%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL538+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 : 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 02:06:52 PM UTC 2026
% Result : Theorem 3.09s 1.27s
% Output : CNFRefutation 3.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 51 ( 20 unt; 0 def)
% Number of atoms : 108 ( 5 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 93 ( 36 ~; 36 |; 10 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 41 !; 4 ?; 17 :)
% 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/sandbox/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_modus_ponens) ).
fof(f51,axiom,
( modus_ponens_strict_implies
<=> ! [X0,X1] :
( ( is_a_theorem(strict_implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',modus_ponens_strict_implies) ).
fof(f55,axiom,
( axiom_M
<=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_M) ).
fof(f75,axiom,
( op_strict_implies
=> ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+1.ax',op_strict_implies) ).
fof(f80,axiom,
axiom_M,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+3.ax',km4b_axiom_M) ).
fof(f86,axiom,
op_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f89,conjecture,
modus_ponens_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_modus_ponens_strict_implies) ).
fof(f90,negated_conjecture,
~ modus_ponens_strict_implies,
inference(negated_conjecture,[status(cth)],[f89]) ).
fof(f91,plain,
~ modus_ponens_strict_implies,
inference(flattening,[],[f90]) ).
fof(f94,plain,
( axiom_M
=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
inference(unused_predicate_definition_removal,[],[f55]) ).
fof(f96,plain,
( ! [X0,X1] :
( ( is_a_theorem(strict_implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) )
=> modus_ponens_strict_implies ),
inference(unused_predicate_definition_removal,[],[f51]) ).
fof(f112,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(f117,plain,
( ~ modus_ponens
| ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ) ),
inference(ennf_transformation,[],[f112]) ).
fof(f118,plain,
( ~ modus_ponens
| ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ) ),
inference(flattening,[],[f117]) ).
fof(f137,plain,
( ? [X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
& is_a_theorem(X0)
& ~ is_a_theorem(X1) )
| modus_ponens_strict_implies ),
inference(ennf_transformation,[],[f96]) ).
fof(f138,plain,
( ? [X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
& is_a_theorem(X0)
& ~ is_a_theorem(X1) )
| modus_ponens_strict_implies ),
inference(flattening,[],[f137]) ).
fof(f140,plain,
( ~ axiom_M
| ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
inference(ennf_transformation,[],[f94]) ).
fof(f144,plain,
( ~ op_strict_implies
| ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
inference(ennf_transformation,[],[f75]) ).
fof(f146,plain,
( ( is_a_theorem(strict_implies(sK0,sK1))
& is_a_theorem(sK0)
& ~ is_a_theorem(sK1) )
| modus_ponens_strict_implies ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f138]) ).
fof(f147,plain,
! [X0,X1] :
( ~ modus_ponens
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(cnf_transformation,[],[f118]) ).
fof(f168,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f184,plain,
( is_a_theorem(strict_implies(sK0,sK1))
| modus_ponens_strict_implies ),
inference(cnf_transformation,[],[f146]) ).
fof(f185,plain,
( is_a_theorem(sK0)
| modus_ponens_strict_implies ),
inference(cnf_transformation,[],[f146]) ).
fof(f186,plain,
( ~ is_a_theorem(sK1)
| modus_ponens_strict_implies ),
inference(cnf_transformation,[],[f146]) ).
fof(f188,plain,
! [X0] :
( ~ axiom_M
| is_a_theorem(implies(necessarily(X0),X0)) ),
inference(cnf_transformation,[],[f140]) ).
fof(f192,plain,
! [X0,X1] :
( ~ op_strict_implies
| strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
inference(cnf_transformation,[],[f144]) ).
fof(f197,plain,
axiom_M,
inference(cnf_transformation,[],[f80]) ).
fof(f202,plain,
op_strict_implies,
inference(cnf_transformation,[],[f86]) ).
fof(f205,plain,
~ modus_ponens_strict_implies,
inference(cnf_transformation,[],[f91]) ).
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,[],[f147]) ).
tcf(c_70,plain,
modus_ponens,
inference(cnf_transformation,[],[f168]) ).
tcf(c_86,plain,
( modus_ponens_strict_implies
| ~ is_a_theorem(sK1) ),
inference(cnf_transformation,[],[f186]) ).
tcf(c_87,plain,
( modus_ponens_strict_implies
| is_a_theorem(sK0) ),
inference(cnf_transformation,[],[f185]) ).
tcf(c_88,plain,
( modus_ponens_strict_implies
| is_a_theorem(strict_implies(sK0,sK1)) ),
inference(cnf_transformation,[],[f184]) ).
tcf(c_90,plain,
! [X0: $i] :
( is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(cnf_transformation,[],[f188]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i] :
( ( necessarily(implies(X0,X1)) = strict_implies(X0,X1) )
| ~ op_strict_implies ),
inference(cnf_transformation,[],[f192]) ).
tcf(c_99,plain,
axiom_M,
inference(cnf_transformation,[],[f197]) ).
tcf(c_104,plain,
op_strict_implies,
inference(cnf_transformation,[],[f202]) ).
tcf(c_107,negated_conjecture,
~ modus_ponens_strict_implies,
inference(cnf_transformation,[],[f205]) ).
tcf(c_137,plain,
is_a_theorem(strict_implies(sK0,sK1)),
inference(global_subsumption_just,[status(thm)],[c_88,c_107,c_88]) ).
tcf(c_139,plain,
! [X0: $i] : is_a_theorem(implies(necessarily(X0),X0)),
inference(global_subsumption_just,[status(thm)],[c_90,c_99,c_90]) ).
tcf(c_175,plain,
! [X0: $i,X1: $i] : necessarily(implies(X0,X1)) = strict_implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_94,c_104,c_94]) ).
tcf(c_190,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_70,c_49]) ).
tcf(c_191,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(renaming,[status(thm)],[c_190]) ).
tcf(c_696,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(strict_implies(X0,X1),implies(X0,X1))),
inference(superposition,[status(thm)],[c_175,c_139]) ).
tcf(c_777,plain,
! [X0: $i] :
( is_a_theorem(sK1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,sK1)) ),
inference(instantiation,[status(thm)],[c_191]) ).
tcf(c_778,plain,
( is_a_theorem(sK1)
| ~ is_a_theorem(sK0)
| ~ is_a_theorem(implies(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_777]) ).
tcf(c_1094,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_696,c_191]) ).
tcf(c_1459,plain,
is_a_theorem(implies(sK0,sK1)),
inference(superposition,[status(thm)],[c_137,c_1094]) ).
tcf(c_1485,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1459,c_778,c_86,c_87,c_107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL538+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n001.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Wed Sep 23 23:46:51 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 0.11/0.41
% 0.11/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.41
% 0.11/0.41 % Detected problem language: tptp
% 0.11/0.42 % Proving...
% 3.09/1.27 % SZS status Started for theBenchmark.p
% 3.09/1.27 % SZS status Theorem for theBenchmark.p
% 3.09/1.27
% 3.09/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.09/1.27
% 3.09/1.27 % ------ iProver source info
% 3.09/1.27
% 3.09/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 3.09/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.09/1.27 % git: non_committed_changes: false
% 3.09/1.27
% 3.09/1.27 % ------ Parsing...
% 3.09/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.09/1.27
% 3.09/1.27 % ------ Preprocessing... sup_sim: 3 sf_s rm: 28 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.09/1.27
% 3.09/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.09/1.27
% 3.09/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.09/1.27 % ------ Proving...
% 3.09/1.27 % ------ Problem Properties
% 3.09/1.27
% 3.09/1.27 %
% 3.09/1.27 % clauses 29
% 3.09/1.27 % conjectures 0
% 3.09/1.27 % EPR 2
% 3.09/1.27 % Horn 29
% 3.09/1.27 % unary 26
% 3.09/1.27 % binary 2
% 3.09/1.27 % lits 33
% 3.09/1.27 % lits eq 7
% 3.09/1.27 % fd_pure 0
% 3.09/1.27 % fd_pseudo 0
% 3.09/1.27 % fd_cond 0
% 3.09/1.27 % fd_pseudo_cond 1
% 3.09/1.27 % AC symbols 0
% 3.09/1.27
% 3.09/1.27 % ------ Schedule dynamic 5 is on
% 3.09/1.27
% 3.09/1.27 % ------ no conjectures: strip conj schedule
% 3.09/1.27
% 3.09/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.09/1.27
% 3.09/1.27
% 3.09/1.27 % ------
% 3.09/1.27 % Current options:
% 3.09/1.27 % ------
% 3.09/1.27
% 3.09/1.27
% 3.09/1.27 %
% 3.09/1.27
% 3.09/1.27 % ------ Proving...
% 3.09/1.27 %
% 3.09/1.27
% 3.09/1.27 % SZS status Theorem for theBenchmark.p
% 3.09/1.27
% 3.09/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.09/1.28
% 3.09/1.28
%------------------------------------------------------------------------------