%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL536+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 : n010.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 02:06:51 PM UTC 2026
% Result : Theorem 2.41s 6.51s
% Output : CNFRefutation 2.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 41 ( 19 unt; 0 def)
% Number of atoms : 68 ( 5 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 50 ( 23 ~; 18 |; 0 &)
% ( 3 <=>; 6 =>; 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 : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 27 !; 1 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
fof(f50,axiom,
( necessitation
<=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',necessitation) ).
fof(f58,axiom,
( axiom_5
<=> ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_5) ).
fof(f72,axiom,
( axiom_m10
<=> ! [X0] : is_a_theorem(strict_implies(possibly(X0),necessarily(possibly(X0)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_m10) ).
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(f78,axiom,
necessitation,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+2.ax',km5_necessitation) ).
fof(f81,axiom,
axiom_5,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+2.ax',km5_axiom_5) ).
fof(f85,axiom,
op_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f88,conjecture,
axiom_m10,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_m10_axiom_m10) ).
fof(f89,negated_conjecture,
~ axiom_m10,
inference(negated_conjecture,[status(cth)],[f88]) ).
fof(f90,plain,
~ axiom_m10,
inference(flattening,[],[f89]) ).
fof(f91,plain,
( ! [X0] : is_a_theorem(strict_implies(possibly(X0),necessarily(possibly(X0))))
=> axiom_m10 ),
inference(unused_predicate_definition_removal,[],[f72]) ).
fof(f92,plain,
( axiom_5
=> ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
inference(unused_predicate_definition_removal,[],[f58]) ).
fof(f95,plain,
( necessitation
=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
inference(unused_predicate_definition_removal,[],[f50]) ).
fof(f134,plain,
( ~ necessitation
| ! [X0] :
( ~ is_a_theorem(X0)
| is_a_theorem(necessarily(X0)) ) ),
inference(ennf_transformation,[],[f95]) ).
fof(f137,plain,
( ~ axiom_5
| ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
inference(ennf_transformation,[],[f92]) ).
fof(f138,plain,
( ? [X0] : ~ is_a_theorem(strict_implies(possibly(X0),necessarily(possibly(X0))))
| axiom_m10 ),
inference(ennf_transformation,[],[f91]) ).
fof(f140,plain,
( ~ op_strict_implies
| ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
inference(ennf_transformation,[],[f75]) ).
fof(f142,plain,
( ~ is_a_theorem(strict_implies(possibly(sK0),necessarily(possibly(sK0))))
| axiom_m10 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f138]) ).
fof(f179,plain,
! [X0] :
( ~ necessitation
| ~ is_a_theorem(X0)
| is_a_theorem(necessarily(X0)) ),
inference(cnf_transformation,[],[f134]) ).
fof(f182,plain,
! [X0] :
( ~ axiom_5
| is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
inference(cnf_transformation,[],[f137]) ).
fof(f183,plain,
( ~ is_a_theorem(strict_implies(possibly(sK0),necessarily(possibly(sK0))))
| axiom_m10 ),
inference(cnf_transformation,[],[f142]) ).
fof(f185,plain,
! [X0,X1] :
( ~ op_strict_implies
| strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
inference(cnf_transformation,[],[f140]) ).
fof(f188,plain,
necessitation,
inference(cnf_transformation,[],[f78]) ).
fof(f191,plain,
axiom_5,
inference(cnf_transformation,[],[f81]) ).
fof(f194,plain,
op_strict_implies,
inference(cnf_transformation,[],[f85]) ).
fof(f197,plain,
~ axiom_m10,
inference(cnf_transformation,[],[f90]) ).
tcf(c_85,plain,
! [X0: $i] :
( is_a_theorem(necessarily(X0))
| ~ necessitation
| ~ is_a_theorem(X0) ),
inference(cnf_transformation,[],[f179]) ).
tcf(c_88,plain,
! [X0: $i] :
( is_a_theorem(implies(possibly(X0),necessarily(possibly(X0))))
| ~ axiom_5 ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_89,plain,
( axiom_m10
| ~ is_a_theorem(strict_implies(possibly(sK0),necessarily(possibly(sK0)))) ),
inference(cnf_transformation,[],[f183]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i] :
( ( necessarily(implies(X0,X1)) = strict_implies(X0,X1) )
| ~ op_strict_implies ),
inference(cnf_transformation,[],[f185]) ).
tcf(c_94,plain,
necessitation,
inference(cnf_transformation,[],[f188]) ).
tcf(c_97,plain,
axiom_5,
inference(cnf_transformation,[],[f191]) ).
tcf(c_100,plain,
op_strict_implies,
inference(cnf_transformation,[],[f194]) ).
tcf(c_103,negated_conjecture,
~ axiom_m10,
inference(cnf_transformation,[],[f197]) ).
tcf(c_131,plain,
! [X0: $i] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_85,c_94,c_85]) ).
tcf(c_147,plain,
~ is_a_theorem(strict_implies(possibly(sK0),necessarily(possibly(sK0)))),
inference(global_subsumption_just,[status(thm)],[c_89,c_103,c_89]) ).
tcf(c_149,plain,
! [X0: $i] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))),
inference(global_subsumption_just,[status(thm)],[c_88,c_97,c_88]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i] : necessarily(implies(X0,X1)) = strict_implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_91,c_100,c_91]) ).
tcf(c_668,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_163,c_131]) ).
tcf(c_723,plain,
! [X0: $i] : is_a_theorem(strict_implies(possibly(X0),necessarily(possibly(X0)))),
inference(superposition,[status(thm)],[c_149,c_668]) ).
tcf(c_730,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_147,c_723]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL536+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/5.59 % Computer : n010.cluster.edu
% 0.10/5.59 % Model : x86_64 x86_64
% 0.10/5.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.59 % Memory : 8046.5625MB
% 0.10/5.59 % OS : Linux 6.8.0-71-generic
% 0.10/5.59 % CPULimit : 300
% 0.10/5.59 % WCLimit : 300
% 0.10/5.59 % DateTime : Wed Sep 23 23:41:10 UTC 2026
% 0.13/5.60 % CPUTime :
% 0.13/5.60 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/5.64 Running first-order theorem proving
% 0.13/5.64 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
% 0.13/5.65
% 0.13/5.65 % ======== iProver multi-core TPTP/SMT =========
% 0.13/5.65
% 0.13/5.65 % Detected problem language: tptp
% 0.13/5.66 % Proving...
% 2.41/6.51 % SZS status Started for theBenchmark.p
% 2.41/6.51 % SZS status Theorem for theBenchmark.p
% 2.41/6.51
% 2.41/6.51 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.41/6.51
% 2.41/6.51 % ------ iProver source info
% 2.41/6.51
% 2.41/6.51 % git: date: 2026-07-19 20:42:38 +0200
% 2.41/6.51 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.41/6.51 % git: non_committed_changes: false
% 2.41/6.51
% 2.41/6.51 % ------ Parsing...
% 2.41/6.51 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.41/6.51
% 2.41/6.51 % ------ Preprocessing... sup_sim: 3 sf_s rm: 27 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.41/6.51
% 2.41/6.51 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.41/6.51
% 2.41/6.51 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.41/6.51 % ------ Proving...
% 2.41/6.51 % ------ Problem Properties
% 2.41/6.51
% 2.41/6.51 %
% 2.41/6.51 % clauses 26
% 2.41/6.51 % conjectures 0
% 2.41/6.51 % EPR 0
% 2.41/6.51 % Horn 26
% 2.41/6.51 % unary 23
% 2.41/6.51 % binary 2
% 2.41/6.51 % lits 30
% 2.41/6.51 % lits eq 7
% 2.41/6.51 % fd_pure 0
% 2.41/6.51 % fd_pseudo 0
% 2.41/6.51 % fd_cond 0
% 2.41/6.51 % fd_pseudo_cond 1
% 2.41/6.51 % AC symbols 0
% 2.41/6.51
% 2.41/6.51 % ------ Schedule dynamic 5 is on
% 2.41/6.51
% 2.41/6.51 % ------ no conjectures: strip conj schedule
% 2.41/6.51
% 2.41/6.51 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.41/6.51
% 2.41/6.51
% 2.41/6.51 % ------
% 2.41/6.51 % Current options:
% 2.41/6.51 % ------
% 2.41/6.51
% 2.41/6.51
% 2.41/6.51 %
% 2.41/6.51
% 2.41/6.51 % ------ Proving...
% 2.41/6.51 %
% 2.41/6.51
% 2.41/6.51 % SZS status Theorem for theBenchmark.p
% 2.41/6.51
% 2.41/6.51 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.41/6.51
% 2.41/6.51
%------------------------------------------------------------------------------