%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM317+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 : n016.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 02:23:41 PM UTC 2026
% Result : Theorem 19.07s 3.51s
% Output : CNFRefutation 19.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 56 ( 30 unt; 0 def)
% Number of atoms : 135 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 153 ( 74 ~; 70 |; 6 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 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 : 9 ( 9 usr; 6 con; 0-1 aty)
% Number of variables : 81 ( 0 sgn 81 !; 0 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
rdn_translate(n3,rdn_pos(rdnn(n3))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdn3) ).
fof(f6,axiom,
rdn_translate(n5,rdn_pos(rdnn(n5))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdn5) ).
fof(f130,axiom,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdnn2) ).
fof(f268,axiom,
rdn_positive_less(rdnn(n2),rdnn(n3)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+1.ax',rdn_positive_less23) ).
fof(f269,axiom,
rdn_positive_less(rdnn(n3),rdnn(n4)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+1.ax',rdn_positive_less34) ).
fof(f270,axiom,
rdn_positive_less(rdnn(n4),rdnn(n5)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+1.ax',rdn_positive_less45) ).
fof(f275,axiom,
! [X0,X1,X2] :
( ( rdn_positive_less(rdnn(X1),rdnn(X2))
& rdn_positive_less(rdnn(X0),rdnn(X1)) )
=> rdn_positive_less(rdnn(X0),rdnn(X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+1.ax',rdn_positive_less_transitivity) ).
fof(f290,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( rdn_translate(X2,rdn_pos(X5))
& rdn_add_with_carry(rdnn(n0),X4,X5,X3)
& rdn_positive_less(X4,X3)
& rdn_translate(X1,rdn_neg(X4))
& rdn_translate(X0,rdn_pos(X3)) )
=> sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+2.ax',sum_entry_point_pos_neg_2) ).
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(f325,axiom,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n5_n0_n5_n0) ).
fof(f402,conjecture,
sum(n5,nn2,n3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_n5_nn2_n3) ).
fof(f403,negated_conjecture,
~ sum(n5,nn2,n3),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f404,plain,
~ sum(n5,nn2,n3),
inference(flattening,[],[f403]) ).
fof(f409,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ rdn_translate(X2,rdn_pos(X5))
| ~ rdn_add_with_carry(rdnn(n0),X4,X5,X3)
| ~ rdn_positive_less(X4,X3)
| ~ rdn_translate(X1,rdn_neg(X4))
| ~ rdn_translate(X0,rdn_pos(X3))
| sum(X0,X1,X2) ),
inference(ennf_transformation,[],[f290]) ).
fof(f410,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ rdn_translate(X2,rdn_pos(X5))
| ~ rdn_add_with_carry(rdnn(n0),X4,X5,X3)
| ~ rdn_positive_less(X4,X3)
| ~ rdn_translate(X1,rdn_neg(X4))
| ~ rdn_translate(X0,rdn_pos(X3))
| sum(X0,X1,X2) ),
inference(flattening,[],[f409]) ).
fof(f418,plain,
! [X0,X1,X2] :
( ~ rdn_positive_less(rdnn(X1),rdnn(X2))
| ~ rdn_positive_less(rdnn(X0),rdnn(X1))
| rdn_positive_less(rdnn(X0),rdnn(X2)) ),
inference(ennf_transformation,[],[f275]) ).
fof(f419,plain,
! [X0,X1,X2] :
( ~ rdn_positive_less(rdnn(X1),rdnn(X2))
| ~ rdn_positive_less(rdnn(X0),rdnn(X1))
| rdn_positive_less(rdnn(X0),rdnn(X2)) ),
inference(flattening,[],[f418]) ).
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(n5,nn2,n3),
inference(cnf_transformation,[],[f404]) ).
fof(f457,plain,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f325]) ).
fof(f462,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(cnf_transformation,[],[f4]) ).
fof(f465,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ rdn_translate(X2,rdn_pos(X5))
| ~ rdn_add_with_carry(rdnn(n0),X4,X5,X3)
| ~ rdn_positive_less(X4,X3)
| ~ rdn_translate(X1,rdn_neg(X4))
| ~ rdn_translate(X0,rdn_pos(X3))
| sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f410]) ).
fof(f483,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f352]) ).
fof(f490,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(cnf_transformation,[],[f6]) ).
fof(f491,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
inference(cnf_transformation,[],[f130]) ).
fof(f553,plain,
! [X2,X0,X1] :
( ~ rdn_positive_less(rdnn(X1),rdnn(X2))
| ~ rdn_positive_less(rdnn(X0),rdnn(X1))
| rdn_positive_less(rdnn(X0),rdnn(X2)) ),
inference(cnf_transformation,[],[f419]) ).
fof(f558,plain,
rdn_positive_less(rdnn(n4),rdnn(n5)),
inference(cnf_transformation,[],[f270]) ).
fof(f559,plain,
rdn_positive_less(rdnn(n3),rdnn(n4)),
inference(cnf_transformation,[],[f269]) ).
fof(f560,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(cnf_transformation,[],[f268]) ).
fof(f567,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(n5,nn2,n3),
inference(cnf_transformation,[],[f434]) ).
tcf(c_72,plain,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f457]) ).
tcf(c_77,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(cnf_transformation,[],[f462]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sum(X3,X4,X5)
| ~ rdn_positive_less(X0,X2)
| ~ rdn_translate(X5,rdn_pos(X1))
| ~ rdn_translate(X4,rdn_neg(X0))
| ~ rdn_translate(X3,rdn_pos(X2))
| ~ rdn_add_with_carry(rdnn(n0),X0,X1,X2) ),
inference(cnf_transformation,[],[f465]) ).
tcf(c_98,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f483]) ).
tcf(c_105,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(cnf_transformation,[],[f490]) ).
tcf(c_106,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
inference(cnf_transformation,[],[f491]) ).
tcf(c_168,plain,
! [X0: $i,X1: $i,X2: $i] :
( rdn_positive_less(rdnn(X0),rdnn(X2))
| ~ rdn_positive_less(rdnn(X1),rdnn(X2))
| ~ rdn_positive_less(rdnn(X0),rdnn(X1)) ),
inference(cnf_transformation,[],[f553]) ).
tcf(c_173,plain,
rdn_positive_less(rdnn(n4),rdnn(n5)),
inference(cnf_transformation,[],[f558]) ).
tcf(c_174,plain,
rdn_positive_less(rdnn(n3),rdnn(n4)),
inference(cnf_transformation,[],[f559]) ).
tcf(c_175,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(cnf_transformation,[],[f560]) ).
tcf(c_182,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,[],[f567]) ).
tcf(c_1199,plain,
! [X0: $i] :
( rdn_positive_less(rdnn(n3),rdnn(X0))
| ~ rdn_positive_less(rdnn(n3),rdnn(n4))
| ~ rdn_positive_less(rdnn(n4),rdnn(X0)) ),
inference(instantiation,[status(thm)],[c_168]) ).
tcf(c_1201,plain,
! [X0: $i] :
( rdn_positive_less(rdnn(n2),rdnn(X0))
| ~ rdn_positive_less(rdnn(n2),rdnn(n3))
| ~ rdn_positive_less(rdnn(n3),rdnn(X0)) ),
inference(instantiation,[status(thm)],[c_168]) ).
tcf(c_1335,plain,
( rdn_positive_less(rdnn(n3),rdnn(n5))
| ~ rdn_positive_less(rdnn(n4),rdnn(n5))
| ~ rdn_positive_less(rdnn(n3),rdnn(n4)) ),
inference(instantiation,[status(thm)],[c_1199]) ).
tcf(c_4592,plain,
( rdn_positive_less(rdnn(n2),rdnn(n5))
| ~ rdn_positive_less(rdnn(n2),rdnn(n3))
| ~ rdn_positive_less(rdnn(n3),rdnn(n5)) ),
inference(instantiation,[status(thm)],[c_1201]) ).
tcf(c_5493,plain,
! [X0: $i,X1: $i] :
( rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(X1))
| ~ rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(X0),rdnn(n0))
| ~ rdn_digit_add(rdnn(X0),rdnn(n0),rdnn(X1),rdnn(n0)) ),
inference(instantiation,[status(thm)],[c_182]) ).
tcf(c_10478,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(n5,nn2,n3)
| ~ rdn_positive_less(X0,X2)
| ~ rdn_translate(n3,rdn_pos(X1))
| ~ rdn_translate(nn2,rdn_neg(X0))
| ~ rdn_translate(n5,rdn_pos(X2))
| ~ rdn_add_with_carry(rdnn(n0),X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_80]) ).
tcf(c_10671,plain,
! [X0: $i] :
( rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(X0))
| ~ rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0))
| ~ rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(X0),rdnn(n0)) ),
inference(instantiation,[status(thm)],[c_5493]) ).
tcf(c_12174,plain,
! [X0: $i,X1: $i] :
( sum(n5,nn2,n3)
| ~ rdn_positive_less(X0,rdnn(n5))
| ~ rdn_translate(n3,rdn_pos(X1))
| ~ rdn_translate(nn2,rdn_neg(X0))
| ~ rdn_translate(n5,rdn_pos(rdnn(n5)))
| ~ rdn_add_with_carry(rdnn(n0),X0,X1,rdnn(n5)) ),
inference(instantiation,[status(thm)],[c_10478]) ).
tcf(c_14952,plain,
( rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5))
| ~ rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0))
| ~ rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)) ),
inference(instantiation,[status(thm)],[c_10671]) ).
tcf(c_17327,plain,
! [X0: $i] :
( sum(n5,nn2,n3)
| ~ rdn_translate(n3,rdn_pos(X0))
| ~ rdn_positive_less(rdnn(n2),rdnn(n5))
| ~ rdn_translate(nn2,rdn_neg(rdnn(n2)))
| ~ rdn_translate(n5,rdn_pos(rdnn(n5)))
| ~ rdn_add_with_carry(rdnn(n0),rdnn(n2),X0,rdnn(n5)) ),
inference(instantiation,[status(thm)],[c_12174]) ).
tcf(c_22238,plain,
( sum(n5,nn2,n3)
| ~ rdn_positive_less(rdnn(n2),rdnn(n5))
| ~ rdn_translate(n3,rdn_pos(rdnn(n3)))
| ~ rdn_translate(nn2,rdn_neg(rdnn(n2)))
| ~ rdn_translate(n5,rdn_pos(rdnn(n5)))
| ~ rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5)) ),
inference(instantiation,[status(thm)],[c_17327]) ).
tcf(c_22239,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_22238,c_14952,c_4592,c_1335,c_72,c_98,c_77,c_105,c_106,c_173,c_174,c_175,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM317+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.39 % Computer : n016.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Thu Sep 24 03:40:14 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.18/0.46 Running first-order theorem proving
% 0.18/0.46 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
% 0.18/0.47
% 0.18/0.47 % ======== iProver multi-core TPTP/SMT =========
% 0.18/0.47
% 0.18/0.48 % Detected problem language: tptp
% 0.18/0.49 % Proving...
% 19.07/3.51 % SZS status Started for theBenchmark.p
% 19.07/3.51 % SZS status Theorem for theBenchmark.p
% 19.07/3.51
% 19.07/3.51 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 19.07/3.51
% 19.07/3.51 % ------ iProver source info
% 19.07/3.51
% 19.07/3.51 % git: date: 2026-07-19 20:42:38 +0200
% 19.07/3.51 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 19.07/3.51 % git: non_committed_changes: false
% 19.07/3.51
% 19.07/3.51 % ------ Parsing...
% 19.07/3.51 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 19.07/3.51
% 19.07/3.51 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 19.07/3.51
% 19.07/3.51 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 19.07/3.51 % ------ Proving...
% 19.07/3.51 % ------ Problem Properties
% 19.07/3.51
% 19.07/3.51 %
% 19.07/3.51 % clauses 146
% 19.07/3.51 % conjectures 1
% 19.07/3.51 % EPR 1
% 19.07/3.51 % Horn 146
% 19.07/3.51 % unary 130
% 19.07/3.51 % binary 4
% 19.07/3.51 % lits 195
% 19.07/3.51 % lits eq 0
% 19.07/3.51 % fd_pure 0
% 19.07/3.51 % fd_pseudo 0
% 19.07/3.51 % fd_cond 0
% 19.07/3.51 % fd_pseudo_cond 0
% 19.07/3.51 % AC symbols 0
% 19.07/3.51
% 19.07/3.51 % ------ Schedule dynamic 5 is on
% 19.07/3.51
% 19.07/3.51 % ------ no equalities: superposition off
% 19.07/3.51
% 19.07/3.51 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 19.07/3.51
% 19.07/3.51
% 19.07/3.51 % ------
% 19.07/3.51 % Current options:
% 19.07/3.51 % ------
% 19.07/3.51
% 19.07/3.51
% 19.07/3.51 %
% 19.07/3.51
% 19.07/3.51 % ------ Proving...
% 19.07/3.51 %
% 19.07/3.51
% 19.07/3.51 % SZS status Theorem for theBenchmark.p
% 19.07/3.51
% 19.07/3.51 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 19.07/3.51
% 19.07/3.51
%------------------------------------------------------------------------------