%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM342+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n020.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 02:23:44 PM UTC 2026
% Result : Theorem 10.35s 2.27s
% Output : CNFRefutation 10.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 53 ( 19 unt; 0 def)
% Number of atoms : 132 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 155 ( 76 ~; 69 |; 7 &)
% ( 1 <=>; 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 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 100 ( 0 sgn 96 !; 4 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
rdn_translate(n0,rdn_pos(rdnn(n0))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn0) ).
fof(f5,axiom,
rdn_translate(n4,rdn_pos(rdnn(n4))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn4) ).
fof(f9,axiom,
rdn_translate(n8,rdn_pos(rdnn(n8))),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/NUM005+2.ax',sum_entry_point_pos_pos) ).
fof(f296,axiom,
! [X0,X1,X2] :
( sum(X1,X2,X0)
<=> difference(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',minus_entry_point) ).
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/sandbox/benchmark/Axioms/NUM005+2.ax',add_digit_digit_digit) ).
fof(f342,axiom,
rdn_digit_add(rdnn(n4),rdnn(n0),rdnn(n4),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n4_n0_n4_n0) ).
fof(f346,axiom,
rdn_digit_add(rdnn(n4),rdnn(n4),rdnn(n8),rdnn(n0)),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n8_n0_n8_n0) ).
fof(f402,conjecture,
? [X0,X1] :
( difference(X0,X1,n0)
& sum(X0,X1,n8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_and_difference) ).
fof(f403,negated_conjecture,
~ ? [X0,X1] :
( difference(X0,X1,n0)
& sum(X0,X1,n8) ),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f404,plain,
! [X0,X1] :
( ~ difference(X0,X1,n0)
| ~ sum(X0,X1,n8) ),
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,X1,X2] :
( ( ~ sum(X1,X2,X0)
| difference(X0,X1,X2) )
& ( ~ difference(X0,X1,X2)
| sum(X1,X2,X0) ) ),
inference(nnf_transformation,[],[f296]) ).
fof(f435,plain,
! [X0,X1] :
( ~ difference(X0,X1,n0)
| ~ sum(X0,X1,n8) ),
inference(cnf_transformation,[],[f404]) ).
fof(f442,plain,
rdn_translate(n0,rdn_pos(rdnn(n0))),
inference(cnf_transformation,[],[f1]) ).
fof(f448,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(f449,plain,
! [X2,X0,X1] :
( ~ sum(X1,X2,X0)
| difference(X0,X1,X2) ),
inference(cnf_transformation,[],[f434]) ).
fof(f462,plain,
rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(n8),rdnn(n0)),
inference(cnf_transformation,[],[f382]) ).
fof(f470,plain,
rdn_digit_add(rdnn(n4),rdnn(n4),rdnn(n8),rdnn(n0)),
inference(cnf_transformation,[],[f346]) ).
fof(f478,plain,
rdn_translate(n8,rdn_pos(rdnn(n8))),
inference(cnf_transformation,[],[f9]) ).
fof(f529,plain,
rdn_digit_add(rdnn(n4),rdnn(n0),rdnn(n4),rdnn(n0)),
inference(cnf_transformation,[],[f342]) ).
fof(f563,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]) ).
fof(f568,plain,
rdn_translate(n4,rdn_pos(rdnn(n4))),
inference(cnf_transformation,[],[f5]) ).
tcf(c_49,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ difference(X0,X1,n0)
| ~ sum(X0,X1,n8) ),
inference(cnf_transformation,[],[f435]) ).
tcf(c_56,plain,
rdn_translate(n0,rdn_pos(rdnn(n0))),
inference(cnf_transformation,[],[f442]) ).
tcf(c_62,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,[],[f448]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( difference(X2,X0,X1)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f449]) ).
tcf(c_76,plain,
rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(n8),rdnn(n0)),
inference(cnf_transformation,[],[f462]) ).
tcf(c_84,plain,
rdn_digit_add(rdnn(n4),rdnn(n4),rdnn(n8),rdnn(n0)),
inference(cnf_transformation,[],[f470]) ).
tcf(c_92,plain,
rdn_translate(n8,rdn_pos(rdnn(n8))),
inference(cnf_transformation,[],[f478]) ).
tcf(c_143,plain,
rdn_digit_add(rdnn(n4),rdnn(n0),rdnn(n4),rdnn(n0)),
inference(cnf_transformation,[],[f529]) ).
tcf(c_177,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,[],[f563]) ).
tcf(c_182,plain,
rdn_translate(n4,rdn_pos(rdnn(n4))),
inference(cnf_transformation,[],[f568]) ).
tcf(c_616,plain,
! [X0: $i,X1: $i] :
( ~ sum(X1,n0,X0)
| ~ sum(X0,X1,n8) ),
inference(resolution,[status(thm)],[c_49,c_64]) ).
tcf(c_1010,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sum(n4,X2,X3)
| ~ rdn_translate(X3,rdn_pos(X1))
| ~ rdn_translate(X2,rdn_pos(X0))
| ~ rdn_translate(n4,rdn_pos(rdnn(n4)))
| ~ rdn_add_with_carry(rdnn(n0),rdnn(n4),X0,X1) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_1156,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(n4,X2,n8)
| ~ rdn_translate(n8,rdn_pos(X1))
| ~ rdn_translate(X2,rdn_pos(X0))
| ~ rdn_translate(n4,rdn_pos(rdnn(n4)))
| ~ rdn_add_with_carry(rdnn(n0),rdnn(n4),X0,X1) ),
inference(instantiation,[status(thm)],[c_1010]) ).
tcf(c_1157,plain,
! [X0: $i] :
( ~ sum(n4,X0,n8)
| ~ sum(X0,n0,n4) ),
inference(instantiation,[status(thm)],[c_616]) ).
tcf(c_5195,plain,
! [X0: $i,X1: $i] :
( sum(n4,n0,X1)
| ~ rdn_translate(X1,rdn_pos(X0))
| ~ rdn_translate(n4,rdn_pos(rdnn(n4)))
| ~ rdn_translate(n0,rdn_pos(rdnn(n0)))
| ~ rdn_add_with_carry(rdnn(n0),rdnn(n4),rdnn(n0),X0) ),
inference(instantiation,[status(thm)],[c_1010]) ).
tcf(c_5225,plain,
! [X0: $i,X1: $i] :
( sum(n4,X1,n8)
| ~ rdn_translate(X1,rdn_pos(X0))
| ~ rdn_translate(n4,rdn_pos(rdnn(n4)))
| ~ rdn_translate(n8,rdn_pos(rdnn(n8)))
| ~ rdn_add_with_carry(rdnn(n0),rdnn(n4),X0,rdnn(n8)) ),
inference(instantiation,[status(thm)],[c_1156]) ).
tcf(c_5369,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( rdn_add_with_carry(rdnn(X1),rdnn(n4),rdnn(X3),rdnn(X2))
| ~ rdn_digit_add(rdnn(n4),rdnn(X3),rdnn(X0),rdnn(n0))
| ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(n0)) ),
inference(instantiation,[status(thm)],[c_177]) ).
tcf(c_10751,plain,
( sum(n4,n0,n4)
| ~ rdn_translate(n4,rdn_pos(rdnn(n4)))
| ~ rdn_translate(n0,rdn_pos(rdnn(n0)))
| ~ rdn_add_with_carry(rdnn(n0),rdnn(n4),rdnn(n0),rdnn(n4)) ),
inference(instantiation,[status(thm)],[c_5195]) ).
tcf(c_10832,plain,
! [X0: $i,X1: $i] :
( rdn_add_with_carry(rdnn(X0),rdnn(n4),rdnn(n4),rdnn(X1))
| ~ rdn_digit_add(rdnn(n4),rdnn(n4),rdnn(n8),rdnn(n0))
| ~ rdn_digit_add(rdnn(n8),rdnn(X0),rdnn(X1),rdnn(n0)) ),
inference(instantiation,[status(thm)],[c_5369]) ).
tcf(c_10837,plain,
! [X0: $i,X1: $i] :
( rdn_add_with_carry(rdnn(X0),rdnn(n4),rdnn(n0),rdnn(X1))
| ~ rdn_digit_add(rdnn(n4),rdnn(n0),rdnn(n4),rdnn(n0))
| ~ rdn_digit_add(rdnn(n4),rdnn(X0),rdnn(X1),rdnn(n0)) ),
inference(instantiation,[status(thm)],[c_5369]) ).
tcf(c_11196,plain,
( rdn_add_with_carry(rdnn(n0),rdnn(n4),rdnn(n4),rdnn(n8))
| ~ rdn_digit_add(rdnn(n4),rdnn(n4),rdnn(n8),rdnn(n0))
| ~ rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(n8),rdnn(n0)) ),
inference(instantiation,[status(thm)],[c_10832]) ).
tcf(c_11215,plain,
( rdn_add_with_carry(rdnn(n0),rdnn(n4),rdnn(n0),rdnn(n4))
| ~ rdn_digit_add(rdnn(n4),rdnn(n0),rdnn(n4),rdnn(n0)) ),
inference(instantiation,[status(thm)],[c_10837]) ).
tcf(c_13788,plain,
! [X0: $i] :
( sum(n4,X0,n8)
| ~ rdn_translate(n4,rdn_pos(rdnn(n4)))
| ~ rdn_translate(n8,rdn_pos(rdnn(n8)))
| ~ rdn_translate(X0,rdn_pos(rdnn(n4)))
| ~ rdn_add_with_carry(rdnn(n0),rdnn(n4),rdnn(n4),rdnn(n8)) ),
inference(instantiation,[status(thm)],[c_5225]) ).
tcf(c_13900,plain,
( ~ sum(n4,n4,n8)
| ~ sum(n4,n0,n4) ),
inference(instantiation,[status(thm)],[c_1157]) ).
tcf(c_17863,plain,
( sum(n4,n4,n8)
| ~ rdn_translate(n4,rdn_pos(rdnn(n4)))
| ~ rdn_translate(n8,rdn_pos(rdnn(n8)))
| ~ rdn_add_with_carry(rdnn(n0),rdnn(n4),rdnn(n4),rdnn(n8)) ),
inference(instantiation,[status(thm)],[c_13788]) ).
tcf(c_17864,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_17863,c_13900,c_11215,c_11196,c_10751,c_76,c_84,c_143,c_56,c_92,c_182]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM342+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n020.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 03:40:03 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.41 % Detected problem language: tptp
% 0.09/0.42 % Proving...
% 10.35/2.27 % SZS status Started for theBenchmark.p
% 10.35/2.27 % SZS status Theorem for theBenchmark.p
% 10.35/2.27
% 10.35/2.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.35/2.27
% 10.35/2.27 % ------ iProver source info
% 10.35/2.27
% 10.35/2.27 % git: date: 2026-07-19 20:42:38 +0200
% 10.35/2.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.35/2.27 % git: non_committed_changes: false
% 10.35/2.27
% 10.35/2.27 % ------ Parsing...
% 10.35/2.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.35/2.27
% 10.35/2.27 % ------ 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 %
% 10.35/2.27
% 10.35/2.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 10.35/2.27 % ------ Proving...
% 10.35/2.27 % ------ Problem Properties
% 10.35/2.27
% 10.35/2.27 %
% 10.35/2.27 % clauses 127
% 10.35/2.27 % conjectures 0
% 10.35/2.27 % EPR 1
% 10.35/2.27 % Horn 127
% 10.35/2.27 % unary 119
% 10.35/2.27 % binary 3
% 10.35/2.27 % lits 152
% 10.35/2.27 % lits eq 0
% 10.35/2.27 % fd_pure 0
% 10.35/2.27 % fd_pseudo 0
% 10.35/2.27 % fd_cond 0
% 10.35/2.27 % fd_pseudo_cond 0
% 10.35/2.27 % AC symbols 0
% 10.35/2.27
% 10.35/2.27 % ------ Schedule dynamic 5 is on
% 10.35/2.27
% 10.35/2.27 % ------ no conjectures: strip conj schedule
% 10.35/2.27
% 10.35/2.27 % ------ no equalities: superposition off
% 10.35/2.27
% 10.35/2.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 10.35/2.27
% 10.35/2.27
% 10.35/2.27 % ------
% 10.35/2.27 % Current options:
% 10.35/2.27 % ------
% 10.35/2.27
% 10.35/2.27
% 10.35/2.27 %
% 10.35/2.27
% 10.35/2.27 % ------ Proving...
% 10.35/2.27 %
% 10.35/2.27
% 10.35/2.27 % SZS status Theorem for theBenchmark.p
% 10.35/2.27
% 10.35/2.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.35/2.27
% 10.35/2.27
%------------------------------------------------------------------------------