%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL520+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n009.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 02:06:49 PM UTC 2026
% Result : Theorem 4.19s 1.20s
% Output : CNFRefutation 4.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 24
% Syntax : Number of formulae : 137 ( 56 unt; 0 def)
% Number of atoms : 247 ( 50 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 218 ( 108 ~; 91 |; 2 &)
% ( 5 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 11 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 166 ( 0 sgn 164 !; 2 ?; 96 :)
% 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/sandbox2/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
fof(f16,axiom,
( kn1
<=> ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',kn1) ).
fof(f17,axiom,
( kn2
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',kn2) ).
fof(f18,axiom,
( kn3
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',kn3) ).
fof(f24,axiom,
( r3
<=> ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r3) ).
fof(f27,axiom,
( op_or
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_or) ).
fof(f28,axiom,
( op_and
=> ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_and) ).
fof(f29,axiom,
( op_implies_and
=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_implies_and) ).
fof(f30,axiom,
( op_implies_or
=> ! [X0,X1] : implies(X0,X1) = or(not(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_implies_or) ).
fof(f31,axiom,
( op_equiv
=> ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_equiv) ).
fof(f32,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_op_or) ).
fof(f33,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_op_implies_and) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_modus_ponens) ).
fof(f36,axiom,
kn1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_kn1) ).
fof(f37,axiom,
kn2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_kn2) ).
fof(f38,axiom,
kn3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_kn3) ).
fof(f40,axiom,
op_implies_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_implies_or) ).
fof(f41,axiom,
op_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_and) ).
fof(f42,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_equiv) ).
fof(f43,conjecture,
r3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r3) ).
fof(f44,negated_conjecture,
~ r3,
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f45,plain,
~ r3,
inference(flattening,[],[f44]) ).
fof(f46,plain,
( ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0)))
=> r3 ),
inference(unused_predicate_definition_removal,[],[f24]) ).
fof(f47,plain,
( kn3
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
inference(unused_predicate_definition_removal,[],[f18]) ).
fof(f48,plain,
( kn2
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(unused_predicate_definition_removal,[],[f17]) ).
fof(f49,plain,
( kn1
=> ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
inference(unused_predicate_definition_removal,[],[f16]) ).
fof(f51,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(f52,plain,
( ~ modus_ponens
| ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ) ),
inference(ennf_transformation,[],[f51]) ).
fof(f53,plain,
( ~ modus_ponens
| ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ) ),
inference(flattening,[],[f52]) ).
fof(f55,plain,
( ~ kn1
| ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
inference(ennf_transformation,[],[f49]) ).
fof(f56,plain,
( ~ kn2
| ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(ennf_transformation,[],[f48]) ).
fof(f57,plain,
( ~ kn3
| ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
inference(ennf_transformation,[],[f47]) ).
fof(f58,plain,
( ? [X0,X1] : ~ is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| r3 ),
inference(ennf_transformation,[],[f46]) ).
fof(f59,plain,
( ~ op_or
| ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(ennf_transformation,[],[f27]) ).
fof(f60,plain,
( ~ op_and
| ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))) ),
inference(ennf_transformation,[],[f28]) ).
fof(f61,plain,
( ~ op_implies_and
| ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
inference(ennf_transformation,[],[f29]) ).
fof(f62,plain,
( ~ op_implies_or
| ! [X0,X1] : implies(X0,X1) = or(not(X0),X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f63,plain,
( ~ op_equiv
| ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
inference(ennf_transformation,[],[f31]) ).
fof(f64,plain,
( ~ is_a_theorem(implies(or(sK0,sK1),or(sK1,sK0)))
| r3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f58]) ).
fof(f65,plain,
! [X0,X1] :
( ~ modus_ponens
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f67,plain,
! [X0] :
( ~ kn1
| is_a_theorem(implies(X0,and(X0,X0))) ),
inference(cnf_transformation,[],[f55]) ).
fof(f68,plain,
! [X0,X1] :
( ~ kn2
| is_a_theorem(implies(and(X0,X1),X0)) ),
inference(cnf_transformation,[],[f56]) ).
fof(f69,plain,
! [X2,X0,X1] :
( ~ kn3
| is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
inference(cnf_transformation,[],[f57]) ).
fof(f70,plain,
( ~ is_a_theorem(implies(or(sK0,sK1),or(sK1,sK0)))
| r3 ),
inference(cnf_transformation,[],[f64]) ).
fof(f71,plain,
! [X0,X1] :
( ~ op_or
| or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(cnf_transformation,[],[f59]) ).
fof(f72,plain,
! [X0,X1] :
( ~ op_and
| and(X0,X1) = not(or(not(X0),not(X1))) ),
inference(cnf_transformation,[],[f60]) ).
fof(f73,plain,
! [X0,X1] :
( ~ op_implies_and
| implies(X0,X1) = not(and(X0,not(X1))) ),
inference(cnf_transformation,[],[f61]) ).
fof(f74,plain,
! [X0,X1] :
( ~ op_implies_or
| implies(X0,X1) = or(not(X0),X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f75,plain,
! [X0,X1] :
( ~ op_equiv
| equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
inference(cnf_transformation,[],[f63]) ).
fof(f76,plain,
op_or,
inference(cnf_transformation,[],[f32]) ).
fof(f77,plain,
op_implies_and,
inference(cnf_transformation,[],[f33]) ).
fof(f79,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f80,plain,
kn1,
inference(cnf_transformation,[],[f36]) ).
fof(f81,plain,
kn2,
inference(cnf_transformation,[],[f37]) ).
fof(f82,plain,
kn3,
inference(cnf_transformation,[],[f38]) ).
fof(f84,plain,
op_implies_or,
inference(cnf_transformation,[],[f40]) ).
fof(f85,plain,
op_and,
inference(cnf_transformation,[],[f41]) ).
fof(f86,plain,
op_equiv,
inference(cnf_transformation,[],[f42]) ).
fof(f87,plain,
~ r3,
inference(cnf_transformation,[],[f45]) ).
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,[],[f65]) ).
tcf(c_51,plain,
! [X0: $i] :
( is_a_theorem(implies(X0,and(X0,X0)))
| ~ kn1 ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ kn2 ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))
| ~ kn3 ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_54,plain,
( r3
| ~ is_a_theorem(implies(or(sK0,sK1),or(sK1,sK0))) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ( not(and(not(X0),not(X1))) = or(X0,X1) )
| ~ op_or ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( ( not(or(not(X0),not(X1))) = and(X0,X1) )
| ~ op_and ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ( not(and(X0,not(X1))) = implies(X0,X1) )
| ~ op_implies_and ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ( or(not(X0),X1) = implies(X0,X1) )
| ~ op_implies_or ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( ( and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1) )
| ~ op_equiv ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_60,plain,
op_or,
inference(cnf_transformation,[],[f76]) ).
tcf(c_61,plain,
op_implies_and,
inference(cnf_transformation,[],[f77]) ).
tcf(c_63,plain,
modus_ponens,
inference(cnf_transformation,[],[f79]) ).
tcf(c_64,plain,
kn1,
inference(cnf_transformation,[],[f80]) ).
tcf(c_65,plain,
kn2,
inference(cnf_transformation,[],[f81]) ).
tcf(c_66,plain,
kn3,
inference(cnf_transformation,[],[f82]) ).
tcf(c_68,plain,
op_implies_or,
inference(cnf_transformation,[],[f84]) ).
tcf(c_69,plain,
op_and,
inference(cnf_transformation,[],[f85]) ).
tcf(c_70,plain,
op_equiv,
inference(cnf_transformation,[],[f86]) ).
tcf(c_71,negated_conjecture,
~ r3,
inference(cnf_transformation,[],[f87]) ).
tcf(c_72,plain,
( is_a_theorem(implies(and(sK0,sK0),sK0))
| ~ kn2 ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_73,plain,
( is_a_theorem(implies(sK0,and(sK0,sK0)))
| ~ kn1 ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(and(X0,X1),X0)),
inference(global_subsumption_just,[status(thm)],[c_52,c_65,c_52]) ).
tcf(c_84,plain,
! [X0: $i] : is_a_theorem(implies(X0,and(X0,X0))),
inference(global_subsumption_just,[status(thm)],[c_51,c_64,c_51]) ).
tcf(c_87,plain,
~ is_a_theorem(implies(or(sK0,sK1),or(sK1,sK0))),
inference(global_subsumption_just,[status(thm)],[c_54,c_71,c_54]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i] : or(not(X0),X1) = implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_58,c_68,c_58]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] : not(and(X0,not(X1))) = implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_57,c_61,c_57]) ).
tcf(c_98,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_63,c_49]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(renaming,[status(thm)],[c_98]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i] : not(or(not(X0),not(X1))) = and(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_56,c_69,c_56]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i] : not(and(not(X0),not(X1))) = or(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_55,c_60,c_55]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i] : and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_59,c_70,c_59]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))),
inference(global_subsumption_just,[status(thm)],[c_53,c_66,c_53]) ).
tcf(c_206,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_208,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_209,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(X1)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_210,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( implies(X0,X2) = implies(X1,X3) )
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_381,plain,
! [X0: $i] :
( ~ is_a_theorem(X0)
| ( implies(or(sK0,sK1),or(sK1,sK0)) != X0 ) ),
inference(resolution,[status(thm)],[c_209,c_87]) ).
tcf(c_392,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,and(X0,X0)))
| ~ is_a_theorem(implies(implies(X0,and(X0,X0)),X1)) ),
inference(instantiation,[status(thm)],[c_99]) ).
tcf(c_404,plain,
! [X0: $i,X1: $i] :
( ~ is_a_theorem(X1)
| ( X1 != X0 )
| ( implies(or(sK0,sK1),or(sK1,sK0)) != X0 ) ),
inference(resolution,[status(thm)],[c_381,c_208]) ).
tcf(c_405,plain,
! [X0: $i] :
( is_a_theorem(and(X0,X0))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_84,c_99]) ).
tcf(c_406,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(X0,X1)) ),
inference(superposition,[status(thm)],[c_81,c_99]) ).
tcf(c_420,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(implies(and(X1,X2),X1))
| ( X0 != implies(and(X1,X2),X1) ) ),
inference(instantiation,[status(thm)],[c_209]) ).
tcf(c_431,plain,
! [X0: $i,X1: $i] : not(implies(X0,not(X1))) = and(X0,X1),
inference(superposition,[status(thm)],[c_89,c_100]) ).
tcf(c_458,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(not(and(and(X0,X0),X1)),not(and(X1,X0))))
| ~ is_a_theorem(implies(X0,and(X0,X0)))
| ~ is_a_theorem(implies(implies(X0,and(X0,X0)),implies(not(and(and(X0,X0),X1)),not(and(X1,X0))))) ),
inference(instantiation,[status(thm)],[c_392]) ).
tcf(c_459,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(implies(X0,and(X0,X0)),implies(not(and(and(X0,X0),X1)),not(and(X1,X0))))),
inference(instantiation,[status(thm)],[c_109]) ).
tcf(c_531,plain,
! [X0: $i,X1: $i] : implies(not(X0),X1) = or(X0,X1),
inference(superposition,[status(thm)],[c_103,c_95]) ).
tcf(c_570,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(not(and(and(X0,X1),not(X0))))
| ~ is_a_theorem(implies(and(X0,X1),X0))
| ( not(and(and(X0,X1),not(X0))) != implies(and(X0,X1),X0) ) ),
inference(instantiation,[status(thm)],[c_420]) ).
tcf(c_571,plain,
! [X0: $i,X1: $i] : not(and(and(X0,X1),not(X0))) = implies(and(X0,X1),X0),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_572,plain,
( is_a_theorem(not(and(and(sK0,sK0),not(sK0))))
| ~ is_a_theorem(implies(and(sK0,sK0),sK0))
| ( not(and(and(sK0,sK0),not(sK0))) != implies(and(sK0,sK0),sK0) ) ),
inference(instantiation,[status(thm)],[c_570]) ).
tcf(c_573,plain,
not(and(and(sK0,sK0),not(sK0))) = implies(and(sK0,sK0),sK0),
inference(instantiation,[status(thm)],[c_571]) ).
tcf(c_697,plain,
! [X0: $i] :
( is_a_theorem(equiv(X0,X0))
| ~ is_a_theorem(implies(X0,X0)) ),
inference(superposition,[status(thm)],[c_106,c_405]) ).
tcf(c_795,plain,
! [X0: $i,X1: $i] : not(or(X0,not(X1))) = and(not(X0),X1),
inference(superposition,[status(thm)],[c_531,c_431]) ).
tcf(c_923,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X2)
| ~ is_a_theorem(not(and(and(X0,X1),not(X0))))
| ~ is_a_theorem(implies(not(and(and(X0,X1),not(X0))),X2)) ),
inference(instantiation,[status(thm)],[c_99]) ).
tcf(c_971,plain,
! [X0: $i,X1: $i] : and(not(not(X0)),X1) = and(X0,X1),
inference(superposition,[status(thm)],[c_795,c_100]) ).
tcf(c_1128,plain,
! [X0: $i] :
( is_a_theorem(equiv(not(X0),not(X0)))
| ~ is_a_theorem(or(X0,not(X0))) ),
inference(superposition,[status(thm)],[c_531,c_697]) ).
tcf(c_1132,plain,
( is_a_theorem(equiv(not(sK0),not(sK0)))
| ~ is_a_theorem(or(sK0,not(sK0))) ),
inference(instantiation,[status(thm)],[c_1128]) ).
tcf(c_1358,plain,
! [X0: $i] :
( is_a_theorem(and(X0,not(not(X0))))
| ~ is_a_theorem(not(not(X0))) ),
inference(superposition,[status(thm)],[c_971,c_405]) ).
tcf(c_1454,plain,
! [X0: $i] :
( ~ is_a_theorem(X0)
| ( X0 != implies(or(sK0,sK1),or(sK1,sK0)) ) ),
inference(resolution,[status(thm)],[c_404,c_206]) ).
tcf(c_1476,plain,
! [X0: $i] :
( is_a_theorem(not(and(not(X0),X0)))
| ~ is_a_theorem(not(and(and(X0,X0),not(X0))))
| ~ is_a_theorem(implies(not(and(and(X0,X0),not(X0))),not(and(not(X0),X0)))) ),
inference(instantiation,[status(thm)],[c_923]) ).
tcf(c_1477,plain,
! [X0: $i] :
( is_a_theorem(implies(not(and(and(X0,X0),not(X0))),not(and(not(X0),X0))))
| ~ is_a_theorem(implies(X0,and(X0,X0)))
| ~ is_a_theorem(implies(implies(X0,and(X0,X0)),implies(not(and(and(X0,X0),not(X0))),not(and(not(X0),X0))))) ),
inference(instantiation,[status(thm)],[c_458]) ).
tcf(c_1478,plain,
( is_a_theorem(not(and(not(sK0),sK0)))
| ~ is_a_theorem(not(and(and(sK0,sK0),not(sK0))))
| ~ is_a_theorem(implies(not(and(and(sK0,sK0),not(sK0))),not(and(not(sK0),sK0)))) ),
inference(instantiation,[status(thm)],[c_1476]) ).
tcf(c_1479,plain,
( is_a_theorem(implies(not(and(and(sK0,sK0),not(sK0))),not(and(not(sK0),sK0))))
| ~ is_a_theorem(implies(sK0,and(sK0,sK0)))
| ~ is_a_theorem(implies(implies(sK0,and(sK0,sK0)),implies(not(and(and(sK0,sK0),not(sK0))),not(and(not(sK0),sK0))))) ),
inference(instantiation,[status(thm)],[c_1477]) ).
tcf(c_1517,plain,
! [X0: $i,X1: $i] :
( ~ is_a_theorem(implies(X0,X1))
| ( X1 != or(sK1,sK0) )
| ( X0 != or(sK0,sK1) ) ),
inference(resolution,[status(thm)],[c_1454,c_210]) ).
tcf(c_4552,plain,
! [X0: $i] : is_a_theorem(implies(implies(X0,and(X0,X0)),implies(not(and(and(X0,X0),not(X0))),not(and(not(X0),X0))))),
inference(instantiation,[status(thm)],[c_459]) ).
tcf(c_4553,plain,
is_a_theorem(implies(implies(sK0,and(sK0,sK0)),implies(not(and(and(sK0,sK0),not(sK0))),not(and(not(sK0),sK0))))),
inference(instantiation,[status(thm)],[c_4552]) ).
tcf(c_4725,plain,
! [X0: $i] :
( ~ is_a_theorem(implies(X0,not(and(not(sK1),not(sK0)))))
| ( X0 != or(sK0,sK1) ) ),
inference(resolution,[status(thm)],[c_1517,c_103]) ).
tcf(c_5393,plain,
~ is_a_theorem(implies(not(and(not(sK0),not(sK1))),not(and(not(sK1),not(sK0))))),
inference(resolution,[status(thm)],[c_4725,c_103]) ).
tcf(c_5428,plain,
! [X0: $i] :
( ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,implies(not(and(not(sK0),not(sK1))),not(and(not(sK1),not(sK0)))))) ),
inference(resolution,[status(thm)],[c_5393,c_99]) ).
tcf(c_6103,plain,
~ is_a_theorem(implies(not(sK0),not(sK0))),
inference(resolution,[status(thm)],[c_5428,c_109]) ).
tcf(c_6159,plain,
! [X0: $i] :
( ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,implies(not(sK0),not(sK0)))) ),
inference(resolution,[status(thm)],[c_6103,c_99]) ).
tcf(c_6484,plain,
! [X0: $i] : ~ is_a_theorem(and(implies(not(sK0),not(sK0)),X0)),
inference(resolution,[status(thm)],[c_6159,c_81]) ).
tcf(c_6494,plain,
! [X0: $i,X1: $i] :
( ~ is_a_theorem(X1)
| ( and(implies(not(sK0),not(sK0)),X0) != X1 ) ),
inference(resolution,[status(thm)],[c_6484,c_209]) ).
tcf(c_6739,plain,
~ is_a_theorem(equiv(not(sK0),not(sK0))),
inference(resolution,[status(thm)],[c_6494,c_106]) ).
tcf(c_8968,plain,
! [X0: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(not(not(X0))) ),
inference(superposition,[status(thm)],[c_1358,c_406]) ).
tcf(c_9028,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X0,not(X1)))
| ~ is_a_theorem(not(and(not(X0),X1))) ),
inference(superposition,[status(thm)],[c_795,c_8968]) ).
tcf(c_9029,plain,
( is_a_theorem(or(sK0,not(sK0)))
| ~ is_a_theorem(not(and(not(sK0),sK0))) ),
inference(instantiation,[status(thm)],[c_9028]) ).
tcf(c_9030,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_9029,c_6739,c_4553,c_1479,c_1478,c_1132,c_573,c_572,c_73,c_72,c_64,c_65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL520+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n009.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 23:38:14 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 4.19/1.20 % SZS status Started for theBenchmark.p
% 4.19/1.20 % SZS status Theorem for theBenchmark.p
% 4.19/1.20
% 4.19/1.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.19/1.20
% 4.19/1.20 % ------ iProver source info
% 4.19/1.20
% 4.19/1.20 % git: date: 2026-07-19 20:42:38 +0200
% 4.19/1.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.19/1.20 % git: non_committed_changes: false
% 4.19/1.20
% 4.19/1.20 % ------ Parsing...
% 4.19/1.20 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.19/1.20
% 4.19/1.20 % ------ Preprocessing... sup_sim: 0 sf_s rm: 12 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 4.19/1.20
% 4.19/1.20 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.19/1.20
% 4.19/1.20 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.19/1.20 % ------ Proving...
% 4.19/1.20 % ------ Problem Properties
% 4.19/1.20
% 4.19/1.20 %
% 4.19/1.20 % clauses 11
% 4.19/1.20 % conjectures 0
% 4.19/1.20 % EPR 0
% 4.19/1.20 % Horn 11
% 4.19/1.20 % unary 9
% 4.19/1.20 % binary 1
% 4.19/1.20 % lits 14
% 4.19/1.20 % lits eq 6
% 4.19/1.20 % fd_pure 0
% 4.19/1.20 % fd_pseudo 0
% 4.19/1.20 % fd_cond 0
% 4.19/1.20 % fd_pseudo_cond 1
% 4.19/1.20 % AC symbols 0
% 4.19/1.20
% 4.19/1.20 % ------ Input Options Time Limit: Unbounded
% 4.19/1.20
% 4.19/1.20
% 4.19/1.20 % ------
% 4.19/1.20 % Current options:
% 4.19/1.20 % ------
% 4.19/1.20
% 4.19/1.20
% 4.19/1.20 %
% 4.19/1.20
% 4.19/1.20 % ------ Proving...
% 4.19/1.20 %
% 4.19/1.20
% 4.19/1.20 % SZS status Theorem for theBenchmark.p
% 4.19/1.20
% 4.19/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.19/1.20
% 4.19/1.20
%------------------------------------------------------------------------------