%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL504+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 : n014.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 02:06:47 PM UTC 2026
% Result : Theorem 194.13s 34.25s
% Output : CNFRefutation 194.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 16
% Syntax : Number of formulae : 149 ( 72 unt; 0 def)
% Number of atoms : 244 ( 20 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 179 ( 84 ~; 78 |; 2 &)
% ( 5 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 11 ( 9 usr; 9 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 240 ( 0 sgn 238 !; 2 ?; 182 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( modus_ponens
<=> ! [X0,X1] :
( ( is_a_theorem(implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
fof(f5,axiom,
( implies_2
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',implies_2) ).
fof(f16,axiom,
( kn1
<=> ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',kn1) ).
fof(f17,axiom,
( kn2
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL006+0.ax',kn3) ).
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(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(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(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_modus_ponens) ).
fof(f36,axiom,
kn1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_kn1) ).
fof(f37,axiom,
kn2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_kn2) ).
fof(f38,axiom,
kn3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_kn3) ).
fof(f40,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(f41,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(f42,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_equiv) ).
fof(f43,conjecture,
implies_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_2) ).
fof(f44,negated_conjecture,
~ implies_2,
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f45,plain,
~ implies_2,
inference(flattening,[],[f44]) ).
fof(f46,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(f47,plain,
( kn2
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(unused_predicate_definition_removal,[],[f17]) ).
fof(f48,plain,
( kn1
=> ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
inference(unused_predicate_definition_removal,[],[f16]) ).
fof(f49,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
=> implies_2 ),
inference(unused_predicate_definition_removal,[],[f5]) ).
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(f54,plain,
( ~ modus_ponens
| ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ) ),
inference(ennf_transformation,[],[f51]) ).
fof(f55,plain,
( ~ modus_ponens
| ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ) ),
inference(flattening,[],[f54]) ).
fof(f57,plain,
( ? [X0,X1] : ~ is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| implies_2 ),
inference(ennf_transformation,[],[f49]) ).
fof(f58,plain,
( ~ kn1
| ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
inference(ennf_transformation,[],[f48]) ).
fof(f59,plain,
( ~ kn2
| ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(ennf_transformation,[],[f47]) ).
fof(f60,plain,
( ~ kn3
| ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
inference(ennf_transformation,[],[f46]) ).
fof(f61,plain,
( ~ op_or
| ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(ennf_transformation,[],[f27]) ).
fof(f62,plain,
( ~ op_implies_and
| ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
inference(ennf_transformation,[],[f29]) ).
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(implies(sK0,implies(sK0,sK1)),implies(sK0,sK1)))
| implies_2 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f57]) ).
fof(f65,plain,
! [X0,X1] :
( ~ modus_ponens
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f67,plain,
( ~ is_a_theorem(implies(implies(sK0,implies(sK0,sK1)),implies(sK0,sK1)))
| implies_2 ),
inference(cnf_transformation,[],[f64]) ).
fof(f68,plain,
! [X0] :
( ~ kn1
| is_a_theorem(implies(X0,and(X0,X0))) ),
inference(cnf_transformation,[],[f58]) ).
fof(f69,plain,
! [X0,X1] :
( ~ kn2
| is_a_theorem(implies(and(X0,X1),X0)) ),
inference(cnf_transformation,[],[f59]) ).
fof(f70,plain,
! [X2,X0,X1] :
( ~ kn3
| is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
inference(cnf_transformation,[],[f60]) ).
fof(f71,plain,
! [X0,X1] :
( ~ op_or
| or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(cnf_transformation,[],[f61]) ).
fof(f72,plain,
! [X0,X1] :
( ~ op_implies_and
| implies(X0,X1) = not(and(X0,not(X1))) ),
inference(cnf_transformation,[],[f62]) ).
fof(f73,plain,
! [X0,X1] :
( ~ op_equiv
| equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
inference(cnf_transformation,[],[f63]) ).
fof(f77,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f78,plain,
kn1,
inference(cnf_transformation,[],[f36]) ).
fof(f79,plain,
kn2,
inference(cnf_transformation,[],[f37]) ).
fof(f80,plain,
kn3,
inference(cnf_transformation,[],[f38]) ).
fof(f82,plain,
op_or,
inference(cnf_transformation,[],[f40]) ).
fof(f83,plain,
op_implies_and,
inference(cnf_transformation,[],[f41]) ).
fof(f84,plain,
op_equiv,
inference(cnf_transformation,[],[f42]) ).
fof(f85,plain,
~ implies_2,
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,
( implies_2
| ~ is_a_theorem(implies(implies(sK0,implies(sK0,sK1)),implies(sK0,sK1))) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_52,plain,
! [X0: $i] :
( is_a_theorem(implies(X0,and(X0,X0)))
| ~ kn1 ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ kn2 ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_54,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,[],[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(and(X0,not(X1))) = implies(X0,X1) )
| ~ op_implies_and ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ( and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1) )
| ~ op_equiv ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_61,plain,
modus_ponens,
inference(cnf_transformation,[],[f77]) ).
tcf(c_62,plain,
kn1,
inference(cnf_transformation,[],[f78]) ).
tcf(c_63,plain,
kn2,
inference(cnf_transformation,[],[f79]) ).
tcf(c_64,plain,
kn3,
inference(cnf_transformation,[],[f80]) ).
tcf(c_66,plain,
op_or,
inference(cnf_transformation,[],[f82]) ).
tcf(c_67,plain,
op_implies_and,
inference(cnf_transformation,[],[f83]) ).
tcf(c_68,plain,
op_equiv,
inference(cnf_transformation,[],[f84]) ).
tcf(c_69,negated_conjecture,
~ implies_2,
inference(cnf_transformation,[],[f85]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(and(X0,X1),X0)),
inference(global_subsumption_just,[status(thm)],[c_53,c_63,c_53]) ).
tcf(c_80,plain,
! [X0: $i] : is_a_theorem(implies(X0,and(X0,X0))),
inference(global_subsumption_just,[status(thm)],[c_52,c_62,c_52]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i] : not(and(X0,not(X1))) = implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_56,c_67,c_56]) ).
tcf(c_89,plain,
~ is_a_theorem(implies(implies(sK0,implies(sK0,sK1)),implies(sK0,sK1))),
inference(global_subsumption_just,[status(thm)],[c_51,c_69,c_51]) ).
tcf(c_91,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_61,c_49]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(renaming,[status(thm)],[c_91]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i] : not(and(not(X0),not(X1))) = or(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_55,c_66,c_55]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i] : and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_57,c_68,c_57]) ).
tcf(c_99,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_54,c_64,c_54]) ).
tcf(c_312,plain,
! [X0: $i] :
( is_a_theorem(and(X0,X0))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_80,c_92]) ).
tcf(c_325,plain,
! [X0: $i,X1: $i] : implies(not(X0),X1) = or(X0,X1),
inference(superposition,[status(thm)],[c_93,c_86]) ).
tcf(c_332,plain,
! [X0: $i] :
( is_a_theorem(equiv(X0,X0))
| ~ is_a_theorem(implies(X0,X0)) ),
inference(superposition,[status(thm)],[c_96,c_312]) ).
tcf(c_333,plain,
! [X0: $i] : is_a_theorem(implies(implies(X0,X0),equiv(X0,X0))),
inference(superposition,[status(thm)],[c_96,c_80]) ).
tcf(c_335,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))),
inference(superposition,[status(thm)],[c_96,c_77]) ).
tcf(c_341,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),not(and(not(X2),X0))))),
inference(superposition,[status(thm)],[c_86,c_99]) ).
tcf(c_368,plain,
! [X0: $i,X1: $i,X2: $i] : or(and(not(X0),not(X1)),X2) = implies(or(X0,X1),X2),
inference(superposition,[status(thm)],[c_93,c_325]) ).
tcf(c_375,plain,
! [X0: $i] : is_a_theorem(or(X0,and(not(X0),not(X0)))),
inference(superposition,[status(thm)],[c_325,c_80]) ).
tcf(c_376,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(X0,X1),or(and(X1,X2),not(and(X2,X0))))),
inference(superposition,[status(thm)],[c_325,c_99]) ).
tcf(c_407,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(and(X0,not(X1)),and(implies(X0,X1),implies(X0,X1)))),
inference(superposition,[status(thm)],[c_86,c_375]) ).
tcf(c_534,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(not(X0),X1),or(and(X1,X2),implies(X2,X0)))),
inference(superposition,[status(thm)],[c_86,c_376]) ).
tcf(c_574,plain,
! [X0: $i] : is_a_theorem(or(and(X0,not(X0)),equiv(X0,X0))),
inference(superposition,[status(thm)],[c_96,c_407]) ).
tcf(c_703,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(or(X0,X1),or(and(X1,X2),implies(X2,X0)))),
inference(superposition,[status(thm)],[c_325,c_534]) ).
tcf(c_739,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(and(X1,X2),implies(X2,X0)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_703,c_92]) ).
tcf(c_864,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(not(X0),X1),implies(implies(X1,X2),or(X2,X0)))),
inference(superposition,[status(thm)],[c_93,c_341]) ).
tcf(c_902,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),or(X2,X0)))),
inference(superposition,[status(thm)],[c_325,c_864]) ).
tcf(c_964,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(implies(X1,X2),or(X2,X0)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_902,c_92]) ).
tcf(c_1073,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X2,X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_964,c_92]) ).
tcf(c_4501,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(and(X1,X1),X0))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_80,c_1073]) ).
tcf(c_4502,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(or(X0,and(X1,X2))) ),
inference(superposition,[status(thm)],[c_77,c_1073]) ).
tcf(c_4504,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(equiv(X1,X1),X0))
| ~ is_a_theorem(or(X0,implies(X1,X1))) ),
inference(superposition,[status(thm)],[c_333,c_1073]) ).
tcf(c_4505,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(implies(X1,X2),X0))
| ~ is_a_theorem(or(X0,equiv(X1,X2))) ),
inference(superposition,[status(thm)],[c_335,c_1073]) ).
tcf(c_4787,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(or(X1,X1),X0))
| ~ is_a_theorem(or(X0,not(X1))) ),
inference(superposition,[status(thm)],[c_368,c_4501]) ).
tcf(c_4803,plain,
! [X0: $i] : is_a_theorem(or(not(X0),X0)),
inference(superposition,[status(thm)],[c_375,c_4502]) ).
tcf(c_4808,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X0,and(X2,X2)))
| ~ is_a_theorem(or(and(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_4501,c_4502]) ).
tcf(c_4856,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,not(and(X0,X1)))),
inference(superposition,[status(thm)],[c_4803,c_4502]) ).
tcf(c_8587,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(or(X1,X1))
| ~ is_a_theorem(or(X0,not(X1))) ),
inference(superposition,[status(thm)],[c_4787,c_92]) ).
tcf(c_13255,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(equiv(X0,X0),and(X1,X0)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_739,c_4504]) ).
tcf(c_14384,plain,
! [X0: $i] : is_a_theorem(or(implies(X0,X0),and(X0,not(X0)))),
inference(superposition,[status(thm)],[c_574,c_4505]) ).
tcf(c_14552,plain,
! [X0: $i] : is_a_theorem(or(X0,implies(X0,X0))),
inference(superposition,[status(thm)],[c_14384,c_4502]) ).
tcf(c_20760,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X1,and(X0,X0)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_4501,c_4808]) ).
tcf(c_65267,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(or(and(X0,X1),and(X0,X1))) ),
inference(superposition,[status(thm)],[c_4856,c_8587]) ).
tcf(c_67414,plain,
! [X0: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(or(X0,and(X0,X0))) ),
inference(superposition,[status(thm)],[c_20760,c_65267]) ).
tcf(c_67744,plain,
! [X0: $i] :
( is_a_theorem(implies(X0,X0))
| ~ is_a_theorem(or(implies(X0,X0),equiv(X0,X0))) ),
inference(superposition,[status(thm)],[c_96,c_67414]) ).
tcf(c_91354,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X1,equiv(X0,X0)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_13255,c_4502]) ).
tcf(c_91382,plain,
! [X0: $i] :
( is_a_theorem(implies(X0,X0))
| ~ is_a_theorem(or(X0,implies(X0,X0))) ),
inference(superposition,[status(thm)],[c_91354,c_67744]) ).
tcf(c_151588,plain,
! [X0: $i] :
( is_a_theorem(and(X0,X0))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_80,c_92]) ).
tcf(c_151589,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(X0,X1)) ),
inference(superposition,[status(thm)],[c_77,c_92]) ).
tcf(c_151599,plain,
! [X0: $i,X1: $i] : implies(not(X0),X1) = or(X0,X1),
inference(superposition,[status(thm)],[c_93,c_86]) ).
tcf(c_151600,plain,
! [X0: $i] :
( is_a_theorem(equiv(X0,X0))
| ~ is_a_theorem(implies(X0,X0)) ),
inference(superposition,[status(thm)],[c_96,c_151588]) ).
tcf(c_151602,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(equiv(X0,X1)) ),
inference(superposition,[status(thm)],[c_96,c_151589]) ).
tcf(c_151619,plain,
! [X0: $i,X1: $i,X2: $i] : or(and(not(X0),not(X1)),X2) = implies(or(X0,X1),X2),
inference(superposition,[status(thm)],[c_93,c_151599]) ).
tcf(c_151620,plain,
! [X0: $i,X1: $i,X2: $i] : or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
inference(superposition,[status(thm)],[c_86,c_151599]) ).
tcf(c_151625,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(not(X0))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_151599,c_92]) ).
tcf(c_151626,plain,
! [X0: $i] : is_a_theorem(or(X0,and(not(X0),not(X0)))),
inference(superposition,[status(thm)],[c_151599,c_80]) ).
tcf(c_151627,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(X0,X1),or(and(X1,X2),not(and(X2,X0))))),
inference(superposition,[status(thm)],[c_151599,c_99]) ).
tcf(c_151648,plain,
! [X0: $i] : is_a_theorem(equiv(X0,X0)),
inference(global_subsumption_just,[status(thm)],[c_151600,c_332,c_14552,c_91382]) ).
tcf(c_151651,plain,
! [X0: $i] : is_a_theorem(implies(X0,X0)),
inference(superposition,[status(thm)],[c_151648,c_151602]) ).
tcf(c_151652,plain,
! [X0: $i] : is_a_theorem(or(X0,not(X0))),
inference(superposition,[status(thm)],[c_151599,c_151651]) ).
tcf(c_151655,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(and(X0,not(X1)),implies(X0,X1))),
inference(superposition,[status(thm)],[c_86,c_151652]) ).
tcf(c_151685,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(not(and(X0,not(X1)))) ),
inference(superposition,[status(thm)],[c_151655,c_151625]) ).
tcf(c_151743,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(not(X0),X1),or(and(X1,X2),implies(X2,X0)))),
inference(superposition,[status(thm)],[c_86,c_151627]) ).
tcf(c_151877,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(not(X0),X1))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_93,c_151685]) ).
tcf(c_151885,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(implies(X0,X1),X2))
| ~ is_a_theorem(or(and(X0,not(X1)),X2)) ),
inference(superposition,[status(thm)],[c_86,c_151877]) ).
tcf(c_151956,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(or(X0,X1),or(and(X1,X2),implies(X2,X0)))),
inference(superposition,[status(thm)],[c_151599,c_151743]) ).
tcf(c_152064,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),implies(not(X2),X0)))),
inference(superposition,[status(thm)],[c_151620,c_151956]) ).
tcf(c_152066,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(or(X0,X1),or(and(X1,not(X2)),or(X2,X0)))),
inference(superposition,[status(thm)],[c_151599,c_151956]) ).
tcf(c_152309,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),or(X2,X0)))),
inference(superposition,[status(thm)],[c_151599,c_152064]) ).
tcf(c_152327,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(implies(X1,X2),or(X2,X0)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_152309,c_92]) ).
tcf(c_152344,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(and(X1,not(X2)),or(X2,X0)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_152066,c_92]) ).
tcf(c_152883,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X2,X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_152327,c_92]) ).
tcf(c_156873,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(or(X0,and(X1,X2))) ),
inference(superposition,[status(thm)],[c_77,c_152883]) ).
tcf(c_156875,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_151651,c_152883]) ).
tcf(c_157263,plain,
! [X0: $i] : is_a_theorem(or(and(not(X0),not(X0)),X0)),
inference(superposition,[status(thm)],[c_151626,c_156875]) ).
tcf(c_157266,plain,
! [X0: $i] : is_a_theorem(or(not(X0),X0)),
inference(superposition,[status(thm)],[c_151652,c_156875]) ).
tcf(c_157450,plain,
! [X0: $i] : is_a_theorem(implies(or(X0,X0),X0)),
inference(superposition,[status(thm)],[c_151619,c_157263]) ).
tcf(c_157521,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,not(and(X0,X1)))),
inference(superposition,[status(thm)],[c_157266,c_156873]) ).
tcf(c_157630,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(or(X0,or(X1,X1))) ),
inference(superposition,[status(thm)],[c_157450,c_152883]) ).
tcf(c_157720,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,implies(X0,X1))),
inference(superposition,[status(thm)],[c_86,c_157521]) ).
tcf(c_157812,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(implies(X0,X1),X0)),
inference(superposition,[status(thm)],[c_157720,c_156875]) ).
tcf(c_161879,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X0,and(X1,not(X0))))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_152344,c_157630]) ).
tcf(c_192066,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(and(X1,not(X0)),X0))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_161879,c_156875]) ).
tcf(c_221957,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(implies(X1,X0),X0))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_192066,c_151885]) ).
tcf(c_222290,plain,
~ is_a_theorem(or(implies(sK0,sK1),sK0)),
inference(superposition,[status(thm)],[c_221957,c_89]) ).
tcf(c_222323,plain,
$false,
inference(superposition,[status(thm)],[c_157812,c_222290]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL504+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/5.39 % Computer : n014.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Wed Sep 23 23:35:10 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.17/5.46 Running first-order theorem proving
% 0.17/5.46 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
% 0.17/5.47
% 0.17/5.47 % ======== iProver multi-core TPTP/SMT =========
% 0.17/5.47
% 0.17/5.48 % Detected problem language: tptp
% 0.17/5.49 % Proving...
% 194.13/34.25 % SZS status Started for theBenchmark.p
% 194.13/34.25 % SZS status Theorem for theBenchmark.p
% 194.13/34.25
% 194.13/34.25 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 194.13/34.25
% 194.13/34.25 % ------ iProver source info
% 194.13/34.25
% 194.13/34.25 % git: date: 2026-07-19 20:42:38 +0200
% 194.13/34.25 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 194.13/34.25 % git: non_committed_changes: false
% 194.13/34.25
% 194.13/34.25 % ------ Parsing...
% 194.13/34.25 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 194.13/34.25
% 194.13/34.25 % ------ Preprocessing... sup_sim: 0 sf_s rm: 10 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 194.13/34.25
% 194.13/34.25 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 194.13/34.25
% 194.13/34.25 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 194.13/34.25 % ------ Proving...
% 194.13/34.25 % ------ Problem Properties
% 194.13/34.25
% 194.13/34.25 %
% 194.13/34.25 % clauses 9
% 194.13/34.25 % conjectures 0
% 194.13/34.25 % EPR 0
% 194.13/34.25 % Horn 9
% 194.13/34.25 % unary 7
% 194.13/34.25 % binary 1
% 194.13/34.25 % lits 12
% 194.13/34.25 % lits eq 4
% 194.13/34.25 % fd_pure 0
% 194.13/34.25 % fd_pseudo 0
% 194.13/34.25 % fd_cond 0
% 194.13/34.25 % fd_pseudo_cond 1
% 194.13/34.25 % AC symbols 0
% 194.13/34.25
% 194.13/34.25 % ------ Input Options Time Limit: Unbounded
% 194.13/34.25
% 194.13/34.25
% 194.13/34.25 % ------
% 194.13/34.25 % Current options:
% 194.13/34.25 % ------
% 194.13/34.25
% 194.13/34.25
% 194.13/34.25 %
% 194.13/34.25
% 194.13/34.25 % ------ Proving...
% 194.13/34.25 %
% 194.13/34.25
% 194.13/34.25 % ------ Proving...
% 194.13/34.25 %
% 194.13/34.25
% 194.13/34.25 % SZS status Theorem for theBenchmark.p
% 194.13/34.25
% 194.13/34.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 194.13/34.26
% 194.13/34.26
%------------------------------------------------------------------------------