%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL498+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 : n017.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 02:06:46 PM UTC 2026
% Result : Theorem 81.92s 13.46s
% Output : CNFRefutation 81.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 21
% Syntax : Number of formulae : 134 ( 45 unt; 0 def)
% Number of atoms : 265 ( 73 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 247 ( 116 ~; 112 |; 2 &)
% ( 7 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 9 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 223 ( 0 sgn 222 !; 1 ?; 160 :)
% 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(f21,axiom,
( cn3
<=> ! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',cn3) ).
fof(f22,axiom,
( r1
<=> ! [X0] : is_a_theorem(implies(or(X0,X0),X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r1) ).
fof(f23,axiom,
( r2
<=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r2) ).
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(f25,axiom,
( r4
<=> ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r4) ).
fof(f26,axiom,
( r5
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r5) ).
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(f32,axiom,
op_implies_or,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_op_implies_or) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_modus_ponens) ).
fof(f36,axiom,
r1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r1) ).
fof(f37,axiom,
r2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r2) ).
fof(f38,axiom,
r3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r3) ).
fof(f39,axiom,
r4,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r4) ).
fof(f40,axiom,
r5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r5) ).
fof(f45,conjecture,
cn3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',luka_cn3) ).
fof(f46,negated_conjecture,
~ cn3,
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f47,plain,
~ cn3,
inference(flattening,[],[f46]) ).
fof(f48,plain,
( r5
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) ),
inference(unused_predicate_definition_removal,[],[f26]) ).
fof(f49,plain,
( r4
=> ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
inference(unused_predicate_definition_removal,[],[f25]) ).
fof(f50,plain,
( r3
=> ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f24]) ).
fof(f51,plain,
( r2
=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f23]) ).
fof(f52,plain,
( r1
=> ! [X0] : is_a_theorem(implies(or(X0,X0),X0)) ),
inference(unused_predicate_definition_removal,[],[f22]) ).
fof(f53,plain,
( ! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0))
=> cn3 ),
inference(unused_predicate_definition_removal,[],[f21]) ).
fof(f55,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(f58,plain,
( ~ modus_ponens
| ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ) ),
inference(ennf_transformation,[],[f55]) ).
fof(f59,plain,
( ~ modus_ponens
| ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ) ),
inference(flattening,[],[f58]) ).
fof(f61,plain,
( ? [X0] : ~ is_a_theorem(implies(implies(not(X0),X0),X0))
| cn3 ),
inference(ennf_transformation,[],[f53]) ).
fof(f62,plain,
( ~ r1
| ! [X0] : is_a_theorem(implies(or(X0,X0),X0)) ),
inference(ennf_transformation,[],[f52]) ).
fof(f63,plain,
( ~ r2
| ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
inference(ennf_transformation,[],[f51]) ).
fof(f64,plain,
( ~ r3
| ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(ennf_transformation,[],[f50]) ).
fof(f65,plain,
( ~ r4
| ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
inference(ennf_transformation,[],[f49]) ).
fof(f66,plain,
( ~ r5
| ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) ),
inference(ennf_transformation,[],[f48]) ).
fof(f69,plain,
( ~ op_implies_or
| ! [X0,X1] : implies(X0,X1) = or(not(X0),X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f71,plain,
( ~ is_a_theorem(implies(implies(not(sK0),sK0),sK0))
| cn3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f61]) ).
fof(f72,plain,
! [X0,X1] :
( ~ modus_ponens
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f74,plain,
( ~ is_a_theorem(implies(implies(not(sK0),sK0),sK0))
| cn3 ),
inference(cnf_transformation,[],[f71]) ).
fof(f75,plain,
! [X0] :
( ~ r1
| is_a_theorem(implies(or(X0,X0),X0)) ),
inference(cnf_transformation,[],[f62]) ).
fof(f76,plain,
! [X0,X1] :
( ~ r2
| is_a_theorem(implies(X1,or(X0,X1))) ),
inference(cnf_transformation,[],[f63]) ).
fof(f77,plain,
! [X0,X1] :
( ~ r3
| is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(cnf_transformation,[],[f64]) ).
fof(f78,plain,
! [X2,X0,X1] :
( ~ r4
| is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
inference(cnf_transformation,[],[f65]) ).
fof(f79,plain,
! [X2,X0,X1] :
( ~ r5
| is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) ),
inference(cnf_transformation,[],[f66]) ).
fof(f82,plain,
! [X0,X1] :
( ~ op_implies_or
| implies(X0,X1) = or(not(X0),X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f84,plain,
op_implies_or,
inference(cnf_transformation,[],[f32]) ).
fof(f87,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f88,plain,
r1,
inference(cnf_transformation,[],[f36]) ).
fof(f89,plain,
r2,
inference(cnf_transformation,[],[f37]) ).
fof(f90,plain,
r3,
inference(cnf_transformation,[],[f38]) ).
fof(f91,plain,
r4,
inference(cnf_transformation,[],[f39]) ).
fof(f92,plain,
r5,
inference(cnf_transformation,[],[f40]) ).
fof(f96,plain,
~ cn3,
inference(cnf_transformation,[],[f47]) ).
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,[],[f72]) ).
tcf(c_51,plain,
( cn3
| ~ is_a_theorem(implies(implies(not(sK0),sK0),sK0)) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_52,plain,
! [X0: $i] :
( is_a_theorem(implies(or(X0,X0),X0))
| ~ r1 ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,or(X1,X0)))
| ~ r2 ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))
| ~ r4 ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1))))
| ~ r5 ),
inference(cnf_transformation,[],[f79]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( ( or(not(X0),X1) = implies(X0,X1) )
| ~ op_implies_or ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_61,plain,
op_implies_or,
inference(cnf_transformation,[],[f84]) ).
tcf(c_64,plain,
modus_ponens,
inference(cnf_transformation,[],[f87]) ).
tcf(c_65,plain,
r1,
inference(cnf_transformation,[],[f88]) ).
tcf(c_66,plain,
r2,
inference(cnf_transformation,[],[f89]) ).
tcf(c_67,plain,
r3,
inference(cnf_transformation,[],[f90]) ).
tcf(c_68,plain,
r4,
inference(cnf_transformation,[],[f91]) ).
tcf(c_69,plain,
r5,
inference(cnf_transformation,[],[f92]) ).
tcf(c_73,negated_conjecture,
~ cn3,
inference(cnf_transformation,[],[f96]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,or(X1,X0))),
inference(global_subsumption_just,[status(thm)],[c_53,c_66,c_53]) ).
tcf(c_87,plain,
! [X0: $i] : is_a_theorem(implies(or(X0,X0),X0)),
inference(global_subsumption_just,[status(thm)],[c_52,c_65,c_52]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(or(X0,X1),or(X1,X0))),
inference(global_subsumption_just,[status(thm)],[c_54,c_67,c_54]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] : or(not(X0),X1) = implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_59,c_61,c_59]) ).
tcf(c_101,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_64,c_49]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(renaming,[status(thm)],[c_101]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
inference(global_subsumption_just,[status(thm)],[c_56,c_69,c_56]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
inference(global_subsumption_just,[status(thm)],[c_55,c_68,c_55]) ).
tcf(c_236,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_238,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_239,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(X1)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_240,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( implies(X0,X2) = implies(X1,X3) )
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_241,plain,
! [X0: $i,X1: $i] :
( ( not(X0) = not(X1) )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_245,plain,
( ( not(sK0) = not(sK0) )
| ( sK0 != sK0 ) ),
inference(instantiation,[status(thm)],[c_241]) ).
tcf(c_248,plain,
sK0 = sK0,
inference(instantiation,[status(thm)],[c_236]) ).
tcf(c_598,plain,
! [X0: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(or(X0,X0)) ),
inference(resolution,[status(thm)],[c_102,c_87]) ).
tcf(c_602,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[c_102,c_92]) ).
tcf(c_667,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(not(X0),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[c_239,c_95]) ).
tcf(c_838,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(or(X2,X0),or(X2,X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[c_112,c_102]) ).
tcf(c_841,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X1,or(X0,X2)))
| ~ is_a_theorem(or(X0,or(X1,X2))) ),
inference(resolution,[status(thm)],[c_115,c_102]) ).
tcf(c_879,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = or(X0,X1) )
| ( X3 != X2 )
| ( or(X0,X1) != X2 ) ),
inference(instantiation,[status(thm)],[c_238]) ).
tcf(c_1000,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X2,X1))
| ~ is_a_theorem(or(X2,X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[c_838,c_102]) ).
tcf(c_1018,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X1,or(not(X0),X2)))
| ~ is_a_theorem(implies(X0,or(X1,X2))) ),
inference(resolution,[status(thm)],[c_841,c_667]) ).
tcf(c_1165,plain,
! [X0: $i,X1: $i] :
( ( X1 = X0 )
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_238,c_236]) ).
tcf(c_1268,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = or(not(X0),X1) )
| ( X2 != implies(X0,X1) )
| ( or(not(X0),X1) != implies(X0,X1) ) ),
inference(instantiation,[status(thm)],[c_879]) ).
tcf(c_1286,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(implies(X1,X3))
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_240,c_239]) ).
tcf(c_1465,plain,
! [X0: $i,X1: $i] : implies(X0,X1) = or(not(X0),X1),
inference(resolution,[status(thm)],[c_1165,c_95]) ).
tcf(c_1630,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(or(not(X0),X1)) ),
inference(resolution,[status(thm)],[c_1465,c_239]) ).
tcf(c_3040,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(implies(X0,X2))
| ( X2 != or(X3,X1) )
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_1286,c_84]) ).
tcf(c_3727,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( implies(X2,X3) = or(not(X0),X1) )
| ( implies(X2,X3) != implies(X0,X1) )
| ( or(not(X0),X1) != implies(X0,X1) ) ),
inference(instantiation,[status(thm)],[c_1268]) ).
tcf(c_10178,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(X0,or(X2,X1)))
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_3040,c_236]) ).
tcf(c_12797,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X2,X1))
| ~ is_a_theorem(X0)
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_10178,c_102]) ).
tcf(c_13001,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( implies(X0,X3) = implies(or(X1,X2),X4) )
| ( X3 != X4 )
| ( X0 != or(X1,X2) ) ),
inference(instantiation,[status(thm)],[c_240]) ).
tcf(c_13185,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X2,or(not(X0),X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[c_12797,c_1465]) ).
tcf(c_15292,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(not(X0),or(X2,X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[c_13185,c_841]) ).
tcf(c_15604,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(X0,or(X2,X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[c_15292,c_1630]) ).
tcf(c_15625,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X2,X1))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[c_15604,c_102]) ).
tcf(c_15792,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X2,or(X1,X0)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[c_15625,c_92]) ).
tcf(c_17131,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X1,or(X2,X0)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[c_15792,c_841]) ).
tcf(c_17426,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(or(X0,or(X1,X0))) ),
inference(resolution,[status(thm)],[c_17131,c_598]) ).
tcf(c_21510,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(implies(X1,X2))
| ( X0 != implies(X1,X2) ) ),
inference(instantiation,[status(thm)],[c_239]) ).
tcf(c_23267,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( implies(implies(X0,X1),X4) = implies(or(not(X2),X3),X5) )
| ( X4 != X5 )
| ( implies(X0,X1) != or(not(X2),X3) ) ),
inference(instantiation,[status(thm)],[c_13001]) ).
tcf(c_35298,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X2,X3))
| ( implies(X0,X1) != implies(X2,X3) ) ),
inference(instantiation,[status(thm)],[c_21510]) ).
tcf(c_39056,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(not(X0),X1))
| ~ is_a_theorem(implies(X0,or(X1,X1))) ),
inference(resolution,[status(thm)],[c_1018,c_17426]) ).
tcf(c_39252,plain,
! [X0: $i] : is_a_theorem(or(not(X0),X0)),
inference(resolution,[status(thm)],[c_39056,c_84]) ).
tcf(c_39700,plain,
! [X0: $i] : is_a_theorem(or(X0,not(X0))),
inference(resolution,[status(thm)],[c_39252,c_602]) ).
tcf(c_39704,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,or(not(or(X0,X1)),X1))),
inference(resolution,[status(thm)],[c_39252,c_841]) ).
tcf(c_39902,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(implies(not(X0),X1)) ),
inference(resolution,[status(thm)],[c_39700,c_1000]) ).
tcf(c_41994,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,or(not(or(not(X0),X1)),X1))),
inference(resolution,[status(thm)],[c_39704,c_1630]) ).
tcf(c_49303,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(implies(not(sK0),sK0),sK0))
| ~ is_a_theorem(implies(X0,X1))
| ( implies(implies(not(sK0),sK0),sK0) != implies(X0,X1) ) ),
inference(instantiation,[status(thm)],[c_35298]) ).
tcf(c_67590,plain,
! [X0: $i,X1: $i] :
( ( implies(not(sK0),sK0) = implies(X0,X1) )
| ( sK0 != X1 )
| ( not(sK0) != X0 ) ),
inference(instantiation,[status(thm)],[c_240]) ).
tcf(c_67595,plain,
! [X0: $i,X1: $i] :
( ( implies(not(sK0),sK0) = or(not(X0),X1) )
| ( implies(not(sK0),sK0) != implies(X0,X1) )
| ( or(not(X0),X1) != implies(X0,X1) ) ),
inference(instantiation,[status(thm)],[c_3727]) ).
tcf(c_69363,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,or(not(or(not(not(X0)),X1)),X1))),
inference(resolution,[status(thm)],[c_41994,c_39902]) ).
tcf(c_75719,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( implies(implies(not(sK0),sK0),sK0) = implies(or(not(X0),X1),X2) )
| ( sK0 != X2 )
| ( implies(not(sK0),sK0) != or(not(X0),X1) ) ),
inference(instantiation,[status(thm)],[c_23267]) ).
tcf(c_75721,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(implies(not(sK0),sK0),sK0))
| ~ is_a_theorem(implies(or(not(X0),X1),X2))
| ( implies(implies(not(sK0),sK0),sK0) != implies(or(not(X0),X1),X2) ) ),
inference(instantiation,[status(thm)],[c_49303]) ).
tcf(c_77032,plain,
! [X0: $i,X1: $i] :
( ( implies(not(sK0),sK0) = implies(not(X0),X1) )
| ( sK0 != X1 )
| ( not(sK0) != not(X0) ) ),
inference(instantiation,[status(thm)],[c_67590]) ).
tcf(c_77034,plain,
( ( implies(not(sK0),sK0) = implies(not(sK0),sK0) )
| ( sK0 != sK0 )
| ( not(sK0) != not(sK0) ) ),
inference(instantiation,[status(thm)],[c_77032]) ).
tcf(c_89402,plain,
( ( implies(not(sK0),sK0) = or(not(not(sK0)),sK0) )
| ( implies(not(sK0),sK0) != implies(not(sK0),sK0) )
| ( or(not(not(sK0)),sK0) != implies(not(sK0),sK0) ) ),
inference(instantiation,[status(thm)],[c_67595]) ).
tcf(c_90143,plain,
or(not(not(sK0)),sK0) = implies(not(sK0),sK0),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_102270,plain,
! [X0: $i] : is_a_theorem(or(not(or(not(not(X0)),X0)),X0)),
inference(resolution,[status(thm)],[c_69363,c_17426]) ).
tcf(c_102433,plain,
! [X0: $i] : is_a_theorem(implies(or(not(not(X0)),X0),X0)),
inference(resolution,[status(thm)],[c_102270,c_1630]) ).
tcf(c_102436,plain,
is_a_theorem(implies(or(not(not(sK0)),sK0),sK0)),
inference(instantiation,[status(thm)],[c_102433]) ).
tcf(c_104622,plain,
! [X0: $i] :
( ( implies(implies(not(sK0),sK0),sK0) = implies(or(not(not(sK0)),sK0),X0) )
| ( sK0 != X0 )
| ( implies(not(sK0),sK0) != or(not(not(sK0)),sK0) ) ),
inference(instantiation,[status(thm)],[c_75719]) ).
tcf(c_104623,plain,
( ( implies(implies(not(sK0),sK0),sK0) = implies(or(not(not(sK0)),sK0),sK0) )
| ( sK0 != sK0 )
| ( implies(not(sK0),sK0) != or(not(not(sK0)),sK0) ) ),
inference(instantiation,[status(thm)],[c_104622]) ).
tcf(c_117913,plain,
! [X0: $i] :
( is_a_theorem(implies(implies(not(sK0),sK0),sK0))
| ~ is_a_theorem(implies(or(not(not(sK0)),sK0),X0))
| ( implies(implies(not(sK0),sK0),sK0) != implies(or(not(not(sK0)),sK0),X0) ) ),
inference(instantiation,[status(thm)],[c_75721]) ).
tcf(c_117914,plain,
( is_a_theorem(implies(implies(not(sK0),sK0),sK0))
| ~ is_a_theorem(implies(or(not(not(sK0)),sK0),sK0))
| ( implies(implies(not(sK0),sK0),sK0) != implies(or(not(not(sK0)),sK0),sK0) ) ),
inference(instantiation,[status(thm)],[c_117913]) ).
tcf(c_117915,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_117914,c_104623,c_102436,c_90143,c_89402,c_77034,c_248,c_245,c_51,c_73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL498+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n017.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Wed Sep 23 23:29:31 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 0.11/0.44
% 0.11/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.44
% 0.11/0.44 % Detected problem language: tptp
% 0.11/0.45 % Proving...
% 81.92/13.46 % SZS status Started for theBenchmark.p
% 81.92/13.46 % SZS status Theorem for theBenchmark.p
% 81.92/13.46
% 81.92/13.46 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 81.92/13.46
% 81.92/13.46 % ------ iProver source info
% 81.92/13.46
% 81.92/13.46 % git: date: 2026-07-19 20:42:38 +0200
% 81.92/13.46 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 81.92/13.46 % git: non_committed_changes: false
% 81.92/13.46
% 81.92/13.46 % ------ Parsing...
% 81.92/13.46 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 81.92/13.46
% 81.92/13.46 % ------ Preprocessing... sup_sim: 1 sf_s rm: 13 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 81.92/13.46
% 81.92/13.46 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 81.92/13.46
% 81.92/13.46 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 81.92/13.46 % ------ Proving...
% 81.92/13.46 % ------ Problem Properties
% 81.92/13.46
% 81.92/13.46 %
% 81.92/13.46 % clauses 12
% 81.92/13.46 % conjectures 0
% 81.92/13.46 % EPR 0
% 81.92/13.46 % Horn 12
% 81.92/13.46 % unary 10
% 81.92/13.46 % binary 1
% 81.92/13.46 % lits 15
% 81.92/13.46 % lits eq 5
% 81.92/13.46 % fd_pure 0
% 81.92/13.46 % fd_pseudo 0
% 81.92/13.46 % fd_cond 0
% 81.92/13.46 % fd_pseudo_cond 1
% 81.92/13.46 % AC symbols 0
% 81.92/13.46
% 81.92/13.46 % ------ Input Options Time Limit: Unbounded
% 81.92/13.46
% 81.92/13.46
% 81.92/13.46 % ------
% 81.92/13.46 % Current options:
% 81.92/13.46 % ------
% 81.92/13.46
% 81.92/13.46
% 81.92/13.46 %
% 81.92/13.46
% 81.92/13.46 % ------ Proving...
% 81.92/13.46 %
% 81.92/13.46
% 81.92/13.46 % SZS status Theorem for theBenchmark.p
% 81.92/13.46
% 81.92/13.46 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 81.92/13.46
% 81.92/13.46
%------------------------------------------------------------------------------