TSTP Solution File: SEU310+1 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SEU310+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n020.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 03:05:26 EDT 2024
% Result : Theorem 3.93s 1.18s
% Output : CNFRefutation 3.93s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named definition)
% 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/sandbox2/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/sandbox2/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_2663,plain,
the_carrier(sK1) = sP0_iProver_def,
definition ).
cnf(c_2664,plain,
powerset(sP0_iProver_def) = sP1_iProver_def,
definition ).
cnf(c_2665,plain,
powerset(sP1_iProver_def) = sP2_iProver_def,
definition ).
cnf(c_2666,plain,
cast_as_carrier_subset(sK1) = sP3_iProver_def,
definition ).
cnf(c_2667,negated_conjecture,
element(sK2,sP2_iProver_def),
inference(demodulation,[status(thm)],[c_52,c_2663,c_2664,c_2665]) ).
cnf(c_2668,negated_conjecture,
( in(sK3(X0),X0)
| in(sK3(X0),sP1_iProver_def) ),
inference(demodulation,[status(thm)],[c_51]) ).
cnf(c_2669,negated_conjecture,
( in(set_difference(sP3_iProver_def,sK3(X0)),sK2)
| in(sK3(X0),X0) ),
inference(demodulation,[status(thm)],[c_50,c_2666]) ).
cnf(c_2670,negated_conjecture,
( ~ in(set_difference(sP3_iProver_def,sK3(X0)),sK2)
| ~ in(sK3(X0),X0)
| ~ in(sK3(X0),sP1_iProver_def) ),
inference(demodulation,[status(thm)],[c_49]) ).
cnf(c_3052,plain,
( ~ in(X0,sK11(sK1,X1))
| ~ element(X1,sP2_iProver_def)
| in(set_difference(sP3_iProver_def,X0),X1)
| sP0(X1,sK1) ),
inference(light_normalisation,[status(thm)],[c_851,c_2663,c_2664,c_2665,c_2666]) ).
cnf(c_3061,plain,
( ~ element(X0,sP2_iProver_def)
| in(set_difference(sP3_iProver_def,sK3(sK11(sK1,X0))),X0)
| in(set_difference(sP3_iProver_def,sK3(sK11(sK1,X0))),sK2)
| sP0(X0,sK1) ),
inference(superposition,[status(thm)],[c_2669,c_3052]) ).
cnf(c_3094,plain,
( ~ in(X0,sK11(sK1,X1))
| ~ element(X1,sP2_iProver_def)
| sK12(sK1,X1,X0) = X0
| sP0(X1,sK1) ),
inference(light_normalisation,[status(thm)],[c_833,c_2663,c_2664,c_2665]) ).
cnf(c_3104,plain,
( ~ element(X0,sP2_iProver_def)
| sK12(sK1,X0,sK3(sK11(sK1,X0))) = sK3(sK11(sK1,X0))
| in(sK3(sK11(sK1,X0)),sP1_iProver_def)
| sP0(X0,sK1) ),
inference(superposition,[status(thm)],[c_2668,c_3094]) ).
cnf(c_3135,plain,
( ~ element(sK2,sP2_iProver_def)
| in(set_difference(sP3_iProver_def,sK3(sK11(sK1,sK2))),sK2)
| sP0(sK2,sK1) ),
inference(equality_factoring,[status(thm)],[c_3061]) ).
cnf(c_3137,plain,
( in(set_difference(sP3_iProver_def,sK3(sK11(sK1,sK2))),sK2)
| sP0(sK2,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3135,c_2667]) ).
cnf(c_3164,plain,
( ~ in(sK3(sK11(sK1,sK2)),sK11(sK1,sK2))
| ~ in(sK3(sK11(sK1,sK2)),sP1_iProver_def)
| sP0(sK2,sK1) ),
inference(superposition,[status(thm)],[c_3137,c_2670]) ).
cnf(c_3176,plain,
( ~ in(X0,sK11(sK1,X1))
| ~ element(X1,sP2_iProver_def)
| in(sK12(sK1,X1,X0),sP1_iProver_def)
| sP0(X1,sK1) ),
inference(light_normalisation,[status(thm)],[c_815,c_2663,c_2664,c_2665]) ).
cnf(c_3193,plain,
( ~ in(set_difference(sP3_iProver_def,X0),X1)
| ~ in(X0,sP1_iProver_def)
| ~ element(X1,sP2_iProver_def)
| in(X0,sK11(sK1,X1))
| sP0(X1,sK1) ),
inference(light_normalisation,[status(thm)],[c_869,c_2663,c_2664,c_2665,c_2666]) ).
cnf(c_3208,plain,
( ~ in(sK3(sK11(sK1,sK2)),sP1_iProver_def)
| ~ element(sK2,sP2_iProver_def)
| in(sK3(sK11(sK1,sK2)),sK11(sK1,sK2))
| sP0(sK2,sK1) ),
inference(superposition,[status(thm)],[c_3137,c_3193]) ).
cnf(c_3209,plain,
( ~ in(sK3(sK11(sK1,sK2)),sP1_iProver_def)
| in(sK3(sK11(sK1,sK2)),sK11(sK1,sK2))
| sP0(sK2,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3208,c_2667]) ).
cnf(c_3323,plain,
( ~ in(sK3(sK11(sK1,sK2)),sP1_iProver_def)
| sP0(sK2,sK1) ),
inference(global_subsumption_just,[status(thm)],[c_3209,c_3164,c_3209]) ).
cnf(c_3329,plain,
( in(sK3(sK11(sK1,sK2)),sK11(sK1,sK2))
| sP0(sK2,sK1) ),
inference(superposition,[status(thm)],[c_2668,c_3323]) ).
cnf(c_3330,plain,
( ~ element(sK2,sP2_iProver_def)
| sK12(sK1,sK2,sK3(sK11(sK1,sK2))) = sK3(sK11(sK1,sK2))
| sP0(sK2,sK1) ),
inference(superposition,[status(thm)],[c_3104,c_3323]) ).
cnf(c_3333,plain,
( sK12(sK1,sK2,sK3(sK11(sK1,sK2))) = sK3(sK11(sK1,sK2))
| sP0(sK2,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3330,c_2667]) ).
cnf(c_3430,plain,
( sK12(sK1,sK2,sK3(sK11(sK1,sK2))) = sK3(sK11(sK1,sK2))
| sK10(sK2,sK1) = sK8(sK2,sK1) ),
inference(superposition,[status(thm)],[c_3333,c_111]) ).
cnf(c_3468,plain,
( sK12(sK1,sK2,sK3(sK11(sK1,sK2))) = sK3(sK11(sK1,sK2))
| sK9(sK2,sK1) = sK8(sK2,sK1) ),
inference(superposition,[status(thm)],[c_3333,c_113]) ).
cnf(c_3619,plain,
( ~ in(sK3(sK11(sK1,sK2)),sK11(sK1,sK2))
| ~ element(sK2,sP2_iProver_def)
| sK10(sK2,sK1) = sK8(sK2,sK1)
| in(sK3(sK11(sK1,sK2)),sP1_iProver_def)
| sP0(sK2,sK1) ),
inference(superposition,[status(thm)],[c_3430,c_3176]) ).
cnf(c_3620,plain,
( ~ in(sK3(sK11(sK1,sK2)),sK11(sK1,sK2))
| sK10(sK2,sK1) = sK8(sK2,sK1)
| in(sK3(sK11(sK1,sK2)),sP1_iProver_def)
| sP0(sK2,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3619,c_2667]) ).
cnf(c_3680,plain,
( ~ in(sK3(sK11(sK1,sK2)),sK11(sK1,sK2))
| ~ element(sK2,sP2_iProver_def)
| sK9(sK2,sK1) = sK8(sK2,sK1)
| in(sK3(sK11(sK1,sK2)),sP1_iProver_def)
| sP0(sK2,sK1) ),
inference(superposition,[status(thm)],[c_3468,c_3176]) ).
cnf(c_3681,plain,
( ~ in(sK3(sK11(sK1,sK2)),sK11(sK1,sK2))
| sK9(sK2,sK1) = sK8(sK2,sK1)
| in(sK3(sK11(sK1,sK2)),sP1_iProver_def)
| sP0(sK2,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3680,c_2667]) ).
cnf(c_3707,plain,
( sK10(sK2,sK1) = sK8(sK2,sK1)
| sP0(sK2,sK1) ),
inference(global_subsumption_just,[status(thm)],[c_3620,c_3323,c_3329,c_3620]) ).
cnf(c_3711,plain,
sK10(sK2,sK1) = sK8(sK2,sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_3707,c_111]) ).
cnf(c_3716,plain,
( sK9(sK2,sK1) = sK8(sK2,sK1)
| sP0(sK2,sK1) ),
inference(global_subsumption_just,[status(thm)],[c_3681,c_3323,c_3329,c_3681]) ).
cnf(c_3718,plain,
( sK9(sK2,sK1) = sK10(sK2,sK1)
| sP0(sK2,sK1) ),
inference(light_normalisation,[status(thm)],[c_3716,c_3711]) ).
cnf(c_3723,plain,
( sK9(sK2,sK1) = sK10(sK2,sK1)
| sK9(sK2,sK1) = sK8(sK2,sK1) ),
inference(superposition,[status(thm)],[c_3718,c_113]) ).
cnf(c_3725,plain,
sK9(sK2,sK1) = sK10(sK2,sK1),
inference(light_normalisation,[status(thm)],[c_3723,c_3711]) ).
cnf(c_3939,plain,
~ sP0(sK2,sK1),
inference(superposition,[status(thm)],[c_3725,c_109]) ).
cnf(c_3950,plain,
sK12(sK1,sK2,sK3(sK11(sK1,sK2))) = sK3(sK11(sK1,sK2)),
inference(backward_subsumption_resolution,[status(thm)],[c_3333,c_3939]) ).
cnf(c_3951,plain,
in(sK3(sK11(sK1,sK2)),sK11(sK1,sK2)),
inference(backward_subsumption_resolution,[status(thm)],[c_3329,c_3939]) ).
cnf(c_3952,plain,
~ in(sK3(sK11(sK1,sK2)),sP1_iProver_def),
inference(backward_subsumption_resolution,[status(thm)],[c_3323,c_3939]) ).
cnf(c_4021,plain,
( ~ in(sK3(sK11(sK1,sK2)),sK11(sK1,sK2))
| ~ element(sK2,sP2_iProver_def)
| in(sK3(sK11(sK1,sK2)),sP1_iProver_def)
| sP0(sK2,sK1) ),
inference(superposition,[status(thm)],[c_3950,c_3176]) ).
cnf(c_4022,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4021,c_3939,c_3952,c_2667,c_3951]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU310+1 : TPTP v8.1.2. Released v3.3.0.
% 0.08/0.14 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n020.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 2 17:28:31 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 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
% 3.93/1.18 % SZS status Started for theBenchmark.p
% 3.93/1.18 % SZS status Theorem for theBenchmark.p
% 3.93/1.18
% 3.93/1.18 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.93/1.18
% 3.93/1.18 ------ iProver source info
% 3.93/1.18
% 3.93/1.18 git: date: 2024-05-02 19:28:25 +0000
% 3.93/1.18 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.93/1.18 git: non_committed_changes: false
% 3.93/1.18
% 3.93/1.18 ------ Parsing...
% 3.93/1.18 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.93/1.18
% 3.93/1.18 ------ 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
% 3.93/1.18
% 3.93/1.18 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.93/1.18
% 3.93/1.18 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.93/1.18 ------ Proving...
% 3.93/1.18 ------ Problem Properties
% 3.93/1.18
% 3.93/1.18
% 3.93/1.18 clauses 26
% 3.93/1.18 conjectures 4
% 3.93/1.18 EPR 3
% 3.93/1.18 Horn 19
% 3.93/1.18 unary 11
% 3.93/1.18 binary 10
% 3.93/1.18 lits 51
% 3.93/1.18 lits eq 8
% 3.93/1.18 fd_pure 0
% 3.93/1.18 fd_pseudo 0
% 3.93/1.18 fd_cond 0
% 3.93/1.18 fd_pseudo_cond 0
% 3.93/1.18 AC symbols 0
% 3.93/1.18
% 3.93/1.18 ------ Schedule dynamic 5 is on
% 3.93/1.18
% 3.93/1.18 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.93/1.18
% 3.93/1.18
% 3.93/1.18 ------
% 3.93/1.18 Current options:
% 3.93/1.18 ------
% 3.93/1.18
% 3.93/1.18
% 3.93/1.18
% 3.93/1.18
% 3.93/1.18 ------ Proving...
% 3.93/1.18
% 3.93/1.18
% 3.93/1.18 % SZS status Theorem for theBenchmark.p
% 3.93/1.18
% 3.93/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.93/1.19
% 3.93/1.19
%------------------------------------------------------------------------------