%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL458+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 : n010.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 02:06:42 PM UTC 2026
% Result : Theorem 108.18s 17.96s
% Output : CNFRefutation 108.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 22
% Syntax : Number of formulae : 136 ( 77 unt; 0 def)
% Number of atoms : 216 ( 52 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 144 ( 64 ~; 57 |; 2 &)
% ( 6 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 204 ( 0 sgn 201 !; 3 ?; 119 :)
% 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(f2,axiom,
( substitution_of_equivalents
<=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',substitution_of_equivalents) ).
fof(f3,axiom,
( modus_tollens
<=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',modus_tollens) ).
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(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(f26,axiom,
( r5
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/LCL006+1.ax',op_equiv) ).
fof(f32,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_op_or) ).
fof(f33,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_op_implies_and) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_modus_ponens) ).
fof(f36,axiom,
modus_tollens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_modus_tollens) ).
fof(f39,axiom,
implies_3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_implies_3) ).
fof(f42,axiom,
and_3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_and_3) ).
fof(f49,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',use_substitution_of_equivalents) ).
fof(f50,axiom,
op_implies_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_implies_or) ).
fof(f51,axiom,
op_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_and) ).
fof(f52,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_equiv) ).
fof(f53,conjecture,
r5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r5) ).
fof(f54,negated_conjecture,
~ r5,
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f55,plain,
~ r5,
inference(flattening,[],[f54]) ).
fof(f56,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2))))
=> r5 ),
inference(unused_predicate_definition_removal,[],[f26]) ).
fof(f63,plain,
( and_3
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(unused_predicate_definition_removal,[],[f9]) ).
fof(f66,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(f69,plain,
( modus_tollens
=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f3]) ).
fof(f70,plain,
( substitution_of_equivalents
=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f71,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(f72,plain,
( ~ modus_ponens
| ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ) ),
inference(ennf_transformation,[],[f71]) ).
fof(f73,plain,
( ~ modus_ponens
| ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ) ),
inference(flattening,[],[f72]) ).
fof(f74,plain,
( ~ substitution_of_equivalents
| ! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ) ),
inference(ennf_transformation,[],[f70]) ).
fof(f75,plain,
( ~ modus_tollens
| ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
inference(ennf_transformation,[],[f69]) ).
fof(f78,plain,
( ~ implies_3
| ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(ennf_transformation,[],[f66]) ).
fof(f81,plain,
( ~ and_3
| ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(ennf_transformation,[],[f63]) ).
fof(f88,plain,
( ? [X0,X1,X2] : ~ is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2))))
| r5 ),
inference(ennf_transformation,[],[f56]) ).
fof(f89,plain,
( ~ op_or
| ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(ennf_transformation,[],[f27]) ).
fof(f90,plain,
( ~ op_and
| ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))) ),
inference(ennf_transformation,[],[f28]) ).
fof(f91,plain,
( ~ op_implies_and
| ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
inference(ennf_transformation,[],[f29]) ).
fof(f92,plain,
( ~ op_implies_or
| ! [X0,X1] : implies(X0,X1) = or(not(X0),X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f93,plain,
( ~ op_equiv
| ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
inference(ennf_transformation,[],[f31]) ).
fof(f94,plain,
( ~ is_a_theorem(implies(implies(sK1,sK2),implies(or(sK0,sK1),or(sK0,sK2))))
| r5 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f88]) ).
fof(f95,plain,
! [X0,X1] :
( ~ modus_ponens
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f96,plain,
! [X0,X1] :
( ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f74]) ).
fof(f97,plain,
! [X0,X1] :
( ~ modus_tollens
| is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
inference(cnf_transformation,[],[f75]) ).
fof(f100,plain,
! [X2,X0,X1] :
( ~ implies_3
| is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(cnf_transformation,[],[f78]) ).
fof(f103,plain,
! [X0,X1] :
( ~ and_3
| is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(cnf_transformation,[],[f81]) ).
fof(f110,plain,
( ~ is_a_theorem(implies(implies(sK1,sK2),implies(or(sK0,sK1),or(sK0,sK2))))
| r5 ),
inference(cnf_transformation,[],[f94]) ).
fof(f111,plain,
! [X0,X1] :
( ~ op_or
| or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(cnf_transformation,[],[f89]) ).
fof(f112,plain,
! [X0,X1] :
( ~ op_and
| and(X0,X1) = not(or(not(X0),not(X1))) ),
inference(cnf_transformation,[],[f90]) ).
fof(f113,plain,
! [X0,X1] :
( ~ op_implies_and
| implies(X0,X1) = not(and(X0,not(X1))) ),
inference(cnf_transformation,[],[f91]) ).
fof(f114,plain,
! [X0,X1] :
( ~ op_implies_or
| implies(X0,X1) = or(not(X0),X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f115,plain,
! [X0,X1] :
( ~ op_equiv
| equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
inference(cnf_transformation,[],[f93]) ).
fof(f116,plain,
op_or,
inference(cnf_transformation,[],[f32]) ).
fof(f117,plain,
op_implies_and,
inference(cnf_transformation,[],[f33]) ).
fof(f119,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f120,plain,
modus_tollens,
inference(cnf_transformation,[],[f36]) ).
fof(f123,plain,
implies_3,
inference(cnf_transformation,[],[f39]) ).
fof(f126,plain,
and_3,
inference(cnf_transformation,[],[f42]) ).
fof(f133,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f49]) ).
fof(f134,plain,
op_implies_or,
inference(cnf_transformation,[],[f50]) ).
fof(f135,plain,
op_and,
inference(cnf_transformation,[],[f51]) ).
fof(f136,plain,
op_equiv,
inference(cnf_transformation,[],[f52]) ).
fof(f137,plain,
~ r5,
inference(cnf_transformation,[],[f55]) ).
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,[],[f95]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X0,X1)) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0)))
| ~ modus_tollens ),
inference(cnf_transformation,[],[f97]) ).
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,[],[f100]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_64,plain,
( r5
| ~ is_a_theorem(implies(implies(sK1,sK2),implies(or(sK0,sK1),or(sK0,sK2)))) ),
inference(cnf_transformation,[],[f110]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( ( not(and(not(X0),not(X1))) = or(X0,X1) )
| ~ op_or ),
inference(cnf_transformation,[],[f111]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( ( not(or(not(X0),not(X1))) = and(X0,X1) )
| ~ op_and ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( ( not(and(X0,not(X1))) = implies(X0,X1) )
| ~ op_implies_and ),
inference(cnf_transformation,[],[f113]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( ( or(not(X0),X1) = implies(X0,X1) )
| ~ op_implies_or ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( ( and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1) )
| ~ op_equiv ),
inference(cnf_transformation,[],[f115]) ).
tcf(c_70,plain,
op_or,
inference(cnf_transformation,[],[f116]) ).
tcf(c_71,plain,
op_implies_and,
inference(cnf_transformation,[],[f117]) ).
tcf(c_73,plain,
modus_ponens,
inference(cnf_transformation,[],[f119]) ).
tcf(c_74,plain,
modus_tollens,
inference(cnf_transformation,[],[f120]) ).
tcf(c_77,plain,
implies_3,
inference(cnf_transformation,[],[f123]) ).
tcf(c_80,plain,
and_3,
inference(cnf_transformation,[],[f126]) ).
tcf(c_87,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f133]) ).
tcf(c_88,plain,
op_implies_or,
inference(cnf_transformation,[],[f134]) ).
tcf(c_89,plain,
op_and,
inference(cnf_transformation,[],[f135]) ).
tcf(c_90,plain,
op_equiv,
inference(cnf_transformation,[],[f136]) ).
tcf(c_91,negated_conjecture,
~ r5,
inference(cnf_transformation,[],[f137]) ).
tcf(c_129,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))),
inference(global_subsumption_just,[status(thm)],[c_57,c_80,c_57]) ).
tcf(c_132,plain,
! [X0: $i,X1: $i] : or(not(X0),X1) = implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_68,c_88,c_68]) ).
tcf(c_135,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ is_a_theorem(equiv(X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_50,c_87,c_50]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i] : not(and(X0,not(X1))) = implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_67,c_71,c_67]) ).
tcf(c_144,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))),
inference(global_subsumption_just,[status(thm)],[c_51,c_74,c_51]) ).
tcf(c_147,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_73,c_49]) ).
tcf(c_148,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(renaming,[status(thm)],[c_147]) ).
tcf(c_149,plain,
! [X0: $i,X1: $i] : not(or(not(X0),not(X1))) = and(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_66,c_89,c_66]) ).
tcf(c_152,plain,
! [X0: $i,X1: $i] : not(and(not(X0),not(X1))) = or(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_65,c_70,c_65]) ).
tcf(c_155,plain,
! [X0: $i,X1: $i] : and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_69,c_90,c_69]) ).
tcf(c_158,plain,
~ is_a_theorem(implies(implies(sK1,sK2),implies(or(sK0,sK1),or(sK0,sK2)))),
inference(global_subsumption_just,[status(thm)],[c_64,c_91,c_64]) ).
tcf(c_163,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_77,c_54]) ).
tcf(c_267,plain,
! [X0: $i,X1: $i] : implies(not(X0),X1) = or(X0,X1),
inference(demodulation,[status(thm)],[c_152,c_138]) ).
tcf(c_268,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0))),
inference(demodulation,[status(thm)],[c_144,c_267]) ).
tcf(c_269,plain,
! [X0: $i,X1: $i] : not(implies(X0,not(X1))) = and(X0,X1),
inference(demodulation,[status(thm)],[c_149,c_132]) ).
tcf(c_193102,plain,
! [X0: $i,X1: $i,X2: $i] : or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
inference(superposition,[status(thm)],[c_138,c_267]) ).
tcf(c_197708,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(implies(X0,not(X1)),implies(X1,not(X0)))),
inference(superposition,[status(thm)],[c_132,c_268]) ).
tcf(c_197737,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(implies(X0,not(not(X1))),or(X1,not(X0)))),
inference(superposition,[status(thm)],[c_267,c_197708]) ).
tcf(c_197841,plain,
! [X0: $i,X1: $i,X2: $i] : implies(implies(X0,not(X1)),X2) = or(and(X0,X1),X2),
inference(superposition,[status(thm)],[c_269,c_132]) ).
tcf(c_197955,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(implies(X0,X1),or(X1,not(X0)))),
inference(demodulation,[status(thm)],[c_197737,c_193102,c_197841]) ).
tcf(c_199199,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X1,and(X0,X1)))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_129,c_148]) ).
tcf(c_200905,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_199199,c_148]) ).
tcf(c_222146,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(equiv(X0,X1))
| ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_155,c_200905]) ).
tcf(c_244773,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(equiv(implies(X0,X1),or(X1,not(X0))))
| ~ is_a_theorem(implies(implies(X0,X1),or(X1,not(X0)))) ),
inference(superposition,[status(thm)],[c_268,c_222146]) ).
tcf(c_244901,plain,
! [X0: $i,X1: $i] : is_a_theorem(equiv(implies(X0,X1),or(X1,not(X0)))),
inference(forward_subsumption_resolution,[status(thm)],[c_244773,c_197955]) ).
tcf(c_254663,plain,
! [X0: $i,X1: $i] : or(X0,not(X1)) = implies(X1,X0),
inference(superposition,[status(thm)],[c_244901,c_135]) ).
tcf(c_278144,plain,
! [X0: $i,X1: $i] : implies(X0,not(X1)) = implies(X1,not(X0)),
inference(superposition,[status(thm)],[c_132,c_254663]) ).
tcf(c_278244,plain,
! [X0: $i,X1: $i] : not(or(X0,not(X1))) = and(not(X0),X1),
inference(superposition,[status(thm)],[c_267,c_269]) ).
tcf(c_278261,plain,
! [X0: $i,X1: $i] : not(implies(X0,X1)) = and(not(X1),X0),
inference(light_normalisation,[status(thm)],[c_278244,c_254663]) ).
tcf(c_278342,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(not(X0),X1),implies(implies(X1,X2),or(X0,X2)))),
inference(superposition,[status(thm)],[c_267,c_163]) ).
tcf(c_278343,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),or(X0,X2)))),
inference(light_normalisation,[status(thm)],[c_278342,c_267]) ).
tcf(c_278662,plain,
! [X0: $i,X1: $i] : implies(X0,not(not(X1))) = or(X1,not(X0)),
inference(superposition,[status(thm)],[c_278144,c_267]) ).
tcf(c_278663,plain,
! [X0: $i,X1: $i] : not(implies(X0,not(X1))) = and(X1,X0),
inference(superposition,[status(thm)],[c_278144,c_269]) ).
tcf(c_278712,plain,
! [X0: $i,X1: $i] : not(or(X0,not(X1))) = and(X1,not(X0)),
inference(superposition,[status(thm)],[c_267,c_278663]) ).
tcf(c_278741,plain,
! [X0: $i,X1: $i] : not(implies(X0,X1)) = and(X0,not(X1)),
inference(light_normalisation,[status(thm)],[c_278712,c_254663]) ).
tcf(c_278745,plain,
! [X0: $i,X1: $i] : not(not(implies(X0,X1))) = implies(X0,X1),
inference(demodulation,[status(thm)],[c_138,c_278741]) ).
tcf(c_279236,plain,
! [X0: $i,X1: $i] : not(implies(not(X0),X1)) = not(implies(not(X1),X0)),
inference(superposition,[status(thm)],[c_278741,c_278261]) ).
tcf(c_279237,plain,
! [X0: $i,X1: $i] : not(implies(not(X0),X1)) = not(or(X1,X0)),
inference(light_normalisation,[status(thm)],[c_279236,c_267]) ).
tcf(c_279238,plain,
! [X0: $i,X1: $i] : not(or(X0,X1)) = not(or(X1,X0)),
inference(light_normalisation,[status(thm)],[c_279237,c_267]) ).
tcf(c_279273,plain,
! [X0: $i,X1: $i] : not(not(or(X0,X1))) = or(X0,X1),
inference(superposition,[status(thm)],[c_267,c_278745]) ).
tcf(c_279735,plain,
! [X0: $i,X1: $i] : not(not(or(X0,X1))) = or(X1,X0),
inference(superposition,[status(thm)],[c_279238,c_279273]) ).
tcf(c_280030,plain,
! [X0: $i,X1: $i] : or(X0,X1) = or(X1,X0),
inference(superposition,[status(thm)],[c_279735,c_279273]) ).
tcf(c_280049,plain,
~ is_a_theorem(implies(implies(sK1,sK2),implies(or(sK1,sK0),or(sK0,sK2)))),
inference(demodulation,[status(thm)],[c_158,c_280030]) ).
tcf(c_280600,plain,
! [X0: $i,X1: $i] : implies(X0,not(not(X1))) = implies(X0,X1),
inference(demodulation,[status(thm)],[c_278662,c_254663]) ).
tcf(c_280604,plain,
! [X0: $i,X1: $i,X2: $i] : implies(X0,or(X1,X2)) = implies(X0,or(X2,X1)),
inference(superposition,[status(thm)],[c_279735,c_280600]) ).
tcf(c_282469,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(or(X0,not(X1)),implies(or(X1,X2),or(X0,X2)))),
inference(superposition,[status(thm)],[c_267,c_278343]) ).
tcf(c_282483,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(X0,X1),implies(or(X0,X2),or(X1,X2)))),
inference(light_normalisation,[status(thm)],[c_282469,c_254663]) ).
tcf(c_284738,plain,
~ is_a_theorem(implies(implies(sK1,sK2),implies(or(sK1,sK0),or(sK2,sK0)))),
inference(demodulation,[status(thm)],[c_280049,c_280604]) ).
tcf(c_285133,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_284738,c_282483]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL458+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n010.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Wed Sep 23 23:27:27 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 0.11/0.41
% 0.11/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.41
% 0.11/0.41 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 108.18/17.96 % SZS status Started for theBenchmark.p
% 108.18/17.96 % SZS status Theorem for theBenchmark.p
% 108.18/17.96
% 108.18/17.96 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 108.18/17.96
% 108.18/17.96 % ------ iProver source info
% 108.18/17.96
% 108.18/17.96 % git: date: 2026-07-19 20:42:38 +0200
% 108.18/17.96 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 108.18/17.96 % git: non_committed_changes: false
% 108.18/17.96
% 108.18/17.96 % ------ Parsing...
% 108.18/17.96 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 108.18/17.96
% 108.18/17.96 % ------ Preprocessing... sup_sim: 3 sf_s rm: 22 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 108.18/17.96
% 108.18/17.96 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 108.18/17.96
% 108.18/17.96 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 108.18/17.96 % ------ Proving...
% 108.18/17.96 % ------ Problem Properties
% 108.18/17.96
% 108.18/17.96 %
% 108.18/17.96 % clauses 21
% 108.18/17.96 % conjectures 0
% 108.18/17.96 % EPR 0
% 108.18/17.96 % Horn 21
% 108.18/17.96 % unary 19
% 108.18/17.96 % binary 1
% 108.18/17.96 % lits 24
% 108.18/17.96 % lits eq 6
% 108.18/17.96 % fd_pure 0
% 108.18/17.96 % fd_pseudo 0
% 108.18/17.96 % fd_cond 0
% 108.18/17.96 % fd_pseudo_cond 1
% 108.18/17.96 % AC symbols 0
% 108.18/17.96
% 108.18/17.96 % ------ Schedule dynamic 5 is on
% 108.18/17.96
% 108.18/17.96 % ------ no conjectures: strip conj schedule
% 108.18/17.96
% 108.18/17.96 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 108.18/17.96
% 108.18/17.96
% 108.18/17.96 % ------
% 108.18/17.96 % Current options:
% 108.18/17.96 % ------
% 108.18/17.96
% 108.18/17.96
% 108.18/17.96 %
% 108.18/17.96
% 108.18/17.96 % ------ Proving...
% 108.18/17.96 % Proof_search_loop: time out after: 5446 full_loop iterations
% 108.18/17.96
% 108.18/17.96 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" stripped conjectures Time Limit: 15.
% 108.18/17.96
% 108.18/17.96
% 108.18/17.96 % ------
% 108.18/17.96 % Current options:
% 108.18/17.96 % ------
% 108.18/17.96
% 108.18/17.96
% 108.18/17.96 %
% 108.18/17.96
% 108.18/17.96 % ------ Proving...
% 108.18/17.96 %
% 108.18/17.96
% 108.18/17.96 % SZS status Theorem for theBenchmark.p
% 108.18/17.96
% 108.18/17.96 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 108.18/17.97
% 108.18/17.97
%------------------------------------------------------------------------------