%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM344+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 : n003.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 02:23:44 PM UTC 2026
% Result : Theorem 4.40s 1.27s
% Output : CNFRefutation 4.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 14 unt; 0 def)
% Number of atoms : 83 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 86 ( 41 ~; 36 |; 6 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-1 aty)
% Number of variables : 76 ( 0 sgn 72 !; 4 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
rdn_translate(n0,rdn_pos(rdnn(n0))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn0) ).
fof(f2,axiom,
rdn_translate(n1,rdn_pos(rdnn(n1))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn1) ).
fof(f129,axiom,
rdn_translate(nn1,rdn_neg(rdnn(n1))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdnn1) ).
fof(f282,axiom,
! [X0,X1,X2,X3] :
( ( rdn_translate(X1,rdn_pos(X3))
& rdn_translate(X0,rdn_neg(X2)) )
=> less(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',less_entry_point_neg_pos) ).
fof(f291,axiom,
! [X0,X1,X2] :
( ( rdn_translate(X1,rdn_neg(X2))
& rdn_translate(X0,rdn_pos(X2)) )
=> sum(X0,X1,n0) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',sum_entry_point_posx_negx) ).
fof(f292,axiom,
! [X0,X1,X2,X3,X4] :
( ( sum(X1,X0,X2)
& rdn_translate(X1,rdn_pos(X4))
& rdn_translate(X0,rdn_neg(X3)) )
=> sum(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',sum_entry_point_neg_pos) ).
fof(f402,conjecture,
? [X0,X1] :
( less(X0,X1)
& sum(X0,n1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exist_bigger_plus_one) ).
fof(f403,negated_conjecture,
~ ? [X0,X1] :
( less(X0,X1)
& sum(X0,n1,X1) ),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f415,plain,
! [X0,X1,X2,X3] :
( ~ rdn_translate(X1,rdn_pos(X3))
| ~ rdn_translate(X0,rdn_neg(X2))
| less(X0,X1) ),
inference(ennf_transformation,[],[f282]) ).
fof(f416,plain,
! [X0,X1,X2,X3] :
( ~ rdn_translate(X1,rdn_pos(X3))
| ~ rdn_translate(X0,rdn_neg(X2))
| less(X0,X1) ),
inference(flattening,[],[f415]) ).
fof(f431,plain,
! [X0,X1,X2] :
( ~ rdn_translate(X1,rdn_neg(X2))
| ~ rdn_translate(X0,rdn_pos(X2))
| sum(X0,X1,n0) ),
inference(ennf_transformation,[],[f291]) ).
fof(f432,plain,
! [X0,X1,X2] :
( ~ rdn_translate(X1,rdn_neg(X2))
| ~ rdn_translate(X0,rdn_pos(X2))
| sum(X0,X1,n0) ),
inference(flattening,[],[f431]) ).
fof(f433,plain,
! [X0,X1,X2,X3,X4] :
( ~ sum(X1,X0,X2)
| ~ rdn_translate(X1,rdn_pos(X4))
| ~ rdn_translate(X0,rdn_neg(X3))
| sum(X0,X1,X2) ),
inference(ennf_transformation,[],[f292]) ).
fof(f434,plain,
! [X0,X1,X2,X3,X4] :
( ~ sum(X1,X0,X2)
| ~ rdn_translate(X1,rdn_pos(X4))
| ~ rdn_translate(X0,rdn_neg(X3))
| sum(X0,X1,X2) ),
inference(flattening,[],[f433]) ).
fof(f450,plain,
! [X0,X1] :
( ~ less(X0,X1)
| ~ sum(X0,n1,X1) ),
inference(ennf_transformation,[],[f403]) ).
fof(f454,plain,
rdn_translate(n0,rdn_pos(rdnn(n0))),
inference(cnf_transformation,[],[f1]) ).
fof(f455,plain,
rdn_translate(n1,rdn_pos(rdnn(n1))),
inference(cnf_transformation,[],[f2]) ).
fof(f582,plain,
rdn_translate(nn1,rdn_neg(rdnn(n1))),
inference(cnf_transformation,[],[f129]) ).
fof(f735,plain,
! [X2,X3,X0,X1] :
( ~ rdn_translate(X1,rdn_pos(X3))
| ~ rdn_translate(X0,rdn_neg(X2))
| less(X0,X1) ),
inference(cnf_transformation,[],[f416]) ).
fof(f746,plain,
! [X2,X0,X1] :
( ~ rdn_translate(X1,rdn_neg(X2))
| ~ rdn_translate(X0,rdn_pos(X2))
| sum(X0,X1,n0) ),
inference(cnf_transformation,[],[f432]) ).
fof(f747,plain,
! [X2,X3,X0,X1,X4] :
( ~ sum(X1,X0,X2)
| ~ rdn_translate(X1,rdn_pos(X4))
| ~ rdn_translate(X0,rdn_neg(X3))
| sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f434]) ).
fof(f858,plain,
! [X0,X1] :
( ~ less(X0,X1)
| ~ sum(X0,n1,X1) ),
inference(cnf_transformation,[],[f450]) ).
tcf(c_49,plain,
rdn_translate(n0,rdn_pos(rdnn(n0))),
inference(cnf_transformation,[],[f454]) ).
tcf(c_50,plain,
rdn_translate(n1,rdn_pos(rdnn(n1))),
inference(cnf_transformation,[],[f455]) ).
tcf(c_177,plain,
rdn_translate(nn1,rdn_neg(rdnn(n1))),
inference(cnf_transformation,[],[f582]) ).
tcf(c_330,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( less(X0,X2)
| ~ rdn_translate(X2,rdn_pos(X3))
| ~ rdn_translate(X0,rdn_neg(X1)) ),
inference(cnf_transformation,[],[f735]) ).
tcf(c_341,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X0,X2,n0)
| ~ rdn_translate(X2,rdn_neg(X1))
| ~ rdn_translate(X0,rdn_pos(X1)) ),
inference(cnf_transformation,[],[f746]) ).
tcf(c_342,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sum(X1,X0,X2)
| ~ rdn_translate(X1,rdn_neg(X3))
| ~ rdn_translate(X0,rdn_pos(X4))
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f747]) ).
tcf(c_453,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ less(X0,X1)
| ~ sum(X0,n1,X1) ),
inference(cnf_transformation,[],[f858]) ).
tcf(c_591,plain,
! [X0: $i,X1: $i] :
( less(X0,n0)
| ~ rdn_translate(X0,rdn_neg(X1)) ),
inference(superposition,[status(thm)],[c_49,c_330]) ).
tcf(c_632,plain,
! [X0: $i] :
( sum(n1,X0,n0)
| ~ rdn_translate(X0,rdn_neg(rdnn(n1))) ),
inference(superposition,[status(thm)],[c_50,c_341]) ).
tcf(c_877,plain,
less(nn1,n0),
inference(superposition,[status(thm)],[c_177,c_591]) ).
tcf(c_888,plain,
sum(n1,nn1,n0),
inference(superposition,[status(thm)],[c_177,c_632]) ).
tcf(c_1177,plain,
! [X0: $i,X1: $i] :
( sum(nn1,n1,n0)
| ~ rdn_translate(nn1,rdn_neg(X1))
| ~ rdn_translate(n1,rdn_pos(X0)) ),
inference(superposition,[status(thm)],[c_888,c_342]) ).
tcf(c_1467,plain,
! [X0: $i] :
( sum(nn1,n1,n0)
| ~ rdn_translate(nn1,rdn_neg(X0)) ),
inference(superposition,[status(thm)],[c_50,c_1177]) ).
tcf(c_1611,plain,
sum(nn1,n1,n0),
inference(superposition,[status(thm)],[c_177,c_1467]) ).
tcf(c_1642,plain,
~ less(nn1,n0),
inference(superposition,[status(thm)],[c_1611,c_453]) ).
tcf(c_1647,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_877,c_1642]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM344+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n003.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 03:40:50 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.41 % Proving...
% 4.40/1.27 % SZS status Started for theBenchmark.p
% 4.40/1.27 % SZS status Theorem for theBenchmark.p
% 4.40/1.27
% 4.40/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.40/1.27
% 4.40/1.27 % ------ iProver source info
% 4.40/1.27
% 4.40/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 4.40/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.40/1.27 % git: non_committed_changes: false
% 4.40/1.27
% 4.40/1.27 % ------ Parsing...
% 4.40/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 4.40/1.27 % ------ Proving...
% 4.40/1.27 % ------ Problem Properties
% 4.40/1.27
% 4.40/1.27 %
% 4.40/1.27 % clauses 405
% 4.40/1.27 % conjectures 1
% 4.40/1.27 % EPR 11
% 4.40/1.27 % Horn 403
% 4.40/1.27 % unary 375
% 4.40/1.27 % binary 9
% 4.40/1.27 % lits 479
% 4.40/1.27 % lits eq 5
% 4.40/1.27 % fd_pure 0
% 4.40/1.27 % fd_pseudo 0
% 4.40/1.27 % fd_cond 0
% 4.40/1.27 % fd_pseudo_cond 5
% 4.40/1.27 % AC symbols 0
% 4.40/1.27
% 4.40/1.27 % ------ Input Options Time Limit: Unbounded
% 4.40/1.27
% 4.40/1.27
% 4.40/1.27 % ------
% 4.40/1.27 % Current options:
% 4.40/1.27 % ------
% 4.40/1.27
% 4.40/1.27
% 4.40/1.27 %
% 4.40/1.27
% 4.40/1.27 % ------ Proving...
% 4.40/1.27 %
% 4.40/1.27
% 4.40/1.27 % ------ Proving...
% 4.40/1.27 %
% 4.40/1.27
% 4.40/1.27 % SZS status Theorem for theBenchmark.p
% 4.40/1.27
% 4.40/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.40/1.27
% 4.40/1.27
%------------------------------------------------------------------------------