%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL528+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 : n011.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 02:06:50 PM UTC 2026
% Result : Theorem 130.74s 20.70s
% Output : CNFRefutation 146.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 21
% Syntax : Number of formulae : 115 ( 44 unt; 0 def)
% Number of atoms : 214 ( 13 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 181 ( 82 ~; 76 |; 2 &)
% ( 8 <=>; 13 =>; 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 : 12 ( 10 usr; 10 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 138 ( 0 sgn 136 !; 2 ?; 68 :)
% 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(f6,axiom,
( implies_3
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',implies_3) ).
fof(f7,axiom,
( and_1
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',and_1) ).
fof(f8,axiom,
( and_2
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',and_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(f39,axiom,
implies_3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_implies_3) ).
fof(f40,axiom,
and_1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_and_1) ).
fof(f41,axiom,
and_2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_and_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(f63,axiom,
( axiom_m1
<=> ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_m1) ).
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_m1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_axiom_m1) ).
fof(f89,negated_conjecture,
~ axiom_m1,
inference(negated_conjecture,[status(cth)],[f88]) ).
fof(f90,plain,
~ axiom_m1,
inference(flattening,[],[f89]) ).
fof(f91,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))
=> axiom_m1 ),
inference(unused_predicate_definition_removal,[],[f63]) ).
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(f103,plain,
( and_2
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
inference(unused_predicate_definition_removal,[],[f8]) ).
fof(f104,plain,
( and_1
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(unused_predicate_definition_removal,[],[f7]) ).
fof(f105,plain,
( implies_3
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(unused_predicate_definition_removal,[],[f6]) ).
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(f121,plain,
( ~ implies_3
| ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(ennf_transformation,[],[f105]) ).
fof(f122,plain,
( ~ and_1
| ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(ennf_transformation,[],[f104]) ).
fof(f123,plain,
( ~ and_2
| ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
inference(ennf_transformation,[],[f103]) ).
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,X1] : ~ is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))
| axiom_m1 ),
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(and(sK0,sK1),and(sK1,sK0)))
| axiom_m1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[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(f148,plain,
! [X2,X0,X1] :
( ~ implies_3
| is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(cnf_transformation,[],[f121]) ).
fof(f149,plain,
! [X0,X1] :
( ~ and_1
| is_a_theorem(implies(and(X0,X1),X0)) ),
inference(cnf_transformation,[],[f122]) ).
fof(f150,plain,
! [X0,X1] :
( ~ and_2
| is_a_theorem(implies(and(X0,X1),X1)) ),
inference(cnf_transformation,[],[f123]) ).
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(f168,plain,
implies_3,
inference(cnf_transformation,[],[f39]) ).
fof(f169,plain,
and_1,
inference(cnf_transformation,[],[f40]) ).
fof(f170,plain,
and_2,
inference(cnf_transformation,[],[f41]) ).
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(and(sK0,sK1),and(sK1,sK0)))
| axiom_m1 ),
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_m1,
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_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ implies_3 ),
inference(cnf_transformation,[],[f148]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(cnf_transformation,[],[f149]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(cnf_transformation,[],[f150]) ).
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_74,plain,
implies_3,
inference(cnf_transformation,[],[f168]) ).
tcf(c_75,plain,
and_1,
inference(cnf_transformation,[],[f169]) ).
tcf(c_76,plain,
and_2,
inference(cnf_transformation,[],[f170]) ).
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_m1
| ~ is_a_theorem(strict_implies(and(sK0,sK1),and(sK1,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_m1,
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_139,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(and(X0,X1),X1)),
inference(global_subsumption_just,[status(thm)],[c_56,c_76,c_56]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(and(X0,X1),X0)),
inference(global_subsumption_just,[status(thm)],[c_55,c_75,c_55]) ).
tcf(c_153,plain,
~ is_a_theorem(strict_implies(and(sK0,sK1),and(sK1,sK0))),
inference(global_subsumption_just,[status(thm)],[c_89,c_103,c_89]) ).
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_195,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),
inference(global_subsumption_just,[status(thm)],[c_54,c_74,c_54]) ).
tcf(c_423,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_425,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_426,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(X1)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1649,plain,
! [X0: $i,X1: $i] :
( ( X1 = X0 )
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_425,c_423]) ).
tcf(c_1660,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_1661,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(implies(X1,X2),implies(X0,X2)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_195,c_179]) ).
tcf(c_1792,plain,
! [X0: $i,X1: $i] : strict_implies(X0,X1) = necessarily(implies(X0,X1)),
inference(resolution,[status(thm)],[c_1649,c_163]) ).
tcf(c_2027,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(necessarily(implies(X0,X1))) ),
inference(resolution,[status(thm)],[c_1792,c_426]) ).
tcf(c_2233,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[c_2027,c_131]) ).
tcf(c_2293,plain,
~ is_a_theorem(implies(and(sK0,sK1),and(sK1,sK0))),
inference(resolution,[status(thm)],[c_153,c_2233]) ).
tcf(c_147454,plain,
( is_a_theorem(implies(and(sK0,sK1),and(sK1,sK0)))
| ~ is_a_theorem(implies(and(sK0,sK1),implies(and(sK0,sK1),and(sK1,sK0)))) ),
inference(instantiation,[status(thm)],[c_1660]) ).
tcf(c_149808,plain,
! [X0: $i] :
( is_a_theorem(implies(and(sK0,sK1),implies(and(sK0,sK1),and(sK1,sK0))))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,implies(and(sK0,sK1),implies(and(sK0,sK1),and(sK1,sK0))))) ),
inference(instantiation,[status(thm)],[c_179]) ).
tcf(c_150068,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X1,implies(and(sK0,sK1),and(sK1,sK0))))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,implies(X1,implies(and(sK0,sK1),and(sK1,sK0))))) ),
inference(instantiation,[status(thm)],[c_179]) ).
tcf(c_150126,plain,
! [X0: $i] :
( is_a_theorem(implies(implies(X0,and(sK1,sK0)),implies(and(sK0,sK1),and(sK1,sK0))))
| ~ is_a_theorem(implies(and(sK0,sK1),X0)) ),
inference(instantiation,[status(thm)],[c_1661]) ).
tcf(c_150128,plain,
( is_a_theorem(implies(implies(sK0,and(sK1,sK0)),implies(and(sK0,sK1),and(sK1,sK0))))
| ~ is_a_theorem(implies(and(sK0,sK1),sK0)) ),
inference(instantiation,[status(thm)],[c_150126]) ).
tcf(c_153211,plain,
! [X0: $i] :
( is_a_theorem(implies(and(sK0,sK1),implies(and(sK0,sK1),and(sK1,sK0))))
| ~ is_a_theorem(implies(X0,implies(and(sK0,sK1),and(sK1,sK0))))
| ~ is_a_theorem(implies(implies(X0,implies(and(sK0,sK1),and(sK1,sK0))),implies(and(sK0,sK1),implies(and(sK0,sK1),and(sK1,sK0))))) ),
inference(instantiation,[status(thm)],[c_149808]) ).
tcf(c_153212,plain,
! [X0: $i] :
( is_a_theorem(implies(implies(X0,implies(and(sK0,sK1),and(sK1,sK0))),implies(and(sK0,sK1),implies(and(sK0,sK1),and(sK1,sK0)))))
| ~ is_a_theorem(implies(and(sK0,sK1),X0)) ),
inference(instantiation,[status(thm)],[c_1661]) ).
tcf(c_153269,plain,
! [X0: $i] : is_a_theorem(implies(and(X0,sK1),sK1)),
inference(instantiation,[status(thm)],[c_139]) ).
tcf(c_153271,plain,
is_a_theorem(implies(and(sK0,sK1),sK1)),
inference(instantiation,[status(thm)],[c_153269]) ).
tcf(c_153671,plain,
is_a_theorem(implies(and(sK0,sK1),sK0)),
inference(instantiation,[status(thm)],[c_142]) ).
tcf(c_154435,plain,
is_a_theorem(implies(sK1,implies(sK0,and(sK1,sK0)))),
inference(instantiation,[status(thm)],[c_160]) ).
tcf(c_154533,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X1,implies(and(sK0,sK1),and(sK1,sK0))))
| ~ is_a_theorem(implies(X0,implies(and(sK0,sK1),and(sK1,sK0))))
| ~ is_a_theorem(implies(implies(X0,implies(and(sK0,sK1),and(sK1,sK0))),implies(X1,implies(and(sK0,sK1),and(sK1,sK0))))) ),
inference(instantiation,[status(thm)],[c_150068]) ).
tcf(c_154534,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(implies(X1,implies(and(sK0,sK1),and(sK1,sK0))),implies(X0,implies(and(sK0,sK1),and(sK1,sK0)))))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(instantiation,[status(thm)],[c_1661]) ).
tcf(c_158816,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X1,implies(and(sK0,sK1),and(sK1,sK0))))
| ~ is_a_theorem(implies(implies(X0,and(sK1,sK0)),implies(and(sK0,sK1),and(sK1,sK0))))
| ~ is_a_theorem(implies(implies(implies(X0,and(sK1,sK0)),implies(and(sK0,sK1),and(sK1,sK0))),implies(X1,implies(and(sK0,sK1),and(sK1,sK0))))) ),
inference(instantiation,[status(thm)],[c_154533]) ).
tcf(c_166126,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(implies(implies(X1,and(sK1,sK0)),implies(and(sK0,sK1),and(sK1,sK0))),implies(X0,implies(and(sK0,sK1),and(sK1,sK0)))))
| ~ is_a_theorem(implies(X0,implies(X1,and(sK1,sK0)))) ),
inference(instantiation,[status(thm)],[c_154534]) ).
tcf(c_173684,plain,
( is_a_theorem(implies(implies(implies(sK0,and(sK1,sK0)),implies(and(sK0,sK1),and(sK1,sK0))),implies(sK1,implies(and(sK0,sK1),and(sK1,sK0)))))
| ~ is_a_theorem(implies(sK1,implies(sK0,and(sK1,sK0)))) ),
inference(instantiation,[status(thm)],[c_166126]) ).
tcf(c_176153,plain,
( is_a_theorem(implies(sK1,implies(and(sK0,sK1),and(sK1,sK0))))
| ~ is_a_theorem(implies(implies(sK0,and(sK1,sK0)),implies(and(sK0,sK1),and(sK1,sK0))))
| ~ is_a_theorem(implies(implies(implies(sK0,and(sK1,sK0)),implies(and(sK0,sK1),and(sK1,sK0))),implies(sK1,implies(and(sK0,sK1),and(sK1,sK0))))) ),
inference(instantiation,[status(thm)],[c_158816]) ).
tcf(c_187291,plain,
( is_a_theorem(implies(and(sK0,sK1),implies(and(sK0,sK1),and(sK1,sK0))))
| ~ is_a_theorem(implies(sK1,implies(and(sK0,sK1),and(sK1,sK0))))
| ~ is_a_theorem(implies(implies(sK1,implies(and(sK0,sK1),and(sK1,sK0))),implies(and(sK0,sK1),implies(and(sK0,sK1),and(sK1,sK0))))) ),
inference(instantiation,[status(thm)],[c_153211]) ).
tcf(c_201306,plain,
( is_a_theorem(implies(implies(sK1,implies(and(sK0,sK1),and(sK1,sK0))),implies(and(sK0,sK1),implies(and(sK0,sK1),and(sK1,sK0)))))
| ~ is_a_theorem(implies(and(sK0,sK1),sK1)) ),
inference(instantiation,[status(thm)],[c_153212]) ).
tcf(c_201307,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_201306,c_187291,c_176153,c_173684,c_154435,c_153671,c_153271,c_150128,c_147454,c_2293]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL528+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.39 % Computer : n011.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Wed Sep 23 23:39:44 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.44 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
% 0.12/0.45
% 0.12/0.45 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.45
% 0.12/0.45 % Detected problem language: tptp
% 0.12/0.46 % Proving...
% 130.74/20.70 % SZS status Started for theBenchmark.p
% 130.74/20.70 % SZS status Theorem for theBenchmark.p
% 130.74/20.70
% 130.74/20.70 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 130.74/20.70
% 130.74/20.70 % ------ iProver source info
% 130.74/20.70
% 130.74/20.70 % git: date: 2026-07-19 20:42:38 +0200
% 130.74/20.70 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 130.74/20.70 % git: non_committed_changes: false
% 130.74/20.70
% 130.74/20.70 % ------ Parsing...
% 130.74/20.70 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 130.74/20.70
% 130.74/20.70 % ------ 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 %
% 130.74/20.70
% 130.74/20.70 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 130.74/20.70
% 130.74/20.70 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 130.74/20.70 % ------ Proving...
% 130.74/20.70 % ------ Problem Properties
% 130.74/20.70
% 130.74/20.70 %
% 130.74/20.70 % clauses 26
% 130.74/20.70 % conjectures 0
% 130.74/20.70 % EPR 0
% 130.74/20.70 % Horn 26
% 130.74/20.70 % unary 23
% 130.74/20.70 % binary 2
% 130.74/20.70 % lits 30
% 130.74/20.70 % lits eq 7
% 130.74/20.70 % fd_pure 0
% 130.74/20.70 % fd_pseudo 0
% 130.74/20.70 % fd_cond 0
% 130.74/20.70 % fd_pseudo_cond 1
% 130.74/20.70 % AC symbols 0
% 130.74/20.70
% 130.74/20.70 % ------ Input Options Time Limit: Unbounded
% 130.74/20.70
% 130.74/20.70
% 130.74/20.70 % ------
% 130.74/20.70 % Current options:
% 130.74/20.70 % ------
% 130.74/20.70
% 130.74/20.70
% 130.74/20.70 %
% 130.74/20.70
% 130.74/20.70 % ------ Proving...
% 130.74/20.70 %
% 130.74/20.70
% 130.74/20.70 % SZS status Theorem for theBenchmark.p
% 130.74/20.70
% 130.74/20.70 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 146.25/20.70
% 146.25/20.70
%------------------------------------------------------------------------------