%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL487+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 : n019.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 02:06:45 PM UTC 2026
% Result : Theorem 108.83s 18.47s
% Output : CNFRefutation 108.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 28
% Syntax : Number of formulae : 148 ( 62 unt; 0 def)
% Number of atoms : 262 ( 56 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 211 ( 97 ~; 92 |; 2 &)
% ( 7 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 14 ( 12 usr; 12 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 239 ( 0 sgn 237 !; 2 ?; 155 :)
% 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(f7,axiom,
( and_1
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',and_1) ).
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(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(f32,axiom,
op_implies_or,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_op_implies_or) ).
fof(f33,axiom,
op_and,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_op_and) ).
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(f42,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(f43,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(f45,conjecture,
and_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_1) ).
fof(f46,negated_conjecture,
~ and_1,
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f47,plain,
~ and_1,
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,X1] : is_a_theorem(implies(and(X0,X1),X0))
=> and_1 ),
inference(unused_predicate_definition_removal,[],[f7]) ).
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(f56,plain,
( ~ modus_ponens
| ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ) ),
inference(ennf_transformation,[],[f55]) ).
fof(f57,plain,
( ~ modus_ponens
| ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ) ),
inference(flattening,[],[f56]) ).
fof(f59,plain,
( ? [X0,X1] : ~ is_a_theorem(implies(and(X0,X1),X0))
| and_1 ),
inference(ennf_transformation,[],[f53]) ).
fof(f60,plain,
( ~ r1
| ! [X0] : is_a_theorem(implies(or(X0,X0),X0)) ),
inference(ennf_transformation,[],[f52]) ).
fof(f61,plain,
( ~ r2
| ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
inference(ennf_transformation,[],[f51]) ).
fof(f62,plain,
( ~ r3
| ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(ennf_transformation,[],[f50]) ).
fof(f63,plain,
( ~ r4
| ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
inference(ennf_transformation,[],[f49]) ).
fof(f64,plain,
( ~ r5
| ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) ),
inference(ennf_transformation,[],[f48]) ).
fof(f65,plain,
( ~ op_or
| ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(ennf_transformation,[],[f27]) ).
fof(f66,plain,
( ~ op_and
| ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))) ),
inference(ennf_transformation,[],[f28]) ).
fof(f67,plain,
( ~ op_implies_and
| ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
inference(ennf_transformation,[],[f29]) ).
fof(f68,plain,
( ~ op_implies_or
| ! [X0,X1] : implies(X0,X1) = or(not(X0),X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f70,plain,
( ~ is_a_theorem(implies(and(sK0,sK1),sK0))
| and_1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f59]) ).
fof(f71,plain,
! [X0,X1] :
( ~ modus_ponens
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f73,plain,
( ~ is_a_theorem(implies(and(sK0,sK1),sK0))
| and_1 ),
inference(cnf_transformation,[],[f70]) ).
fof(f74,plain,
! [X0] :
( ~ r1
| is_a_theorem(implies(or(X0,X0),X0)) ),
inference(cnf_transformation,[],[f60]) ).
fof(f75,plain,
! [X0,X1] :
( ~ r2
| is_a_theorem(implies(X1,or(X0,X1))) ),
inference(cnf_transformation,[],[f61]) ).
fof(f76,plain,
! [X0,X1] :
( ~ r3
| is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(cnf_transformation,[],[f62]) ).
fof(f77,plain,
! [X2,X0,X1] :
( ~ r4
| is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
inference(cnf_transformation,[],[f63]) ).
fof(f78,plain,
! [X2,X0,X1] :
( ~ r5
| is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) ),
inference(cnf_transformation,[],[f64]) ).
fof(f79,plain,
! [X0,X1] :
( ~ op_or
| or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(cnf_transformation,[],[f65]) ).
fof(f80,plain,
! [X0,X1] :
( ~ op_and
| and(X0,X1) = not(or(not(X0),not(X1))) ),
inference(cnf_transformation,[],[f66]) ).
fof(f81,plain,
! [X0,X1] :
( ~ op_implies_and
| implies(X0,X1) = not(and(X0,not(X1))) ),
inference(cnf_transformation,[],[f67]) ).
fof(f82,plain,
! [X0,X1] :
( ~ op_implies_or
| implies(X0,X1) = or(not(X0),X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f84,plain,
op_implies_or,
inference(cnf_transformation,[],[f32]) ).
fof(f85,plain,
op_and,
inference(cnf_transformation,[],[f33]) ).
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(f94,plain,
op_or,
inference(cnf_transformation,[],[f42]) ).
fof(f95,plain,
op_implies_and,
inference(cnf_transformation,[],[f43]) ).
fof(f97,plain,
~ and_1,
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,[],[f71]) ).
tcf(c_51,plain,
( and_1
| ~ is_a_theorem(implies(and(sK0,sK1),sK0)) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_52,plain,
! [X0: $i] :
( is_a_theorem(implies(or(X0,X0),X0))
| ~ r1 ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,or(X1,X0)))
| ~ r2 ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ),
inference(cnf_transformation,[],[f76]) ).
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,[],[f77]) ).
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,[],[f78]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ( not(and(not(X0),not(X1))) = or(X0,X1) )
| ~ op_or ),
inference(cnf_transformation,[],[f79]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ( not(or(not(X0),not(X1))) = and(X0,X1) )
| ~ op_and ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( ( not(and(X0,not(X1))) = implies(X0,X1) )
| ~ op_implies_and ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( ( or(not(X0),X1) = implies(X0,X1) )
| ~ op_implies_or ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_62,plain,
op_implies_or,
inference(cnf_transformation,[],[f84]) ).
tcf(c_63,plain,
op_and,
inference(cnf_transformation,[],[f85]) ).
tcf(c_65,plain,
modus_ponens,
inference(cnf_transformation,[],[f87]) ).
tcf(c_66,plain,
r1,
inference(cnf_transformation,[],[f88]) ).
tcf(c_67,plain,
r2,
inference(cnf_transformation,[],[f89]) ).
tcf(c_68,plain,
r3,
inference(cnf_transformation,[],[f90]) ).
tcf(c_69,plain,
r4,
inference(cnf_transformation,[],[f91]) ).
tcf(c_70,plain,
r5,
inference(cnf_transformation,[],[f92]) ).
tcf(c_72,plain,
op_or,
inference(cnf_transformation,[],[f94]) ).
tcf(c_73,plain,
op_implies_and,
inference(cnf_transformation,[],[f95]) ).
tcf(c_75,negated_conjecture,
~ and_1,
inference(cnf_transformation,[],[f97]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,or(X1,X0))),
inference(global_subsumption_just,[status(thm)],[c_53,c_67,c_53]) ).
tcf(c_90,plain,
! [X0: $i] : is_a_theorem(implies(or(X0,X0),X0)),
inference(global_subsumption_just,[status(thm)],[c_52,c_66,c_52]) ).
tcf(c_93,plain,
~ is_a_theorem(implies(and(sK0,sK1),sK0)),
inference(global_subsumption_just,[status(thm)],[c_51,c_75,c_51]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(or(X0,X1),or(X1,X0))),
inference(global_subsumption_just,[status(thm)],[c_54,c_68,c_54]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i] : or(not(X0),X1) = implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_60,c_62,c_60]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i] : not(and(X0,not(X1))) = implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_59,c_73,c_59]) ).
tcf(c_107,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_65,c_49]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(renaming,[status(thm)],[c_107]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i] : not(or(not(X0),not(X1))) = and(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_58,c_63,c_58]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i] : not(and(not(X0),not(X1))) = or(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_57,c_72,c_57]) ).
tcf(c_118,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_70,c_56]) ).
tcf(c_121,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_69,c_55]) ).
tcf(c_140,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_142,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_143,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(X1)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_144,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( implies(X0,X2) = implies(X1,X3) )
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_146,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( or(X0,X2) = or(X1,X3) )
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_147,plain,
! [X0: $i,X1: $i] :
( ( not(X0) = not(X1) )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_198,plain,
! [X0: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(or(X0,X0)) ),
inference(resolution,[status(thm)],[c_108,c_90]) ).
tcf(c_202,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[c_108,c_95]) ).
tcf(c_288,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(not(and(X0,not(X1))))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[c_143,c_104]) ).
tcf(c_290,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(not(X0),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[c_143,c_98]) ).
tcf(c_389,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_118,c_108]) ).
tcf(c_396,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X1,not(X0)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[c_290,c_202]) ).
tcf(c_414,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_121,c_108]) ).
tcf(c_595,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_389,c_108]) ).
tcf(c_679,plain,
! [X0: $i,X1: $i] :
( ( X1 = X0 )
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_142,c_140]) ).
tcf(c_680,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( not(X0) = X2 )
| ( X2 != not(X1) )
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_142,c_147]) ).
tcf(c_730,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_144,c_143]) ).
tcf(c_780,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(or(X0,X2))
| ~ is_a_theorem(or(X1,X3))
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_146,c_143]) ).
tcf(c_835,plain,
! [X0: $i,X1: $i] : or(X0,X1) = not(and(not(X0),not(X1))),
inference(resolution,[status(thm)],[c_679,c_112]) ).
tcf(c_837,plain,
! [X0: $i,X1: $i] : and(X0,X1) = not(or(not(X0),not(X1))),
inference(resolution,[status(thm)],[c_679,c_109]) ).
tcf(c_841,plain,
! [X0: $i,X1: $i] : implies(X0,X1) = or(not(X0),X1),
inference(resolution,[status(thm)],[c_679,c_98]) ).
tcf(c_965,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(or(not(X0),X1)) ),
inference(resolution,[status(thm)],[c_841,c_143]) ).
tcf(c_1050,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X1,not(X0)))
| ~ is_a_theorem(implies(X0,not(X1))) ),
inference(resolution,[status(thm)],[c_965,c_396]) ).
tcf(c_1198,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(not(and(not(X0),not(X1)))) ),
inference(resolution,[status(thm)],[c_835,c_143]) ).
tcf(c_1461,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( not(X0) = and(X1,X2) )
| ( X0 != or(not(X1),not(X2)) ) ),
inference(resolution,[status(thm)],[c_680,c_837]) ).
tcf(c_1890,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(implies(X0,X3))
| ( X3 != or(X2,X1) )
| ( X0 != or(X1,X2) ) ),
inference(resolution,[status(thm)],[c_730,c_95]) ).
tcf(c_2043,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(or(X0,X2))
| ~ is_a_theorem(implies(X1,X3))
| ( X2 != X3 )
| ( X0 != not(X1) ) ),
inference(resolution,[status(thm)],[c_780,c_290]) ).
tcf(c_2934,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(implies(not(X0),X1)) ),
inference(resolution,[status(thm)],[c_1198,c_288]) ).
tcf(c_2944,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,or(X1,not(X0)))),
inference(resolution,[status(thm)],[c_2934,c_87]) ).
tcf(c_3059,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,or(X1,not(X1)))),
inference(resolution,[status(thm)],[c_2944,c_414]) ).
tcf(c_3144,plain,
! [X0: $i] : is_a_theorem(or(X0,not(X0))),
inference(resolution,[status(thm)],[c_3059,c_198]) ).
tcf(c_3182,plain,
! [X0: $i] : is_a_theorem(or(not(X0),X0)),
inference(resolution,[status(thm)],[c_3144,c_202]) ).
tcf(c_3289,plain,
! [X0: $i] : is_a_theorem(implies(X0,X0)),
inference(resolution,[status(thm)],[c_3182,c_965]) ).
tcf(c_7737,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(X0,implies(X2,X1)))
| ( X0 != or(X1,not(X2)) ) ),
inference(resolution,[status(thm)],[c_1890,c_841]) ).
tcf(c_9375,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(not(X2),X0))
| ~ is_a_theorem(implies(X2,X1))
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_2043,c_140]) ).
tcf(c_20210,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(implies(or(X0,not(X1)),X2)) ),
inference(resolution,[status(thm)],[c_595,c_2944]) ).
tcf(c_27192,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0))),
inference(resolution,[status(thm)],[c_7737,c_140]) ).
tcf(c_27348,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(or(X0,not(X1))) ),
inference(resolution,[status(thm)],[c_27192,c_108]) ).
tcf(c_32863,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(not(X1),X0))
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_9375,c_3289]) ).
tcf(c_33589,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X1,X0))
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_32863,c_965]) ).
tcf(c_36438,plain,
! [X0: $i,X1: $i] : not(implies(X0,not(X1))) = and(X0,X1),
inference(resolution,[status(thm)],[c_1461,c_841]) ).
tcf(c_39893,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(and(X0,X1),not(implies(X0,not(X1))))),
inference(resolution,[status(thm)],[c_36438,c_33589]) ).
tcf(c_41687,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(implies(X0,not(X1)),not(and(X0,X1)))),
inference(resolution,[status(thm)],[c_39893,c_1050]) ).
tcf(c_151426,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,implies(X0,X1))),
inference(resolution,[status(thm)],[c_20210,c_27192]) ).
tcf(c_152029,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X0,X2))
| ~ is_a_theorem(implies(implies(X0,X1),X2)) ),
inference(resolution,[status(thm)],[c_151426,c_595]) ).
tcf(c_196062,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,not(and(X0,X1)))),
inference(resolution,[status(thm)],[c_152029,c_41687]) ).
tcf(c_197626,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(and(X0,X1),X0)),
inference(resolution,[status(thm)],[c_196062,c_27348]) ).
tcf(c_197767,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_93,c_197626]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL487+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n019.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 23:33:19 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 108.83/18.47 % SZS status Started for theBenchmark.p
% 108.83/18.47 % SZS status Theorem for theBenchmark.p
% 108.83/18.47
% 108.83/18.47 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 108.83/18.47
% 108.83/18.47 % ------ iProver source info
% 108.83/18.47
% 108.83/18.47 % git: date: 2026-07-19 20:42:38 +0200
% 108.83/18.47 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 108.83/18.47 % git: non_committed_changes: false
% 108.83/18.47
% 108.83/18.47 % ------ Parsing...
% 108.83/18.47 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 108.83/18.47
% 108.83/18.47 % ------ Preprocessing... sf_s rm: 14 0s sf_e sf_s rm: 1 0s sf_e %
% 108.83/18.47
% 108.83/18.47 % ------ Preprocessing...%
% 108.83/18.47
% 108.83/18.47 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 108.83/18.47 % ------ Proving...
% 108.83/18.47 % ------ Problem Properties
% 108.83/18.47
% 108.83/18.47 %
% 108.83/18.47 % clauses 13
% 108.83/18.47 % conjectures 0
% 108.83/18.47 % EPR 0
% 108.83/18.47 % Horn 13
% 108.83/18.47 % unary 11
% 108.83/18.47 % binary 1
% 108.83/18.47 % lits 16
% 108.83/18.47 % lits eq 6
% 108.83/18.47 % fd_pure 0
% 108.83/18.47 % fd_pseudo 0
% 108.83/18.47 % fd_cond 0
% 108.83/18.47 % fd_pseudo_cond 1
% 108.83/18.47 % AC symbols 0
% 108.83/18.47
% 108.83/18.47 % ------ Input Options Time Limit: Unbounded
% 108.83/18.47
% 108.83/18.47
% 108.83/18.47 % ------
% 108.83/18.47 % Current options:
% 108.83/18.47 % ------
% 108.83/18.47
% 108.83/18.47
% 108.83/18.47 %
% 108.83/18.47
% 108.83/18.47 % ------ Proving...
% 108.83/18.47 %
% 108.83/18.47
% 108.83/18.47 % SZS status Theorem for theBenchmark.p
% 108.83/18.47
% 108.83/18.47 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 108.83/18.47
% 108.83/18.47
%------------------------------------------------------------------------------