%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL039-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n012.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 02:05:29 PM UTC 2026
% Result : Unsatisfiable 7.61s 1.50s
% Output : CNFRefutation 7.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 68 ( 25 unt; 0 def)
% Number of atoms : 124 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 115 ( 59 ~; 56 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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 : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 123 ( 0 sgn 123 !; 0 ?; 110 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).
fof(f2,axiom,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_18) ).
fof(f3,axiom,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(implies(X0,X1),implies(X0,X2)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_35) ).
fof(f4,axiom,
! [X0,X1] : is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_49) ).
fof(f5,axiom,
! [X0,X1] : is_a_theorem(implies(necessary(implies(X0,X1)),implies(necessary(X0),necessary(X1)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',necessitation1) ).
fof(f6,axiom,
! [X0] : is_a_theorem(implies(necessary(X0),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',necessitation2) ).
fof(f7,axiom,
! [X0] :
( is_a_theorem(necessary(X0))
| ~ is_a_theorem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_of_necessitation) ).
fof(f8,negated_conjecture,
~ is_a_theorem(implies(necessary(a),not(necessary(not(a))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
tcf(c_57,negated_conjecture,
~ is_a_theorem(implies(necessary(a),not(necessary(not(a))))),
inference(cnf_transformation,[],[f8]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(implies(X0,X1),implies(X0,X2)))),
inference(cnf_transformation,[],[f3]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(cnf_transformation,[],[f2]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))),
inference(cnf_transformation,[],[f4]) ).
tcf(c_62,plain,
! [X0: $i] :
( is_a_theorem(necessary(X0))
| ~ is_a_theorem(X0) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_63,plain,
! [X0: $i] : is_a_theorem(implies(necessary(X0),X0)),
inference(cnf_transformation,[],[f6]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(necessary(implies(X0,X1)),implies(necessary(X0),necessary(X1)))),
inference(cnf_transformation,[],[f5]) ).
tcf(c_183,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_59,c_60]) ).
tcf(c_184,plain,
! [X0: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(necessary(X0)) ),
inference(superposition,[status(thm)],[c_63,c_60]) ).
tcf(c_246,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(implies(X0,X1),implies(X0,X2)))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(superposition,[status(thm)],[c_58,c_60]) ).
tcf(c_250,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(implies(X0,X1),implies(X0,X2)))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(superposition,[status(thm)],[c_58,c_60]) ).
tcf(c_270,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(not(X0),not(X1))) ),
inference(superposition,[status(thm)],[c_61,c_60]) ).
tcf(c_315,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(necessary(X0),necessary(X1)))
| ~ is_a_theorem(necessary(implies(X0,X1))) ),
inference(superposition,[status(thm)],[c_64,c_60]) ).
tcf(c_345,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(necessary(X1))
| ~ is_a_theorem(necessary(X0))
| ~ is_a_theorem(necessary(implies(X0,X1))) ),
inference(superposition,[status(thm)],[c_315,c_60]) ).
tcf(c_471,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(necessary(X1))
| ~ is_a_theorem(necessary(X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_62,c_345]) ).
tcf(c_520,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(necessary(implies(X1,X0)))
| ~ is_a_theorem(necessary(X0)) ),
inference(superposition,[status(thm)],[c_59,c_471]) ).
tcf(c_522,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(necessary(implies(X1,X0)))
| ~ is_a_theorem(necessary(implies(not(X0),not(X1)))) ),
inference(superposition,[status(thm)],[c_61,c_471]) ).
tcf(c_523,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(necessary(implies(necessary(X0),necessary(X1))))
| ~ is_a_theorem(necessary(necessary(implies(X0,X1)))) ),
inference(superposition,[status(thm)],[c_64,c_471]) ).
tcf(c_526,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(necessary(necessary(X1)))
| ~ is_a_theorem(necessary(necessary(X0)))
| ~ is_a_theorem(necessary(implies(X0,X1))) ),
inference(superposition,[status(thm)],[c_315,c_471]) ).
tcf(c_642,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(necessary(X0)) ),
inference(superposition,[status(thm)],[c_520,c_184]) ).
tcf(c_728,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(superposition,[status(thm)],[c_246,c_60]) ).
tcf(c_740,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(superposition,[status(thm)],[c_250,c_60]) ).
tcf(c_763,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(necessary(implies(X1,X0)))
| ~ is_a_theorem(implies(not(X0),not(X1))) ),
inference(superposition,[status(thm)],[c_62,c_522]) ).
tcf(c_864,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(necessary(X0),necessary(X1)))
| ~ is_a_theorem(necessary(necessary(implies(X0,X1)))) ),
inference(superposition,[status(thm)],[c_523,c_184]) ).
tcf(c_878,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_59,c_728]) ).
tcf(c_915,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_59,c_740]) ).
tcf(c_916,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(X0,X2)))
| ~ is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(X0,X1))) ),
inference(superposition,[status(thm)],[c_58,c_740]) ).
tcf(c_919,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(necessary(implies(X0,X1)),X1))
| ~ is_a_theorem(implies(necessary(implies(X0,X1)),X0)) ),
inference(superposition,[status(thm)],[c_63,c_740]) ).
tcf(c_921,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(X2,X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_183,c_740]) ).
tcf(c_1058,plain,
! [X0: $i] : is_a_theorem(implies(X0,X0)),
inference(superposition,[status(thm)],[c_59,c_878]) ).
tcf(c_1068,plain,
! [X0: $i] : is_a_theorem(implies(X0,X0)),
inference(global_subsumption_just,[status(thm)],[c_915,c_1058]) ).
tcf(c_1073,plain,
! [X0: $i] : is_a_theorem(necessary(implies(X0,X0))),
inference(superposition,[status(thm)],[c_1068,c_763]) ).
tcf(c_1515,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(necessary(implies(X0,X1)),X1))
| ~ is_a_theorem(necessary(X0)) ),
inference(superposition,[status(thm)],[c_642,c_919]) ).
tcf(c_2209,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(necessary(X0))
| ~ is_a_theorem(necessary(implies(X0,X1))) ),
inference(superposition,[status(thm)],[c_1515,c_60]) ).
tcf(c_2613,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(necessary(necessary(X1)))
| ~ is_a_theorem(necessary(necessary(X0)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_62,c_526]) ).
tcf(c_3416,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(necessary(X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_62,c_2209]) ).
tcf(c_3557,plain,
! [X0: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(necessary(necessary(X0))) ),
inference(superposition,[status(thm)],[c_63,c_3416]) ).
tcf(c_4291,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(necessary(necessary(implies(X1,X0))))
| ~ is_a_theorem(necessary(necessary(X0))) ),
inference(superposition,[status(thm)],[c_59,c_2613]) ).
tcf(c_4293,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(necessary(necessary(implies(X1,X0))))
| ~ is_a_theorem(necessary(necessary(implies(not(X0),not(X1))))) ),
inference(superposition,[status(thm)],[c_61,c_2613]) ).
tcf(c_4297,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(necessary(necessary(X1)))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(necessary(necessary(X0))) ),
inference(superposition,[status(thm)],[c_183,c_2613]) ).
tcf(c_4464,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(necessary(necessary(X0))) ),
inference(superposition,[status(thm)],[c_4291,c_3557]) ).
tcf(c_5021,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(necessary(necessary(X1)))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(necessary(X0)) ),
inference(superposition,[status(thm)],[c_62,c_4297]) ).
tcf(c_5044,plain,
! [X0: $i] :
( is_a_theorem(necessary(necessary(X0)))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_1073,c_5021]) ).
tcf(c_5089,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(necessary(X0),necessary(X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_5044,c_864]) ).
tcf(c_5106,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(necessary(necessary(implies(X1,X0))))
| ~ is_a_theorem(necessary(implies(not(X0),not(X1)))) ),
inference(superposition,[status(thm)],[c_62,c_4293]) ).
tcf(c_5186,plain,
! [X0: $i] : is_a_theorem(necessary(necessary(implies(X0,X0)))),
inference(superposition,[status(thm)],[c_1073,c_5106]) ).
tcf(c_5426,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,implies(X1,X1))),
inference(superposition,[status(thm)],[c_5186,c_4464]) ).
tcf(c_5438,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))),
inference(superposition,[status(thm)],[c_5426,c_916]) ).
tcf(c_5626,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X0,implies(X0,X1))) ),
inference(superposition,[status(thm)],[c_5438,c_60]) ).
tcf(c_9409,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(X0,implies(X2,X1)))
| ~ is_a_theorem(implies(X0,implies(not(X1),not(X2)))) ),
inference(superposition,[status(thm)],[c_61,c_921]) ).
tcf(c_9411,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X0,necessary(X1))) ),
inference(superposition,[status(thm)],[c_63,c_921]) ).
tcf(c_10477,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(necessary(X0),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_5089,c_9411]) ).
tcf(c_13073,plain,
~ is_a_theorem(implies(a,not(necessary(not(a))))),
inference(superposition,[status(thm)],[c_10477,c_57]) ).
tcf(c_16767,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(not(X0),implies(X0,X1))),
inference(superposition,[status(thm)],[c_59,c_9409]) ).
tcf(c_17320,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(not(not(X0)),implies(X1,X0))),
inference(superposition,[status(thm)],[c_16767,c_9409]) ).
tcf(c_17578,plain,
! [X0: $i] : is_a_theorem(implies(not(not(X0)),X0)),
inference(superposition,[status(thm)],[c_17320,c_5626]) ).
tcf(c_18309,plain,
! [X0: $i] : is_a_theorem(implies(not(not(necessary(X0))),X0)),
inference(superposition,[status(thm)],[c_17578,c_9411]) ).
tcf(c_18894,plain,
! [X0: $i] : is_a_theorem(implies(X0,not(necessary(not(X0))))),
inference(superposition,[status(thm)],[c_18309,c_270]) ).
tcf(c_18918,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_13073,c_18894]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL039-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Wed Sep 23 21:41:36 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.32 Running first-order theorem proving
% 0.03/0.32 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
% 0.03/0.33
% 0.03/0.33 % ======== iProver multi-core TPTP/SMT =========
% 0.03/0.33
% 0.03/0.33 % Detected problem language: tptp
% 0.07/0.33 % Proving...
% 7.61/1.50 % SZS status Started for theBenchmark.p
% 7.61/1.50 % SZS status Unsatisfiable for theBenchmark.p
% 7.61/1.50
% 7.61/1.50 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.61/1.50
% 7.61/1.50 % ------ iProver source info
% 7.61/1.50
% 7.61/1.50 % git: date: 2026-07-19 20:42:38 +0200
% 7.61/1.50 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.61/1.50 % git: non_committed_changes: false
% 7.61/1.50
% 7.61/1.50 % ------ Parsing...% successful
% 7.61/1.50
% 7.61/1.50
% 7.61/1.50 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.61/1.50
% 7.61/1.50 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 7.61/1.50
% 7.61/1.50 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 7.61/1.50 % ------ Proving...
% 7.61/1.50 % ------ Problem Properties
% 7.61/1.50
% 7.61/1.50 %
% 7.61/1.50 % clauses 8
% 7.61/1.50 % conjectures 1
% 7.61/1.50 % EPR 0
% 7.61/1.50 % Horn 8
% 7.61/1.50 % unary 6
% 7.61/1.50 % binary 1
% 7.61/1.50 % lits 11
% 7.61/1.50 % lits eq 0
% 7.61/1.50 % fd_pure 0
% 7.61/1.50 % fd_pseudo 0
% 7.61/1.50 % fd_cond 0
% 7.61/1.50 % fd_pseudo_cond 0
% 7.61/1.50 % AC symbols 0
% 7.61/1.50
% 7.61/1.50 % ------ Schedule dynamic 5 is on
% 7.61/1.50
% 7.61/1.50 % ------ no equalities: superposition off
% 7.61/1.50
% 7.61/1.50 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.61/1.50
% 7.61/1.50
% 7.61/1.50 % ------
% 7.61/1.50 % Current options:
% 7.61/1.50 % ------
% 7.61/1.50
% 7.61/1.50
% 7.61/1.50 %
% 7.61/1.50
% 7.61/1.50 % ------ Proving...
% 7.61/1.50 %
% 7.61/1.50
% 7.61/1.50 % SZS status Unsatisfiable for theBenchmark.p
% 7.61/1.50
% 7.61/1.50 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.61/1.50
% 7.61/1.50
%------------------------------------------------------------------------------