%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM335+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 : n012.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 02:23:43 PM UTC 2026
% Result : Theorem 7.85s 1.51s
% Output : CNFRefutation 7.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 53 ( 24 unt; 0 def)
% Number of atoms : 114 ( 16 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 113 ( 52 ~; 47 |; 8 &)
% ( 1 <=>; 5 =>; 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 : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-1 aty)
% Number of variables : 102 ( 0 sgn 101 !; 1 ?; 30 :)
% 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(f296,axiom,
! [X0,X1,X2] :
( sum(X1,X2,X0)
<=> difference(X0,X1,X2) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/NUM005+2.ax',add_digit_digit_digit) ).
fof(f334,axiom,
rdn_digit_add(rdnn(n3),rdnn(n2),rdnn(n5),rdnn(n0)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n3_n2_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] :
( difference(n5,n3,X0)
=> X0 = n2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diff_n5_n3_only_n2) ).
fof(f403,negated_conjecture,
~ ! [X0] :
( difference(n5,n3,X0)
=> X0 = n2 ),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f404,plain,
? [X0] :
( difference(n5,n3,X0)
& n2 != 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,
( difference(n5,n3,sK0)
& n2 != sK0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f404]) ).
fof(f449,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(f450,plain,
difference(n5,n3,sK0),
inference(cnf_transformation,[],[f446]) ).
fof(f451,plain,
n2 != sK0,
inference(cnf_transformation,[],[f446]) ).
fof(f452,plain,
! [X2,X3,X0,X1] :
( ~ sum(X0,X2,X3)
| ~ sum(X0,X1,X3)
| X1 = X2 ),
inference(cnf_transformation,[],[f406]) ).
fof(f471,plain,
rdn_digit_add(rdnn(n3),rdnn(n2),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f334]) ).
fof(f485,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(cnf_transformation,[],[f3]) ).
fof(f507,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(cnf_transformation,[],[f4]) ).
fof(f519,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f352]) ).
fof(f525,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(cnf_transformation,[],[f6]) ).
fof(f527,plain,
! [X2,X0,X1] :
( ~ difference(X0,X1,X2)
| sum(X1,X2,X0) ),
inference(cnf_transformation,[],[f449]) ).
fof(f533,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(f594,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,
n2 != sK0,
inference(cnf_transformation,[],[f451]) ).
tcf(c_50,negated_conjecture,
difference(n5,n3,sK0),
inference(cnf_transformation,[],[f450]) ).
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,[],[f452]) ).
tcf(c_70,plain,
rdn_digit_add(rdnn(n3),rdnn(n2),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f471]) ).
tcf(c_84,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(cnf_transformation,[],[f485]) ).
tcf(c_106,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(cnf_transformation,[],[f507]) ).
tcf(c_118,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f519]) ).
tcf(c_124,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(cnf_transformation,[],[f525]) ).
tcf(c_125,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X1,X2,X0)
| ~ difference(X0,X1,X2) ),
inference(cnf_transformation,[],[f527]) ).
tcf(c_132,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,[],[f533]) ).
tcf(c_193,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,[],[f594]) ).
tcf(c_887,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X2,X0,X1)
| ( X2 != n3 )
| ( X1 != n5 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_125]) ).
tcf(c_888,plain,
sum(n3,sK0,n5),
inference(unflattening,[status(thm)],[c_887]) ).
tcf(c_2790,plain,
! [X0: $i] :
( ( X0 = sK0 )
| ~ sum(n3,X0,n5) ),
inference(superposition,[status(thm)],[c_888,c_51]) ).
tcf(c_4516,plain,
! [X0: $i,X1: $i] :
( rdn_add_with_carry(rdnn(X0),rdnn(n3),rdnn(n2),rdnn(X1))
| ~ rdn_digit_add(rdnn(n5),rdnn(X0),rdnn(X1),rdnn(n0)) ),
inference(superposition,[status(thm)],[c_70,c_193]) ).
tcf(c_9489,plain,
rdn_add_with_carry(rdnn(n0),rdnn(n3),rdnn(n2),rdnn(n5)),
inference(superposition,[status(thm)],[c_118,c_4516]) ).
tcf(c_9611,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X2,X0,X1)
| ~ rdn_translate(X2,rdn_pos(rdnn(n3)))
| ~ rdn_translate(X1,rdn_pos(rdnn(n5)))
| ~ rdn_translate(X0,rdn_pos(rdnn(n2))) ),
inference(superposition,[status(thm)],[c_9489,c_132]) ).
tcf(c_14489,plain,
! [X0: $i,X1: $i] :
( sum(X1,X0,n5)
| ~ rdn_translate(X1,rdn_pos(rdnn(n3)))
| ~ rdn_translate(X0,rdn_pos(rdnn(n2))) ),
inference(superposition,[status(thm)],[c_124,c_9611]) ).
tcf(c_14500,plain,
! [X0: $i] :
( sum(n3,X0,n5)
| ~ rdn_translate(X0,rdn_pos(rdnn(n2))) ),
inference(superposition,[status(thm)],[c_106,c_14489]) ).
tcf(c_14508,plain,
sum(n3,n2,n5),
inference(superposition,[status(thm)],[c_84,c_14500]) ).
tcf(c_14513,plain,
n2 = sK0,
inference(superposition,[status(thm)],[c_14508,c_2790]) ).
tcf(c_14514,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_14513,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM335+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Thu Sep 24 03:38:05 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.32 Running first-order theorem proving
% 0.03/0.32 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
% 0.07/0.33
% 0.07/0.33 % ======== iProver multi-core TPTP/SMT =========
% 0.07/0.33
% 0.07/0.33 % Detected problem language: tptp
% 0.07/0.34 % Proving...
% 7.85/1.51 % SZS status Started for theBenchmark.p
% 7.85/1.51 % SZS status Theorem for theBenchmark.p
% 7.85/1.51
% 7.85/1.51 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.85/1.51
% 7.85/1.51 % ------ iProver source info
% 7.85/1.51
% 7.85/1.51 % git: date: 2026-07-19 20:42:38 +0200
% 7.85/1.51 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.85/1.51 % git: non_committed_changes: false
% 7.85/1.51
% 7.85/1.51 % ------ Parsing...
% 7.85/1.51 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.85/1.51
% 7.85/1.51 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 7.85/1.51
% 7.85/1.51 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.85/1.51
% 7.85/1.51 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.85/1.51 % ------ Proving...
% 7.85/1.51 % ------ Problem Properties
% 7.85/1.51
% 7.85/1.51 %
% 7.85/1.51 % clauses 156
% 7.85/1.51 % conjectures 1
% 7.85/1.51 % EPR 8
% 7.85/1.51 % Horn 155
% 7.85/1.51 % unary 131
% 7.85/1.51 % binary 6
% 7.85/1.51 % lits 223
% 7.85/1.51 % lits eq 5
% 7.85/1.51 % fd_pure 0
% 7.85/1.51 % fd_pseudo 0
% 7.85/1.51 % fd_cond 0
% 7.85/1.51 % fd_pseudo_cond 4
% 7.85/1.51 % AC symbols 0
% 7.85/1.51
% 7.85/1.51 % ------ Schedule dynamic 5 is on
% 7.85/1.51
% 7.85/1.51 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.85/1.51
% 7.85/1.51
% 7.85/1.51 % ------
% 7.85/1.51 % Current options:
% 7.85/1.51 % ------
% 7.85/1.51
% 7.85/1.51
% 7.85/1.51 %
% 7.85/1.51
% 7.85/1.51 % ------ Proving...
% 7.85/1.51 %
% 7.85/1.51
% 7.85/1.51 % SZS status Theorem for theBenchmark.p
% 7.85/1.51
% 7.85/1.51 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.85/1.51
% 7.85/1.51
%------------------------------------------------------------------------------