%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM313+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 : n008.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 1.45s 1.78s
% Output : CNFRefutation 1.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 47 ( 23 unt; 0 def)
% Number of atoms : 99 ( 13 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 97 ( 45 ~; 40 |; 7 &)
% ( 0 <=>; 5 =>; 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 : 6 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-1 aty)
% Number of variables : 87 ( 0 sgn 86 !; 1 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdn2) ).
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(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/sandbox2/benchmark/Axioms/NUM005+2.ax',sum_entry_point_pos_pos) ).
fof(f295,axiom,
! [X0,X1,X2,X3] :
( ( sum(X0,X2,X3)
& sum(X0,X1,X3) )
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+2.ax',unique_RHS) ).
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,
! [X0] :
( sum(n2,X0,n5)
=> X0 = n3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sumn2_only_n3_n5) ).
fof(f403,negated_conjecture,
~ ! [X0] :
( sum(n2,X0,n5)
=> X0 = n3 ),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f404,plain,
? [X0] :
( sum(n2,X0,n5)
& n3 != X0 ),
inference(ennf_transformation,[],[f403]) ).
fof(f405,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,X2,X3)
| ~ sum(X0,X1,X3)
| X1 = X2 ),
inference(ennf_transformation,[],[f295]) ).
fof(f406,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,X2,X3)
| ~ sum(X0,X1,X3)
| X1 = X2 ),
inference(flattening,[],[f405]) ).
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(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,sK0,n5)
& n3 != sK0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f404]) ).
fof(f449,plain,
sum(n2,sK0,n5),
inference(cnf_transformation,[],[f446]) ).
fof(f450,plain,
n3 != sK0,
inference(cnf_transformation,[],[f446]) ).
fof(f451,plain,
! [X2,X3,X0,X1] :
( ~ sum(X0,X2,X3)
| ~ sum(X0,X1,X3)
| X1 = X2 ),
inference(cnf_transformation,[],[f406]) ).
fof(f477,plain,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f325]) ).
fof(f484,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(cnf_transformation,[],[f3]) ).
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(f524,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f352]) ).
fof(f530,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(cnf_transformation,[],[f6]) ).
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,
n3 != sK0,
inference(cnf_transformation,[],[f450]) ).
tcf(c_50,negated_conjecture,
sum(n2,sK0,n5),
inference(cnf_transformation,[],[f449]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X3 )
| ~ sum(X0,X3,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f451]) ).
tcf(c_77,plain,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f477]) ).
tcf(c_84,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
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(X5,X3,X4)
| ~ rdn_translate(X5,rdn_pos(X0))
| ~ rdn_translate(X4,rdn_pos(X2))
| ~ rdn_translate(X3,rdn_pos(X1))
| ~ rdn_add_with_carry(rdnn(n0),X0,X1,X2) ),
inference(cnf_transformation,[],[f512]) ).
tcf(c_124,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f524]) ).
tcf(c_130,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(cnf_transformation,[],[f530]) ).
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_2038,plain,
! [X0: $i] :
( ( X0 = sK0 )
| ~ sum(n2,X0,n5) ),
inference(superposition,[status(thm)],[c_50,c_51]) ).
tcf(c_3661,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_77,c_191]) ).
tcf(c_9154,plain,
rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5)),
inference(superposition,[status(thm)],[c_124,c_3661]) ).
tcf(c_9176,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X2,X0,X1)
| ~ rdn_translate(X2,rdn_pos(rdnn(n2)))
| ~ rdn_translate(X1,rdn_pos(rdnn(n5)))
| ~ rdn_translate(X0,rdn_pos(rdnn(n3))) ),
inference(superposition,[status(thm)],[c_9154,c_112]) ).
tcf(c_14193,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_84,c_9176]) ).
tcf(c_14204,plain,
! [X0: $i] :
( sum(n2,X0,n5)
| ~ rdn_translate(X0,rdn_pos(rdnn(n3))) ),
inference(superposition,[status(thm)],[c_130,c_14193]) ).
tcf(c_14212,plain,
sum(n2,n3,n5),
inference(superposition,[status(thm)],[c_106,c_14204]) ).
tcf(c_14217,plain,
n3 = sK0,
inference(superposition,[status(thm)],[c_14212,c_2038]) ).
tcf(c_14218,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_14217,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM313+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.38 % Computer : n008.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Thu Sep 24 03:35:24 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.42 Running first-order theorem proving
% 0.09/0.42 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
% 0.09/0.43
% 0.09/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.43
% 0.09/0.43 % Detected problem language: tptp
% 0.09/0.45 % Proving...
% 1.45/1.78 % SZS status Started for theBenchmark.p
% 1.45/1.78 % SZS status Theorem for theBenchmark.p
% 1.45/1.78
% 1.45/1.78 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.45/1.78
% 1.45/1.78 % ------ iProver source info
% 1.45/1.78
% 1.45/1.78 % git: date: 2026-07-19 20:42:38 +0200
% 1.45/1.78 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.45/1.78 % git: non_committed_changes: false
% 1.45/1.78
% 1.45/1.78 % ------ Parsing...
% 1.45/1.78 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.45/1.78
% 1.45/1.78 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.45/1.78
% 1.45/1.78 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.45/1.78
% 1.45/1.78 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.45/1.78 % ------ Proving...
% 1.45/1.78 % ------ Problem Properties
% 1.45/1.78
% 1.45/1.78 %
% 1.45/1.78 % clauses 156
% 1.45/1.78 % conjectures 2
% 1.45/1.78 % EPR 8
% 1.45/1.78 % Horn 155
% 1.45/1.78 % unary 131
% 1.45/1.78 % binary 6
% 1.45/1.78 % lits 223
% 1.45/1.78 % lits eq 5
% 1.45/1.78 % fd_pure 0
% 1.45/1.78 % fd_pseudo 0
% 1.45/1.78 % fd_cond 0
% 1.45/1.78 % fd_pseudo_cond 4
% 1.45/1.78 % AC symbols 0
% 1.45/1.78
% 1.45/1.78 % ------ Schedule dynamic 5 is on
% 1.45/1.78
% 1.45/1.78 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.45/1.78
% 1.45/1.78
% 1.45/1.78 % ------
% 1.45/1.78 % Current options:
% 1.45/1.78 % ------
% 1.45/1.78
% 1.45/1.78
% 1.45/1.78 %
% 1.45/1.78
% 1.45/1.78 % ------ Proving...
% 1.45/1.78 %
% 1.45/1.78
% 1.45/1.78 % SZS status Theorem for theBenchmark.p
% 1.45/1.78
% 1.45/1.78 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.45/1.78
% 1.45/1.78
%------------------------------------------------------------------------------