%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM319+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 : n019.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 8.50s 3.72s
% Output : CNFRefutation 8.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 37 ( 23 unt; 0 def)
% Number of atoms : 74 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 72 ( 35 ~; 31 |; 4 &)
% ( 0 <=>; 2 =>; 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 : 5 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-1 aty)
% Number of variables : 68 ( 0 sgn 66 !; 2 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
fof(f130,axiom,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdnn2) ).
fof(f133,axiom,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdnn5) ).
fof(f135,axiom,
rdn_translate(nn7,rdn_neg(rdnn(n7))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdnn7) ).
fof(f288,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( rdn_translate(X2,rdn_neg(X5))
& rdn_add_with_carry(rdnn(n0),X3,X4,X5)
& rdn_translate(X1,rdn_neg(X4))
& rdn_translate(X0,rdn_neg(X3)) )
=> sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+2.ax',sum_entry_point_neg_neg) ).
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(f327,axiom,
rdn_digit_add(rdnn(n2),rdnn(n5),rdnn(n7),rdnn(n0)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n2_n5_n7_n0) ).
fof(f372,axiom,
rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n7_n0_n7_n0) ).
fof(f402,conjecture,
? [X0] : sum(nn2,nn5,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_nn2_nn5_what) ).
fof(f403,negated_conjecture,
~ ? [X0] : sum(nn2,nn5,X0),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f425,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ rdn_translate(X2,rdn_neg(X5))
| ~ rdn_add_with_carry(rdnn(n0),X3,X4,X5)
| ~ rdn_translate(X1,rdn_neg(X4))
| ~ rdn_translate(X0,rdn_neg(X3))
| sum(X0,X1,X2) ),
inference(ennf_transformation,[],[f288]) ).
fof(f426,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ rdn_translate(X2,rdn_neg(X5))
| ~ rdn_add_with_carry(rdnn(n0),X3,X4,X5)
| ~ rdn_translate(X1,rdn_neg(X4))
| ~ rdn_translate(X0,rdn_neg(X3))
| sum(X0,X1,X2) ),
inference(flattening,[],[f425]) ).
fof(f441,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(f442,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,[],[f441]) ).
fof(f450,plain,
! [X0] : ~ sum(nn2,nn5,X0),
inference(ennf_transformation,[],[f403]) ).
fof(f583,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
inference(cnf_transformation,[],[f130]) ).
fof(f586,plain,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
inference(cnf_transformation,[],[f133]) ).
fof(f588,plain,
rdn_translate(nn7,rdn_neg(rdnn(n7))),
inference(cnf_transformation,[],[f135]) ).
fof(f743,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ rdn_translate(X2,rdn_neg(X5))
| ~ rdn_add_with_carry(rdnn(n0),X3,X4,X5)
| ~ rdn_translate(X1,rdn_neg(X4))
| ~ rdn_translate(X0,rdn_neg(X3))
| sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f426]) ).
fof(f753,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,[],[f442]) ).
fof(f783,plain,
rdn_digit_add(rdnn(n2),rdnn(n5),rdnn(n7),rdnn(n0)),
inference(cnf_transformation,[],[f327]) ).
fof(f828,plain,
rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0)),
inference(cnf_transformation,[],[f372]) ).
fof(f858,plain,
! [X0] : ~ sum(nn2,nn5,X0),
inference(cnf_transformation,[],[f450]) ).
tcf(c_178,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
inference(cnf_transformation,[],[f583]) ).
tcf(c_181,plain,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
inference(cnf_transformation,[],[f586]) ).
tcf(c_183,plain,
rdn_translate(nn7,rdn_neg(rdnn(n7))),
inference(cnf_transformation,[],[f588]) ).
tcf(c_338,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sum(X3,X5,X4)
| ~ rdn_translate(X5,rdn_neg(X1))
| ~ rdn_translate(X4,rdn_neg(X2))
| ~ rdn_translate(X3,rdn_neg(X0))
| ~ rdn_add_with_carry(rdnn(n0),X0,X1,X2) ),
inference(cnf_transformation,[],[f743]) ).
tcf(c_348,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,[],[f753]) ).
tcf(c_378,plain,
rdn_digit_add(rdnn(n2),rdnn(n5),rdnn(n7),rdnn(n0)),
inference(cnf_transformation,[],[f783]) ).
tcf(c_423,plain,
rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0)),
inference(cnf_transformation,[],[f828]) ).
tcf(c_453,negated_conjecture,
! [X0: $i] : ~ sum(nn2,nn5,X0),
inference(cnf_transformation,[],[f858]) ).
tcf(c_15649,plain,
! [X0: $i,X1: $i] :
( rdn_add_with_carry(rdnn(X0),rdnn(n2),rdnn(n5),rdnn(X1))
| ~ rdn_digit_add(rdnn(n7),rdnn(X0),rdnn(X1),rdnn(n0)) ),
inference(superposition,[status(thm)],[c_378,c_348]) ).
tcf(c_16743,plain,
rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n5),rdnn(n7)),
inference(superposition,[status(thm)],[c_423,c_15649]) ).
tcf(c_19957,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X0,X2,X1)
| ~ rdn_translate(X2,rdn_neg(rdnn(n5)))
| ~ rdn_translate(X1,rdn_neg(rdnn(n7)))
| ~ rdn_translate(X0,rdn_neg(rdnn(n2))) ),
inference(superposition,[status(thm)],[c_16743,c_338]) ).
tcf(c_26390,plain,
! [X0: $i,X1: $i] :
( sum(nn2,X1,X0)
| ~ rdn_translate(X1,rdn_neg(rdnn(n5)))
| ~ rdn_translate(X0,rdn_neg(rdnn(n7))) ),
inference(superposition,[status(thm)],[c_178,c_19957]) ).
tcf(c_33058,plain,
! [X0: $i] :
( sum(nn2,X0,nn7)
| ~ rdn_translate(X0,rdn_neg(rdnn(n5))) ),
inference(superposition,[status(thm)],[c_183,c_26390]) ).
tcf(c_35062,plain,
sum(nn2,nn5,nn7),
inference(superposition,[status(thm)],[c_181,c_33058]) ).
tcf(c_36522,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_35062,c_453]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM319+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n019.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 03:35:37 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 0.12/0.40
% 0.12/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.40
% 0.12/0.40 % Detected problem language: tptp
% 0.12/0.41 % Proving...
% 8.50/3.72 % SZS status Started for theBenchmark.p
% 8.50/3.72 % SZS status Theorem for theBenchmark.p
% 8.50/3.72
% 8.50/3.72 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.50/3.72
% 8.50/3.72 % ------ iProver source info
% 8.50/3.72
% 8.50/3.72 % git: date: 2026-07-19 20:42:38 +0200
% 8.50/3.72 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.50/3.72 % git: non_committed_changes: false
% 8.50/3.72
% 8.50/3.72 % ------ Parsing...
% 8.50/3.72 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 8.50/3.72 % ------ Proving...
% 8.50/3.72 % ------ Problem Properties
% 8.50/3.72
% 8.50/3.72 %
% 8.50/3.72 % clauses 405
% 8.50/3.72 % conjectures 1
% 8.50/3.72 % EPR 11
% 8.50/3.72 % Horn 403
% 8.50/3.72 % unary 376
% 8.50/3.72 % binary 8
% 8.50/3.72 % lits 478
% 8.50/3.72 % lits eq 5
% 8.50/3.72 % fd_pure 0
% 8.50/3.72 % fd_pseudo 0
% 8.50/3.72 % fd_cond 0
% 8.50/3.72 % fd_pseudo_cond 5
% 8.50/3.72 % AC symbols 0
% 8.50/3.72
% 8.50/3.72 % ------ Input Options Time Limit: Unbounded
% 8.50/3.72
% 8.50/3.72
% 8.50/3.72 % ------
% 8.50/3.72 % Current options:
% 8.50/3.72 % ------
% 8.50/3.72
% 8.50/3.72
% 8.50/3.72 %
% 8.50/3.72
% 8.50/3.72 % ------ Proving...
% 8.50/3.72 %
% 8.50/3.72
% 8.50/3.72 % ------ Proving...
% 8.50/3.72 %
% 8.50/3.72
% 8.50/3.72 % ------ Proving...
% 8.50/3.72 %
% 8.50/3.72
% 8.50/3.72 % ------ Proving...
% 8.50/3.72 %
% 8.50/3.72
% 8.50/3.72 % ------ Proving...
% 8.50/3.72 %
% 8.50/3.72
% 8.50/3.72 % ------ Proving...
% 8.50/3.72 %
% 8.50/3.72
% 8.50/3.72 % ------ Proving...
% 8.50/3.72 %
% 8.50/3.72
% 8.50/3.72 % ------ Proving...
% 8.50/3.72 %
% 8.50/3.72
% 8.50/3.72 % SZS status Theorem for theBenchmark.p
% 8.50/3.72
% 8.50/3.72 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.50/3.72
% 8.50/3.72
%------------------------------------------------------------------------------