TSTP Solution File: SET770+4 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET770+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 3 03:01:28 EDT 2024
% Result : Theorem 20.34s 3.63s
% Output : CNFRefutation 20.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 9
% Syntax : Number of formulae : 105 ( 21 unt; 0 def)
% Number of atoms : 379 ( 10 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 451 ( 177 ~; 171 |; 70 &)
% ( 8 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 221 ( 3 sgn 134 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set) ).
fof(f12,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> ~ ? [X2] :
( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint) ).
fof(f14,axiom,
! [X0,X6] :
( equivalence(X6,X0)
<=> ( ! [X2,X4,X5] :
( ( member(X5,X0)
& member(X4,X0)
& member(X2,X0) )
=> ( ( apply(X6,X4,X5)
& apply(X6,X2,X4) )
=> apply(X6,X2,X5) ) )
& ! [X2,X4] :
( ( member(X4,X0)
& member(X2,X0) )
=> ( apply(X6,X2,X4)
=> apply(X6,X4,X2) ) )
& ! [X2] :
( member(X2,X0)
=> apply(X6,X2,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence) ).
fof(f15,axiom,
! [X6,X3,X0,X2] :
( member(X2,equivalence_class(X0,X3,X6))
<=> ( apply(X6,X0,X2)
& member(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_class) ).
fof(f17,conjecture,
! [X3,X6,X0,X1] :
( ( member(X1,X3)
& member(X0,X3)
& equivalence(X6,X3) )
=> ( disjoint(equivalence_class(X0,X3,X6),equivalence_class(X1,X3,X6))
| equal_set(equivalence_class(X0,X3,X6),equivalence_class(X1,X3,X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIII06) ).
fof(f18,negated_conjecture,
~ ! [X3,X6,X0,X1] :
( ( member(X1,X3)
& member(X0,X3)
& equivalence(X6,X3) )
=> ( disjoint(equivalence_class(X0,X3,X6),equivalence_class(X1,X3,X6))
| equal_set(equivalence_class(X0,X3,X6),equivalence_class(X1,X3,X6)) ) ),
inference(negated_conjecture,[],[f17]) ).
fof(f29,plain,
! [X0,X1] :
( equivalence(X1,X0)
<=> ( ! [X2,X3,X4] :
( ( member(X4,X0)
& member(X3,X0)
& member(X2,X0) )
=> ( ( apply(X1,X3,X4)
& apply(X1,X2,X3) )
=> apply(X1,X2,X4) ) )
& ! [X5,X6] :
( ( member(X6,X0)
& member(X5,X0) )
=> ( apply(X1,X5,X6)
=> apply(X1,X6,X5) ) )
& ! [X7] :
( member(X7,X0)
=> apply(X1,X7,X7) ) ) ),
inference(rectify,[],[f14]) ).
fof(f30,plain,
! [X0,X1,X2,X3] :
( member(X3,equivalence_class(X2,X1,X0))
<=> ( apply(X0,X2,X3)
& member(X3,X1) ) ),
inference(rectify,[],[f15]) ).
fof(f32,plain,
~ ! [X0,X1,X2,X3] :
( ( member(X3,X0)
& member(X2,X0)
& equivalence(X1,X0) )
=> ( disjoint(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1))
| equal_set(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1)) ) ),
inference(rectify,[],[f18]) ).
fof(f33,plain,
! [X0,X1] :
( equivalence(X1,X0)
=> ( ! [X2,X3,X4] :
( ( member(X4,X0)
& member(X3,X0)
& member(X2,X0) )
=> ( ( apply(X1,X3,X4)
& apply(X1,X2,X3) )
=> apply(X1,X2,X4) ) )
& ! [X5,X6] :
( ( member(X6,X0)
& member(X5,X0) )
=> ( apply(X1,X5,X6)
=> apply(X1,X6,X5) ) )
& ! [X7] :
( member(X7,X0)
=> apply(X1,X7,X7) ) ) ),
inference(unused_predicate_definition_removal,[],[f29]) ).
fof(f34,plain,
! [X0,X1] :
( ~ ? [X2] :
( member(X2,X1)
& member(X2,X0) )
=> disjoint(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f12]) ).
fof(f35,plain,
! [X0,X1] :
( ( subset(X1,X0)
& subset(X0,X1) )
=> equal_set(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f36,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f37,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f38,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(flattening,[],[f37]) ).
fof(f40,plain,
! [X0,X1] :
( disjoint(X0,X1)
| ? [X2] :
( member(X2,X1)
& member(X2,X0) ) ),
inference(ennf_transformation,[],[f34]) ).
fof(f41,plain,
! [X0,X1] :
( ( ! [X2,X3,X4] :
( apply(X1,X2,X4)
| ~ apply(X1,X3,X4)
| ~ apply(X1,X2,X3)
| ~ member(X4,X0)
| ~ member(X3,X0)
| ~ member(X2,X0) )
& ! [X5,X6] :
( apply(X1,X6,X5)
| ~ apply(X1,X5,X6)
| ~ member(X6,X0)
| ~ member(X5,X0) )
& ! [X7] :
( apply(X1,X7,X7)
| ~ member(X7,X0) ) )
| ~ equivalence(X1,X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f42,plain,
! [X0,X1] :
( ( ! [X2,X3,X4] :
( apply(X1,X2,X4)
| ~ apply(X1,X3,X4)
| ~ apply(X1,X2,X3)
| ~ member(X4,X0)
| ~ member(X3,X0)
| ~ member(X2,X0) )
& ! [X5,X6] :
( apply(X1,X6,X5)
| ~ apply(X1,X5,X6)
| ~ member(X6,X0)
| ~ member(X5,X0) )
& ! [X7] :
( apply(X1,X7,X7)
| ~ member(X7,X0) ) )
| ~ equivalence(X1,X0) ),
inference(flattening,[],[f41]) ).
fof(f43,plain,
? [X0,X1,X2,X3] :
( ~ disjoint(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1))
& ~ equal_set(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1))
& member(X3,X0)
& member(X2,X0)
& equivalence(X1,X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f44,plain,
? [X0,X1,X2,X3] :
( ~ disjoint(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1))
& ~ equal_set(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1))
& member(X3,X0)
& member(X2,X0)
& equivalence(X1,X0) ),
inference(flattening,[],[f43]) ).
fof(f45,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f36]) ).
fof(f46,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f45]) ).
fof(f47,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f48,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f46,f47]) ).
fof(f67,plain,
! [X0,X1] :
( ? [X2] :
( member(X2,X1)
& member(X2,X0) )
=> ( member(sK3(X0,X1),X1)
& member(sK3(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f68,plain,
! [X0,X1] :
( disjoint(X0,X1)
| ( member(sK3(X0,X1),X1)
& member(sK3(X0,X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f40,f67]) ).
fof(f69,plain,
! [X0,X1,X2,X3] :
( ( member(X3,equivalence_class(X2,X1,X0))
| ~ apply(X0,X2,X3)
| ~ member(X3,X1) )
& ( ( apply(X0,X2,X3)
& member(X3,X1) )
| ~ member(X3,equivalence_class(X2,X1,X0)) ) ),
inference(nnf_transformation,[],[f30]) ).
fof(f70,plain,
! [X0,X1,X2,X3] :
( ( member(X3,equivalence_class(X2,X1,X0))
| ~ apply(X0,X2,X3)
| ~ member(X3,X1) )
& ( ( apply(X0,X2,X3)
& member(X3,X1) )
| ~ member(X3,equivalence_class(X2,X1,X0)) ) ),
inference(flattening,[],[f69]) ).
fof(f71,plain,
( ? [X0,X1,X2,X3] :
( ~ disjoint(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1))
& ~ equal_set(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1))
& member(X3,X0)
& member(X2,X0)
& equivalence(X1,X0) )
=> ( ~ disjoint(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5))
& ~ equal_set(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5))
& member(sK7,sK4)
& member(sK6,sK4)
& equivalence(sK5,sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f72,plain,
( ~ disjoint(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5))
& ~ equal_set(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5))
& member(sK7,sK4)
& member(sK6,sK4)
& equivalence(sK5,sK4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f44,f71]) ).
fof(f74,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f75,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f76,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
fof(f100,plain,
! [X0,X1] :
( disjoint(X0,X1)
| member(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f101,plain,
! [X0,X1] :
( disjoint(X0,X1)
| member(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f103,plain,
! [X0,X1,X6,X5] :
( apply(X1,X6,X5)
| ~ apply(X1,X5,X6)
| ~ member(X6,X0)
| ~ member(X5,X0)
| ~ equivalence(X1,X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f104,plain,
! [X2,X3,X0,X1,X4] :
( apply(X1,X2,X4)
| ~ apply(X1,X3,X4)
| ~ apply(X1,X2,X3)
| ~ member(X4,X0)
| ~ member(X3,X0)
| ~ member(X2,X0)
| ~ equivalence(X1,X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f105,plain,
! [X2,X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,equivalence_class(X2,X1,X0)) ),
inference(cnf_transformation,[],[f70]) ).
fof(f106,plain,
! [X2,X3,X0,X1] :
( apply(X0,X2,X3)
| ~ member(X3,equivalence_class(X2,X1,X0)) ),
inference(cnf_transformation,[],[f70]) ).
fof(f107,plain,
! [X2,X3,X0,X1] :
( member(X3,equivalence_class(X2,X1,X0))
| ~ apply(X0,X2,X3)
| ~ member(X3,X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f108,plain,
equivalence(sK5,sK4),
inference(cnf_transformation,[],[f72]) ).
fof(f109,plain,
member(sK6,sK4),
inference(cnf_transformation,[],[f72]) ).
fof(f110,plain,
member(sK7,sK4),
inference(cnf_transformation,[],[f72]) ).
fof(f111,plain,
~ equal_set(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),
inference(cnf_transformation,[],[f72]) ).
fof(f112,plain,
~ disjoint(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),
inference(cnf_transformation,[],[f72]) ).
cnf(c_49,plain,
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
cnf(c_50,plain,
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f74]) ).
cnf(c_52,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f76]) ).
cnf(c_76,plain,
( member(sK3(X0,X1),X1)
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f101]) ).
cnf(c_77,plain,
( member(sK3(X0,X1),X0)
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f100]) ).
cnf(c_78,plain,
( ~ apply(X0,X1,X2)
| ~ apply(X0,X3,X1)
| ~ member(X1,X4)
| ~ member(X2,X4)
| ~ member(X3,X4)
| ~ equivalence(X0,X4)
| apply(X0,X3,X2) ),
inference(cnf_transformation,[],[f104]) ).
cnf(c_79,plain,
( ~ apply(X0,X1,X2)
| ~ member(X1,X3)
| ~ member(X2,X3)
| ~ equivalence(X0,X3)
| apply(X0,X2,X1) ),
inference(cnf_transformation,[],[f103]) ).
cnf(c_81,plain,
( ~ apply(X0,X1,X2)
| ~ member(X2,X3)
| member(X2,equivalence_class(X1,X3,X0)) ),
inference(cnf_transformation,[],[f107]) ).
cnf(c_82,plain,
( ~ member(X0,equivalence_class(X1,X2,X3))
| apply(X3,X1,X0) ),
inference(cnf_transformation,[],[f106]) ).
cnf(c_83,plain,
( ~ member(X0,equivalence_class(X1,X2,X3))
| member(X0,X2) ),
inference(cnf_transformation,[],[f105]) ).
cnf(c_84,negated_conjecture,
~ disjoint(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),
inference(cnf_transformation,[],[f112]) ).
cnf(c_85,negated_conjecture,
~ equal_set(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),
inference(cnf_transformation,[],[f111]) ).
cnf(c_86,negated_conjecture,
member(sK7,sK4),
inference(cnf_transformation,[],[f110]) ).
cnf(c_87,negated_conjecture,
member(sK6,sK4),
inference(cnf_transformation,[],[f109]) ).
cnf(c_88,negated_conjecture,
equivalence(sK5,sK4),
inference(cnf_transformation,[],[f108]) ).
cnf(c_165,plain,
( member(sK3(X0,X1),X0)
| disjoint(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_77]) ).
cnf(c_167,plain,
( disjoint(X0,X1)
| member(sK3(X0,X1),X1) ),
inference(prop_impl_just,[status(thm)],[c_76]) ).
cnf(c_168,plain,
( member(sK3(X0,X1),X1)
| disjoint(X0,X1) ),
inference(renaming,[status(thm)],[c_167]) ).
cnf(c_596,plain,
( equivalence_class(sK6,sK4,sK5) != X0
| equivalence_class(sK7,sK4,sK5) != X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(resolution_lifted,[status(thm)],[c_52,c_85]) ).
cnf(c_597,plain,
( ~ subset(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5))
| ~ subset(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5)) ),
inference(unflattening,[status(thm)],[c_596]) ).
cnf(c_606,plain,
( equivalence_class(sK6,sK4,sK5) != X0
| equivalence_class(sK7,sK4,sK5) != X1
| member(sK3(X0,X1),X0) ),
inference(resolution_lifted,[status(thm)],[c_165,c_84]) ).
cnf(c_607,plain,
member(sK3(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),equivalence_class(sK6,sK4,sK5)),
inference(unflattening,[status(thm)],[c_606]) ).
cnf(c_611,plain,
( equivalence_class(sK6,sK4,sK5) != X0
| equivalence_class(sK7,sK4,sK5) != X1
| member(sK3(X0,X1),X1) ),
inference(resolution_lifted,[status(thm)],[c_168,c_84]) ).
cnf(c_612,plain,
member(sK3(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),equivalence_class(sK7,sK4,sK5)),
inference(unflattening,[status(thm)],[c_611]) ).
cnf(c_618,plain,
( X0 != sK5
| X1 != sK4
| ~ apply(X0,X2,X3)
| ~ apply(X0,X4,X2)
| ~ member(X2,X1)
| ~ member(X3,X1)
| ~ member(X4,X1)
| apply(X0,X4,X3) ),
inference(resolution_lifted,[status(thm)],[c_78,c_88]) ).
cnf(c_619,plain,
( ~ apply(sK5,X0,X1)
| ~ apply(sK5,X2,X0)
| ~ member(X0,sK4)
| ~ member(X1,sK4)
| ~ member(X2,sK4)
| apply(sK5,X2,X1) ),
inference(unflattening,[status(thm)],[c_618]) ).
cnf(c_638,plain,
( X0 != sK5
| X1 != sK4
| ~ apply(X0,X2,X3)
| ~ member(X2,X1)
| ~ member(X3,X1)
| apply(X0,X3,X2) ),
inference(resolution_lifted,[status(thm)],[c_79,c_88]) ).
cnf(c_639,plain,
( ~ apply(sK5,X0,X1)
| ~ member(X0,sK4)
| ~ member(X1,sK4)
| apply(sK5,X1,X0) ),
inference(unflattening,[status(thm)],[c_638]) ).
cnf(c_1113,negated_conjecture,
member(sK6,sK4),
inference(demodulation,[status(thm)],[c_87]) ).
cnf(c_1114,negated_conjecture,
member(sK7,sK4),
inference(demodulation,[status(thm)],[c_86]) ).
cnf(c_2051,plain,
( ~ apply(sK5,X0,sK7)
| ~ apply(sK5,sK7,X1)
| ~ member(X0,sK4)
| ~ member(X1,sK4)
| ~ member(sK7,sK4)
| apply(sK5,X0,X1) ),
inference(instantiation,[status(thm)],[c_619]) ).
cnf(c_2052,plain,
( ~ apply(sK5,X0,sK6)
| ~ apply(sK5,sK6,X1)
| ~ member(X0,sK4)
| ~ member(X1,sK4)
| ~ member(sK6,sK4)
| apply(sK5,X0,X1) ),
inference(instantiation,[status(thm)],[c_619]) ).
cnf(c_2093,plain,
( ~ member(sK0(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),equivalence_class(sK7,sK4,sK5))
| subset(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_2094,plain,
( member(sK0(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),equivalence_class(sK6,sK4,sK5))
| subset(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_2117,plain,
member(sK3(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),sK4),
inference(superposition,[status(thm)],[c_607,c_83]) ).
cnf(c_2258,plain,
apply(sK5,sK6,sK3(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5))),
inference(superposition,[status(thm)],[c_607,c_82]) ).
cnf(c_2259,plain,
apply(sK5,sK7,sK3(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5))),
inference(superposition,[status(thm)],[c_612,c_82]) ).
cnf(c_2379,plain,
( ~ member(sK3(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),sK4)
| ~ member(sK6,sK4)
| apply(sK5,sK3(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),sK6) ),
inference(superposition,[status(thm)],[c_2258,c_639]) ).
cnf(c_2380,plain,
apply(sK5,sK3(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),sK6),
inference(forward_subsumption_resolution,[status(thm)],[c_2379,c_1113,c_2117]) ).
cnf(c_2386,plain,
( ~ apply(sK5,X0,sK3(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)))
| ~ member(sK3(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),sK4)
| ~ member(X0,sK4)
| ~ member(sK6,sK4)
| apply(sK5,X0,sK6) ),
inference(superposition,[status(thm)],[c_2380,c_619]) ).
cnf(c_2388,plain,
( ~ apply(sK5,X0,sK3(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)))
| ~ member(X0,sK4)
| apply(sK5,X0,sK6) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2386,c_1113,c_2117]) ).
cnf(c_2921,plain,
( ~ member(sK7,sK4)
| apply(sK5,sK7,sK6) ),
inference(superposition,[status(thm)],[c_2259,c_2388]) ).
cnf(c_2922,plain,
apply(sK5,sK7,sK6),
inference(forward_subsumption_resolution,[status(thm)],[c_2921,c_1114]) ).
cnf(c_2930,plain,
( ~ member(sK6,sK4)
| ~ member(sK7,sK4)
| apply(sK5,sK6,sK7) ),
inference(superposition,[status(thm)],[c_2922,c_639]) ).
cnf(c_2931,plain,
apply(sK5,sK6,sK7),
inference(forward_subsumption_resolution,[status(thm)],[c_2930,c_1114,c_1113]) ).
cnf(c_3409,plain,
( member(sK0(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5)),equivalence_class(sK7,sK4,sK5))
| subset(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_3410,plain,
( ~ member(sK0(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5)),equivalence_class(sK6,sK4,sK5))
| subset(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_5023,plain,
( ~ apply(sK5,sK7,X0)
| ~ apply(sK5,sK6,sK7)
| ~ member(X0,sK4)
| ~ member(sK6,sK4)
| ~ member(sK7,sK4)
| apply(sK5,sK6,X0) ),
inference(instantiation,[status(thm)],[c_2051]) ).
cnf(c_5027,plain,
( ~ apply(sK5,sK6,X0)
| ~ apply(sK5,sK7,sK6)
| ~ member(X0,sK4)
| ~ member(sK6,sK4)
| ~ member(sK7,sK4)
| apply(sK5,sK7,X0) ),
inference(instantiation,[status(thm)],[c_2052]) ).
cnf(c_7457,plain,
( ~ member(sK0(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),equivalence_class(sK6,sK4,sK5))
| apply(sK5,sK6,sK0(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5))) ),
inference(instantiation,[status(thm)],[c_82]) ).
cnf(c_7458,plain,
( ~ member(sK0(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),equivalence_class(sK6,sK4,sK5))
| member(sK0(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),sK4) ),
inference(instantiation,[status(thm)],[c_83]) ).
cnf(c_14597,plain,
( ~ member(sK0(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5)),equivalence_class(sK7,sK4,sK5))
| apply(sK5,sK7,sK0(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5))) ),
inference(instantiation,[status(thm)],[c_82]) ).
cnf(c_14598,plain,
( ~ member(sK0(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5)),equivalence_class(sK7,sK4,sK5))
| member(sK0(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5)),sK4) ),
inference(instantiation,[status(thm)],[c_83]) ).
cnf(c_19405,plain,
( ~ apply(sK5,X0,X1)
| ~ member(X1,X2)
| member(X1,equivalence_class(X0,X2,sK5)) ),
inference(instantiation,[status(thm)],[c_81]) ).
cnf(c_42928,plain,
( ~ apply(sK5,sK7,sK0(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)))
| ~ member(sK0(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),sK4)
| member(sK0(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),equivalence_class(sK7,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_19405]) ).
cnf(c_42929,plain,
( ~ apply(sK5,sK6,sK0(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5)))
| ~ member(sK0(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5)),sK4)
| member(sK0(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5)),equivalence_class(sK6,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_19405]) ).
cnf(c_57936,plain,
( ~ apply(sK5,sK6,sK0(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)))
| ~ member(sK0(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),sK4)
| ~ apply(sK5,sK7,sK6)
| ~ member(sK6,sK4)
| ~ member(sK7,sK4)
| apply(sK5,sK7,sK0(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5))) ),
inference(instantiation,[status(thm)],[c_5027]) ).
cnf(c_58032,plain,
( ~ apply(sK5,sK7,sK0(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5)))
| ~ member(sK0(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5)),sK4)
| ~ apply(sK5,sK6,sK7)
| ~ member(sK6,sK4)
| ~ member(sK7,sK4)
| apply(sK5,sK6,sK0(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5))) ),
inference(instantiation,[status(thm)],[c_5023]) ).
cnf(c_60453,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_58032,c_57936,c_42929,c_42928,c_14597,c_14598,c_7457,c_7458,c_3409,c_3410,c_2931,c_2922,c_2094,c_2093,c_597,c_86,c_87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : SET770+4 : TPTP v8.1.2. Released v2.2.0.
% 0.02/0.11 % Command : run_iprover %s %d THM
% 0.10/0.31 % Computer : n027.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Thu May 2 20:59:20 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.16/0.42 Running first-order theorem proving
% 0.16/0.42 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 20.34/3.63 % SZS status Started for theBenchmark.p
% 20.34/3.63 % SZS status Theorem for theBenchmark.p
% 20.34/3.63
% 20.34/3.63 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 20.34/3.63
% 20.34/3.63 ------ iProver source info
% 20.34/3.63
% 20.34/3.63 git: date: 2024-05-02 19:28:25 +0000
% 20.34/3.63 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 20.34/3.63 git: non_committed_changes: false
% 20.34/3.63
% 20.34/3.63 ------ Parsing...
% 20.34/3.63 ------ Clausification by vclausify_rel & Parsing by iProver...
% 20.34/3.63
% 20.34/3.63 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e
% 20.34/3.63
% 20.34/3.63 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 20.34/3.63
% 20.34/3.63 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 20.34/3.63 ------ Proving...
% 20.34/3.63 ------ Problem Properties
% 20.34/3.63
% 20.34/3.63
% 20.34/3.63 clauses 37
% 20.34/3.63 conjectures 2
% 20.34/3.63 EPR 7
% 20.34/3.63 Horn 32
% 20.34/3.63 unary 8
% 20.34/3.63 binary 19
% 20.34/3.63 lits 80
% 20.34/3.63 lits eq 3
% 20.34/3.63 fd_pure 0
% 20.34/3.63 fd_pseudo 0
% 20.34/3.63 fd_cond 0
% 20.34/3.63 fd_pseudo_cond 2
% 20.34/3.63 AC symbols 0
% 20.34/3.63
% 20.34/3.63 ------ Schedule dynamic 5 is on
% 20.34/3.63
% 20.34/3.63 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 20.34/3.63
% 20.34/3.63
% 20.34/3.63 ------
% 20.34/3.63 Current options:
% 20.34/3.63 ------
% 20.34/3.63
% 20.34/3.63
% 20.34/3.63
% 20.34/3.63
% 20.34/3.63 ------ Proving...
% 20.34/3.63
% 20.34/3.63
% 20.34/3.63 % SZS status Theorem for theBenchmark.p
% 20.34/3.63
% 20.34/3.63 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 20.34/3.63
% 20.34/3.63
%------------------------------------------------------------------------------