%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM345+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 : n011.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 02:23:45 PM UTC 2026
% Result : Theorem 11.65s 17.88s
% Output : CNFRefutation 11.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 62 ( 31 unt; 0 def)
% Number of atoms : 132 ( 7 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 131 ( 61 ~; 55 |; 9 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-1 aty)
% Number of variables : 109 ( 0 sgn 108 !; 1 ?; 30 :)
% 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(f7,axiom,
rdn_translate(n6,rdn_pos(rdnn(n6))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn6) ).
fof(f271,axiom,
rdn_positive_less(rdnn(n5),rdnn(n6)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',rdn_positive_less56) ).
fof(f281,axiom,
! [X0,X1,X2,X3] :
( ( rdn_positive_less(X2,X3)
& rdn_translate(X1,rdn_pos(X3))
& rdn_translate(X0,rdn_pos(X2)) )
=> less(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',less_entry_point_pos_pos) ).
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(f293,axiom,
! [X0,X1,X2,X3] :
( ( sum(X0,X1,X3)
& sum(X0,X1,X2) )
=> X2 = X3 ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',unique_sum) ).
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,
! [X0] :
( sum(n2,n3,X0)
=> less(X0,n6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_n2_n3_less_n6) ).
fof(f403,negated_conjecture,
~ ! [X0] :
( sum(n2,n3,X0)
=> less(X0,n6) ),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f404,plain,
? [X0] :
( sum(n2,n3,X0)
& ~ less(X0,n6) ),
inference(ennf_transformation,[],[f403]) ).
fof(f409,plain,
! [X0,X1,X2,X3] :
( ~ rdn_positive_less(X2,X3)
| ~ rdn_translate(X1,rdn_pos(X3))
| ~ rdn_translate(X0,rdn_pos(X2))
| less(X0,X1) ),
inference(ennf_transformation,[],[f281]) ).
fof(f410,plain,
! [X0,X1,X2,X3] :
( ~ rdn_positive_less(X2,X3)
| ~ rdn_translate(X1,rdn_pos(X3))
| ~ rdn_translate(X0,rdn_pos(X2))
| less(X0,X1) ),
inference(flattening,[],[f409]) ).
fof(f421,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(f422,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,[],[f421]) ).
fof(f427,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2)
| X2 = X3 ),
inference(ennf_transformation,[],[f293]) ).
fof(f428,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2)
| X2 = X3 ),
inference(flattening,[],[f427]) ).
fof(f439,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(f440,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,[],[f439]) ).
fof(f446,plain,
( sum(n2,n3,sK0)
& ~ less(sK0,n6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f404]) ).
fof(f449,plain,
sum(n2,n3,sK0),
inference(cnf_transformation,[],[f446]) ).
fof(f450,plain,
~ less(sK0,n6),
inference(cnf_transformation,[],[f446]) ).
fof(f471,plain,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f325]) ).
fof(f478,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(cnf_transformation,[],[f3]) ).
fof(f484,plain,
! [X2,X3,X0,X1] :
( ~ rdn_positive_less(X2,X3)
| ~ rdn_translate(X1,rdn_pos(X3))
| ~ rdn_translate(X0,rdn_pos(X2))
| less(X0,X1) ),
inference(cnf_transformation,[],[f410]) ).
fof(f506,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(cnf_transformation,[],[f4]) ).
fof(f512,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,[],[f422]) ).
fof(f530,plain,
rdn_translate(n6,rdn_pos(rdnn(n6))),
inference(cnf_transformation,[],[f7]) ).
fof(f549,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f352]) ).
fof(f571,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(cnf_transformation,[],[f6]) ).
fof(f575,plain,
! [X2,X3,X0,X1] :
( ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2)
| X2 = X3 ),
inference(cnf_transformation,[],[f428]) ).
fof(f581,plain,
rdn_positive_less(rdnn(n5),rdnn(n6)),
inference(cnf_transformation,[],[f271]) ).
fof(f591,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,[],[f440]) ).
tcf(c_49,negated_conjecture,
~ less(sK0,n6),
inference(cnf_transformation,[],[f450]) ).
tcf(c_50,negated_conjecture,
sum(n2,n3,sK0),
inference(cnf_transformation,[],[f449]) ).
tcf(c_71,plain,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f471]) ).
tcf(c_78,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(cnf_transformation,[],[f478]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( less(X0,X2)
| ~ rdn_positive_less(X1,X3)
| ~ rdn_translate(X2,rdn_pos(X3))
| ~ rdn_translate(X0,rdn_pos(X1)) ),
inference(cnf_transformation,[],[f484]) ).
tcf(c_106,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(cnf_transformation,[],[f506]) ).
tcf(c_112,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,[],[f512]) ).
tcf(c_130,plain,
rdn_translate(n6,rdn_pos(rdnn(n6))),
inference(cnf_transformation,[],[f530]) ).
tcf(c_149,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f549]) ).
tcf(c_171,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(cnf_transformation,[],[f571]) ).
tcf(c_175,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = X3 )
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f575]) ).
tcf(c_181,plain,
rdn_positive_less(rdnn(n5),rdnn(n6)),
inference(cnf_transformation,[],[f581]) ).
tcf(c_191,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,[],[f591]) ).
tcf(c_2116,plain,
! [X0: $i,X1: $i] :
( less(X0,n6)
| ~ rdn_positive_less(X1,rdnn(n6))
| ~ rdn_translate(X0,rdn_pos(X1)) ),
inference(superposition,[status(thm)],[c_130,c_84]) ).
tcf(c_2200,plain,
! [X0: $i] :
( ( X0 = sK0 )
| ~ sum(n2,n3,X0) ),
inference(superposition,[status(thm)],[c_50,c_175]) ).
tcf(c_3491,plain,
! [X0: $i,X1: $i] :
( rdn_add_with_carry(rdnn(X0),rdnn(n2),rdnn(n3),rdnn(X1))
| ~ rdn_digit_add(rdnn(n5),rdnn(X0),rdnn(X1),rdnn(n0)) ),
inference(superposition,[status(thm)],[c_71,c_191]) ).
tcf(c_6782,plain,
( less(n5,n6)
| ~ rdn_positive_less(rdnn(n5),rdnn(n6)) ),
inference(superposition,[status(thm)],[c_171,c_2116]) ).
tcf(c_6786,plain,
less(n5,n6),
inference(forward_subsumption_resolution,[status(thm)],[c_6782,c_181]) ).
tcf(c_9310,plain,
rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5)),
inference(superposition,[status(thm)],[c_149,c_3491]) ).
tcf(c_9335,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X0,X1,X2)
| ~ rdn_translate(X2,rdn_pos(rdnn(n5)))
| ~ rdn_translate(X1,rdn_pos(rdnn(n3)))
| ~ rdn_translate(X0,rdn_pos(rdnn(n2))) ),
inference(superposition,[status(thm)],[c_9310,c_112]) ).
tcf(c_15104,plain,
! [X0: $i,X1: $i] :
( sum(n2,X0,X1)
| ~ rdn_translate(X1,rdn_pos(rdnn(n5)))
| ~ rdn_translate(X0,rdn_pos(rdnn(n3))) ),
inference(superposition,[status(thm)],[c_78,c_9335]) ).
tcf(c_15115,plain,
! [X0: $i] :
( sum(n2,n3,X0)
| ~ rdn_translate(X0,rdn_pos(rdnn(n5))) ),
inference(superposition,[status(thm)],[c_106,c_15104]) ).
tcf(c_15123,plain,
sum(n2,n3,n5),
inference(superposition,[status(thm)],[c_171,c_15115]) ).
tcf(c_15127,plain,
sK0 = n5,
inference(superposition,[status(thm)],[c_15123,c_2200]) ).
tcf(c_15139,plain,
~ less(n5,n6),
inference(demodulation,[status(thm)],[c_49,c_15127]) ).
tcf(c_15140,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_15139,c_6786]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM345+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.11/15.47 % CPULimit : 300
% 0.11/15.47 % WCLimit : 300
% 0.11/15.47 % DateTime : Thu Sep 24 03:43:12 UTC 2026
% 0.11/15.48 % CPUTime :
% 0.11/15.48 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.37/15.52 Running first-order theorem proving
% 0.37/15.52 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
% 0.37/15.53
% 0.37/15.53 % ======== iProver multi-core TPTP/SMT =========
% 0.37/15.53
% 0.37/15.53 % Detected problem language: tptp
% 0.37/15.54 % Proving...
% 11.65/17.88 % SZS status Started for theBenchmark.p
% 11.65/17.88 % SZS status Theorem for theBenchmark.p
% 11.65/17.88
% 11.65/17.88 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 11.65/17.88
% 11.65/17.88 % ------ iProver source info
% 11.65/17.88
% 11.65/17.88 % git: date: 2026-07-19 20:42:38 +0200
% 11.65/17.88 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 11.65/17.88 % git: non_committed_changes: false
% 11.65/17.88
% 11.65/17.88 % ------ Parsing...
% 11.65/17.88 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 11.65/17.88
% 11.65/17.88 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 11.65/17.88
% 11.65/17.88 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 11.65/17.88
% 11.65/17.88 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 11.65/17.88 % ------ Proving...
% 11.65/17.88 % ------ Problem Properties
% 11.65/17.88
% 11.65/17.88 %
% 11.65/17.88 % clauses 156
% 11.65/17.88 % conjectures 2
% 11.65/17.88 % EPR 8
% 11.65/17.88 % Horn 155
% 11.65/17.88 % unary 131
% 11.65/17.88 % binary 6
% 11.65/17.88 % lits 223
% 11.65/17.88 % lits eq 4
% 11.65/17.88 % fd_pure 0
% 11.65/17.88 % fd_pseudo 0
% 11.65/17.88 % fd_cond 0
% 11.65/17.88 % fd_pseudo_cond 4
% 11.65/17.88 % AC symbols 0
% 11.65/17.88
% 11.65/17.88 % ------ Schedule dynamic 5 is on
% 11.65/17.88
% 11.65/17.88 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 11.65/17.88
% 11.65/17.88
% 11.65/17.88 % ------
% 11.65/17.88 % Current options:
% 11.65/17.88 % ------
% 11.65/17.88
% 11.65/17.88
% 11.65/17.88 %
% 11.65/17.88
% 11.65/17.88 % ------ Proving...
% 11.65/17.88 %
% 11.65/17.88
% 11.65/17.88 % SZS status Theorem for theBenchmark.p
% 11.65/17.88
% 11.65/17.88 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 11.65/17.88
% 11.65/17.88
%------------------------------------------------------------------------------