TSTP Solution File: SET768+4 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET768+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n011.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 65.10s 9.68s
% Output : CNFRefutation 65.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 89 ( 7 unt; 0 def)
% Number of atoms : 380 ( 0 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 472 ( 181 ~; 184 |; 73 &)
% ( 10 <=>; 22 =>; 0 <=; 2 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 210 ( 4 sgn 126 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_set) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',equivalence_class) ).
fof(f17,conjecture,
! [X3,X6,X0,X1] :
( ( member(X1,X3)
& member(X0,X3)
& equivalence(X6,X3) )
=> ( equal_set(equivalence_class(X0,X3,X6),equivalence_class(X1,X3,X6))
<=> apply(X6,X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIII04) ).
fof(f18,negated_conjecture,
~ ! [X3,X6,X0,X1] :
( ( member(X1,X3)
& member(X0,X3)
& equivalence(X6,X3) )
=> ( equal_set(equivalence_class(X0,X3,X6),equivalence_class(X1,X3,X6))
<=> apply(X6,X0,X1) ) ),
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) )
=> ( equal_set(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1))
<=> apply(X1,X2,X3) ) ),
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] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f36,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(f37,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,[],[f36]) ).
fof(f38,plain,
? [X0,X1,X2,X3] :
( ( equal_set(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1))
<~> apply(X1,X2,X3) )
& member(X3,X0)
& member(X2,X0)
& equivalence(X1,X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f39,plain,
? [X0,X1,X2,X3] :
( ( equal_set(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1))
<~> apply(X1,X2,X3) )
& member(X3,X0)
& member(X2,X0)
& equivalence(X1,X0) ),
inference(flattening,[],[f38]) ).
fof(f40,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,[],[f34]) ).
fof(f41,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,[],[f40]) ).
fof(f42,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f43,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])],[f41,f42]) ).
fof(f44,plain,
! [X0,X1] :
( ( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| ~ equal_set(X0,X1) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f45,plain,
! [X0,X1] :
( ( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| ~ equal_set(X0,X1) ) ),
inference(flattening,[],[f44]) ).
fof(f64,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(f65,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,[],[f64]) ).
fof(f66,plain,
? [X0,X1,X2,X3] :
( ( ~ apply(X1,X2,X3)
| ~ equal_set(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1)) )
& ( apply(X1,X2,X3)
| equal_set(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1)) )
& member(X3,X0)
& member(X2,X0)
& equivalence(X1,X0) ),
inference(nnf_transformation,[],[f39]) ).
fof(f67,plain,
? [X0,X1,X2,X3] :
( ( ~ apply(X1,X2,X3)
| ~ equal_set(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1)) )
& ( apply(X1,X2,X3)
| equal_set(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1)) )
& member(X3,X0)
& member(X2,X0)
& equivalence(X1,X0) ),
inference(flattening,[],[f66]) ).
fof(f68,plain,
( ? [X0,X1,X2,X3] :
( ( ~ apply(X1,X2,X3)
| ~ equal_set(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1)) )
& ( apply(X1,X2,X3)
| equal_set(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1)) )
& member(X3,X0)
& member(X2,X0)
& equivalence(X1,X0) )
=> ( ( ~ apply(sK4,sK5,sK6)
| ~ equal_set(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4)) )
& ( apply(sK4,sK5,sK6)
| equal_set(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4)) )
& member(sK6,sK3)
& member(sK5,sK3)
& equivalence(sK4,sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f69,plain,
( ( ~ apply(sK4,sK5,sK6)
| ~ equal_set(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4)) )
& ( apply(sK4,sK5,sK6)
| equal_set(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4)) )
& member(sK6,sK3)
& member(sK5,sK3)
& equivalence(sK4,sK3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f67,f68]) ).
fof(f70,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f71,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f72,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f74,plain,
! [X0,X1] :
( subset(X1,X0)
| ~ equal_set(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f75,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f99,plain,
! [X0,X1,X7] :
( apply(X1,X7,X7)
| ~ member(X7,X0)
| ~ equivalence(X1,X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f100,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,[],[f37]) ).
fof(f101,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,[],[f37]) ).
fof(f102,plain,
! [X2,X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,equivalence_class(X2,X1,X0)) ),
inference(cnf_transformation,[],[f65]) ).
fof(f103,plain,
! [X2,X3,X0,X1] :
( apply(X0,X2,X3)
| ~ member(X3,equivalence_class(X2,X1,X0)) ),
inference(cnf_transformation,[],[f65]) ).
fof(f104,plain,
! [X2,X3,X0,X1] :
( member(X3,equivalence_class(X2,X1,X0))
| ~ apply(X0,X2,X3)
| ~ member(X3,X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f105,plain,
equivalence(sK4,sK3),
inference(cnf_transformation,[],[f69]) ).
fof(f106,plain,
member(sK5,sK3),
inference(cnf_transformation,[],[f69]) ).
fof(f107,plain,
member(sK6,sK3),
inference(cnf_transformation,[],[f69]) ).
fof(f108,plain,
( apply(sK4,sK5,sK6)
| equal_set(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4)) ),
inference(cnf_transformation,[],[f69]) ).
fof(f109,plain,
( ~ apply(sK4,sK5,sK6)
| ~ equal_set(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4)) ),
inference(cnf_transformation,[],[f69]) ).
cnf(c_49,plain,
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
cnf(c_50,plain,
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f71]) ).
cnf(c_51,plain,
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f70]) ).
cnf(c_52,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
cnf(c_53,plain,
( ~ equal_set(X0,X1)
| subset(X1,X0) ),
inference(cnf_transformation,[],[f74]) ).
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,[],[f101]) ).
cnf(c_79,plain,
( ~ apply(X0,X1,X2)
| ~ member(X1,X3)
| ~ member(X2,X3)
| ~ equivalence(X0,X3)
| apply(X0,X2,X1) ),
inference(cnf_transformation,[],[f100]) ).
cnf(c_80,plain,
( ~ member(X0,X1)
| ~ equivalence(X2,X1)
| apply(X2,X0,X0) ),
inference(cnf_transformation,[],[f99]) ).
cnf(c_81,plain,
( ~ apply(X0,X1,X2)
| ~ member(X2,X3)
| member(X2,equivalence_class(X1,X3,X0)) ),
inference(cnf_transformation,[],[f104]) ).
cnf(c_82,plain,
( ~ member(X0,equivalence_class(X1,X2,X3))
| apply(X3,X1,X0) ),
inference(cnf_transformation,[],[f103]) ).
cnf(c_83,plain,
( ~ member(X0,equivalence_class(X1,X2,X3))
| member(X0,X2) ),
inference(cnf_transformation,[],[f102]) ).
cnf(c_84,negated_conjecture,
( ~ equal_set(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4))
| ~ apply(sK4,sK5,sK6) ),
inference(cnf_transformation,[],[f109]) ).
cnf(c_85,negated_conjecture,
( equal_set(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4))
| apply(sK4,sK5,sK6) ),
inference(cnf_transformation,[],[f108]) ).
cnf(c_86,negated_conjecture,
member(sK6,sK3),
inference(cnf_transformation,[],[f107]) ).
cnf(c_87,negated_conjecture,
member(sK5,sK3),
inference(cnf_transformation,[],[f106]) ).
cnf(c_88,negated_conjecture,
equivalence(sK4,sK3),
inference(cnf_transformation,[],[f105]) ).
cnf(c_577,plain,
( ~ subset(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4))
| ~ subset(equivalence_class(sK6,sK3,sK4),equivalence_class(sK5,sK3,sK4))
| equal_set(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_595,plain,
( ~ apply(sK4,sK5,sK6)
| ~ member(sK5,X0)
| ~ member(sK6,X0)
| ~ equivalence(sK4,X0)
| apply(sK4,sK6,sK5) ),
inference(instantiation,[status(thm)],[c_79]) ).
cnf(c_598,plain,
( ~ apply(sK4,sK5,sK6)
| ~ member(sK5,sK3)
| ~ member(sK6,sK3)
| ~ equivalence(sK4,sK3)
| apply(sK4,sK6,sK5) ),
inference(instantiation,[status(thm)],[c_595]) ).
cnf(c_599,plain,
( ~ apply(sK4,sK6,X0)
| ~ apply(sK4,sK5,sK6)
| ~ member(X0,X1)
| ~ member(sK5,X1)
| ~ member(sK6,X1)
| ~ equivalence(sK4,X1)
| apply(sK4,sK5,X0) ),
inference(instantiation,[status(thm)],[c_78]) ).
cnf(c_1655,plain,
( subset(equivalence_class(sK6,sK3,sK4),equivalence_class(sK5,sK3,sK4))
| apply(sK4,sK5,sK6) ),
inference(superposition,[status(thm)],[c_85,c_53]) ).
cnf(c_1872,plain,
( ~ equivalence(X0,sK3)
| apply(X0,sK6,sK6) ),
inference(superposition,[status(thm)],[c_86,c_80]) ).
cnf(c_2091,plain,
( ~ subset(equivalence_class(X0,X1,X2),X3)
| ~ apply(X2,X0,X4)
| ~ member(X4,X1)
| member(X4,X3) ),
inference(superposition,[status(thm)],[c_81,c_51]) ).
cnf(c_2235,plain,
( ~ apply(sK4,sK6,X0)
| ~ member(X0,sK3)
| member(X0,equivalence_class(sK5,sK3,sK4))
| apply(sK4,sK5,sK6) ),
inference(superposition,[status(thm)],[c_1655,c_2091]) ).
cnf(c_2328,plain,
( ~ apply(sK4,sK6,X0)
| ~ member(X0,sK3)
| apply(sK4,sK5,X0)
| apply(sK4,sK5,sK6) ),
inference(superposition,[status(thm)],[c_2235,c_82]) ).
cnf(c_3004,plain,
( ~ member(sK6,sK3)
| ~ equivalence(sK4,sK3)
| apply(sK4,sK5,sK6) ),
inference(superposition,[status(thm)],[c_1872,c_2328]) ).
cnf(c_4211,plain,
( member(sK0(equivalence_class(sK6,sK3,sK4),equivalence_class(sK5,sK3,sK4)),equivalence_class(sK6,sK3,sK4))
| subset(equivalence_class(sK6,sK3,sK4),equivalence_class(sK5,sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_4212,plain,
( ~ member(sK0(equivalence_class(sK6,sK3,sK4),equivalence_class(sK5,sK3,sK4)),equivalence_class(sK5,sK3,sK4))
| subset(equivalence_class(sK6,sK3,sK4),equivalence_class(sK5,sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_4237,plain,
( ~ member(X0,equivalence_class(sK6,X1,sK4))
| apply(sK4,sK6,X0) ),
inference(instantiation,[status(thm)],[c_82]) ).
cnf(c_7483,plain,
( member(sK0(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4)),equivalence_class(sK5,sK3,sK4))
| subset(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_7484,plain,
( ~ member(sK0(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4)),equivalence_class(sK6,sK3,sK4))
| subset(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_13550,plain,
( ~ member(sK0(equivalence_class(sK6,sK3,sK4),equivalence_class(sK5,sK3,sK4)),equivalence_class(sK6,sK3,sK4))
| member(sK0(equivalence_class(sK6,sK3,sK4),equivalence_class(sK5,sK3,sK4)),sK3) ),
inference(instantiation,[status(thm)],[c_83]) ).
cnf(c_13551,plain,
( ~ member(sK0(equivalence_class(sK6,sK3,sK4),equivalence_class(sK5,sK3,sK4)),equivalence_class(sK6,sK3,sK4))
| apply(sK4,sK6,sK0(equivalence_class(sK6,sK3,sK4),equivalence_class(sK5,sK3,sK4))) ),
inference(instantiation,[status(thm)],[c_4237]) ).
cnf(c_15954,plain,
( ~ apply(sK4,X0,X1)
| ~ apply(sK4,X2,X0)
| ~ member(X0,sK3)
| ~ member(X1,sK3)
| ~ member(X2,sK3)
| ~ equivalence(sK4,sK3)
| apply(sK4,X2,X1) ),
inference(instantiation,[status(thm)],[c_78]) ).
cnf(c_18797,plain,
( ~ apply(sK4,X0,X1)
| ~ member(X1,X2)
| member(X1,equivalence_class(X0,X2,sK4)) ),
inference(instantiation,[status(thm)],[c_81]) ).
cnf(c_18856,plain,
( ~ apply(sK4,X0,X1)
| ~ apply(sK4,sK6,X0)
| ~ member(X0,sK3)
| ~ member(X1,sK3)
| ~ member(sK6,sK3)
| ~ equivalence(sK4,sK3)
| apply(sK4,sK6,X1) ),
inference(instantiation,[status(thm)],[c_15954]) ).
cnf(c_19007,plain,
( ~ member(sK0(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4)),equivalence_class(sK5,sK3,sK4))
| apply(sK4,sK5,sK0(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4))) ),
inference(instantiation,[status(thm)],[c_82]) ).
cnf(c_19008,plain,
( ~ member(sK0(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4)),equivalence_class(sK5,sK3,sK4))
| member(sK0(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4)),sK3) ),
inference(instantiation,[status(thm)],[c_83]) ).
cnf(c_26513,plain,
( ~ apply(sK4,sK5,sK0(equivalence_class(sK6,sK3,sK4),equivalence_class(sK5,sK3,sK4)))
| ~ member(sK0(equivalence_class(sK6,sK3,sK4),equivalence_class(sK5,sK3,sK4)),sK3)
| member(sK0(equivalence_class(sK6,sK3,sK4),equivalence_class(sK5,sK3,sK4)),equivalence_class(sK5,sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_18797]) ).
cnf(c_31077,plain,
( ~ apply(sK4,sK6,sK0(equivalence_class(sK6,sK3,sK4),equivalence_class(sK5,sK3,sK4)))
| ~ member(sK0(equivalence_class(sK6,sK3,sK4),equivalence_class(sK5,sK3,sK4)),X0)
| ~ apply(sK4,sK5,sK6)
| ~ member(sK5,X0)
| ~ member(sK6,X0)
| ~ equivalence(sK4,X0)
| apply(sK4,sK5,sK0(equivalence_class(sK6,sK3,sK4),equivalence_class(sK5,sK3,sK4))) ),
inference(instantiation,[status(thm)],[c_599]) ).
cnf(c_31078,plain,
( ~ apply(sK4,sK6,sK0(equivalence_class(sK6,sK3,sK4),equivalence_class(sK5,sK3,sK4)))
| ~ member(sK0(equivalence_class(sK6,sK3,sK4),equivalence_class(sK5,sK3,sK4)),sK3)
| ~ apply(sK4,sK5,sK6)
| ~ member(sK5,sK3)
| ~ member(sK6,sK3)
| ~ equivalence(sK4,sK3)
| apply(sK4,sK5,sK0(equivalence_class(sK6,sK3,sK4),equivalence_class(sK5,sK3,sK4))) ),
inference(instantiation,[status(thm)],[c_31077]) ).
cnf(c_32631,plain,
( ~ apply(sK4,sK5,X0)
| ~ apply(sK4,sK6,sK5)
| ~ member(X0,sK3)
| ~ member(sK5,sK3)
| ~ member(sK6,sK3)
| ~ equivalence(sK4,sK3)
| apply(sK4,sK6,X0) ),
inference(instantiation,[status(thm)],[c_18856]) ).
cnf(c_62588,plain,
( ~ apply(sK4,sK5,sK0(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4)))
| ~ member(sK0(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4)),sK3)
| ~ apply(sK4,sK6,sK5)
| ~ member(sK5,sK3)
| ~ member(sK6,sK3)
| ~ equivalence(sK4,sK3)
| apply(sK4,sK6,sK0(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4))) ),
inference(instantiation,[status(thm)],[c_32631]) ).
cnf(c_77847,plain,
( ~ apply(sK4,X0,X1)
| ~ member(X1,X2)
| member(X1,equivalence_class(X0,X2,sK4)) ),
inference(instantiation,[status(thm)],[c_81]) ).
cnf(c_80823,plain,
( ~ apply(sK4,sK6,sK0(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4)))
| ~ member(sK0(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4)),sK3)
| member(sK0(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4)),equivalence_class(sK6,sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_77847]) ).
cnf(c_81822,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_80823,c_62588,c_31078,c_26513,c_19007,c_19008,c_13551,c_13550,c_7483,c_7484,c_4211,c_4212,c_3004,c_598,c_577,c_84,c_86,c_87,c_88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET768+4 : TPTP v8.1.2. Released v2.2.0.
% 0.09/0.11 % Command : run_iprover %s %d THM
% 0.10/0.31 % Computer : n011.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 20:24:18 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 65.10/9.68 % SZS status Started for theBenchmark.p
% 65.10/9.68 % SZS status Theorem for theBenchmark.p
% 65.10/9.68
% 65.10/9.68 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 65.10/9.68
% 65.10/9.68 ------ iProver source info
% 65.10/9.68
% 65.10/9.68 git: date: 2024-05-02 19:28:25 +0000
% 65.10/9.68 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 65.10/9.68 git: non_committed_changes: false
% 65.10/9.68
% 65.10/9.68 ------ Parsing...
% 65.10/9.68 ------ Clausification by vclausify_rel & Parsing by iProver...
% 65.10/9.68
% 65.10/9.68 ------ Preprocessing... sf_s rm: 1 0s sf_e
% 65.10/9.68
% 65.10/9.68 ------ Preprocessing...
% 65.10/9.68
% 65.10/9.68 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 65.10/9.68 ------ Proving...
% 65.10/9.68 ------ Problem Properties
% 65.10/9.68
% 65.10/9.68
% 65.10/9.68 clauses 40
% 65.10/9.68 conjectures 5
% 65.10/9.68 EPR 11
% 65.10/9.68 Horn 34
% 65.10/9.68 unary 7
% 65.10/9.68 binary 21
% 65.10/9.68 lits 91
% 65.10/9.68 lits eq 3
% 65.10/9.68 fd_pure 0
% 65.10/9.68 fd_pseudo 0
% 65.10/9.68 fd_cond 0
% 65.10/9.68 fd_pseudo_cond 2
% 65.10/9.68 AC symbols 0
% 65.10/9.68
% 65.10/9.68 ------ Input Options Time Limit: Unbounded
% 65.10/9.68
% 65.10/9.68
% 65.10/9.68 ------
% 65.10/9.68 Current options:
% 65.10/9.68 ------
% 65.10/9.68
% 65.10/9.68
% 65.10/9.68
% 65.10/9.68
% 65.10/9.68 ------ Proving...
% 65.10/9.68
% 65.10/9.68
% 65.10/9.68 % SZS status Theorem for theBenchmark.p
% 65.10/9.68
% 65.10/9.68 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 65.10/9.68
% 65.10/9.69
%------------------------------------------------------------------------------