TSTP Solution File: SEU322+1 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SEU322+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n018.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 03:05:28 EDT 2024
% Result : Theorem 17.58s 3.21s
% Output : CNFRefutation 17.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 20
% Syntax : Number of formulae : 151 ( 16 unt; 0 def)
% Number of atoms : 431 ( 30 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 516 ( 236 ~; 221 |; 28 &)
% ( 8 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 251 ( 2 sgn 131 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f17,axiom,
! [X0] :
( one_sorted_str(X0)
=> ( empty_carrier(X0)
<=> empty(the_carrier(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_struct_0) ).
fof(f18,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> interior(X0,X1) = subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tops_1) ).
fof(f19,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f20,axiom,
! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& top_str(X0) )
=> element(interior(X0,X1),powerset(the_carrier(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tops_1) ).
fof(f23,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> element(subset_complement(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).
fof(f24,axiom,
! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& top_str(X0) )
=> element(topstr_closure(X0,X1),powerset(the_carrier(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_pre_topc) ).
fof(f25,axiom,
! [X0] :
( top_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
fof(f35,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( in(X2,subset_complement(the_carrier(X0),X1))
<=> ~ in(X2,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l40_tops_1) ).
fof(f42,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f43,conjecture,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset(interior(X0,X1),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_tops_1) ).
fof(f44,negated_conjecture,
~ ! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset(interior(X0,X1),X1) ) ),
inference(negated_conjecture,[],[f43]) ).
fof(f45,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset(X1,topstr_closure(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_pre_topc) ).
fof(f46,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f47,axiom,
! [X0,X1,X2] :
( element(X2,powerset(X0))
=> ~ ( in(X1,X2)
& in(X1,subset_complement(X0,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_subset_1) ).
fof(f48,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f68,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f79,plain,
! [X0] :
( ( empty_carrier(X0)
<=> empty(the_carrier(X0)) )
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f80,plain,
! [X0] :
( ! [X1] :
( interior(X0,X1) = subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1)))
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f81,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f82,plain,
! [X0,X1] :
( element(interior(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f83,plain,
! [X0,X1] :
( element(interior(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(flattening,[],[f82]) ).
fof(f84,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f23]) ).
fof(f85,plain,
! [X0,X1] :
( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f86,plain,
! [X0,X1] :
( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(flattening,[],[f85]) ).
fof(f87,plain,
! [X0] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f91,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( in(X2,subset_complement(the_carrier(X0),X1))
<=> ~ in(X2,X1) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f92,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( in(X2,subset_complement(the_carrier(X0),X1))
<=> ~ in(X2,X1) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f91]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ~ subset(interior(X0,X1),X1)
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f99,plain,
! [X0] :
( ! [X1] :
( subset(X1,topstr_closure(X0,X1))
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f45]) ).
fof(f100,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f46]) ).
fof(f101,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f100]) ).
fof(f102,plain,
! [X0,X1,X2] :
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0)) ),
inference(ennf_transformation,[],[f47]) ).
fof(f103,plain,
! [X0,X1,X2] :
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0)) ),
inference(flattening,[],[f102]) ).
fof(f104,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f48]) ).
fof(f108,plain,
! [X0] :
( ( ( empty_carrier(X0)
| ~ empty(the_carrier(X0)) )
& ( empty(the_carrier(X0))
| ~ empty_carrier(X0) ) )
| ~ one_sorted_str(X0) ),
inference(nnf_transformation,[],[f79]) ).
fof(f109,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f81]) ).
fof(f110,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f109]) ).
fof(f111,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK0(X0,X1),X1)
& in(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f112,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK0(X0,X1),X1)
& in(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f110,f111]) ).
fof(f119,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( in(X2,subset_complement(the_carrier(X0),X1))
| in(X2,X1) )
& ( ~ in(X2,X1)
| ~ in(X2,subset_complement(the_carrier(X0),X1)) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(nnf_transformation,[],[f92]) ).
fof(f126,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f42]) ).
fof(f127,plain,
( ? [X0] :
( ? [X1] :
( ~ subset(interior(X0,X1),X1)
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0) )
=> ( ? [X1] :
( ~ subset(interior(sK7,X1),X1)
& element(X1,powerset(the_carrier(sK7))) )
& top_str(sK7) ) ),
introduced(choice_axiom,[]) ).
fof(f128,plain,
( ? [X1] :
( ~ subset(interior(sK7,X1),X1)
& element(X1,powerset(the_carrier(sK7))) )
=> ( ~ subset(interior(sK7,sK8),sK8)
& element(sK8,powerset(the_carrier(sK7))) ) ),
introduced(choice_axiom,[]) ).
fof(f129,plain,
( ~ subset(interior(sK7,sK8),sK8)
& element(sK8,powerset(the_carrier(sK7)))
& top_str(sK7) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f98,f128,f127]) ).
fof(f130,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f155,plain,
! [X0] :
( empty(the_carrier(X0))
| ~ empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f157,plain,
! [X0,X1] :
( interior(X0,X1) = subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f158,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f112]) ).
fof(f159,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f160,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f112]) ).
fof(f161,plain,
! [X0,X1] :
( element(interior(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f162,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f84]) ).
fof(f163,plain,
! [X0,X1] :
( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f164,plain,
! [X0] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f177,plain,
! [X2,X0,X1] :
( in(X2,subset_complement(the_carrier(X0),X1))
| in(X2,X1)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f191,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f126]) ).
fof(f192,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f126]) ).
fof(f193,plain,
top_str(sK7),
inference(cnf_transformation,[],[f129]) ).
fof(f194,plain,
element(sK8,powerset(the_carrier(sK7))),
inference(cnf_transformation,[],[f129]) ).
fof(f195,plain,
~ subset(interior(sK7,sK8),sK8),
inference(cnf_transformation,[],[f129]) ).
fof(f196,plain,
! [X0,X1] :
( subset(X1,topstr_closure(X0,X1))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f197,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f101]) ).
fof(f198,plain,
! [X2,X0,X1] :
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0)) ),
inference(cnf_transformation,[],[f103]) ).
fof(f199,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f104]) ).
cnf(c_49,plain,
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f130]) ).
cnf(c_75,plain,
( ~ empty_carrier(X0)
| ~ one_sorted_str(X0)
| empty(the_carrier(X0)) ),
inference(cnf_transformation,[],[f155]) ).
cnf(c_76,plain,
( ~ element(X0,powerset(the_carrier(X1)))
| ~ top_str(X1)
| subset_complement(the_carrier(X1),topstr_closure(X1,subset_complement(the_carrier(X1),X0))) = interior(X1,X0) ),
inference(cnf_transformation,[],[f157]) ).
cnf(c_77,plain,
( ~ in(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f160]) ).
cnf(c_78,plain,
( in(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f159]) ).
cnf(c_79,plain,
( ~ in(X0,X1)
| ~ subset(X1,X2)
| in(X0,X2) ),
inference(cnf_transformation,[],[f158]) ).
cnf(c_80,plain,
( ~ element(X0,powerset(the_carrier(X1)))
| ~ top_str(X1)
| element(interior(X1,X0),powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f161]) ).
cnf(c_81,plain,
( ~ element(X0,powerset(X1))
| element(subset_complement(X1,X0),powerset(X1)) ),
inference(cnf_transformation,[],[f162]) ).
cnf(c_82,plain,
( ~ element(X0,powerset(the_carrier(X1)))
| ~ top_str(X1)
| element(topstr_closure(X1,X0),powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f163]) ).
cnf(c_83,plain,
( ~ top_str(X0)
| one_sorted_str(X0) ),
inference(cnf_transformation,[],[f164]) ).
cnf(c_95,plain,
( ~ element(X0,powerset(the_carrier(X1)))
| ~ element(X2,the_carrier(X1))
| ~ one_sorted_str(X1)
| in(X2,subset_complement(the_carrier(X1),X0))
| in(X2,X0)
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f177]) ).
cnf(c_110,plain,
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f192]) ).
cnf(c_111,plain,
( ~ element(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f191]) ).
cnf(c_112,negated_conjecture,
~ subset(interior(sK7,sK8),sK8),
inference(cnf_transformation,[],[f195]) ).
cnf(c_113,negated_conjecture,
element(sK8,powerset(the_carrier(sK7))),
inference(cnf_transformation,[],[f194]) ).
cnf(c_114,negated_conjecture,
top_str(sK7),
inference(cnf_transformation,[],[f193]) ).
cnf(c_115,plain,
( ~ element(X0,powerset(the_carrier(X1)))
| ~ top_str(X1)
| subset(X0,topstr_closure(X1,X0)) ),
inference(cnf_transformation,[],[f196]) ).
cnf(c_116,plain,
( ~ element(X0,powerset(X1))
| ~ in(X2,X0)
| element(X2,X1) ),
inference(cnf_transformation,[],[f197]) ).
cnf(c_117,plain,
( ~ in(X0,subset_complement(X1,X2))
| ~ element(X2,powerset(X1))
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f198]) ).
cnf(c_118,plain,
( ~ element(X0,powerset(X1))
| ~ in(X2,X0)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f199]) ).
cnf(c_143,plain,
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(prop_impl_just,[status(thm)],[c_110]) ).
cnf(c_189,plain,
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(prop_impl_just,[status(thm)],[c_83]) ).
cnf(c_190,plain,
( ~ top_str(X0)
| one_sorted_str(X0) ),
inference(renaming,[status(thm)],[c_189]) ).
cnf(c_191,plain,
( ~ in(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_77]) ).
cnf(c_193,plain,
( ~ subset(X0,X1)
| element(subset_complement(X1,X0),powerset(X1)) ),
inference(prop_impl_just,[status(thm)],[c_110,c_81]) ).
cnf(c_203,plain,
( subset(X0,X1)
| in(sK0(X0,X1),X0) ),
inference(prop_impl_just,[status(thm)],[c_78]) ).
cnf(c_204,plain,
( in(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(renaming,[status(thm)],[c_203]) ).
cnf(c_317,plain,
( ~ in(X0,X1)
| ~ subset(X1,X2)
| element(X0,X2) ),
inference(bin_hyper_res,[status(thm)],[c_116,c_143]) ).
cnf(c_318,plain,
( ~ in(X0,X1)
| ~ subset(X1,X2)
| ~ empty(X2) ),
inference(bin_hyper_res,[status(thm)],[c_118,c_143]) ).
cnf(c_685,plain,
( X0 != sK7
| ~ element(X1,powerset(the_carrier(X0)))
| subset(X1,topstr_closure(X0,X1)) ),
inference(resolution_lifted,[status(thm)],[c_115,c_114]) ).
cnf(c_686,plain,
( ~ element(X0,powerset(the_carrier(sK7)))
| subset(X0,topstr_closure(sK7,X0)) ),
inference(unflattening,[status(thm)],[c_685]) ).
cnf(c_694,plain,
( X0 != sK7
| ~ element(X1,powerset(the_carrier(X0)))
| element(topstr_closure(X0,X1),powerset(the_carrier(X0))) ),
inference(resolution_lifted,[status(thm)],[c_82,c_114]) ).
cnf(c_695,plain,
( ~ element(X0,powerset(the_carrier(sK7)))
| element(topstr_closure(sK7,X0),powerset(the_carrier(sK7))) ),
inference(unflattening,[status(thm)],[c_694]) ).
cnf(c_703,plain,
( X0 != sK7
| ~ element(X1,powerset(the_carrier(X0)))
| element(interior(X0,X1),powerset(the_carrier(X0))) ),
inference(resolution_lifted,[status(thm)],[c_80,c_114]) ).
cnf(c_704,plain,
( ~ element(X0,powerset(the_carrier(sK7)))
| element(interior(sK7,X0),powerset(the_carrier(sK7))) ),
inference(unflattening,[status(thm)],[c_703]) ).
cnf(c_712,plain,
( X0 != sK7
| ~ element(X1,powerset(the_carrier(X0)))
| subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1))) = interior(X0,X1) ),
inference(resolution_lifted,[status(thm)],[c_76,c_114]) ).
cnf(c_713,plain,
( ~ element(X0,powerset(the_carrier(sK7)))
| subset_complement(the_carrier(sK7),topstr_closure(sK7,subset_complement(the_carrier(sK7),X0))) = interior(sK7,X0) ),
inference(unflattening,[status(thm)],[c_712]) ).
cnf(c_726,plain,
( X0 != sK7
| one_sorted_str(X0) ),
inference(resolution_lifted,[status(thm)],[c_190,c_114]) ).
cnf(c_727,plain,
one_sorted_str(sK7),
inference(unflattening,[status(thm)],[c_726]) ).
cnf(c_906,plain,
( X0 != sK7
| ~ element(X1,powerset(the_carrier(X0)))
| ~ element(X2,the_carrier(X0))
| in(X2,subset_complement(the_carrier(X0),X1))
| in(X2,X1)
| empty_carrier(X0) ),
inference(resolution_lifted,[status(thm)],[c_95,c_727]) ).
cnf(c_907,plain,
( ~ element(X0,powerset(the_carrier(sK7)))
| ~ element(X1,the_carrier(sK7))
| in(X1,subset_complement(the_carrier(sK7),X0))
| in(X1,X0)
| empty_carrier(sK7) ),
inference(unflattening,[status(thm)],[c_906]) ).
cnf(c_1027,plain,
( X0 != sK7
| ~ empty_carrier(X0)
| empty(the_carrier(X0)) ),
inference(resolution_lifted,[status(thm)],[c_75,c_727]) ).
cnf(c_1028,plain,
( ~ empty_carrier(sK7)
| empty(the_carrier(sK7)) ),
inference(unflattening,[status(thm)],[c_1027]) ).
cnf(c_1274,plain,
( interior(sK7,sK8) != X0
| X1 != sK8
| in(sK0(X0,X1),X0) ),
inference(resolution_lifted,[status(thm)],[c_204,c_112]) ).
cnf(c_1275,plain,
in(sK0(interior(sK7,sK8),sK8),interior(sK7,sK8)),
inference(unflattening,[status(thm)],[c_1274]) ).
cnf(c_1279,plain,
( interior(sK7,sK8) != X0
| X1 != sK8
| ~ in(sK0(X0,X1),X1) ),
inference(resolution_lifted,[status(thm)],[c_191,c_112]) ).
cnf(c_1280,plain,
~ in(sK0(interior(sK7,sK8),sK8),sK8),
inference(unflattening,[status(thm)],[c_1279]) ).
cnf(c_2202,plain,
( ~ subset(X0,X1)
| element(subset_complement(X1,X0),powerset(X1)) ),
inference(prop_impl_just,[status(thm)],[c_193]) ).
cnf(c_2236,plain,
( ~ element(X0,powerset(the_carrier(sK7)))
| subset(X0,topstr_closure(sK7,X0)) ),
inference(prop_impl_just,[status(thm)],[c_686]) ).
cnf(c_2238,plain,
( ~ element(X0,powerset(the_carrier(sK7)))
| element(topstr_closure(sK7,X0),powerset(the_carrier(sK7))) ),
inference(prop_impl_just,[status(thm)],[c_695]) ).
cnf(c_2240,plain,
( ~ element(X0,powerset(the_carrier(sK7)))
| element(interior(sK7,X0),powerset(the_carrier(sK7))) ),
inference(prop_impl_just,[status(thm)],[c_704]) ).
cnf(c_2242,plain,
( ~ element(X0,powerset(the_carrier(sK7)))
| subset_complement(the_carrier(sK7),topstr_closure(sK7,subset_complement(the_carrier(sK7),X0))) = interior(sK7,X0) ),
inference(prop_impl_just,[status(thm)],[c_713]) ).
cnf(c_3642,plain,
X0 = X0,
theory(equality) ).
cnf(c_3645,plain,
( X0 != X1
| X2 != X3
| ~ in(X1,X3)
| in(X0,X2) ),
theory(equality) ).
cnf(c_4685,plain,
( ~ subset(X0,the_carrier(sK7))
| ~ in(X1,X0)
| element(X1,the_carrier(sK7)) ),
inference(instantiation,[status(thm)],[c_317]) ).
cnf(c_4730,plain,
( ~ in(sK0(interior(sK7,sK8),sK8),interior(sK7,sK8))
| ~ subset(interior(sK7,sK8),the_carrier(sK7))
| element(sK0(interior(sK7,sK8),sK8),the_carrier(sK7)) ),
inference(instantiation,[status(thm)],[c_4685]) ).
cnf(c_4731,plain,
( ~ in(sK0(interior(sK7,sK8),sK8),interior(sK7,sK8))
| ~ subset(interior(sK7,sK8),X0)
| ~ empty(X0) ),
inference(instantiation,[status(thm)],[c_318]) ).
cnf(c_4764,plain,
( ~ element(interior(sK7,sK8),powerset(the_carrier(sK7)))
| subset(interior(sK7,sK8),the_carrier(sK7)) ),
inference(instantiation,[status(thm)],[c_111]) ).
cnf(c_4793,plain,
( X0 != sK0(interior(sK7,sK8),sK8)
| X1 != interior(sK7,sK8)
| ~ in(sK0(interior(sK7,sK8),sK8),interior(sK7,sK8))
| in(X0,X1) ),
inference(instantiation,[status(thm)],[c_3645]) ).
cnf(c_4960,plain,
( ~ element(sK8,powerset(the_carrier(sK7)))
| element(interior(sK7,sK8),powerset(the_carrier(sK7))) ),
inference(instantiation,[status(thm)],[c_2240]) ).
cnf(c_5060,plain,
( ~ element(sK0(interior(sK7,sK8),sK8),the_carrier(sK7))
| ~ element(X0,powerset(the_carrier(sK7)))
| in(sK0(interior(sK7,sK8),sK8),subset_complement(the_carrier(sK7),X0))
| in(sK0(interior(sK7,sK8),sK8),X0)
| empty_carrier(sK7) ),
inference(instantiation,[status(thm)],[c_907]) ).
cnf(c_5099,plain,
( ~ in(sK0(interior(sK7,sK8),sK8),interior(sK7,sK8))
| ~ subset(interior(sK7,sK8),the_carrier(sK7))
| ~ empty(the_carrier(sK7)) ),
inference(instantiation,[status(thm)],[c_4731]) ).
cnf(c_5123,plain,
( ~ in(X0,subset_complement(the_carrier(sK7),X1))
| ~ element(X1,powerset(the_carrier(sK7)))
| ~ in(X0,X1) ),
inference(instantiation,[status(thm)],[c_117]) ).
cnf(c_5170,plain,
( subset_complement(the_carrier(sK7),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8))) != interior(sK7,sK8)
| X0 != sK0(interior(sK7,sK8),sK8)
| ~ in(sK0(interior(sK7,sK8),sK8),interior(sK7,sK8))
| in(X0,subset_complement(the_carrier(sK7),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)))) ),
inference(instantiation,[status(thm)],[c_4793]) ).
cnf(c_5172,plain,
( in(X1,X0)
| in(X1,subset_complement(the_carrier(sK7),X0))
| ~ element(X1,the_carrier(sK7))
| ~ element(X0,powerset(the_carrier(sK7))) ),
inference(global_subsumption_just,[status(thm)],[c_907,c_113,c_907,c_1028,c_1275,c_4764,c_4960,c_5099]) ).
cnf(c_5173,plain,
( ~ element(X0,powerset(the_carrier(sK7)))
| ~ element(X1,the_carrier(sK7))
| in(X1,subset_complement(the_carrier(sK7),X0))
| in(X1,X0) ),
inference(renaming,[status(thm)],[c_5172]) ).
cnf(c_5266,plain,
subset(sK8,the_carrier(sK7)),
inference(superposition,[status(thm)],[c_113,c_111]) ).
cnf(c_5336,plain,
( ~ element(sK0(X0,subset_complement(the_carrier(sK7),X1)),the_carrier(sK7))
| ~ element(X1,powerset(the_carrier(sK7)))
| in(sK0(X0,subset_complement(the_carrier(sK7),X1)),X1)
| subset(X0,subset_complement(the_carrier(sK7),X1)) ),
inference(superposition,[status(thm)],[c_5173,c_77]) ).
cnf(c_5539,plain,
( ~ subset(X0,the_carrier(sK7))
| element(subset_complement(the_carrier(sK7),X0),powerset(the_carrier(sK7))) ),
inference(instantiation,[status(thm)],[c_2202]) ).
cnf(c_6532,plain,
( ~ element(sK8,powerset(the_carrier(sK7)))
| subset_complement(the_carrier(sK7),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8))) = interior(sK7,sK8) ),
inference(instantiation,[status(thm)],[c_2242]) ).
cnf(c_8671,plain,
( ~ in(sK0(interior(sK7,sK8),sK8),subset_complement(the_carrier(sK7),X0))
| ~ subset(subset_complement(the_carrier(sK7),X0),X1)
| in(sK0(interior(sK7,sK8),sK8),X1) ),
inference(instantiation,[status(thm)],[c_79]) ).
cnf(c_8692,plain,
( ~ in(sK0(interior(sK7,sK8),sK8),subset_complement(the_carrier(sK7),X0))
| ~ in(sK0(interior(sK7,sK8),sK8),X0)
| ~ element(X0,powerset(the_carrier(sK7))) ),
inference(instantiation,[status(thm)],[c_5123]) ).
cnf(c_9735,plain,
( subset_complement(the_carrier(sK7),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8))) != interior(sK7,sK8)
| sK0(interior(sK7,sK8),sK8) != sK0(interior(sK7,sK8),sK8)
| ~ in(sK0(interior(sK7,sK8),sK8),interior(sK7,sK8))
| in(sK0(interior(sK7,sK8),sK8),subset_complement(the_carrier(sK7),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)))) ),
inference(instantiation,[status(thm)],[c_5170]) ).
cnf(c_9931,plain,
( ~ element(subset_complement(the_carrier(sK7),sK8),powerset(the_carrier(sK7)))
| subset(subset_complement(the_carrier(sK7),sK8),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8))) ),
inference(instantiation,[status(thm)],[c_2236]) ).
cnf(c_10009,plain,
( ~ subset(sK8,the_carrier(sK7))
| element(subset_complement(the_carrier(sK7),sK8),powerset(the_carrier(sK7))) ),
inference(instantiation,[status(thm)],[c_5539]) ).
cnf(c_15468,plain,
sK0(interior(sK7,sK8),sK8) = sK0(interior(sK7,sK8),sK8),
inference(instantiation,[status(thm)],[c_3642]) ).
cnf(c_18555,plain,
( ~ in(sK0(interior(sK7,sK8),sK8),subset_complement(the_carrier(sK7),sK8))
| ~ subset(subset_complement(the_carrier(sK7),sK8),X0)
| in(sK0(interior(sK7,sK8),sK8),X0) ),
inference(instantiation,[status(thm)],[c_8671]) ).
cnf(c_26970,plain,
( ~ element(sK0(interior(sK7,sK8),sK8),the_carrier(sK7))
| ~ element(sK8,powerset(the_carrier(sK7)))
| in(sK0(interior(sK7,sK8),sK8),subset_complement(the_carrier(sK7),sK8))
| in(sK0(interior(sK7,sK8),sK8),sK8)
| empty_carrier(sK7) ),
inference(instantiation,[status(thm)],[c_5060]) ).
cnf(c_43122,plain,
subset_complement(the_carrier(sK7),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8))) = interior(sK7,sK8),
inference(superposition,[status(thm)],[c_113,c_2242]) ).
cnf(c_43144,plain,
( ~ element(topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)),powerset(the_carrier(sK7)))
| ~ element(sK0(X0,interior(sK7,sK8)),the_carrier(sK7))
| in(sK0(X0,subset_complement(the_carrier(sK7),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)))),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)))
| subset(X0,subset_complement(the_carrier(sK7),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)))) ),
inference(superposition,[status(thm)],[c_43122,c_5336]) ).
cnf(c_43245,plain,
( ~ in(topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)),sK0(X0,subset_complement(the_carrier(sK7),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)))))
| ~ element(topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)),powerset(the_carrier(sK7)))
| ~ element(sK0(X0,interior(sK7,sK8)),the_carrier(sK7))
| subset(X0,subset_complement(the_carrier(sK7),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)))) ),
inference(superposition,[status(thm)],[c_43144,c_49]) ).
cnf(c_50490,plain,
( ~ subset(subset_complement(the_carrier(sK7),sK8),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)))
| ~ in(sK0(interior(sK7,sK8),sK8),subset_complement(the_carrier(sK7),sK8))
| in(sK0(interior(sK7,sK8),sK8),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8))) ),
inference(instantiation,[status(thm)],[c_18555]) ).
cnf(c_57530,plain,
( ~ in(sK0(interior(sK7,sK8),sK8),subset_complement(the_carrier(sK7),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8))))
| ~ in(sK0(interior(sK7,sK8),sK8),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)))
| ~ element(topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)),powerset(the_carrier(sK7))) ),
inference(instantiation,[status(thm)],[c_8692]) ).
cnf(c_58335,plain,
~ element(topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)),powerset(the_carrier(sK7))),
inference(global_subsumption_just,[status(thm)],[c_43245,c_113,c_1028,c_1275,c_1280,c_4730,c_4764,c_4960,c_5099,c_5266,c_6532,c_9735,c_9931,c_10009,c_15468,c_26970,c_50490,c_57530]) ).
cnf(c_58338,plain,
~ element(subset_complement(the_carrier(sK7),sK8),powerset(the_carrier(sK7))),
inference(superposition,[status(thm)],[c_2238,c_58335]) ).
cnf(c_58339,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_58338,c_10009,c_5266]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU322+1 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.14 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n018.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 18:01:16 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 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
% 17.58/3.21 % SZS status Started for theBenchmark.p
% 17.58/3.21 % SZS status Theorem for theBenchmark.p
% 17.58/3.21
% 17.58/3.21 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 17.58/3.21
% 17.58/3.21 ------ iProver source info
% 17.58/3.21
% 17.58/3.21 git: date: 2024-05-02 19:28:25 +0000
% 17.58/3.21 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 17.58/3.21 git: non_committed_changes: false
% 17.58/3.21
% 17.58/3.21 ------ Parsing...
% 17.58/3.21 ------ Clausification by vclausify_rel & Parsing by iProver...
% 17.58/3.21
% 17.58/3.21 ------ Preprocessing... sup_sim: 0 sf_s rm: 40 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
% 17.58/3.21
% 17.58/3.21 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 17.58/3.21
% 17.58/3.21 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 17.58/3.21 ------ Proving...
% 17.58/3.21 ------ Problem Properties
% 17.58/3.21
% 17.58/3.21
% 17.58/3.21 clauses 50
% 17.58/3.21 conjectures 2
% 17.58/3.21 EPR 13
% 17.58/3.21 Horn 41
% 17.58/3.21 unary 10
% 17.58/3.21 binary 30
% 17.58/3.21 lits 107
% 17.58/3.21 lits eq 5
% 17.58/3.21 fd_pure 0
% 17.58/3.21 fd_pseudo 0
% 17.58/3.21 fd_cond 1
% 17.58/3.21 fd_pseudo_cond 1
% 17.58/3.21 AC symbols 0
% 17.58/3.21
% 17.58/3.21 ------ Input Options Time Limit: Unbounded
% 17.58/3.21
% 17.58/3.21
% 17.58/3.21 ------
% 17.58/3.21 Current options:
% 17.58/3.21 ------
% 17.58/3.21
% 17.58/3.21
% 17.58/3.21
% 17.58/3.21
% 17.58/3.21 ------ Proving...
% 17.58/3.21
% 17.58/3.21
% 17.58/3.21 % SZS status Theorem for theBenchmark.p
% 17.58/3.21
% 17.58/3.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.58/3.22
% 17.58/3.22
%------------------------------------------------------------------------------