TSTP Solution File: SEU310+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU310+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n008.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 : Thu Aug 31 17:05:41 EDT 2023
% Result : Theorem 3.13s 1.16s
% Output : CNFRefutation 3.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 8
% Syntax : Number of formulae : 100 ( 14 unt; 0 def)
% Number of atoms : 483 ( 88 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 580 ( 197 ~; 247 |; 114 &)
% ( 7 <=>; 13 =>; 0 <=; 2 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 2 con; 0-3 aty)
% Number of variables : 210 ( 0 sgn; 91 !; 55 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1] :
( ( element(X1,powerset(powerset(the_carrier(X0))))
& top_str(X0)
& topological_space(X0) )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& in(X3,powerset(the_carrier(X0))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e2_37_1_1__pre_topc__1) ).
fof(f2,negated_conjecture,
~ ! [X0,X1] :
( ( element(X1,powerset(powerset(the_carrier(X0))))
& top_str(X0)
& topological_space(X0) )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& in(X3,powerset(the_carrier(X0))) ) ) ),
inference(negated_conjecture,[],[f1]) ).
fof(f37,axiom,
! [X0,X1] :
( ( element(X1,powerset(powerset(the_carrier(X0))))
& top_str(X0)
& topological_space(X0) )
=> ( ! [X2,X3,X4] :
( ( in(set_difference(cast_as_carrier_subset(X0),X4),X1)
& X2 = X4
& in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& X2 = X3 )
=> X3 = X4 )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& X3 = X4
& in(X4,powerset(the_carrier(X0))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e2_37_1_1__pre_topc__1) ).
fof(f38,plain,
! [X0,X1] :
( ( element(X1,powerset(powerset(the_carrier(X0))))
& top_str(X0)
& topological_space(X0) )
=> ( ! [X2,X3,X4] :
( ( in(set_difference(cast_as_carrier_subset(X0),X4),X1)
& X2 = X4
& in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& X2 = X3 )
=> X3 = X4 )
=> ? [X5] :
! [X6] :
( in(X6,X5)
<=> ? [X7] :
( in(set_difference(cast_as_carrier_subset(X0),X6),X1)
& X6 = X7
& in(X7,powerset(the_carrier(X0))) ) ) ) ),
inference(rectify,[],[f37]) ).
fof(f56,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( in(X3,X2)
<~> ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& in(X3,powerset(the_carrier(X0))) ) )
& element(X1,powerset(powerset(the_carrier(X0))))
& top_str(X0)
& topological_space(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f57,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( in(X3,X2)
<~> ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& in(X3,powerset(the_carrier(X0))) ) )
& element(X1,powerset(powerset(the_carrier(X0))))
& top_str(X0)
& topological_space(X0) ),
inference(flattening,[],[f56]) ).
fof(f79,plain,
! [X0,X1] :
( ? [X5] :
! [X6] :
( in(X6,X5)
<=> ? [X7] :
( in(set_difference(cast_as_carrier_subset(X0),X6),X1)
& X6 = X7
& in(X7,powerset(the_carrier(X0))) ) )
| ? [X2,X3,X4] :
( X3 != X4
& in(set_difference(cast_as_carrier_subset(X0),X4),X1)
& X2 = X4
& in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& X2 = X3 )
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f80,plain,
! [X0,X1] :
( ? [X5] :
! [X6] :
( in(X6,X5)
<=> ? [X7] :
( in(set_difference(cast_as_carrier_subset(X0),X6),X1)
& X6 = X7
& in(X7,powerset(the_carrier(X0))) ) )
| ? [X2,X3,X4] :
( X3 != X4
& in(set_difference(cast_as_carrier_subset(X0),X4),X1)
& X2 = X4
& in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& X2 = X3 )
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f79]) ).
fof(f81,plain,
! [X1,X0] :
( ? [X2,X3,X4] :
( X3 != X4
& in(set_difference(cast_as_carrier_subset(X0),X4),X1)
& X2 = X4
& in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& X2 = X3 )
| ~ sP0(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f82,plain,
! [X0,X1] :
( ? [X5] :
! [X6] :
( in(X6,X5)
<=> ? [X7] :
( in(set_difference(cast_as_carrier_subset(X0),X6),X1)
& X6 = X7
& in(X7,powerset(the_carrier(X0))) ) )
| sP0(X1,X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(definition_folding,[],[f80,f81]) ).
fof(f83,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( ( ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| ~ in(X3,powerset(the_carrier(X0)))
| ~ in(X3,X2) )
& ( ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& in(X3,powerset(the_carrier(X0))) )
| in(X3,X2) ) )
& element(X1,powerset(powerset(the_carrier(X0))))
& top_str(X0)
& topological_space(X0) ),
inference(nnf_transformation,[],[f57]) ).
fof(f84,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( ( ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| ~ in(X3,powerset(the_carrier(X0)))
| ~ in(X3,X2) )
& ( ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& in(X3,powerset(the_carrier(X0))) )
| in(X3,X2) ) )
& element(X1,powerset(powerset(the_carrier(X0))))
& top_str(X0)
& topological_space(X0) ),
inference(flattening,[],[f83]) ).
fof(f85,plain,
( ? [X0,X1] :
( ! [X2] :
? [X3] :
( ( ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| ~ in(X3,powerset(the_carrier(X0)))
| ~ in(X3,X2) )
& ( ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& in(X3,powerset(the_carrier(X0))) )
| in(X3,X2) ) )
& element(X1,powerset(powerset(the_carrier(X0))))
& top_str(X0)
& topological_space(X0) )
=> ( ! [X2] :
? [X3] :
( ( ~ in(set_difference(cast_as_carrier_subset(sK1),X3),sK2)
| ~ in(X3,powerset(the_carrier(sK1)))
| ~ in(X3,X2) )
& ( ( in(set_difference(cast_as_carrier_subset(sK1),X3),sK2)
& in(X3,powerset(the_carrier(sK1))) )
| in(X3,X2) ) )
& element(sK2,powerset(powerset(the_carrier(sK1))))
& top_str(sK1)
& topological_space(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f86,plain,
! [X2] :
( ? [X3] :
( ( ~ in(set_difference(cast_as_carrier_subset(sK1),X3),sK2)
| ~ in(X3,powerset(the_carrier(sK1)))
| ~ in(X3,X2) )
& ( ( in(set_difference(cast_as_carrier_subset(sK1),X3),sK2)
& in(X3,powerset(the_carrier(sK1))) )
| in(X3,X2) ) )
=> ( ( ~ in(set_difference(cast_as_carrier_subset(sK1),sK3(X2)),sK2)
| ~ in(sK3(X2),powerset(the_carrier(sK1)))
| ~ in(sK3(X2),X2) )
& ( ( in(set_difference(cast_as_carrier_subset(sK1),sK3(X2)),sK2)
& in(sK3(X2),powerset(the_carrier(sK1))) )
| in(sK3(X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f87,plain,
( ! [X2] :
( ( ~ in(set_difference(cast_as_carrier_subset(sK1),sK3(X2)),sK2)
| ~ in(sK3(X2),powerset(the_carrier(sK1)))
| ~ in(sK3(X2),X2) )
& ( ( in(set_difference(cast_as_carrier_subset(sK1),sK3(X2)),sK2)
& in(sK3(X2),powerset(the_carrier(sK1))) )
| in(sK3(X2),X2) ) )
& element(sK2,powerset(powerset(the_carrier(sK1))))
& top_str(sK1)
& topological_space(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f84,f86,f85]) ).
fof(f96,plain,
! [X1,X0] :
( ? [X2,X3,X4] :
( X3 != X4
& in(set_difference(cast_as_carrier_subset(X0),X4),X1)
& X2 = X4
& in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& X2 = X3 )
| ~ sP0(X1,X0) ),
inference(nnf_transformation,[],[f81]) ).
fof(f97,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( X3 != X4
& in(set_difference(cast_as_carrier_subset(X1),X4),X0)
& X2 = X4
& in(set_difference(cast_as_carrier_subset(X1),X3),X0)
& X2 = X3 )
| ~ sP0(X0,X1) ),
inference(rectify,[],[f96]) ).
fof(f98,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( X3 != X4
& in(set_difference(cast_as_carrier_subset(X1),X4),X0)
& X2 = X4
& in(set_difference(cast_as_carrier_subset(X1),X3),X0)
& X2 = X3 )
=> ( sK9(X0,X1) != sK10(X0,X1)
& in(set_difference(cast_as_carrier_subset(X1),sK10(X0,X1)),X0)
& sK8(X0,X1) = sK10(X0,X1)
& in(set_difference(cast_as_carrier_subset(X1),sK9(X0,X1)),X0)
& sK8(X0,X1) = sK9(X0,X1) ) ),
introduced(choice_axiom,[]) ).
fof(f99,plain,
! [X0,X1] :
( ( sK9(X0,X1) != sK10(X0,X1)
& in(set_difference(cast_as_carrier_subset(X1),sK10(X0,X1)),X0)
& sK8(X0,X1) = sK10(X0,X1)
& in(set_difference(cast_as_carrier_subset(X1),sK9(X0,X1)),X0)
& sK8(X0,X1) = sK9(X0,X1) )
| ~ sP0(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f97,f98]) ).
fof(f100,plain,
! [X0,X1] :
( ? [X5] :
! [X6] :
( ( in(X6,X5)
| ! [X7] :
( ~ in(set_difference(cast_as_carrier_subset(X0),X6),X1)
| X6 != X7
| ~ in(X7,powerset(the_carrier(X0))) ) )
& ( ? [X7] :
( in(set_difference(cast_as_carrier_subset(X0),X6),X1)
& X6 = X7
& in(X7,powerset(the_carrier(X0))) )
| ~ in(X6,X5) ) )
| sP0(X1,X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(nnf_transformation,[],[f82]) ).
fof(f101,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| X3 != X4
| ~ in(X4,powerset(the_carrier(X0))) ) )
& ( ? [X5] :
( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& X3 = X5
& in(X5,powerset(the_carrier(X0))) )
| ~ in(X3,X2) ) )
| sP0(X1,X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(rectify,[],[f100]) ).
fof(f102,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| X3 != X4
| ~ in(X4,powerset(the_carrier(X0))) ) )
& ( ? [X5] :
( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& X3 = X5
& in(X5,powerset(the_carrier(X0))) )
| ~ in(X3,X2) ) )
=> ! [X3] :
( ( in(X3,sK11(X0,X1))
| ! [X4] :
( ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| X3 != X4
| ~ in(X4,powerset(the_carrier(X0))) ) )
& ( ? [X5] :
( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& X3 = X5
& in(X5,powerset(the_carrier(X0))) )
| ~ in(X3,sK11(X0,X1)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f103,plain,
! [X0,X1,X3] :
( ? [X5] :
( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& X3 = X5
& in(X5,powerset(the_carrier(X0))) )
=> ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& sK12(X0,X1,X3) = X3
& in(sK12(X0,X1,X3),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f104,plain,
! [X0,X1] :
( ! [X3] :
( ( in(X3,sK11(X0,X1))
| ! [X4] :
( ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| X3 != X4
| ~ in(X4,powerset(the_carrier(X0))) ) )
& ( ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& sK12(X0,X1,X3) = X3
& in(sK12(X0,X1,X3),powerset(the_carrier(X0))) )
| ~ in(X3,sK11(X0,X1)) ) )
| sP0(X1,X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12])],[f101,f103,f102]) ).
fof(f105,plain,
topological_space(sK1),
inference(cnf_transformation,[],[f87]) ).
fof(f106,plain,
top_str(sK1),
inference(cnf_transformation,[],[f87]) ).
fof(f107,plain,
element(sK2,powerset(powerset(the_carrier(sK1)))),
inference(cnf_transformation,[],[f87]) ).
fof(f108,plain,
! [X2] :
( in(sK3(X2),powerset(the_carrier(sK1)))
| in(sK3(X2),X2) ),
inference(cnf_transformation,[],[f87]) ).
fof(f109,plain,
! [X2] :
( in(set_difference(cast_as_carrier_subset(sK1),sK3(X2)),sK2)
| in(sK3(X2),X2) ),
inference(cnf_transformation,[],[f87]) ).
fof(f110,plain,
! [X2] :
( ~ in(set_difference(cast_as_carrier_subset(sK1),sK3(X2)),sK2)
| ~ in(sK3(X2),powerset(the_carrier(sK1)))
| ~ in(sK3(X2),X2) ),
inference(cnf_transformation,[],[f87]) ).
fof(f165,plain,
! [X0,X1] :
( sK8(X0,X1) = sK9(X0,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f167,plain,
! [X0,X1] :
( sK8(X0,X1) = sK10(X0,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f169,plain,
! [X0,X1] :
( sK9(X0,X1) != sK10(X0,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f170,plain,
! [X3,X0,X1] :
( in(sK12(X0,X1,X3),powerset(the_carrier(X0)))
| ~ in(X3,sK11(X0,X1))
| sP0(X1,X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f171,plain,
! [X3,X0,X1] :
( sK12(X0,X1,X3) = X3
| ~ in(X3,sK11(X0,X1))
| sP0(X1,X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f172,plain,
! [X3,X0,X1] :
( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| ~ in(X3,sK11(X0,X1))
| sP0(X1,X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f173,plain,
! [X3,X0,X1,X4] :
( in(X3,sK11(X0,X1))
| ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| X3 != X4
| ~ in(X4,powerset(the_carrier(X0)))
| sP0(X1,X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f174,plain,
! [X0,X1,X4] :
( in(X4,sK11(X0,X1))
| ~ in(set_difference(cast_as_carrier_subset(X0),X4),X1)
| ~ in(X4,powerset(the_carrier(X0)))
| sP0(X1,X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(equality_resolution,[],[f173]) ).
cnf(c_49,negated_conjecture,
( ~ in(set_difference(cast_as_carrier_subset(sK1),sK3(X0)),sK2)
| ~ in(sK3(X0),powerset(the_carrier(sK1)))
| ~ in(sK3(X0),X0) ),
inference(cnf_transformation,[],[f110]) ).
cnf(c_50,negated_conjecture,
( in(set_difference(cast_as_carrier_subset(sK1),sK3(X0)),sK2)
| in(sK3(X0),X0) ),
inference(cnf_transformation,[],[f109]) ).
cnf(c_51,negated_conjecture,
( in(sK3(X0),powerset(the_carrier(sK1)))
| in(sK3(X0),X0) ),
inference(cnf_transformation,[],[f108]) ).
cnf(c_52,negated_conjecture,
element(sK2,powerset(powerset(the_carrier(sK1)))),
inference(cnf_transformation,[],[f107]) ).
cnf(c_53,negated_conjecture,
top_str(sK1),
inference(cnf_transformation,[],[f106]) ).
cnf(c_54,negated_conjecture,
topological_space(sK1),
inference(cnf_transformation,[],[f105]) ).
cnf(c_109,plain,
( sK9(X0,X1) != sK10(X0,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f169]) ).
cnf(c_111,plain,
( ~ sP0(X0,X1)
| sK10(X0,X1) = sK8(X0,X1) ),
inference(cnf_transformation,[],[f167]) ).
cnf(c_113,plain,
( ~ sP0(X0,X1)
| sK9(X0,X1) = sK8(X0,X1) ),
inference(cnf_transformation,[],[f165]) ).
cnf(c_114,plain,
( ~ in(set_difference(cast_as_carrier_subset(X0),X1),X2)
| ~ element(X2,powerset(powerset(the_carrier(X0))))
| ~ in(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| in(X1,sK11(X0,X2))
| sP0(X2,X0) ),
inference(cnf_transformation,[],[f174]) ).
cnf(c_115,plain,
( ~ element(X0,powerset(powerset(the_carrier(X1))))
| ~ in(X2,sK11(X1,X0))
| ~ top_str(X1)
| ~ topological_space(X1)
| in(set_difference(cast_as_carrier_subset(X1),X2),X0)
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f172]) ).
cnf(c_116,plain,
( ~ element(X0,powerset(powerset(the_carrier(X1))))
| ~ in(X2,sK11(X1,X0))
| ~ top_str(X1)
| ~ topological_space(X1)
| sK12(X1,X0,X2) = X2
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f171]) ).
cnf(c_117,plain,
( ~ element(X0,powerset(powerset(the_carrier(X1))))
| ~ in(X2,sK11(X1,X0))
| ~ top_str(X1)
| ~ topological_space(X1)
| in(sK12(X1,X0,X2),powerset(the_carrier(X1)))
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f170]) ).
cnf(c_811,plain,
( X0 != sK1
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ in(X2,sK11(X0,X1))
| ~ top_str(X0)
| in(sK12(X0,X1,X2),powerset(the_carrier(X0)))
| sP0(X1,X0) ),
inference(resolution_lifted,[status(thm)],[c_54,c_117]) ).
cnf(c_812,plain,
( ~ element(X0,powerset(powerset(the_carrier(sK1))))
| ~ in(X1,sK11(sK1,X0))
| ~ top_str(sK1)
| in(sK12(sK1,X0,X1),powerset(the_carrier(sK1)))
| sP0(X0,sK1) ),
inference(unflattening,[status(thm)],[c_811]) ).
cnf(c_814,plain,
( ~ in(X1,sK11(sK1,X0))
| ~ element(X0,powerset(powerset(the_carrier(sK1))))
| in(sK12(sK1,X0,X1),powerset(the_carrier(sK1)))
| sP0(X0,sK1) ),
inference(global_subsumption_just,[status(thm)],[c_812,c_53,c_812]) ).
cnf(c_815,plain,
( ~ element(X0,powerset(powerset(the_carrier(sK1))))
| ~ in(X1,sK11(sK1,X0))
| in(sK12(sK1,X0,X1),powerset(the_carrier(sK1)))
| sP0(X0,sK1) ),
inference(renaming,[status(thm)],[c_814]) ).
cnf(c_829,plain,
( X0 != sK1
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ in(X2,sK11(X0,X1))
| ~ top_str(X0)
| sK12(X0,X1,X2) = X2
| sP0(X1,X0) ),
inference(resolution_lifted,[status(thm)],[c_54,c_116]) ).
cnf(c_830,plain,
( ~ element(X0,powerset(powerset(the_carrier(sK1))))
| ~ in(X1,sK11(sK1,X0))
| ~ top_str(sK1)
| sK12(sK1,X0,X1) = X1
| sP0(X0,sK1) ),
inference(unflattening,[status(thm)],[c_829]) ).
cnf(c_832,plain,
( ~ in(X1,sK11(sK1,X0))
| ~ element(X0,powerset(powerset(the_carrier(sK1))))
| sK12(sK1,X0,X1) = X1
| sP0(X0,sK1) ),
inference(global_subsumption_just,[status(thm)],[c_830,c_53,c_830]) ).
cnf(c_833,plain,
( ~ element(X0,powerset(powerset(the_carrier(sK1))))
| ~ in(X1,sK11(sK1,X0))
| sK12(sK1,X0,X1) = X1
| sP0(X0,sK1) ),
inference(renaming,[status(thm)],[c_832]) ).
cnf(c_847,plain,
( X0 != sK1
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ in(X2,sK11(X0,X1))
| ~ top_str(X0)
| in(set_difference(cast_as_carrier_subset(X0),X2),X1)
| sP0(X1,X0) ),
inference(resolution_lifted,[status(thm)],[c_54,c_115]) ).
cnf(c_848,plain,
( ~ element(X0,powerset(powerset(the_carrier(sK1))))
| ~ in(X1,sK11(sK1,X0))
| ~ top_str(sK1)
| in(set_difference(cast_as_carrier_subset(sK1),X1),X0)
| sP0(X0,sK1) ),
inference(unflattening,[status(thm)],[c_847]) ).
cnf(c_850,plain,
( ~ in(X1,sK11(sK1,X0))
| ~ element(X0,powerset(powerset(the_carrier(sK1))))
| in(set_difference(cast_as_carrier_subset(sK1),X1),X0)
| sP0(X0,sK1) ),
inference(global_subsumption_just,[status(thm)],[c_848,c_53,c_848]) ).
cnf(c_851,plain,
( ~ element(X0,powerset(powerset(the_carrier(sK1))))
| ~ in(X1,sK11(sK1,X0))
| in(set_difference(cast_as_carrier_subset(sK1),X1),X0)
| sP0(X0,sK1) ),
inference(renaming,[status(thm)],[c_850]) ).
cnf(c_865,plain,
( X0 != sK1
| ~ in(set_difference(cast_as_carrier_subset(X0),X1),X2)
| ~ element(X2,powerset(powerset(the_carrier(X0))))
| ~ in(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| in(X1,sK11(X0,X2))
| sP0(X2,X0) ),
inference(resolution_lifted,[status(thm)],[c_54,c_114]) ).
cnf(c_866,plain,
( ~ in(set_difference(cast_as_carrier_subset(sK1),X0),X1)
| ~ element(X1,powerset(powerset(the_carrier(sK1))))
| ~ in(X0,powerset(the_carrier(sK1)))
| ~ top_str(sK1)
| in(X0,sK11(sK1,X1))
| sP0(X1,sK1) ),
inference(unflattening,[status(thm)],[c_865]) ).
cnf(c_868,plain,
( ~ in(X0,powerset(the_carrier(sK1)))
| ~ element(X1,powerset(powerset(the_carrier(sK1))))
| ~ in(set_difference(cast_as_carrier_subset(sK1),X0),X1)
| in(X0,sK11(sK1,X1))
| sP0(X1,sK1) ),
inference(global_subsumption_just,[status(thm)],[c_866,c_53,c_866]) ).
cnf(c_869,plain,
( ~ in(set_difference(cast_as_carrier_subset(sK1),X0),X1)
| ~ element(X1,powerset(powerset(the_carrier(sK1))))
| ~ in(X0,powerset(the_carrier(sK1)))
| in(X0,sK11(sK1,X1))
| sP0(X1,sK1) ),
inference(renaming,[status(thm)],[c_868]) ).
cnf(c_3031,plain,
( ~ in(X0,sK11(sK1,sK2))
| in(set_difference(cast_as_carrier_subset(sK1),X0),sK2)
| sP0(sK2,sK1) ),
inference(superposition,[status(thm)],[c_52,c_851]) ).
cnf(c_3097,plain,
( ~ in(sK3(X0),powerset(the_carrier(sK1)))
| ~ in(sK3(X0),sK11(sK1,sK2))
| ~ in(sK3(X0),X0)
| sP0(sK2,sK1) ),
inference(superposition,[status(thm)],[c_3031,c_49]) ).
cnf(c_3135,plain,
( ~ in(X0,sK11(sK1,sK2))
| sK12(sK1,sK2,X0) = X0
| sP0(sK2,sK1) ),
inference(superposition,[status(thm)],[c_52,c_833]) ).
cnf(c_3269,plain,
( ~ in(set_difference(cast_as_carrier_subset(sK1),X0),sK2)
| ~ in(X0,powerset(the_carrier(sK1)))
| in(X0,sK11(sK1,sK2))
| sP0(sK2,sK1) ),
inference(superposition,[status(thm)],[c_52,c_869]) ).
cnf(c_3295,plain,
( ~ in(sK3(X0),powerset(the_carrier(sK1)))
| in(sK3(X0),sK11(sK1,sK2))
| in(sK3(X0),X0)
| sP0(sK2,sK1) ),
inference(superposition,[status(thm)],[c_50,c_3269]) ).
cnf(c_3309,plain,
( in(sK3(X0),sK11(sK1,sK2))
| in(sK3(X0),X0)
| sP0(sK2,sK1) ),
inference(global_subsumption_just,[status(thm)],[c_3295,c_51,c_3295]) ).
cnf(c_3324,plain,
( in(sK3(sK11(sK1,sK2)),sK11(sK1,sK2))
| sP0(sK2,sK1) ),
inference(equality_factoring,[status(thm)],[c_3309]) ).
cnf(c_3345,plain,
( sK12(sK1,sK2,sK3(sK11(sK1,sK2))) = sK3(sK11(sK1,sK2))
| sP0(sK2,sK1) ),
inference(superposition,[status(thm)],[c_3324,c_3135]) ).
cnf(c_3459,plain,
( sK12(sK1,sK2,sK3(sK11(sK1,sK2))) = sK3(sK11(sK1,sK2))
| sK9(sK2,sK1) = sK8(sK2,sK1) ),
inference(superposition,[status(thm)],[c_3345,c_113]) ).
cnf(c_3460,plain,
( sK12(sK1,sK2,sK3(sK11(sK1,sK2))) = sK3(sK11(sK1,sK2))
| sK10(sK2,sK1) = sK8(sK2,sK1) ),
inference(superposition,[status(thm)],[c_3345,c_111]) ).
cnf(c_3475,plain,
( ~ in(sK3(sK11(sK1,sK2)),sK11(sK1,sK2))
| ~ element(sK2,powerset(powerset(the_carrier(sK1))))
| sK9(sK2,sK1) = sK8(sK2,sK1)
| in(sK3(sK11(sK1,sK2)),powerset(the_carrier(sK1)))
| sP0(sK2,sK1) ),
inference(superposition,[status(thm)],[c_3459,c_815]) ).
cnf(c_3476,plain,
( ~ in(sK3(sK11(sK1,sK2)),sK11(sK1,sK2))
| sK9(sK2,sK1) = sK8(sK2,sK1)
| in(sK3(sK11(sK1,sK2)),powerset(the_carrier(sK1)))
| sP0(sK2,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3475,c_52]) ).
cnf(c_3481,plain,
( sK9(sK2,sK1) = sK8(sK2,sK1)
| in(sK3(sK11(sK1,sK2)),powerset(the_carrier(sK1)))
| sP0(sK2,sK1) ),
inference(global_subsumption_just,[status(thm)],[c_3476,c_3324,c_3476]) ).
cnf(c_3486,plain,
( sK9(sK2,sK1) = sK8(sK2,sK1)
| in(sK3(sK11(sK1,sK2)),powerset(the_carrier(sK1))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3481,c_113]) ).
cnf(c_3489,plain,
( ~ in(sK3(sK11(sK1,sK2)),sK11(sK1,sK2))
| sK9(sK2,sK1) = sK8(sK2,sK1)
| sP0(sK2,sK1) ),
inference(superposition,[status(thm)],[c_3486,c_3097]) ).
cnf(c_3535,plain,
( sK9(sK2,sK1) = sK8(sK2,sK1)
| sP0(sK2,sK1) ),
inference(global_subsumption_just,[status(thm)],[c_3489,c_3324,c_3489]) ).
cnf(c_3539,plain,
sK9(sK2,sK1) = sK8(sK2,sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_3535,c_113]) ).
cnf(c_3553,plain,
( sK12(sK1,sK2,sK3(sK11(sK1,sK2))) = sK3(sK11(sK1,sK2))
| sK9(sK2,sK1) = sK10(sK2,sK1) ),
inference(light_normalisation,[status(thm)],[c_3460,c_3539]) ).
cnf(c_3559,plain,
( ~ in(sK3(sK11(sK1,sK2)),sK11(sK1,sK2))
| ~ element(sK2,powerset(powerset(the_carrier(sK1))))
| sK9(sK2,sK1) = sK10(sK2,sK1)
| in(sK3(sK11(sK1,sK2)),powerset(the_carrier(sK1)))
| sP0(sK2,sK1) ),
inference(superposition,[status(thm)],[c_3553,c_815]) ).
cnf(c_3560,plain,
( ~ in(sK3(sK11(sK1,sK2)),sK11(sK1,sK2))
| sK9(sK2,sK1) = sK10(sK2,sK1)
| in(sK3(sK11(sK1,sK2)),powerset(the_carrier(sK1)))
| sP0(sK2,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3559,c_52]) ).
cnf(c_3634,plain,
( sK9(sK2,sK1) = sK10(sK2,sK1)
| in(sK3(sK11(sK1,sK2)),powerset(the_carrier(sK1)))
| sP0(sK2,sK1) ),
inference(global_subsumption_just,[status(thm)],[c_3560,c_3324,c_3560]) ).
cnf(c_3642,plain,
( ~ in(sK3(sK11(sK1,sK2)),sK11(sK1,sK2))
| sK9(sK2,sK1) = sK10(sK2,sK1)
| sP0(sK2,sK1) ),
inference(superposition,[status(thm)],[c_3634,c_3097]) ).
cnf(c_3650,plain,
( sK9(sK2,sK1) = sK10(sK2,sK1)
| sP0(sK2,sK1) ),
inference(global_subsumption_just,[status(thm)],[c_3642,c_3324,c_3642]) ).
cnf(c_3657,plain,
( sK9(sK2,sK1) = sK10(sK2,sK1)
| sK10(sK2,sK1) = sK8(sK2,sK1) ),
inference(superposition,[status(thm)],[c_3650,c_111]) ).
cnf(c_3658,plain,
sK9(sK2,sK1) = sK10(sK2,sK1),
inference(light_normalisation,[status(thm)],[c_3657,c_3539]) ).
cnf(c_3727,plain,
~ sP0(sK2,sK1),
inference(superposition,[status(thm)],[c_3658,c_109]) ).
cnf(c_3730,plain,
sK12(sK1,sK2,sK3(sK11(sK1,sK2))) = sK3(sK11(sK1,sK2)),
inference(backward_subsumption_resolution,[status(thm)],[c_3345,c_3727]) ).
cnf(c_3732,plain,
in(sK3(sK11(sK1,sK2)),sK11(sK1,sK2)),
inference(backward_subsumption_resolution,[status(thm)],[c_3324,c_3727]) ).
cnf(c_3741,plain,
( ~ in(sK3(X0),powerset(the_carrier(sK1)))
| ~ in(sK3(X0),sK11(sK1,sK2))
| ~ in(sK3(X0),X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_3097,c_3727]) ).
cnf(c_3913,plain,
( ~ in(sK3(sK11(sK1,sK2)),sK11(sK1,sK2))
| ~ element(sK2,powerset(powerset(the_carrier(sK1))))
| in(sK3(sK11(sK1,sK2)),powerset(the_carrier(sK1)))
| sP0(sK2,sK1) ),
inference(superposition,[status(thm)],[c_3730,c_815]) ).
cnf(c_3914,plain,
in(sK3(sK11(sK1,sK2)),powerset(the_carrier(sK1))),
inference(forward_subsumption_resolution,[status(thm)],[c_3913,c_3727,c_52,c_3732]) ).
cnf(c_3916,plain,
~ in(sK3(sK11(sK1,sK2)),sK11(sK1,sK2)),
inference(superposition,[status(thm)],[c_3914,c_3741]) ).
cnf(c_3918,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3916,c_3732]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU310+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 23 13:07:17 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.13/1.16 % SZS status Started for theBenchmark.p
% 3.13/1.16 % SZS status Theorem for theBenchmark.p
% 3.13/1.16
% 3.13/1.16 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.13/1.16
% 3.13/1.16 ------ iProver source info
% 3.13/1.16
% 3.13/1.16 git: date: 2023-05-31 18:12:56 +0000
% 3.13/1.16 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.13/1.16 git: non_committed_changes: false
% 3.13/1.16 git: last_make_outside_of_git: false
% 3.13/1.16
% 3.13/1.16 ------ Parsing...
% 3.13/1.16 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.13/1.16
% 3.13/1.16 ------ Preprocessing... sup_sim: 0 sf_s rm: 50 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 8 0s sf_e pe_s pe_e
% 3.13/1.16
% 3.13/1.16 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.13/1.16
% 3.13/1.16 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.13/1.16 ------ Proving...
% 3.13/1.16 ------ Problem Properties
% 3.13/1.16
% 3.13/1.16
% 3.13/1.16 clauses 22
% 3.13/1.16 conjectures 4
% 3.13/1.16 EPR 2
% 3.13/1.16 Horn 15
% 3.13/1.16 unary 7
% 3.13/1.16 binary 10
% 3.13/1.16 lits 47
% 3.13/1.16 lits eq 4
% 3.13/1.16 fd_pure 0
% 3.13/1.16 fd_pseudo 0
% 3.13/1.16 fd_cond 0
% 3.13/1.16 fd_pseudo_cond 0
% 3.13/1.16 AC symbols 0
% 3.13/1.16
% 3.13/1.16 ------ Schedule dynamic 5 is on
% 3.13/1.16
% 3.13/1.16 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.13/1.16
% 3.13/1.16
% 3.13/1.16 ------
% 3.13/1.16 Current options:
% 3.13/1.16 ------
% 3.13/1.16
% 3.13/1.16
% 3.13/1.16
% 3.13/1.16
% 3.13/1.16 ------ Proving...
% 3.13/1.16
% 3.13/1.16
% 3.13/1.16 % SZS status Theorem for theBenchmark.p
% 3.13/1.16
% 3.13/1.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.13/1.16
% 3.13/1.16
%------------------------------------------------------------------------------