%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM324+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 : n001.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 02:23:42 PM UTC 2026
% Result : Theorem 13.37s 3.28s
% Output : CNFRefutation 13.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 56 ( 34 unt; 0 def)
% Number of atoms : 114 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 112 ( 54 ~; 49 |; 6 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-1 aty)
% Number of variables : 89 ( 0 sgn 87 !; 2 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn2) ).
fof(f131,axiom,
rdn_translate(nn3,rdn_neg(rdnn(n3))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdnn3) ).
fof(f133,axiom,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdnn5) ).
fof(f268,axiom,
rdn_positive_less(rdnn(n2),rdnn(n3)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',rdn_positive_less23) ).
fof(f269,axiom,
rdn_positive_less(rdnn(n3),rdnn(n4)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',rdn_positive_less34) ).
fof(f270,axiom,
rdn_positive_less(rdnn(n4),rdnn(n5)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',rdn_positive_less45) ).
fof(f275,axiom,
! [X0,X1,X2] :
( ( rdn_positive_less(rdnn(X1),rdnn(X2))
& rdn_positive_less(rdnn(X0),rdnn(X1)) )
=> rdn_positive_less(rdnn(X0),rdnn(X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',rdn_positive_less_transitivity) ).
fof(f289,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( rdn_translate(X2,rdn_neg(X5))
& rdn_add_with_carry(rdnn(n0),X3,X5,X4)
& rdn_positive_less(X3,X4)
& rdn_translate(X1,rdn_neg(X4))
& rdn_translate(X0,rdn_pos(X3)) )
=> sum(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',sum_entry_point_pos_neg_1) ).
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(X0,nn5,nn3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_what_nn5_nn3) ).
fof(f403,negated_conjecture,
~ ? [X0] : sum(X0,nn5,nn3),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f404,plain,
! [X0] : ~ sum(X0,nn5,nn3),
inference(ennf_transformation,[],[f403]) ).
fof(f411,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ rdn_translate(X2,rdn_neg(X5))
| ~ rdn_add_with_carry(rdnn(n0),X3,X5,X4)
| ~ rdn_positive_less(X3,X4)
| ~ rdn_translate(X1,rdn_neg(X4))
| ~ rdn_translate(X0,rdn_pos(X3))
| sum(X0,X1,X2) ),
inference(ennf_transformation,[],[f289]) ).
fof(f412,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ rdn_translate(X2,rdn_neg(X5))
| ~ rdn_add_with_carry(rdnn(n0),X3,X5,X4)
| ~ rdn_positive_less(X3,X4)
| ~ rdn_translate(X1,rdn_neg(X4))
| ~ rdn_translate(X0,rdn_pos(X3))
| sum(X0,X1,X2) ),
inference(flattening,[],[f411]) ).
fof(f418,plain,
! [X0,X1,X2] :
( ~ rdn_positive_less(rdnn(X1),rdnn(X2))
| ~ rdn_positive_less(rdnn(X0),rdnn(X1))
| rdn_positive_less(rdnn(X0),rdnn(X2)) ),
inference(ennf_transformation,[],[f275]) ).
fof(f419,plain,
! [X0,X1,X2] :
( ~ rdn_positive_less(rdnn(X1),rdnn(X2))
| ~ rdn_positive_less(rdnn(X0),rdnn(X1))
| rdn_positive_less(rdnn(X0),rdnn(X2)) ),
inference(flattening,[],[f418]) ).
fof(f427,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(f428,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,[],[f427]) ).
fof(f434,plain,
! [X0] : ~ sum(X0,nn5,nn3),
inference(cnf_transformation,[],[f404]) ).
fof(f438,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ rdn_translate(X2,rdn_neg(X5))
| ~ rdn_add_with_carry(rdnn(n0),X3,X5,X4)
| ~ rdn_positive_less(X3,X4)
| ~ rdn_translate(X1,rdn_neg(X4))
| ~ rdn_translate(X0,rdn_pos(X3))
| sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f412]) ).
fof(f441,plain,
rdn_translate(nn3,rdn_neg(rdnn(n3))),
inference(cnf_transformation,[],[f131]) ).
fof(f442,plain,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
inference(cnf_transformation,[],[f133]) ).
fof(f452,plain,
! [X2,X0,X1] :
( ~ rdn_positive_less(rdnn(X1),rdnn(X2))
| ~ rdn_positive_less(rdnn(X0),rdnn(X1))
| rdn_positive_less(rdnn(X0),rdnn(X2)) ),
inference(cnf_transformation,[],[f419]) ).
fof(f457,plain,
rdn_positive_less(rdnn(n4),rdnn(n5)),
inference(cnf_transformation,[],[f270]) ).
fof(f458,plain,
rdn_positive_less(rdnn(n3),rdnn(n4)),
inference(cnf_transformation,[],[f269]) ).
fof(f459,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(cnf_transformation,[],[f268]) ).
fof(f466,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,[],[f428]) ).
fof(f489,plain,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f325]) ).
fof(f509,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f352]) ).
fof(f531,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(cnf_transformation,[],[f3]) ).
tcf(c_49,negated_conjecture,
! [X0: $i] : ~ sum(X0,nn5,nn3),
inference(cnf_transformation,[],[f434]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sum(X3,X4,X5)
| ~ rdn_positive_less(X0,X2)
| ~ rdn_translate(X5,rdn_neg(X1))
| ~ rdn_translate(X4,rdn_neg(X2))
| ~ rdn_translate(X3,rdn_pos(X0))
| ~ rdn_add_with_carry(rdnn(n0),X0,X1,X2) ),
inference(cnf_transformation,[],[f438]) ).
tcf(c_56,plain,
rdn_translate(nn3,rdn_neg(rdnn(n3))),
inference(cnf_transformation,[],[f441]) ).
tcf(c_57,plain,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
inference(cnf_transformation,[],[f442]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( rdn_positive_less(rdnn(X0),rdnn(X2))
| ~ rdn_positive_less(rdnn(X1),rdnn(X2))
| ~ rdn_positive_less(rdnn(X0),rdnn(X1)) ),
inference(cnf_transformation,[],[f452]) ).
tcf(c_72,plain,
rdn_positive_less(rdnn(n4),rdnn(n5)),
inference(cnf_transformation,[],[f457]) ).
tcf(c_73,plain,
rdn_positive_less(rdnn(n3),rdnn(n4)),
inference(cnf_transformation,[],[f458]) ).
tcf(c_74,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(cnf_transformation,[],[f459]) ).
tcf(c_81,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,[],[f466]) ).
tcf(c_104,plain,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f489]) ).
tcf(c_124,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f509]) ).
tcf(c_146,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(cnf_transformation,[],[f531]) ).
tcf(c_2539,plain,
! [X0: $i] :
( rdn_positive_less(rdnn(n3),rdnn(X0))
| ~ rdn_positive_less(rdnn(n4),rdnn(X0)) ),
inference(superposition,[status(thm)],[c_73,c_67]) ).
tcf(c_2540,plain,
! [X0: $i] :
( rdn_positive_less(rdnn(n2),rdnn(X0))
| ~ rdn_positive_less(rdnn(n3),rdnn(X0)) ),
inference(superposition,[status(thm)],[c_74,c_67]) ).
tcf(c_2947,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_104,c_81]) ).
tcf(c_11646,plain,
rdn_positive_less(rdnn(n3),rdnn(n5)),
inference(superposition,[status(thm)],[c_72,c_2539]) ).
tcf(c_11772,plain,
rdn_positive_less(rdnn(n2),rdnn(n5)),
inference(superposition,[status(thm)],[c_11646,c_2540]) ).
tcf(c_15771,plain,
rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5)),
inference(superposition,[status(thm)],[c_124,c_2947]) ).
tcf(c_15877,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X0,X1,X2)
| ~ rdn_positive_less(rdnn(n2),rdnn(n5))
| ~ rdn_translate(X2,rdn_neg(rdnn(n3)))
| ~ rdn_translate(X1,rdn_neg(rdnn(n5)))
| ~ rdn_translate(X0,rdn_pos(rdnn(n2))) ),
inference(superposition,[status(thm)],[c_15771,c_53]) ).
tcf(c_15892,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X0,X1,X2)
| ~ rdn_translate(X2,rdn_neg(rdnn(n3)))
| ~ rdn_translate(X1,rdn_neg(rdnn(n5)))
| ~ rdn_translate(X0,rdn_pos(rdnn(n2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15877,c_11772]) ).
tcf(c_24963,plain,
! [X0: $i,X1: $i] :
( sum(X0,X1,nn3)
| ~ rdn_translate(X1,rdn_neg(rdnn(n5)))
| ~ rdn_translate(X0,rdn_pos(rdnn(n2))) ),
inference(superposition,[status(thm)],[c_56,c_15892]) ).
tcf(c_24974,plain,
! [X0: $i] :
( sum(X0,nn5,nn3)
| ~ rdn_translate(X0,rdn_pos(rdnn(n2))) ),
inference(superposition,[status(thm)],[c_57,c_24963]) ).
tcf(c_24975,plain,
! [X0: $i] : ~ rdn_translate(X0,rdn_pos(rdnn(n2))),
inference(forward_subsumption_resolution,[status(thm)],[c_24974,c_49]) ).
tcf(c_24976,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_146,c_24975]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM324+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 03:41:36 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 13.37/3.28 % SZS status Started for theBenchmark.p
% 13.37/3.28 % SZS status Theorem for theBenchmark.p
% 13.37/3.28
% 13.37/3.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 13.37/3.28
% 13.37/3.28 % ------ iProver source info
% 13.37/3.28
% 13.37/3.28 % git: date: 2026-07-19 20:42:38 +0200
% 13.37/3.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 13.37/3.28 % git: non_committed_changes: false
% 13.37/3.28
% 13.37/3.28 % ------ Parsing...
% 13.37/3.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 13.37/3.28
% 13.37/3.28 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 13.37/3.28
% 13.37/3.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 13.37/3.28 % ------ Proving...
% 13.37/3.28 % ------ Problem Properties
% 13.37/3.28
% 13.37/3.28 %
% 13.37/3.28 % clauses 147
% 13.37/3.28 % conjectures 1
% 13.37/3.28 % EPR 1
% 13.37/3.28 % Horn 147
% 13.37/3.28 % unary 131
% 13.37/3.28 % binary 4
% 13.37/3.28 % lits 196
% 13.37/3.28 % lits eq 0
% 13.37/3.28 % fd_pure 0
% 13.37/3.28 % fd_pseudo 0
% 13.37/3.28 % fd_cond 0
% 13.37/3.28 % fd_pseudo_cond 0
% 13.37/3.28 % AC symbols 0
% 13.37/3.28
% 13.37/3.28 % ------ Schedule dynamic 5 is on
% 13.37/3.28
% 13.37/3.28 % ------ no equalities: superposition off
% 13.37/3.28
% 13.37/3.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 13.37/3.28
% 13.37/3.28
% 13.37/3.28 % ------
% 13.37/3.28 % Current options:
% 13.37/3.28 % ------
% 13.37/3.28
% 13.37/3.28
% 13.37/3.28 %
% 13.37/3.28
% 13.37/3.28 % ------ Proving...
% 13.37/3.28 %
% 13.37/3.28
% 13.37/3.28 % SZS status Theorem for theBenchmark.p
% 13.37/3.28
% 13.37/3.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 13.37/3.28
% 13.37/3.28
%------------------------------------------------------------------------------