%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL540+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 : n018.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 2.61s 1.29s
% Output : CNFRefutation 2.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 42 ( 14 unt; 0 def)
% Number of atoms : 98 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 92 ( 36 ~; 36 |; 10 &)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 4 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 35 !; 4 ?; 13 :)
% 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(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(f42,axiom,
and_3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_and_3) ).
fof(f52,axiom,
( adjunction
<=> ! [X0,X1] :
( ( is_a_theorem(X1)
& is_a_theorem(X0) )
=> is_a_theorem(and(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',adjunction) ).
fof(f89,conjecture,
adjunction,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_adjunction) ).
fof(f90,negated_conjecture,
~ adjunction,
inference(negated_conjecture,[status(cth)],[f89]) ).
fof(f91,plain,
~ adjunction,
inference(flattening,[],[f90]) ).
fof(f96,plain,
( ! [X0,X1] :
( ( is_a_theorem(X1)
& is_a_theorem(X0) )
=> is_a_theorem(and(X0,X1)) )
=> adjunction ),
inference(unused_predicate_definition_removal,[],[f52]) ).
fof(f104,plain,
( and_3
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(unused_predicate_definition_removal,[],[f9]) ).
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(f126,plain,
( ~ and_3
| ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(ennf_transformation,[],[f104]) ).
fof(f137,plain,
( ? [X0,X1] :
( is_a_theorem(X1)
& is_a_theorem(X0)
& ~ is_a_theorem(and(X0,X1)) )
| adjunction ),
inference(ennf_transformation,[],[f96]) ).
fof(f138,plain,
( ? [X0,X1] :
( is_a_theorem(X1)
& is_a_theorem(X0)
& ~ is_a_theorem(and(X0,X1)) )
| adjunction ),
inference(flattening,[],[f137]) ).
fof(f146,plain,
( ( is_a_theorem(sK1)
& is_a_theorem(sK0)
& ~ is_a_theorem(and(sK0,sK1)) )
| adjunction ),
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(f155,plain,
! [X0,X1] :
( ~ and_3
| is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(cnf_transformation,[],[f126]) ).
fof(f168,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f175,plain,
and_3,
inference(cnf_transformation,[],[f42]) ).
fof(f184,plain,
( is_a_theorem(sK1)
| adjunction ),
inference(cnf_transformation,[],[f146]) ).
fof(f185,plain,
( is_a_theorem(sK0)
| adjunction ),
inference(cnf_transformation,[],[f146]) ).
fof(f186,plain,
( ~ is_a_theorem(and(sK0,sK1))
| adjunction ),
inference(cnf_transformation,[],[f146]) ).
fof(f205,plain,
~ adjunction,
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_57,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[],[f155]) ).
tcf(c_70,plain,
modus_ponens,
inference(cnf_transformation,[],[f168]) ).
tcf(c_77,plain,
and_3,
inference(cnf_transformation,[],[f175]) ).
tcf(c_86,plain,
( adjunction
| ~ is_a_theorem(and(sK0,sK1)) ),
inference(cnf_transformation,[],[f186]) ).
tcf(c_87,plain,
( adjunction
| is_a_theorem(sK0) ),
inference(cnf_transformation,[],[f185]) ).
tcf(c_88,plain,
( adjunction
| is_a_theorem(sK1) ),
inference(cnf_transformation,[],[f184]) ).
tcf(c_107,negated_conjecture,
~ adjunction,
inference(cnf_transformation,[],[f205]) ).
tcf(c_172,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_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_756,plain,
! [X0: $i] :
( is_a_theorem(and(sK0,sK1))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,and(sK0,sK1))) ),
inference(instantiation,[status(thm)],[c_191]) ).
tcf(c_774,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X1,and(sK0,sK1)))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,implies(X1,and(sK0,sK1)))) ),
inference(instantiation,[status(thm)],[c_191]) ).
tcf(c_943,plain,
( is_a_theorem(implies(sK1,and(sK0,sK1)))
| ~ is_a_theorem(sK0)
| ~ is_a_theorem(implies(sK0,implies(sK1,and(sK0,sK1)))) ),
inference(instantiation,[status(thm)],[c_774]) ).
tcf(c_944,plain,
is_a_theorem(implies(sK0,implies(sK1,and(sK0,sK1)))),
inference(instantiation,[status(thm)],[c_172]) ).
tcf(c_1196,plain,
( is_a_theorem(and(sK0,sK1))
| ~ is_a_theorem(sK1)
| ~ is_a_theorem(implies(sK1,and(sK0,sK1))) ),
inference(instantiation,[status(thm)],[c_756]) ).
tcf(c_1197,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1196,c_944,c_943,c_86,c_87,c_88,c_107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL540+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n018.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 23:43:49 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 2.61/1.29 % SZS status Started for theBenchmark.p
% 2.61/1.29 % SZS status Theorem for theBenchmark.p
% 2.61/1.29
% 2.61/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.61/1.29
% 2.61/1.29 % ------ iProver source info
% 2.61/1.29
% 2.61/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 2.61/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.61/1.29 % git: non_committed_changes: false
% 2.61/1.29
% 2.61/1.29 % ------ Parsing...
% 2.61/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.61/1.29
% 2.61/1.29 % ------ 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 %
% 2.61/1.29
% 2.61/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.61/1.29
% 2.61/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.61/1.29 % ------ Proving...
% 2.61/1.29 % ------ Problem Properties
% 2.61/1.29
% 2.61/1.29 %
% 2.61/1.29 % clauses 29
% 2.61/1.29 % conjectures 0
% 2.61/1.29 % EPR 2
% 2.61/1.29 % Horn 29
% 2.61/1.29 % unary 26
% 2.61/1.29 % binary 2
% 2.61/1.29 % lits 33
% 2.61/1.29 % lits eq 7
% 2.61/1.29 % fd_pure 0
% 2.61/1.29 % fd_pseudo 0
% 2.61/1.29 % fd_cond 0
% 2.61/1.29 % fd_pseudo_cond 1
% 2.61/1.29 % AC symbols 0
% 2.61/1.29
% 2.61/1.29 % ------ Schedule dynamic 5 is on
% 2.61/1.29
% 2.61/1.29 % ------ no conjectures: strip conj schedule
% 2.61/1.29
% 2.61/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.61/1.29
% 2.61/1.29
% 2.61/1.29 % ------
% 2.61/1.29 % Current options:
% 2.61/1.29 % ------
% 2.61/1.29
% 2.61/1.29
% 2.61/1.29 %
% 2.61/1.29
% 2.61/1.29 % ------ Proving...
% 2.61/1.29 %
% 2.61/1.29
% 2.61/1.29 % SZS status Theorem for theBenchmark.p
% 2.61/1.29
% 2.61/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.61/1.29
% 2.61/1.29
%------------------------------------------------------------------------------