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 4.41s 1.34s
% Output : CNFRefutation 4.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 12 unt; 0 def)
% Number of atoms : 67 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 82 ( 42 ~; 34 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 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 : 5 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 67 ( 0 sgn 65 !; 2 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
rdn_translate(n0,rdn_pos(rdnn(n0))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdn0) ).
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(f302,axiom,
rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n0_n0_n0_n0) ).
fof(f402,conjecture,
? [X0] : sum(X0,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotent_element) ).
fof(f403,negated_conjecture,
~ ? [X0] : sum(X0,X0,X0),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f404,plain,
! [X0] : ~ sum(X0,X0,X0),
inference(ennf_transformation,[],[f403]) ).
fof(f415,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(f416,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,[],[f415]) ).
fof(f427,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(f428,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,[],[f427]) ).
fof(f434,plain,
! [X0] : ~ sum(X0,X0,X0),
inference(cnf_transformation,[],[f404]) ).
fof(f440,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,[],[f416]) ).
fof(f442,plain,
rdn_translate(n0,rdn_pos(rdnn(n0))),
inference(cnf_transformation,[],[f1]) ).
fof(f448,plain,
rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)),
inference(cnf_transformation,[],[f302]) ).
fof(f464,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,[],[f428]) ).
tcf(c_49,negated_conjecture,
! [X0: $i] : ~ sum(X0,X0,X0),
inference(cnf_transformation,[],[f434]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sum(X3,X4,X5)
| ~ rdn_translate(X5,rdn_pos(X2))
| ~ rdn_translate(X4,rdn_pos(X1))
| ~ rdn_translate(X3,rdn_pos(X0))
| ~ rdn_add_with_carry(rdnn(n0),X0,X1,X2) ),
inference(cnf_transformation,[],[f440]) ).
tcf(c_57,plain,
rdn_translate(n0,rdn_pos(rdnn(n0))),
inference(cnf_transformation,[],[f442]) ).
tcf(c_63,plain,
rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)),
inference(cnf_transformation,[],[f448]) ).
tcf(c_79,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,[],[f464]) ).
tcf(c_205,plain,
( rdn_add_with_carry(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0))
| ~ rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_602,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ rdn_translate(X3,rdn_pos(X2))
| ~ rdn_translate(X3,rdn_pos(X1))
| ~ rdn_translate(X3,rdn_pos(X0))
| ~ rdn_add_with_carry(rdnn(n0),X0,X1,X2) ),
inference(resolution,[status(thm)],[c_49,c_55]) ).
tcf(c_983,plain,
! [X0: $i,X1: $i] :
( ~ rdn_translate(n0,rdn_pos(X1))
| ~ rdn_translate(n0,rdn_pos(X0))
| ~ rdn_translate(n0,rdn_pos(rdnn(n0)))
| ~ rdn_add_with_carry(rdnn(n0),rdnn(n0),X0,X1) ),
inference(instantiation,[status(thm)],[c_602]) ).
tcf(c_1277,plain,
! [X0: $i] :
( ~ rdn_translate(n0,rdn_pos(X0))
| ~ rdn_translate(n0,rdn_pos(rdnn(n0)))
| ~ rdn_add_with_carry(rdnn(n0),rdnn(n0),rdnn(n0),X0) ),
inference(instantiation,[status(thm)],[c_983]) ).
tcf(c_1944,plain,
( ~ rdn_translate(n0,rdn_pos(rdnn(n0)))
| ~ rdn_add_with_carry(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)) ),
inference(instantiation,[status(thm)],[c_1277]) ).
tcf(c_1945,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1944,c_205,c_63,c_57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM329+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.41 % Computer : n003.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Thu Sep 24 03:38:21 UTC 2026
% 0.03/0.41 % CPUTime :
% 0.03/0.41 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.45 Running first-order theorem proving
% 0.03/0.45 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
% 0.03/0.47
% 0.03/0.47 % ======== iProver multi-core TPTP/SMT =========
% 0.03/0.47
% 0.03/0.47 % Detected problem language: tptp
% 0.03/0.48 % Proving...
% 4.41/1.34 % SZS status Started for theBenchmark.p
% 4.41/1.34 % SZS status Theorem for theBenchmark.p
% 4.41/1.34
% 4.41/1.34 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.41/1.34
% 4.41/1.34 % ------ iProver source info
% 4.41/1.34
% 4.41/1.34 % git: date: 2026-07-19 20:42:38 +0200
% 4.41/1.34 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.41/1.34 % git: non_committed_changes: false
% 4.41/1.34
% 4.41/1.34 % ------ Parsing...
% 4.41/1.34 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.41/1.34
% 4.41/1.34 % ------ Preprocessing... sf_s rm: 18 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 4.41/1.34
% 4.41/1.34 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 4.41/1.34 % ------ Proving...
% 4.41/1.34 % ------ Problem Properties
% 4.41/1.34
% 4.41/1.34 %
% 4.41/1.34 % clauses 126
% 4.41/1.34 % conjectures 0
% 4.41/1.34 % EPR 0
% 4.41/1.34 % Horn 126
% 4.41/1.34 % unary 119
% 4.41/1.34 % binary 2
% 4.41/1.34 % lits 149
% 4.41/1.34 % lits eq 0
% 4.41/1.34 % fd_pure 0
% 4.41/1.34 % fd_pseudo 0
% 4.41/1.34 % fd_cond 0
% 4.41/1.34 % fd_pseudo_cond 0
% 4.41/1.34 % AC symbols 0
% 4.41/1.34
% 4.41/1.34 % ------ Schedule dynamic 5 is on
% 4.41/1.34
% 4.41/1.34 % ------ no conjectures: strip conj schedule
% 4.41/1.34
% 4.41/1.34 % ------ no equalities: superposition off
% 4.41/1.34
% 4.41/1.34 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 4.41/1.34
% 4.41/1.34
% 4.41/1.34 % ------
% 4.41/1.34 % Current options:
% 4.41/1.34 % ------
% 4.41/1.34
% 4.41/1.34
% 4.41/1.34 %
% 4.41/1.34
% 4.41/1.34 % ------ Proving...
% 4.41/1.34 %
% 4.41/1.34
% 4.41/1.34 % SZS status Theorem for theBenchmark.p
% 4.41/1.34
% 4.41/1.34 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.41/1.34
% 4.41/1.34
%------------------------------------------------------------------------------