%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM303+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 : n015.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 02:23:39 PM UTC 2026
% Result : Theorem 3.45s 1.39s
% Output : CNFRefutation 3.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 33 ( 17 unt; 0 def)
% Number of atoms : 70 ( 10 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 72 ( 35 ~; 27 |; 7 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 51 !; 0 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
fof(f22,axiom,
rdn_translate(n21,rdn_pos(rdn(rdnn(n1),rdnn(n2)))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn21) ).
fof(f32,axiom,
rdn_translate(n31,rdn_pos(rdn(rdnn(n1),rdnn(n3)))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn31) ).
fof(f268,axiom,
rdn_positive_less(rdnn(n2),rdnn(n3)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',rdn_positive_less23) ).
fof(f276,axiom,
! [X0,X1,X2,X3] :
( rdn_positive_less(X1,X3)
=> rdn_positive_less(rdn(rdnn(X0),X1),rdn(rdnn(X2),X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',rdn_positive_less_multi_digit_high) ).
fof(f281,axiom,
! [X0,X1,X2,X3] :
( ( rdn_positive_less(X2,X3)
& rdn_translate(X1,rdn_pos(X3))
& rdn_translate(X0,rdn_pos(X2)) )
=> less(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',less_entry_point_pos_pos) ).
fof(f284,axiom,
! [X0,X1] :
( less(X0,X1)
<=> ( X1 != X0
& ~ less(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',less_property) ).
fof(f402,conjecture,
n31 != n21,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n31_not_n12) ).
fof(f403,negated_conjecture,
~ ( n31 != n21 ),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f404,plain,
n21 = n31,
inference(flattening,[],[f403]) ).
fof(f427,plain,
! [X0,X1,X2,X3] :
( ~ rdn_positive_less(X2,X3)
| ~ rdn_translate(X1,rdn_pos(X3))
| ~ rdn_translate(X0,rdn_pos(X2))
| less(X0,X1) ),
inference(ennf_transformation,[],[f281]) ).
fof(f428,plain,
! [X0,X1,X2,X3] :
( ~ rdn_positive_less(X2,X3)
| ~ rdn_translate(X1,rdn_pos(X3))
| ~ rdn_translate(X0,rdn_pos(X2))
| less(X0,X1) ),
inference(flattening,[],[f427]) ).
fof(f429,plain,
! [X0,X1,X2,X3] :
( ~ rdn_positive_less(X1,X3)
| rdn_positive_less(rdn(rdnn(X0),X1),rdn(rdnn(X2),X3)) ),
inference(ennf_transformation,[],[f276]) ).
fof(f446,plain,
! [X0,X1] :
( ( ~ less(X0,X1)
| ( X1 != X0
& ~ less(X1,X0) ) )
& ( X0 = X1
| less(X1,X0)
| less(X0,X1) ) ),
inference(nnf_transformation,[],[f284]) ).
fof(f447,plain,
! [X0,X1] :
( ( ~ less(X0,X1)
| ( X1 != X0
& ~ less(X1,X0) ) )
& ( X0 = X1
| less(X1,X0)
| less(X0,X1) ) ),
inference(flattening,[],[f446]) ).
fof(f448,plain,
n21 = n31,
inference(cnf_transformation,[],[f404]) ).
fof(f452,plain,
! [X0,X1] :
( ~ less(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f447]) ).
fof(f455,plain,
rdn_translate(n21,rdn_pos(rdn(rdnn(n1),rdnn(n2)))),
inference(cnf_transformation,[],[f22]) ).
fof(f456,plain,
rdn_translate(n31,rdn_pos(rdn(rdnn(n1),rdnn(n3)))),
inference(cnf_transformation,[],[f32]) ).
fof(f465,plain,
! [X2,X3,X0,X1] :
( ~ rdn_positive_less(X2,X3)
| ~ rdn_translate(X1,rdn_pos(X3))
| ~ rdn_translate(X0,rdn_pos(X2))
| less(X0,X1) ),
inference(cnf_transformation,[],[f428]) ).
fof(f521,plain,
! [X2,X3,X0,X1] :
( ~ rdn_positive_less(X1,X3)
| rdn_positive_less(rdn(rdnn(X0),X1),rdn(rdnn(X2),X3)) ),
inference(cnf_transformation,[],[f429]) ).
fof(f529,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(cnf_transformation,[],[f268]) ).
fof(f605,plain,
rdn_translate(n31,rdn_pos(rdn(rdnn(n1),rdnn(n2)))),
inference(definition_unfolding,[],[f455,f448]) ).
fof(f606,plain,
! [X1] : ~ less(X1,X1),
inference(equality_resolution,[],[f452]) ).
tcf(c_54,plain,
! [X0: $i] : ~ less(X0,X0),
inference(cnf_transformation,[],[f606]) ).
tcf(c_55,negated_conjecture,
rdn_translate(n31,rdn_pos(rdn(rdnn(n1),rdnn(n2)))),
inference(cnf_transformation,[],[f605]) ).
tcf(c_56,plain,
rdn_translate(n31,rdn_pos(rdn(rdnn(n1),rdnn(n3)))),
inference(cnf_transformation,[],[f456]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( less(X2,X0)
| ~ rdn_positive_less(X3,X1)
| ~ rdn_translate(X2,rdn_pos(X3))
| ~ rdn_translate(X0,rdn_pos(X1)) ),
inference(cnf_transformation,[],[f465]) ).
tcf(c_121,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( rdn_positive_less(rdn(rdnn(X2),X0),rdn(rdnn(X3),X1))
| ~ rdn_positive_less(X0,X1) ),
inference(cnf_transformation,[],[f521]) ).
tcf(c_129,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(cnf_transformation,[],[f529]) ).
tcf(c_2242,plain,
! [X0: $i,X1: $i] :
( less(n31,X1)
| ~ rdn_translate(X1,rdn_pos(X0))
| ~ rdn_positive_less(rdn(rdnn(n1),rdnn(n2)),X0) ),
inference(superposition,[status(thm)],[c_55,c_65]) ).
tcf(c_2324,plain,
! [X0: $i,X1: $i,X2: $i] :
( less(n31,X0)
| ~ rdn_positive_less(rdnn(n2),X2)
| ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X1),X2))) ),
inference(superposition,[status(thm)],[c_121,c_2242]) ).
tcf(c_2336,plain,
( less(n31,n31)
| ~ rdn_positive_less(rdnn(n2),rdnn(n3)) ),
inference(superposition,[status(thm)],[c_56,c_2324]) ).
tcf(c_2337,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2336,c_54,c_129]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM303+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.39 % Computer : n015.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Thu Sep 24 03:35:55 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.45 Running first-order theorem proving
% 0.14/0.45 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
% 0.14/0.47
% 0.14/0.47 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.47
% 0.14/0.47 % Detected problem language: tptp
% 0.22/0.49 % Proving...
% 3.45/1.39 % SZS status Started for theBenchmark.p
% 3.45/1.39 % SZS status Theorem for theBenchmark.p
% 3.45/1.39
% 3.45/1.39 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.45/1.39
% 3.45/1.39 % ------ iProver source info
% 3.45/1.39
% 3.45/1.39 % git: date: 2026-07-19 20:42:38 +0200
% 3.45/1.39 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.45/1.39 % git: non_committed_changes: false
% 3.45/1.39
% 3.45/1.39 % ------ Parsing...
% 3.45/1.39 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.45/1.39
% 3.45/1.39 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.45/1.39
% 3.45/1.39 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.45/1.39
% 3.45/1.39 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.45/1.39 % ------ Proving...
% 3.45/1.39 % ------ Problem Properties
% 3.45/1.39
% 3.45/1.39 %
% 3.45/1.39 % clauses 156
% 3.45/1.39 % conjectures 1
% 3.45/1.39 % EPR 6
% 3.45/1.39 % Horn 155
% 3.45/1.39 % unary 131
% 3.45/1.39 % binary 6
% 3.45/1.39 % lits 223
% 3.45/1.39 % lits eq 4
% 3.45/1.39 % fd_pure 0
% 3.45/1.39 % fd_pseudo 0
% 3.45/1.39 % fd_cond 0
% 3.45/1.39 % fd_pseudo_cond 4
% 3.45/1.39 % AC symbols 0
% 3.45/1.39
% 3.45/1.39 % ------ Schedule dynamic 5 is on
% 3.45/1.39
% 3.45/1.39 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.45/1.39
% 3.45/1.39
% 3.45/1.39 % ------
% 3.45/1.39 % Current options:
% 3.45/1.39 % ------
% 3.45/1.39
% 3.45/1.39
% 3.45/1.39 %
% 3.45/1.39
% 3.45/1.39 % ------ Proving...
% 3.45/1.39 %
% 3.45/1.39
% 3.45/1.39 % SZS status Theorem for theBenchmark.p
% 3.45/1.39
% 3.45/1.39 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.45/1.40
% 3.45/1.40
%------------------------------------------------------------------------------