%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL531+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 : n005.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 3.26s 6.27s
% Output : CNFRefutation 3.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 63 ( 27 unt; 0 def)
% Number of atoms : 118 ( 5 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 98 ( 43 ~; 38 |; 2 &)
% ( 5 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 9 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn 64 !; 1 ?; 26 :)
% 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(f5,axiom,
( implies_2
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',implies_2) ).
fof(f9,axiom,
( and_3
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',and_3) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_modus_ponens) ).
fof(f38,axiom,
implies_2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_implies_2) ).
fof(f42,axiom,
and_3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_and_3) ).
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(f66,axiom,
( axiom_m4
<=> ! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_m4) ).
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(f85,axiom,
op_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f88,conjecture,
axiom_m4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_axiom_m4) ).
fof(f89,negated_conjecture,
~ axiom_m4,
inference(negated_conjecture,[status(cth)],[f88]) ).
fof(f90,plain,
~ axiom_m4,
inference(flattening,[],[f89]) ).
fof(f91,plain,
( ! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0)))
=> axiom_m4 ),
inference(unused_predicate_definition_removal,[],[f66]) ).
fof(f95,plain,
( necessitation
=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
inference(unused_predicate_definition_removal,[],[f50]) ).
fof(f102,plain,
( and_3
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(unused_predicate_definition_removal,[],[f9]) ).
fof(f106,plain,
( implies_2
=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f5]) ).
fof(f110,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(f115,plain,
( ~ modus_ponens
| ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ) ),
inference(ennf_transformation,[],[f110]) ).
fof(f116,plain,
( ~ modus_ponens
| ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ) ),
inference(flattening,[],[f115]) ).
fof(f120,plain,
( ~ implies_2
| ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(ennf_transformation,[],[f106]) ).
fof(f124,plain,
( ~ and_3
| ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(ennf_transformation,[],[f102]) ).
fof(f134,plain,
( ~ necessitation
| ! [X0] :
( ~ is_a_theorem(X0)
| is_a_theorem(necessarily(X0)) ) ),
inference(ennf_transformation,[],[f95]) ).
fof(f138,plain,
( ? [X0] : ~ is_a_theorem(strict_implies(X0,and(X0,X0)))
| axiom_m4 ),
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(sK0,and(sK0,sK0)))
| axiom_m4 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f138]) ).
fof(f143,plain,
! [X0,X1] :
( ~ modus_ponens
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(cnf_transformation,[],[f116]) ).
fof(f147,plain,
! [X0,X1] :
( ~ implies_2
| is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(cnf_transformation,[],[f120]) ).
fof(f151,plain,
! [X0,X1] :
( ~ and_3
| is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(cnf_transformation,[],[f124]) ).
fof(f164,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f167,plain,
implies_2,
inference(cnf_transformation,[],[f38]) ).
fof(f171,plain,
and_3,
inference(cnf_transformation,[],[f42]) ).
fof(f179,plain,
! [X0] :
( ~ necessitation
| ~ is_a_theorem(X0)
| is_a_theorem(necessarily(X0)) ),
inference(cnf_transformation,[],[f134]) ).
fof(f183,plain,
( ~ is_a_theorem(strict_implies(sK0,and(sK0,sK0)))
| axiom_m4 ),
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(f194,plain,
op_strict_implies,
inference(cnf_transformation,[],[f85]) ).
fof(f197,plain,
~ axiom_m4,
inference(cnf_transformation,[],[f90]) ).
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,[],[f143]) ).
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,[],[f147]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_70,plain,
modus_ponens,
inference(cnf_transformation,[],[f164]) ).
tcf(c_73,plain,
implies_2,
inference(cnf_transformation,[],[f167]) ).
tcf(c_77,plain,
and_3,
inference(cnf_transformation,[],[f171]) ).
tcf(c_85,plain,
! [X0: $i] :
( is_a_theorem(necessarily(X0))
| ~ necessitation
| ~ is_a_theorem(X0) ),
inference(cnf_transformation,[],[f179]) ).
tcf(c_89,plain,
( axiom_m4
| ~ is_a_theorem(strict_implies(sK0,and(sK0,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_100,plain,
op_strict_implies,
inference(cnf_transformation,[],[f194]) ).
tcf(c_103,negated_conjecture,
~ axiom_m4,
inference(cnf_transformation,[],[f197]) ).
tcf(c_131,plain,
~ is_a_theorem(strict_implies(sK0,and(sK0,sK0))),
inference(global_subsumption_just,[status(thm)],[c_89,c_103,c_89]) ).
tcf(c_133,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_160,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))),
inference(global_subsumption_just,[status(thm)],[c_57,c_77,c_57]) ).
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_172,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_73,c_53]) ).
tcf(c_178,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_179,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(renaming,[status(thm)],[c_178]) ).
tcf(c_656,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_133]) ).
tcf(c_935,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X0,implies(X0,X1))) ),
inference(superposition,[status(thm)],[c_172,c_179]) ).
tcf(c_2334,plain,
! [X0: $i] : is_a_theorem(implies(X0,and(X0,X0))),
inference(superposition,[status(thm)],[c_160,c_935]) ).
tcf(c_2388,plain,
! [X0: $i] : is_a_theorem(strict_implies(X0,and(X0,X0))),
inference(superposition,[status(thm)],[c_2334,c_656]) ).
tcf(c_2391,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_131,c_2388]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL531+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/5.36 % Computer : n005.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Wed Sep 23 23:39:24 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/5.40 Running first-order theorem proving
% 0.15/5.40 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
% 0.15/5.41
% 0.15/5.41 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.41
% 0.15/5.41 % Detected problem language: tptp
% 0.15/5.42 % Proving...
% 3.26/6.27 % SZS status Started for theBenchmark.p
% 3.26/6.27 % SZS status Theorem for theBenchmark.p
% 3.26/6.27
% 3.26/6.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.26/6.27
% 3.26/6.27 % ------ iProver source info
% 3.26/6.27
% 3.26/6.27 % git: date: 2026-07-19 20:42:38 +0200
% 3.26/6.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.26/6.27 % git: non_committed_changes: false
% 3.26/6.27
% 3.26/6.27 % ------ Parsing...
% 3.26/6.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.26/6.27
% 3.26/6.27 % ------ 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 %
% 3.26/6.27
% 3.26/6.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.26/6.27
% 3.26/6.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.26/6.27 % ------ Proving...
% 3.26/6.27 % ------ Problem Properties
% 3.26/6.27
% 3.26/6.27 %
% 3.26/6.27 % clauses 26
% 3.26/6.27 % conjectures 0
% 3.26/6.27 % EPR 0
% 3.26/6.27 % Horn 26
% 3.26/6.27 % unary 23
% 3.26/6.27 % binary 2
% 3.26/6.27 % lits 30
% 3.26/6.27 % lits eq 7
% 3.26/6.27 % fd_pure 0
% 3.26/6.27 % fd_pseudo 0
% 3.26/6.27 % fd_cond 0
% 3.26/6.27 % fd_pseudo_cond 1
% 3.26/6.27 % AC symbols 0
% 3.26/6.27
% 3.26/6.27 % ------ Schedule dynamic 5 is on
% 3.26/6.27
% 3.26/6.27 % ------ no conjectures: strip conj schedule
% 3.26/6.27
% 3.26/6.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.26/6.27
% 3.26/6.27
% 3.26/6.27 % ------
% 3.26/6.27 % Current options:
% 3.26/6.27 % ------
% 3.26/6.27
% 3.26/6.27
% 3.26/6.27 %
% 3.26/6.27
% 3.26/6.27 % ------ Proving...
% 3.26/6.27 %
% 3.26/6.27
% 3.26/6.27 % SZS status Theorem for theBenchmark.p
% 3.26/6.27
% 3.26/6.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.26/6.27
% 3.26/6.27
%------------------------------------------------------------------------------