%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL453+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/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 02:06:41 PM UTC 2026
% Result : Theorem 2.04s 6.36s
% Output : CNFRefutation 2.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of formulae : 74 ( 32 unt; 0 def)
% Number of atoms : 130 ( 11 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 102 ( 46 ~; 40 |; 2 &)
% ( 5 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 8 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 87 ( 0 sgn 86 !; 1 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( modus_ponens
<=> ! [X0,X1] :
( ( is_a_theorem(implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
fof(f4,axiom,
( implies_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',implies_1) ).
fof(f5,axiom,
( implies_2
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',implies_2) ).
fof(f12,axiom,
( or_3
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',or_3) ).
fof(f21,axiom,
( cn3
<=> ! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',cn3) ).
fof(f27,axiom,
( op_or
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL006+1.ax',op_implies_and) ).
fof(f33,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_op_implies_and) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_modus_ponens) ).
fof(f37,axiom,
implies_1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_implies_1) ).
fof(f38,axiom,
implies_2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_implies_2) ).
fof(f45,axiom,
or_3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_or_3) ).
fof(f50,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',luka_op_or) ).
fof(f53,conjecture,
cn3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',luka_cn3) ).
fof(f54,negated_conjecture,
~ cn3,
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f55,plain,
~ cn3,
inference(flattening,[],[f54]) ).
fof(f56,plain,
( ! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0))
=> cn3 ),
inference(unused_predicate_definition_removal,[],[f21]) ).
fof(f60,plain,
( or_3
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))) ),
inference(unused_predicate_definition_removal,[],[f12]) ).
fof(f67,plain,
( implies_2
=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f5]) ).
fof(f68,plain,
( implies_1
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f71,plain,
( modus_ponens
=> ! [X0,X1] :
( ( is_a_theorem(implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f75,plain,
( ~ modus_ponens
| ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ) ),
inference(ennf_transformation,[],[f71]) ).
fof(f76,plain,
( ~ modus_ponens
| ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ) ),
inference(flattening,[],[f75]) ).
fof(f79,plain,
( ~ implies_1
| ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(ennf_transformation,[],[f68]) ).
fof(f80,plain,
( ~ implies_2
| ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(ennf_transformation,[],[f67]) ).
fof(f87,plain,
( ~ or_3
| ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))) ),
inference(ennf_transformation,[],[f60]) ).
fof(f91,plain,
( ? [X0] : ~ is_a_theorem(implies(implies(not(X0),X0),X0))
| cn3 ),
inference(ennf_transformation,[],[f56]) ).
fof(f92,plain,
( ~ op_or
| ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(ennf_transformation,[],[f27]) ).
fof(f93,plain,
( ~ op_implies_and
| ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
inference(ennf_transformation,[],[f29]) ).
fof(f95,plain,
( ~ is_a_theorem(implies(implies(not(sK0),sK0),sK0))
| cn3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f91]) ).
fof(f96,plain,
! [X0,X1] :
( ~ modus_ponens
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(cnf_transformation,[],[f76]) ).
fof(f99,plain,
! [X0,X1] :
( ~ implies_1
| is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(cnf_transformation,[],[f79]) ).
fof(f100,plain,
! [X0,X1] :
( ~ implies_2
| is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(cnf_transformation,[],[f80]) ).
fof(f107,plain,
! [X2,X0,X1] :
( ~ or_3
| is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))) ),
inference(cnf_transformation,[],[f87]) ).
fof(f111,plain,
( ~ is_a_theorem(implies(implies(not(sK0),sK0),sK0))
| cn3 ),
inference(cnf_transformation,[],[f95]) ).
fof(f112,plain,
! [X0,X1] :
( ~ op_or
| or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(cnf_transformation,[],[f92]) ).
fof(f113,plain,
! [X0,X1] :
( ~ op_implies_and
| implies(X0,X1) = not(and(X0,not(X1))) ),
inference(cnf_transformation,[],[f93]) ).
fof(f116,plain,
op_implies_and,
inference(cnf_transformation,[],[f33]) ).
fof(f118,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f120,plain,
implies_1,
inference(cnf_transformation,[],[f37]) ).
fof(f121,plain,
implies_2,
inference(cnf_transformation,[],[f38]) ).
fof(f128,plain,
or_3,
inference(cnf_transformation,[],[f45]) ).
fof(f133,plain,
op_or,
inference(cnf_transformation,[],[f50]) ).
fof(f135,plain,
~ cn3,
inference(cnf_transformation,[],[f55]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ modus_ponens
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(cnf_transformation,[],[f100]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1))))
| ~ or_3 ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_64,plain,
( cn3
| ~ is_a_theorem(implies(implies(not(sK0),sK0),sK0)) ),
inference(cnf_transformation,[],[f111]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( ( not(and(not(X0),not(X1))) = or(X0,X1) )
| ~ op_or ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( ( not(and(X0,not(X1))) = implies(X0,X1) )
| ~ op_implies_and ),
inference(cnf_transformation,[],[f113]) ).
tcf(c_69,plain,
op_implies_and,
inference(cnf_transformation,[],[f116]) ).
tcf(c_71,plain,
modus_ponens,
inference(cnf_transformation,[],[f118]) ).
tcf(c_73,plain,
implies_1,
inference(cnf_transformation,[],[f120]) ).
tcf(c_74,plain,
implies_2,
inference(cnf_transformation,[],[f121]) ).
tcf(c_81,plain,
or_3,
inference(cnf_transformation,[],[f128]) ).
tcf(c_86,plain,
op_or,
inference(cnf_transformation,[],[f133]) ).
tcf(c_88,negated_conjecture,
~ cn3,
inference(cnf_transformation,[],[f135]) ).
tcf(c_93,plain,
( is_a_theorem(implies(sK0,implies(sK0,sK0)))
| ~ implies_1 ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_119,plain,
~ is_a_theorem(implies(implies(not(sK0),sK0),sK0)),
inference(global_subsumption_just,[status(thm)],[c_64,c_88,c_64]) ).
tcf(c_132,plain,
! [X0: $i,X1: $i] : not(and(X0,not(X1))) = implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_66,c_69,c_66]) ).
tcf(c_135,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))),
inference(global_subsumption_just,[status(thm)],[c_53,c_74,c_53]) ).
tcf(c_141,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_49,c_71,c_49]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(renaming,[status(thm)],[c_141]) ).
tcf(c_143,plain,
! [X0: $i,X1: $i] : not(and(not(X0),not(X1))) = or(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_65,c_86,c_65]) ).
tcf(c_155,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1)))),
inference(global_subsumption_just,[status(thm)],[c_60,c_81,c_60]) ).
tcf(c_248,plain,
! [X0: $i,X1: $i] : implies(not(X0),X1) = or(X0,X1),
inference(demodulation,[status(thm)],[c_143,c_132]) ).
tcf(c_250,plain,
~ is_a_theorem(implies(or(sK0,sK0),sK0)),
inference(demodulation,[status(thm)],[c_119,c_248]) ).
tcf(c_554,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X0,implies(X0,X1))) ),
inference(superposition,[status(thm)],[c_135,c_142]) ).
tcf(c_606,plain,
( is_a_theorem(implies(sK0,sK0))
| ~ is_a_theorem(implies(sK0,implies(sK0,sK0))) ),
inference(instantiation,[status(thm)],[c_554]) ).
tcf(c_949,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(implies(X0,X1),implies(or(X0,X0),X1))),
inference(superposition,[status(thm)],[c_155,c_554]) ).
tcf(c_1089,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(or(X0,X0),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_949,c_142]) ).
tcf(c_1092,plain,
( is_a_theorem(implies(or(sK0,sK0),sK0))
| ~ is_a_theorem(implies(sK0,sK0)) ),
inference(instantiation,[status(thm)],[c_1089]) ).
tcf(c_1093,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1092,c_606,c_250,c_93,c_73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL453+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/5.39 % Computer : n002.cluster.edu
% 0.09/5.39 % Model : x86_64 x86_64
% 0.09/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.39 % Memory : 8046.5625MB
% 0.09/5.39 % OS : Linux 6.8.0-71-generic
% 0.09/5.39 % CPULimit : 300
% 0.09/5.39 % WCLimit : 300
% 0.09/5.39 % DateTime : Wed Sep 23 23:28:57 UTC 2026
% 0.09/5.39 % CPUTime :
% 0.09/5.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.45 Running first-order theorem proving
% 0.15/5.45 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
% 0.15/5.47
% 0.15/5.47 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.47
% 0.15/5.47 % Detected problem language: tptp
% 0.15/5.49 % Proving...
% 2.04/6.36 % SZS status Started for theBenchmark.p
% 2.04/6.36 % SZS status Theorem for theBenchmark.p
% 2.04/6.36
% 2.04/6.36 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.04/6.36
% 2.04/6.36 % ------ iProver source info
% 2.04/6.36
% 2.04/6.36 % git: date: 2026-07-19 20:42:38 +0200
% 2.04/6.36 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.04/6.36 % git: non_committed_changes: false
% 2.04/6.36
% 2.04/6.36 % ------ Parsing...
% 2.04/6.36 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.04/6.36
% 2.04/6.36 % ------ Preprocessing... sup_sim: 3 sf_s rm: 20 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.04/6.36
% 2.04/6.36 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.04/6.36
% 2.04/6.36 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.04/6.36 % ------ Proving...
% 2.04/6.36 % ------ Problem Properties
% 2.04/6.36
% 2.04/6.36 %
% 2.04/6.36 % clauses 19
% 2.04/6.36 % conjectures 0
% 2.04/6.36 % EPR 0
% 2.04/6.36 % Horn 19
% 2.04/6.36 % unary 17
% 2.04/6.36 % binary 1
% 2.04/6.36 % lits 22
% 2.04/6.36 % lits eq 4
% 2.04/6.36 % fd_pure 0
% 2.04/6.36 % fd_pseudo 0
% 2.04/6.36 % fd_cond 0
% 2.04/6.36 % fd_pseudo_cond 1
% 2.04/6.36 % AC symbols 0
% 2.04/6.36
% 2.04/6.36 % ------ Schedule dynamic 5 is on
% 2.04/6.36
% 2.04/6.36 % ------ no conjectures: strip conj schedule
% 2.04/6.36
% 2.04/6.36 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.04/6.36
% 2.04/6.36
% 2.04/6.36 % ------
% 2.04/6.36 % Current options:
% 2.04/6.36 % ------
% 2.04/6.36
% 2.04/6.36
% 2.04/6.36 %
% 2.04/6.36
% 2.04/6.36 % ------ Proving...
% 2.04/6.36 %
% 2.04/6.36
% 2.04/6.36 % SZS status Theorem for theBenchmark.p
% 2.04/6.36
% 2.04/6.36 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.04/6.36
% 2.04/6.36
%------------------------------------------------------------------------------