%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM340+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 : n009.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 3.35s 1.19s
% Output : CNFRefutation 3.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 13 unt; 0 def)
% Number of atoms : 78 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 93 ( 47 ~; 38 |; 5 &)
% ( 1 <=>; 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 : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 81 ( 0 sgn 79 !; 2 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
rdn_translate(n0,rdn_pos(rdnn(n0))),
file('/export/starexec/sandbox/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/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(f302,axiom,
rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n0_n0_n0_n0) ).
fof(f402,conjecture,
? [X0] : difference(X0,n0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diff_zero_identity) ).
fof(f403,negated_conjecture,
~ ? [X0] : difference(X0,n0,X0),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f404,plain,
! [X0] : ~ difference(X0,n0,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,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] : ~ difference(X0,n0,X0),
inference(cnf_transformation,[],[f404]) ).
fof(f441,plain,
rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)),
inference(cnf_transformation,[],[f302]) ).
fof(f442,plain,
rdn_translate(n0,rdn_pos(rdnn(n0))),
inference(cnf_transformation,[],[f1]) ).
fof(f443,plain,
! [X2,X0,X1] :
( ~ sum(X1,X2,X0)
| difference(X0,X1,X2) ),
inference(cnf_transformation,[],[f434]) ).
fof(f546,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(f569,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] : ~ difference(X0,n0,X0),
inference(cnf_transformation,[],[f435]) ).
tcf(c_55,plain,
rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)),
inference(cnf_transformation,[],[f441]) ).
tcf(c_56,plain,
rdn_translate(n0,rdn_pos(rdnn(n0))),
inference(cnf_transformation,[],[f442]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( difference(X2,X0,X1)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f443]) ).
tcf(c_160,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,[],[f546]) ).
tcf(c_183,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,[],[f569]) ).
tcf(c_208,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_183]) ).
tcf(c_613,plain,
! [X0: $i] : ~ sum(n0,X0,X0),
inference(resolution,[status(thm)],[c_49,c_58]) ).
tcf(c_620,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ rdn_translate(n0,rdn_pos(X0))
| ~ rdn_translate(X3,rdn_pos(X2))
| ~ rdn_translate(X3,rdn_pos(X1))
| ~ rdn_add_with_carry(rdnn(n0),X0,X1,X2) ),
inference(resolution,[status(thm)],[c_160,c_613]) ).
tcf(c_999,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ rdn_translate(X2,rdn_pos(X1))
| ~ rdn_translate(X2,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_620]) ).
tcf(c_1275,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_999]) ).
tcf(c_1943,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_1275]) ).
tcf(c_1944,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1943,c_208,c_55,c_56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM340+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n009.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 03:39:13 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 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
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 3.35/1.19 % SZS status Started for theBenchmark.p
% 3.35/1.19 % SZS status Theorem for theBenchmark.p
% 3.35/1.19
% 3.35/1.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.35/1.19
% 3.35/1.19 % ------ iProver source info
% 3.35/1.19
% 3.35/1.19 % git: date: 2026-07-19 20:42:38 +0200
% 3.35/1.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.35/1.19 % git: non_committed_changes: false
% 3.35/1.19
% 3.35/1.19 % ------ Parsing...
% 3.35/1.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.35/1.19
% 3.35/1.19 % ------ 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 %
% 3.35/1.19
% 3.35/1.19 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.35/1.19 % ------ Proving...
% 3.35/1.19 % ------ Problem Properties
% 3.35/1.19
% 3.35/1.19 %
% 3.35/1.19 % clauses 126
% 3.35/1.19 % conjectures 0
% 3.35/1.19 % EPR 0
% 3.35/1.19 % Horn 126
% 3.35/1.19 % unary 119
% 3.35/1.19 % binary 2
% 3.35/1.19 % lits 149
% 3.35/1.19 % lits eq 0
% 3.35/1.19 % fd_pure 0
% 3.35/1.19 % fd_pseudo 0
% 3.35/1.19 % fd_cond 0
% 3.35/1.19 % fd_pseudo_cond 0
% 3.35/1.19 % AC symbols 0
% 3.35/1.19
% 3.35/1.19 % ------ Schedule dynamic 5 is on
% 3.35/1.19
% 3.35/1.19 % ------ no conjectures: strip conj schedule
% 3.35/1.19
% 3.35/1.19 % ------ no equalities: superposition off
% 3.35/1.19
% 3.35/1.19 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.35/1.19
% 3.35/1.19
% 3.35/1.19 % ------
% 3.35/1.19 % Current options:
% 3.35/1.19 % ------
% 3.35/1.19
% 3.35/1.19
% 3.35/1.19 %
% 3.35/1.19
% 3.35/1.19 % ------ Proving...
% 3.35/1.19 %
% 3.35/1.19
% 3.35/1.19 % SZS status Theorem for theBenchmark.p
% 3.35/1.19
% 3.35/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.35/1.19
% 3.35/1.19
%------------------------------------------------------------------------------