%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM305+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 : n015.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 02:23:40 PM UTC 2026
% Result : Theorem 6.88s 1.79s
% Output : CNFRefutation 6.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 38 ( 21 unt; 0 def)
% Number of atoms : 86 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 98 ( 50 ~; 42 |; 4 &)
% ( 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 : 5 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 67 ( 0 sgn 67 !; 0 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn2) ).
fof(f4,axiom,
rdn_translate(n3,rdn_pos(rdnn(n3))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn3) ).
fof(f6,axiom,
rdn_translate(n5,rdn_pos(rdnn(n5))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn5) ).
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(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(f325,axiom,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n2_n3_n5_n0) ).
fof(f352,axiom,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n5_n0_n5_n0) ).
fof(f402,conjecture,
sum(n2,n3,n5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_n2_n3_n5) ).
fof(f403,negated_conjecture,
~ sum(n2,n3,n5),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f404,plain,
~ sum(n2,n3,n5),
inference(flattening,[],[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,
~ sum(n2,n3,n5),
inference(cnf_transformation,[],[f404]) ).
fof(f455,plain,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f325]) ).
fof(f462,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(cnf_transformation,[],[f3]) ).
fof(f484,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(cnf_transformation,[],[f4]) ).
fof(f490,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(f502,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f352]) ).
fof(f508,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(cnf_transformation,[],[f6]) ).
fof(f566,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,
~ sum(n2,n3,n5),
inference(cnf_transformation,[],[f434]) ).
tcf(c_70,plain,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f455]) ).
tcf(c_77,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(cnf_transformation,[],[f462]) ).
tcf(c_99,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(cnf_transformation,[],[f484]) ).
tcf(c_105,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,[],[f490]) ).
tcf(c_117,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f502]) ).
tcf(c_123,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(cnf_transformation,[],[f508]) ).
tcf(c_181,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,[],[f566]) ).
tcf(c_600,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ rdn_translate(n5,rdn_pos(X2))
| ~ rdn_translate(n3,rdn_pos(X1))
| ~ rdn_translate(n2,rdn_pos(X0))
| ~ rdn_add_with_carry(rdnn(n0),X0,X1,X2) ),
inference(resolution,[status(thm)],[c_49,c_105]) ).
tcf(c_1263,plain,
! [X0: $i,X1: $i] :
( ~ rdn_translate(n5,rdn_pos(X1))
| ~ rdn_translate(n3,rdn_pos(X0))
| ~ rdn_translate(n2,rdn_pos(rdnn(n2)))
| ~ rdn_add_with_carry(rdnn(n0),rdnn(n2),X0,X1) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_1359,plain,
! [X0: $i] :
( ~ rdn_translate(n5,rdn_pos(X0))
| ~ rdn_translate(n3,rdn_pos(rdnn(n3)))
| ~ rdn_translate(n2,rdn_pos(rdnn(n2)))
| ~ rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),X0) ),
inference(instantiation,[status(thm)],[c_1263]) ).
tcf(c_2189,plain,
( ~ rdn_translate(n5,rdn_pos(rdnn(n5)))
| ~ rdn_translate(n3,rdn_pos(rdnn(n3)))
| ~ rdn_translate(n2,rdn_pos(rdnn(n2)))
| ~ rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5)) ),
inference(instantiation,[status(thm)],[c_1359]) ).
tcf(c_4589,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( rdn_add_with_carry(rdnn(X1),rdnn(n2),rdnn(X3),rdnn(X2))
| ~ rdn_digit_add(rdnn(n2),rdnn(X3),rdnn(X0),rdnn(n0))
| ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(n0)) ),
inference(instantiation,[status(thm)],[c_181]) ).
tcf(c_6995,plain,
! [X0: $i,X1: $i] :
( rdn_add_with_carry(rdnn(X0),rdnn(n2),rdnn(n3),rdnn(X1))
| ~ rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0))
| ~ rdn_digit_add(rdnn(n5),rdnn(X0),rdnn(X1),rdnn(n0)) ),
inference(instantiation,[status(thm)],[c_4589]) ).
tcf(c_10694,plain,
( rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5))
| ~ rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0))
| ~ rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)) ),
inference(instantiation,[status(thm)],[c_6995]) ).
tcf(c_10695,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_10694,c_2189,c_70,c_117,c_77,c_99,c_123]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM305+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.37 % Computer : n015.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Thu Sep 24 03:36:10 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 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
% 0.13/0.43
% 0.13/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.43
% 0.13/0.43 % Detected problem language: tptp
% 0.13/0.44 % Proving...
% 6.88/1.79 % SZS status Started for theBenchmark.p
% 6.88/1.79 % SZS status Theorem for theBenchmark.p
% 6.88/1.79
% 6.88/1.79 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.88/1.79
% 6.88/1.79 % ------ iProver source info
% 6.88/1.79
% 6.88/1.79 % git: date: 2026-07-19 20:42:38 +0200
% 6.88/1.79 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.88/1.79 % git: non_committed_changes: false
% 6.88/1.79
% 6.88/1.79 % ------ Parsing...
% 6.88/1.79 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 6.88/1.79
% 6.88/1.79 % ------ Preprocessing... sf_s rm: 18 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sf_s rm: 7 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 6.88/1.79
% 6.88/1.79 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 6.88/1.79 % ------ Proving...
% 6.88/1.79 % ------ Problem Properties
% 6.88/1.79
% 6.88/1.79 %
% 6.88/1.79 % clauses 119
% 6.88/1.79 % conjectures 0
% 6.88/1.79 % EPR 0
% 6.88/1.79 % Horn 119
% 6.88/1.79 % unary 112
% 6.88/1.79 % binary 2
% 6.88/1.79 % lits 142
% 6.88/1.79 % lits eq 0
% 6.88/1.79 % fd_pure 0
% 6.88/1.79 % fd_pseudo 0
% 6.88/1.79 % fd_cond 0
% 6.88/1.79 % fd_pseudo_cond 0
% 6.88/1.79 % AC symbols 0
% 6.88/1.79
% 6.88/1.79 % ------ Schedule dynamic 5 is on
% 6.88/1.79
% 6.88/1.79 % ------ no conjectures: strip conj schedule
% 6.88/1.79
% 6.88/1.79 % ------ no equalities: superposition off
% 6.88/1.79
% 6.88/1.79 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 6.88/1.79
% 6.88/1.79
% 6.88/1.79 % ------
% 6.88/1.79 % Current options:
% 6.88/1.79 % ------
% 6.88/1.79
% 6.88/1.79
% 6.88/1.79 %
% 6.88/1.79
% 6.88/1.79 % ------ Proving...
% 6.88/1.79 %
% 6.88/1.79
% 6.88/1.79 % SZS status Theorem for theBenchmark.p
% 6.88/1.79
% 6.88/1.79 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.88/1.79
% 6.88/1.79
%------------------------------------------------------------------------------