%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL469+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n002.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 02:06:44 PM UTC 2026
% Result : Theorem 1.87s 1.28s
% Output : CNFRefutation 1.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 40 ( 21 unt; 0 def)
% Number of atoms : 59 ( 11 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 37 ( 18 ~; 13 |; 0 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn 40 !; 2 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
( or_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',or_1) ).
fof(f20,axiom,
( cn2
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',cn2) ).
fof(f27,axiom,
( op_or
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_or) ).
fof(f29,axiom,
( op_implies_and
=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_implies_and) ).
fof(f37,axiom,
cn2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+3.ax',luka_cn2) ).
fof(f40,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(f41,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(f43,conjecture,
or_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_or_1) ).
fof(f44,negated_conjecture,
~ or_1,
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f45,plain,
~ or_1,
inference(flattening,[],[f44]) ).
fof(f47,plain,
( cn2
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1))) ),
inference(unused_predicate_definition_removal,[],[f20]) ).
fof(f49,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1)))
=> or_1 ),
inference(unused_predicate_definition_removal,[],[f10]) ).
fof(f58,plain,
( ? [X0,X1] : ~ is_a_theorem(implies(X0,or(X0,X1)))
| or_1 ),
inference(ennf_transformation,[],[f49]) ).
fof(f60,plain,
( ~ cn2
| ! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1))) ),
inference(ennf_transformation,[],[f47]) ).
fof(f62,plain,
( ~ op_or
| ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(ennf_transformation,[],[f27]) ).
fof(f63,plain,
( ~ op_implies_and
| ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
inference(ennf_transformation,[],[f29]) ).
fof(f65,plain,
( ~ is_a_theorem(implies(sK0,or(sK0,sK1)))
| or_1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f58]) ).
fof(f68,plain,
( ~ is_a_theorem(implies(sK0,or(sK0,sK1)))
| or_1 ),
inference(cnf_transformation,[],[f65]) ).
fof(f70,plain,
! [X0,X1] :
( ~ cn2
| is_a_theorem(implies(X0,implies(not(X0),X1))) ),
inference(cnf_transformation,[],[f60]) ).
fof(f72,plain,
! [X0,X1] :
( ~ op_or
| or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(cnf_transformation,[],[f62]) ).
fof(f73,plain,
! [X0,X1] :
( ~ op_implies_and
| implies(X0,X1) = not(and(X0,not(X1))) ),
inference(cnf_transformation,[],[f63]) ).
fof(f79,plain,
cn2,
inference(cnf_transformation,[],[f37]) ).
fof(f82,plain,
op_or,
inference(cnf_transformation,[],[f40]) ).
fof(f83,plain,
op_implies_and,
inference(cnf_transformation,[],[f41]) ).
fof(f85,plain,
~ or_1,
inference(cnf_transformation,[],[f45]) ).
tcf(c_51,plain,
( or_1
| ~ is_a_theorem(implies(sK0,or(sK0,sK1))) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,implies(not(X0),X1)))
| ~ cn2 ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ( not(and(not(X0),not(X1))) = or(X0,X1) )
| ~ op_or ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( ( not(and(X0,not(X1))) = implies(X0,X1) )
| ~ op_implies_and ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_62,plain,
cn2,
inference(cnf_transformation,[],[f79]) ).
tcf(c_65,plain,
op_or,
inference(cnf_transformation,[],[f82]) ).
tcf(c_66,plain,
op_implies_and,
inference(cnf_transformation,[],[f83]) ).
tcf(c_68,negated_conjecture,
~ or_1,
inference(cnf_transformation,[],[f85]) ).
tcf(c_76,plain,
~ is_a_theorem(implies(sK0,or(sK0,sK1))),
inference(global_subsumption_just,[status(thm)],[c_51,c_68,c_51]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,implies(not(X0),X1))),
inference(global_subsumption_just,[status(thm)],[c_53,c_62,c_53]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i] : not(and(X0,not(X1))) = implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_56,c_66,c_56]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i] : not(and(not(X0),not(X1))) = or(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_55,c_65,c_55]) ).
tcf(c_151,plain,
! [X0: $i,X1: $i] : implies(not(X0),X1) = or(X0,X1),
inference(demodulation,[status(thm)],[c_92,c_87]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,or(X0,X1))),
inference(demodulation,[status(thm)],[c_81,c_151]) ).
tcf(c_154,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_76,c_153]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL469+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n002.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 23:32:03 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 1.87/1.28 % SZS status Started for theBenchmark.p
% 1.87/1.28 % SZS status Theorem for theBenchmark.p
% 1.87/1.28
% 1.87/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.87/1.28
% 1.87/1.28 % ------ iProver source info
% 1.87/1.28
% 1.87/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 1.87/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.87/1.28 % git: non_committed_changes: false
% 1.87/1.28
% 1.87/1.28 % ------ Parsing...
% 1.87/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.87/1.28
% 1.87/1.28 % ------ Preprocessing...%
% 1.87/1.28
% 1.87/1.28 % SZS status Theorem for theBenchmark.p
% 1.87/1.28
% 1.87/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.87/1.28
% 1.87/1.28
%------------------------------------------------------------------------------