TSTP Solution File: LCL950_17 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : LCL950_17 : TPTP v8.2.0. Released v8.2.0.
% 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 : Fri May 3 02:40:21 EDT 2024
% Result : Theorem 1.78s 1.11s
% Output : CNFRefutation 1.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 15
% Syntax : Number of formulae : 52 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 598 ( 0 equ)
% Maximal formula atoms : 26 ( 11 avg)
% Number of connectives : 580 ( 178 ~; 150 |; 181 &)
% ( 0 <=>; 71 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 10 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 144 ( 144 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 18 ( 17 usr; 11 prp; 0-3 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 323 ( 12 sgn 162 !; 108 ?; 197 :)
% Comments :
%------------------------------------------------------------------------------
tff(f1,axiom,
! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_universal) ).
tff(f2,axiom,
! [X0: '$ki_world',X2] : '$ki_exists_in_world_$i'(X0,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$ki_exists_in_world_$i_const') ).
tff(f4,axiom,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X3] :
( '$ki_exists_in_world_$i'(X0,X3)
=> ! [X4: '$ki_world'] :
( '$ki_accessible'(X0,X4)
=> ! [X5] :
( '$ki_exists_in_world_$i'(X4,X5)
=> ( ! [X6: '$ki_world'] :
( '$ki_accessible'(X4,X6)
=> ( ? [X8] :
( ! [X7: '$ki_world'] :
( '$ki_accessible'(X6,X7)
=> member(X7,X8,X5) )
& ! [X7: '$ki_world'] :
( '$ki_accessible'(X6,X7)
=> member(X7,X8,X3) )
& '$ki_exists_in_world_$i'(X6,X8) )
=> ! [X7: '$ki_world'] :
( '$ki_accessible'(X6,X7)
=> intersect(X7,X3,X5) ) ) )
& ! [X6: '$ki_world'] :
( '$ki_accessible'(X4,X6)
=> ( ! [X7: '$ki_world'] :
( '$ki_accessible'(X6,X7)
=> intersect(X7,X3,X5) )
=> ? [X8] :
( ! [X7: '$ki_world'] :
( '$ki_accessible'(X6,X7)
=> member(X7,X8,X5) )
& ! [X7: '$ki_world'] :
( '$ki_accessible'(X6,X7)
=> member(X7,X8,X3) )
& '$ki_exists_in_world_$i'(X6,X8) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersect_defn) ).
tff(f6,conjecture,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X3] :
( '$ki_exists_in_world_$i'(X0,X3)
=> ! [X4: '$ki_world'] :
( '$ki_accessible'(X0,X4)
=> ! [X5] :
( '$ki_exists_in_world_$i'(X4,X5)
=> ! [X6: '$ki_world'] :
( '$ki_accessible'(X4,X6)
=> ! [X8] :
( '$ki_exists_in_world_$i'(X6,X8)
=> ! [X7: '$ki_world'] :
( '$ki_accessible'(X6,X7)
=> ( ( ! [X9: '$ki_world'] :
( '$ki_accessible'(X7,X9)
=> member(X9,X3,X8) )
& ! [X9: '$ki_world'] :
( '$ki_accessible'(X7,X9)
=> member(X9,X3,X5) ) )
=> ! [X9: '$ki_world'] :
( '$ki_accessible'(X7,X9)
=> intersect(X9,X5,X8) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).
tff(f7,negated_conjecture,
~ ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X3] :
( '$ki_exists_in_world_$i'(X0,X3)
=> ! [X4: '$ki_world'] :
( '$ki_accessible'(X0,X4)
=> ! [X5] :
( '$ki_exists_in_world_$i'(X4,X5)
=> ! [X6: '$ki_world'] :
( '$ki_accessible'(X4,X6)
=> ! [X8] :
( '$ki_exists_in_world_$i'(X6,X8)
=> ! [X7: '$ki_world'] :
( '$ki_accessible'(X6,X7)
=> ( ( ! [X9: '$ki_world'] :
( '$ki_accessible'(X7,X9)
=> member(X9,X3,X8) )
& ! [X9: '$ki_world'] :
( '$ki_accessible'(X7,X9)
=> member(X9,X3,X5) ) )
=> ! [X9: '$ki_world'] :
( '$ki_accessible'(X7,X9)
=> intersect(X9,X5,X8) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[],[f6]) ).
tff(f8,plain,
! [X0: '$ki_world',X1] : '$ki_exists_in_world_$i'(X0,X1),
inference(rectify,[],[f2]) ).
tff(f10,plain,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X1] :
( '$ki_exists_in_world_$i'(X0,X1)
=> ! [X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
=> ! [X3] :
( '$ki_exists_in_world_$i'(X2,X3)
=> ( ! [X4: '$ki_world'] :
( '$ki_accessible'(X2,X4)
=> ( ? [X5] :
( ! [X6: '$ki_world'] :
( '$ki_accessible'(X4,X6)
=> member(X6,X5,X3) )
& ! [X7: '$ki_world'] :
( '$ki_accessible'(X4,X7)
=> member(X7,X5,X1) )
& '$ki_exists_in_world_$i'(X4,X5) )
=> ! [X8: '$ki_world'] :
( '$ki_accessible'(X4,X8)
=> intersect(X8,X1,X3) ) ) )
& ! [X9: '$ki_world'] :
( '$ki_accessible'(X2,X9)
=> ( ! [X10: '$ki_world'] :
( '$ki_accessible'(X9,X10)
=> intersect(X10,X1,X3) )
=> ? [X11] :
( ! [X12: '$ki_world'] :
( '$ki_accessible'(X9,X12)
=> member(X12,X11,X3) )
& ! [X13: '$ki_world'] :
( '$ki_accessible'(X9,X13)
=> member(X13,X11,X1) )
& '$ki_exists_in_world_$i'(X9,X11) ) ) ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
tff(f12,plain,
~ ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X1] :
( '$ki_exists_in_world_$i'(X0,X1)
=> ! [X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
=> ! [X3] :
( '$ki_exists_in_world_$i'(X2,X3)
=> ! [X4: '$ki_world'] :
( '$ki_accessible'(X2,X4)
=> ! [X5] :
( '$ki_exists_in_world_$i'(X4,X5)
=> ! [X6: '$ki_world'] :
( '$ki_accessible'(X4,X6)
=> ( ( ! [X7: '$ki_world'] :
( '$ki_accessible'(X6,X7)
=> member(X7,X1,X5) )
& ! [X8: '$ki_world'] :
( '$ki_accessible'(X6,X8)
=> member(X8,X1,X3) ) )
=> ! [X9: '$ki_world'] :
( '$ki_accessible'(X6,X9)
=> intersect(X9,X3,X5) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f7]) ).
tff(f13,plain,
! [X0: '$ki_world'] :
( ! [X1] :
( ! [X2: '$ki_world'] :
( ! [X3] :
( ( ! [X4: '$ki_world'] :
( ! [X8: '$ki_world'] :
( intersect(X8,X1,X3)
| ~ '$ki_accessible'(X4,X8) )
| ! [X5] :
( ? [X6: '$ki_world'] :
( ~ member(X6,X5,X3)
& '$ki_accessible'(X4,X6) )
| ? [X7: '$ki_world'] :
( ~ member(X7,X5,X1)
& '$ki_accessible'(X4,X7) )
| ~ '$ki_exists_in_world_$i'(X4,X5) )
| ~ '$ki_accessible'(X2,X4) )
& ! [X9: '$ki_world'] :
( ? [X11] :
( ! [X12: '$ki_world'] :
( member(X12,X11,X3)
| ~ '$ki_accessible'(X9,X12) )
& ! [X13: '$ki_world'] :
( member(X13,X11,X1)
| ~ '$ki_accessible'(X9,X13) )
& '$ki_exists_in_world_$i'(X9,X11) )
| ? [X10: '$ki_world'] :
( ~ intersect(X10,X1,X3)
& '$ki_accessible'(X9,X10) )
| ~ '$ki_accessible'(X2,X9) ) )
| ~ '$ki_exists_in_world_$i'(X2,X3) )
| ~ '$ki_accessible'(X0,X2) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(ennf_transformation,[],[f10]) ).
tff(f14,plain,
! [X0: '$ki_world'] :
( ! [X1] :
( ! [X2: '$ki_world'] :
( ! [X3] :
( ( ! [X4: '$ki_world'] :
( ! [X8: '$ki_world'] :
( intersect(X8,X1,X3)
| ~ '$ki_accessible'(X4,X8) )
| ! [X5] :
( ? [X6: '$ki_world'] :
( ~ member(X6,X5,X3)
& '$ki_accessible'(X4,X6) )
| ? [X7: '$ki_world'] :
( ~ member(X7,X5,X1)
& '$ki_accessible'(X4,X7) )
| ~ '$ki_exists_in_world_$i'(X4,X5) )
| ~ '$ki_accessible'(X2,X4) )
& ! [X9: '$ki_world'] :
( ? [X11] :
( ! [X12: '$ki_world'] :
( member(X12,X11,X3)
| ~ '$ki_accessible'(X9,X12) )
& ! [X13: '$ki_world'] :
( member(X13,X11,X1)
| ~ '$ki_accessible'(X9,X13) )
& '$ki_exists_in_world_$i'(X9,X11) )
| ? [X10: '$ki_world'] :
( ~ intersect(X10,X1,X3)
& '$ki_accessible'(X9,X10) )
| ~ '$ki_accessible'(X2,X9) ) )
| ~ '$ki_exists_in_world_$i'(X2,X3) )
| ~ '$ki_accessible'(X0,X2) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(flattening,[],[f13]) ).
tff(f17,plain,
? [X0: '$ki_world'] :
( ? [X1] :
( ? [X2: '$ki_world'] :
( ? [X3] :
( ? [X4: '$ki_world'] :
( ? [X5] :
( ? [X6: '$ki_world'] :
( ? [X9: '$ki_world'] :
( ~ intersect(X9,X3,X5)
& '$ki_accessible'(X6,X9) )
& ! [X7: '$ki_world'] :
( member(X7,X1,X5)
| ~ '$ki_accessible'(X6,X7) )
& ! [X8: '$ki_world'] :
( member(X8,X1,X3)
| ~ '$ki_accessible'(X6,X8) )
& '$ki_accessible'(X4,X6) )
& '$ki_exists_in_world_$i'(X4,X5) )
& '$ki_accessible'(X2,X4) )
& '$ki_exists_in_world_$i'(X2,X3) )
& '$ki_accessible'(X0,X2) )
& '$ki_exists_in_world_$i'(X0,X1) )
& '$ki_accessible'('$ki_local_world',X0) ),
inference(ennf_transformation,[],[f12]) ).
tff(f18,plain,
? [X0: '$ki_world'] :
( ? [X1] :
( ? [X2: '$ki_world'] :
( ? [X3] :
( ? [X4: '$ki_world'] :
( ? [X5] :
( ? [X6: '$ki_world'] :
( ? [X9: '$ki_world'] :
( ~ intersect(X9,X3,X5)
& '$ki_accessible'(X6,X9) )
& ! [X7: '$ki_world'] :
( member(X7,X1,X5)
| ~ '$ki_accessible'(X6,X7) )
& ! [X8: '$ki_world'] :
( member(X8,X1,X3)
| ~ '$ki_accessible'(X6,X8) )
& '$ki_accessible'(X4,X6) )
& '$ki_exists_in_world_$i'(X4,X5) )
& '$ki_accessible'(X2,X4) )
& '$ki_exists_in_world_$i'(X2,X3) )
& '$ki_accessible'(X0,X2) )
& '$ki_exists_in_world_$i'(X0,X1) )
& '$ki_accessible'('$ki_local_world',X0) ),
inference(flattening,[],[f17]) ).
tff(f19,plain,
! [X3,X1,X2: '$ki_world'] :
( ! [X9: '$ki_world'] :
( ? [X11] :
( ! [X12: '$ki_world'] :
( member(X12,X11,X3)
| ~ '$ki_accessible'(X9,X12) )
& ! [X13: '$ki_world'] :
( member(X13,X11,X1)
| ~ '$ki_accessible'(X9,X13) )
& '$ki_exists_in_world_$i'(X9,X11) )
| ? [X10: '$ki_world'] :
( ~ intersect(X10,X1,X3)
& '$ki_accessible'(X9,X10) )
| ~ '$ki_accessible'(X2,X9) )
| ~ sP0(X3,X1,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f20,plain,
! [X0: '$ki_world'] :
( ! [X1] :
( ! [X2: '$ki_world'] :
( ! [X3] :
( ( ! [X4: '$ki_world'] :
( ! [X8: '$ki_world'] :
( intersect(X8,X1,X3)
| ~ '$ki_accessible'(X4,X8) )
| ! [X5] :
( ? [X6: '$ki_world'] :
( ~ member(X6,X5,X3)
& '$ki_accessible'(X4,X6) )
| ? [X7: '$ki_world'] :
( ~ member(X7,X5,X1)
& '$ki_accessible'(X4,X7) )
| ~ '$ki_exists_in_world_$i'(X4,X5) )
| ~ '$ki_accessible'(X2,X4) )
& sP0(X3,X1,X2) )
| ~ '$ki_exists_in_world_$i'(X2,X3) )
| ~ '$ki_accessible'(X0,X2) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(definition_folding,[],[f14,f19]) ).
tff(f28,plain,
! [X0: '$ki_world'] :
( ! [X1] :
( ! [X2: '$ki_world'] :
( ! [X3] :
( ( ! [X4: '$ki_world'] :
( ! [X5: '$ki_world'] :
( intersect(X5,X1,X3)
| ~ '$ki_accessible'(X4,X5) )
| ! [X6] :
( ? [X7: '$ki_world'] :
( ~ member(X7,X6,X3)
& '$ki_accessible'(X4,X7) )
| ? [X8: '$ki_world'] :
( ~ member(X8,X6,X1)
& '$ki_accessible'(X4,X8) )
| ~ '$ki_exists_in_world_$i'(X4,X6) )
| ~ '$ki_accessible'(X2,X4) )
& sP0(X3,X1,X2) )
| ~ '$ki_exists_in_world_$i'(X2,X3) )
| ~ '$ki_accessible'(X0,X2) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(rectify,[],[f20]) ).
tff(f29,plain,
! [X3,X4: '$ki_world',X6] :
( ? [X7: '$ki_world'] :
( ~ member(X7,X6,X3)
& '$ki_accessible'(X4,X7) )
=> ( ~ member(sK4(X3,X4,X6),X6,X3)
& '$ki_accessible'(X4,sK4(X3,X4,X6)) ) ),
introduced(choice_axiom,[]) ).
tff(f30,plain,
! [X1,X4: '$ki_world',X6] :
( ? [X8: '$ki_world'] :
( ~ member(X8,X6,X1)
& '$ki_accessible'(X4,X8) )
=> ( ~ member(sK5(X1,X4,X6),X6,X1)
& '$ki_accessible'(X4,sK5(X1,X4,X6)) ) ),
introduced(choice_axiom,[]) ).
tff(f31,plain,
! [X0: '$ki_world'] :
( ! [X1] :
( ! [X2: '$ki_world'] :
( ! [X3] :
( ( ! [X4: '$ki_world'] :
( ! [X5: '$ki_world'] :
( intersect(X5,X1,X3)
| ~ '$ki_accessible'(X4,X5) )
| ! [X6] :
( ( ~ member(sK4(X3,X4,X6),X6,X3)
& '$ki_accessible'(X4,sK4(X3,X4,X6)) )
| ( ~ member(sK5(X1,X4,X6),X6,X1)
& '$ki_accessible'(X4,sK5(X1,X4,X6)) )
| ~ '$ki_exists_in_world_$i'(X4,X6) )
| ~ '$ki_accessible'(X2,X4) )
& sP0(X3,X1,X2) )
| ~ '$ki_exists_in_world_$i'(X2,X3) )
| ~ '$ki_accessible'(X0,X2) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f28,f30,f29]) ).
tff(f35,plain,
? [X0: '$ki_world'] :
( ? [X1] :
( ? [X2: '$ki_world'] :
( ? [X3] :
( ? [X4: '$ki_world'] :
( ? [X5] :
( ? [X6: '$ki_world'] :
( ? [X7: '$ki_world'] :
( ~ intersect(X7,X3,X5)
& '$ki_accessible'(X6,X7) )
& ! [X8: '$ki_world'] :
( member(X8,X1,X5)
| ~ '$ki_accessible'(X6,X8) )
& ! [X9: '$ki_world'] :
( member(X9,X1,X3)
| ~ '$ki_accessible'(X6,X9) )
& '$ki_accessible'(X4,X6) )
& '$ki_exists_in_world_$i'(X4,X5) )
& '$ki_accessible'(X2,X4) )
& '$ki_exists_in_world_$i'(X2,X3) )
& '$ki_accessible'(X0,X2) )
& '$ki_exists_in_world_$i'(X0,X1) )
& '$ki_accessible'('$ki_local_world',X0) ),
inference(rectify,[],[f18]) ).
tff(f36,plain,
( ? [X0: '$ki_world'] :
( ? [X1] :
( ? [X2: '$ki_world'] :
( ? [X3] :
( ? [X4: '$ki_world'] :
( ? [X5] :
( ? [X6: '$ki_world'] :
( ? [X7: '$ki_world'] :
( ~ intersect(X7,X3,X5)
& '$ki_accessible'(X6,X7) )
& ! [X8: '$ki_world'] :
( member(X8,X1,X5)
| ~ '$ki_accessible'(X6,X8) )
& ! [X9: '$ki_world'] :
( member(X9,X1,X3)
| ~ '$ki_accessible'(X6,X9) )
& '$ki_accessible'(X4,X6) )
& '$ki_exists_in_world_$i'(X4,X5) )
& '$ki_accessible'(X2,X4) )
& '$ki_exists_in_world_$i'(X2,X3) )
& '$ki_accessible'(X0,X2) )
& '$ki_exists_in_world_$i'(X0,X1) )
& '$ki_accessible'('$ki_local_world',X0) )
=> ( ? [X1] :
( ? [X2: '$ki_world'] :
( ? [X3] :
( ? [X4: '$ki_world'] :
( ? [X5] :
( ? [X6: '$ki_world'] :
( ? [X7: '$ki_world'] :
( ~ intersect(X7,X3,X5)
& '$ki_accessible'(X6,X7) )
& ! [X8: '$ki_world'] :
( member(X8,X1,X5)
| ~ '$ki_accessible'(X6,X8) )
& ! [X9: '$ki_world'] :
( member(X9,X1,X3)
| ~ '$ki_accessible'(X6,X9) )
& '$ki_accessible'(X4,X6) )
& '$ki_exists_in_world_$i'(X4,X5) )
& '$ki_accessible'(X2,X4) )
& '$ki_exists_in_world_$i'(X2,X3) )
& '$ki_accessible'(sK7,X2) )
& '$ki_exists_in_world_$i'(sK7,X1) )
& '$ki_accessible'('$ki_local_world',sK7) ) ),
introduced(choice_axiom,[]) ).
tff(f37,plain,
( ? [X1] :
( ? [X2: '$ki_world'] :
( ? [X3] :
( ? [X4: '$ki_world'] :
( ? [X5] :
( ? [X6: '$ki_world'] :
( ? [X7: '$ki_world'] :
( ~ intersect(X7,X3,X5)
& '$ki_accessible'(X6,X7) )
& ! [X8: '$ki_world'] :
( member(X8,X1,X5)
| ~ '$ki_accessible'(X6,X8) )
& ! [X9: '$ki_world'] :
( member(X9,X1,X3)
| ~ '$ki_accessible'(X6,X9) )
& '$ki_accessible'(X4,X6) )
& '$ki_exists_in_world_$i'(X4,X5) )
& '$ki_accessible'(X2,X4) )
& '$ki_exists_in_world_$i'(X2,X3) )
& '$ki_accessible'(sK7,X2) )
& '$ki_exists_in_world_$i'(sK7,X1) )
=> ( ? [X2: '$ki_world'] :
( ? [X3] :
( ? [X4: '$ki_world'] :
( ? [X5] :
( ? [X6: '$ki_world'] :
( ? [X7: '$ki_world'] :
( ~ intersect(X7,X3,X5)
& '$ki_accessible'(X6,X7) )
& ! [X8: '$ki_world'] :
( member(X8,sK8,X5)
| ~ '$ki_accessible'(X6,X8) )
& ! [X9: '$ki_world'] :
( member(X9,sK8,X3)
| ~ '$ki_accessible'(X6,X9) )
& '$ki_accessible'(X4,X6) )
& '$ki_exists_in_world_$i'(X4,X5) )
& '$ki_accessible'(X2,X4) )
& '$ki_exists_in_world_$i'(X2,X3) )
& '$ki_accessible'(sK7,X2) )
& '$ki_exists_in_world_$i'(sK7,sK8) ) ),
introduced(choice_axiom,[]) ).
tff(f38,plain,
( ? [X2: '$ki_world'] :
( ? [X3] :
( ? [X4: '$ki_world'] :
( ? [X5] :
( ? [X6: '$ki_world'] :
( ? [X7: '$ki_world'] :
( ~ intersect(X7,X3,X5)
& '$ki_accessible'(X6,X7) )
& ! [X8: '$ki_world'] :
( member(X8,sK8,X5)
| ~ '$ki_accessible'(X6,X8) )
& ! [X9: '$ki_world'] :
( member(X9,sK8,X3)
| ~ '$ki_accessible'(X6,X9) )
& '$ki_accessible'(X4,X6) )
& '$ki_exists_in_world_$i'(X4,X5) )
& '$ki_accessible'(X2,X4) )
& '$ki_exists_in_world_$i'(X2,X3) )
& '$ki_accessible'(sK7,X2) )
=> ( ? [X3] :
( ? [X4: '$ki_world'] :
( ? [X5] :
( ? [X6: '$ki_world'] :
( ? [X7: '$ki_world'] :
( ~ intersect(X7,X3,X5)
& '$ki_accessible'(X6,X7) )
& ! [X8: '$ki_world'] :
( member(X8,sK8,X5)
| ~ '$ki_accessible'(X6,X8) )
& ! [X9: '$ki_world'] :
( member(X9,sK8,X3)
| ~ '$ki_accessible'(X6,X9) )
& '$ki_accessible'(X4,X6) )
& '$ki_exists_in_world_$i'(X4,X5) )
& '$ki_accessible'(sK9,X4) )
& '$ki_exists_in_world_$i'(sK9,X3) )
& '$ki_accessible'(sK7,sK9) ) ),
introduced(choice_axiom,[]) ).
tff(f39,plain,
( ? [X3] :
( ? [X4: '$ki_world'] :
( ? [X5] :
( ? [X6: '$ki_world'] :
( ? [X7: '$ki_world'] :
( ~ intersect(X7,X3,X5)
& '$ki_accessible'(X6,X7) )
& ! [X8: '$ki_world'] :
( member(X8,sK8,X5)
| ~ '$ki_accessible'(X6,X8) )
& ! [X9: '$ki_world'] :
( member(X9,sK8,X3)
| ~ '$ki_accessible'(X6,X9) )
& '$ki_accessible'(X4,X6) )
& '$ki_exists_in_world_$i'(X4,X5) )
& '$ki_accessible'(sK9,X4) )
& '$ki_exists_in_world_$i'(sK9,X3) )
=> ( ? [X4: '$ki_world'] :
( ? [X5] :
( ? [X6: '$ki_world'] :
( ? [X7: '$ki_world'] :
( ~ intersect(X7,sK10,X5)
& '$ki_accessible'(X6,X7) )
& ! [X8: '$ki_world'] :
( member(X8,sK8,X5)
| ~ '$ki_accessible'(X6,X8) )
& ! [X9: '$ki_world'] :
( member(X9,sK8,sK10)
| ~ '$ki_accessible'(X6,X9) )
& '$ki_accessible'(X4,X6) )
& '$ki_exists_in_world_$i'(X4,X5) )
& '$ki_accessible'(sK9,X4) )
& '$ki_exists_in_world_$i'(sK9,sK10) ) ),
introduced(choice_axiom,[]) ).
tff(f40,plain,
( ? [X4: '$ki_world'] :
( ? [X5] :
( ? [X6: '$ki_world'] :
( ? [X7: '$ki_world'] :
( ~ intersect(X7,sK10,X5)
& '$ki_accessible'(X6,X7) )
& ! [X8: '$ki_world'] :
( member(X8,sK8,X5)
| ~ '$ki_accessible'(X6,X8) )
& ! [X9: '$ki_world'] :
( member(X9,sK8,sK10)
| ~ '$ki_accessible'(X6,X9) )
& '$ki_accessible'(X4,X6) )
& '$ki_exists_in_world_$i'(X4,X5) )
& '$ki_accessible'(sK9,X4) )
=> ( ? [X5] :
( ? [X6: '$ki_world'] :
( ? [X7: '$ki_world'] :
( ~ intersect(X7,sK10,X5)
& '$ki_accessible'(X6,X7) )
& ! [X8: '$ki_world'] :
( member(X8,sK8,X5)
| ~ '$ki_accessible'(X6,X8) )
& ! [X9: '$ki_world'] :
( member(X9,sK8,sK10)
| ~ '$ki_accessible'(X6,X9) )
& '$ki_accessible'(sK11,X6) )
& '$ki_exists_in_world_$i'(sK11,X5) )
& '$ki_accessible'(sK9,sK11) ) ),
introduced(choice_axiom,[]) ).
tff(f41,plain,
( ? [X5] :
( ? [X6: '$ki_world'] :
( ? [X7: '$ki_world'] :
( ~ intersect(X7,sK10,X5)
& '$ki_accessible'(X6,X7) )
& ! [X8: '$ki_world'] :
( member(X8,sK8,X5)
| ~ '$ki_accessible'(X6,X8) )
& ! [X9: '$ki_world'] :
( member(X9,sK8,sK10)
| ~ '$ki_accessible'(X6,X9) )
& '$ki_accessible'(sK11,X6) )
& '$ki_exists_in_world_$i'(sK11,X5) )
=> ( ? [X6: '$ki_world'] :
( ? [X7: '$ki_world'] :
( ~ intersect(X7,sK10,sK12)
& '$ki_accessible'(X6,X7) )
& ! [X8: '$ki_world'] :
( member(X8,sK8,sK12)
| ~ '$ki_accessible'(X6,X8) )
& ! [X9: '$ki_world'] :
( member(X9,sK8,sK10)
| ~ '$ki_accessible'(X6,X9) )
& '$ki_accessible'(sK11,X6) )
& '$ki_exists_in_world_$i'(sK11,sK12) ) ),
introduced(choice_axiom,[]) ).
tff(f42,plain,
( ? [X6: '$ki_world'] :
( ? [X7: '$ki_world'] :
( ~ intersect(X7,sK10,sK12)
& '$ki_accessible'(X6,X7) )
& ! [X8: '$ki_world'] :
( member(X8,sK8,sK12)
| ~ '$ki_accessible'(X6,X8) )
& ! [X9: '$ki_world'] :
( member(X9,sK8,sK10)
| ~ '$ki_accessible'(X6,X9) )
& '$ki_accessible'(sK11,X6) )
=> ( ? [X7: '$ki_world'] :
( ~ intersect(X7,sK10,sK12)
& '$ki_accessible'(sK13,X7) )
& ! [X8: '$ki_world'] :
( member(X8,sK8,sK12)
| ~ '$ki_accessible'(sK13,X8) )
& ! [X9: '$ki_world'] :
( member(X9,sK8,sK10)
| ~ '$ki_accessible'(sK13,X9) )
& '$ki_accessible'(sK11,sK13) ) ),
introduced(choice_axiom,[]) ).
tff(f43,plain,
( ? [X7: '$ki_world'] :
( ~ intersect(X7,sK10,sK12)
& '$ki_accessible'(sK13,X7) )
=> ( ~ intersect(sK14,sK10,sK12)
& '$ki_accessible'(sK13,sK14) ) ),
introduced(choice_axiom,[]) ).
tff(f44,plain,
( ~ intersect(sK14,sK10,sK12)
& '$ki_accessible'(sK13,sK14)
& ! [X8: '$ki_world'] :
( member(X8,sK8,sK12)
| ~ '$ki_accessible'(sK13,X8) )
& ! [X9: '$ki_world'] :
( member(X9,sK8,sK10)
| ~ '$ki_accessible'(sK13,X9) )
& '$ki_accessible'(sK11,sK13)
& '$ki_exists_in_world_$i'(sK11,sK12)
& '$ki_accessible'(sK9,sK11)
& '$ki_exists_in_world_$i'(sK9,sK10)
& '$ki_accessible'(sK7,sK9)
& '$ki_exists_in_world_$i'(sK7,sK8)
& '$ki_accessible'('$ki_local_world',sK7) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10,sK11,sK12,sK13,sK14])],[f35,f43,f42,f41,f40,f39,f38,f37,f36]) ).
tff(f45,plain,
! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X0,X1),
inference(cnf_transformation,[],[f1]) ).
tff(f46,plain,
! [X0: '$ki_world',X1: $i] : '$ki_exists_in_world_$i'(X0,X1),
inference(cnf_transformation,[],[f8]) ).
tff(f58,plain,
! [X2: '$ki_world',X3: $i,X0: '$ki_world',X1: $i,X6: $i,X4: '$ki_world',X5: '$ki_world'] :
( intersect(X5,X1,X3)
| ~ '$ki_accessible'(X4,X5)
| ~ member(sK4(X3,X4,X6),X6,X3)
| ~ member(sK5(X1,X4,X6),X6,X1)
| ~ '$ki_exists_in_world_$i'(X4,X6)
| ~ '$ki_accessible'(X2,X4)
| ~ '$ki_exists_in_world_$i'(X2,X3)
| ~ '$ki_accessible'(X0,X2)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(cnf_transformation,[],[f31]) ).
tff(f68,plain,
! [X9: '$ki_world'] :
( member(X9,sK8,sK10)
| ~ '$ki_accessible'(sK13,X9) ),
inference(cnf_transformation,[],[f44]) ).
tff(f69,plain,
! [X8: '$ki_world'] :
( member(X8,sK8,sK12)
| ~ '$ki_accessible'(sK13,X8) ),
inference(cnf_transformation,[],[f44]) ).
tff(f71,plain,
~ intersect(sK14,sK10,sK12),
inference(cnf_transformation,[],[f44]) ).
cnf(c_49,plain,
'$ki_accessible'(X0_13,X1_13),
inference(cnf_transformation,[],[f45]) ).
cnf(c_50,plain,
'$ki_exists_in_world_$i'(X0_13,X0),
inference(cnf_transformation,[],[f46]) ).
cnf(c_58,plain,
( ~ member(sK4(X0,X0_13,X1),X1,X0)
| ~ member(sK5(X2,X0_13,X1),X1,X2)
| ~ '$ki_accessible'(X0_13,X2_13)
| ~ '$ki_accessible'(X1_13,X0_13)
| ~ '$ki_accessible'(X3_13,X1_13)
| ~ '$ki_exists_in_world_$i'(X0_13,X1)
| ~ '$ki_exists_in_world_$i'(X1_13,X0)
| ~ '$ki_exists_in_world_$i'(X3_13,X2)
| ~ '$ki_accessible'('$ki_local_world',X3_13)
| intersect(X2_13,X2,X0) ),
inference(cnf_transformation,[],[f58]) ).
cnf(c_65,negated_conjecture,
~ intersect(sK14,sK10,sK12),
inference(cnf_transformation,[],[f71]) ).
cnf(c_67,negated_conjecture,
( ~ '$ki_accessible'(sK13,X0_13)
| member(X0_13,sK8,sK12) ),
inference(cnf_transformation,[],[f69]) ).
cnf(c_68,negated_conjecture,
( ~ '$ki_accessible'(sK13,X0_13)
| member(X0_13,sK8,sK10) ),
inference(cnf_transformation,[],[f68]) ).
cnf(c_121,plain,
member(X0_13,sK8,sK12),
inference(backward_subsumption_resolution,[status(thm)],[c_67,c_49]) ).
cnf(c_122,plain,
member(X0_13,sK8,sK10),
inference(backward_subsumption_resolution,[status(thm)],[c_68,c_49]) ).
cnf(c_127,plain,
( ~ member(sK4(X0,X0_13,X1),X1,X0)
| ~ member(sK5(X2,X0_13,X1),X1,X2)
| ~ '$ki_accessible'(X0_13,X1_13)
| ~ '$ki_accessible'(X2_13,X0_13)
| ~ '$ki_accessible'(X3_13,X2_13)
| ~ '$ki_exists_in_world_$i'(X0_13,X1)
| ~ '$ki_exists_in_world_$i'(X2_13,X0)
| ~ '$ki_exists_in_world_$i'(X3_13,X2)
| intersect(X1_13,X2,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_58,c_49]) ).
cnf(c_128,plain,
( ~ member(sK5(X2,X0_13,X1),X1,X2)
| ~ member(sK4(X0,X0_13,X1),X1,X0)
| ~ '$ki_accessible'(X2_13,X0_13)
| ~ '$ki_accessible'(X3_13,X2_13)
| ~ '$ki_exists_in_world_$i'(X0_13,X1)
| ~ '$ki_exists_in_world_$i'(X2_13,X0)
| ~ '$ki_exists_in_world_$i'(X3_13,X2)
| intersect(X1_13,X2,X0) ),
inference(global_subsumption_just,[status(thm)],[c_127,c_49,c_127]) ).
cnf(c_129,plain,
( ~ member(sK4(X0,X0_13,X1),X1,X0)
| ~ member(sK5(X2,X0_13,X1),X1,X2)
| ~ '$ki_accessible'(X1_13,X0_13)
| ~ '$ki_accessible'(X2_13,X1_13)
| ~ '$ki_exists_in_world_$i'(X0_13,X1)
| ~ '$ki_exists_in_world_$i'(X1_13,X0)
| ~ '$ki_exists_in_world_$i'(X2_13,X2)
| intersect(X3_13,X2,X0) ),
inference(renaming,[status(thm)],[c_128]) ).
cnf(c_138,plain,
( ~ member(sK4(X0,X0_13,X1),X1,X0)
| ~ member(sK5(X2,X0_13,X1),X1,X2)
| ~ '$ki_accessible'(X1_13,X0_13)
| ~ '$ki_accessible'(X2_13,X1_13)
| ~ '$ki_exists_in_world_$i'(X1_13,X0)
| ~ '$ki_exists_in_world_$i'(X2_13,X2)
| intersect(X3_13,X2,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_129,c_50]) ).
cnf(c_192,plain,
( ~ member(sK4(X0,X0_13,X1),X1,X0)
| ~ member(sK5(X2,X0_13,X1),X1,X2)
| intersect(X1_13,X2,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_138,c_50,c_50,c_49,c_49]) ).
cnf(c_235,plain,
( ~ member(sK4(sK12,X0_13,X0),X0,sK12)
| ~ member(sK5(sK10,X0_13,X0),X0,sK10)
| intersect(sK14,sK10,sK12) ),
inference(instantiation,[status(thm)],[c_192]) ).
cnf(c_241,plain,
( ~ member(sK4(sK12,X0_13,sK8),sK8,sK12)
| ~ member(sK5(sK10,X0_13,sK8),sK8,sK10)
| intersect(sK14,sK10,sK12) ),
inference(instantiation,[status(thm)],[c_235]) ).
cnf(c_242,plain,
member(sK4(sK12,X0_13,sK8),sK8,sK12),
inference(instantiation,[status(thm)],[c_121]) ).
cnf(c_260,plain,
member(sK5(sK10,X0_13,sK8),sK8,sK10),
inference(instantiation,[status(thm)],[c_122]) ).
cnf(c_261,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_260,c_242,c_241,c_65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.10 % Problem : LCL950_17 : TPTP v8.2.0. Released v8.2.0.
% 0.08/0.11 % Command : run_iprover %s %d THM
% 0.10/0.31 % Computer : n008.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 19:00:12 EDT 2024
% 0.16/0.31 % CPUTime :
% 0.16/0.42 Running first-order theorem proving
% 0.16/0.42 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
% 1.78/1.11 % SZS status Started for theBenchmark.p
% 1.78/1.11 % SZS status Theorem for theBenchmark.p
% 1.78/1.11
% 1.78/1.11 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 1.78/1.11
% 1.78/1.11 ------ iProver source info
% 1.78/1.11
% 1.78/1.11 git: date: 2024-05-02 19:28:25 +0000
% 1.78/1.11 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 1.78/1.11 git: non_committed_changes: false
% 1.78/1.11
% 1.78/1.11 ------ Parsing...
% 1.78/1.11 ------ Clausification by vclausify_rel & Parsing by iProver...------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 1.78/1.11
% 1.78/1.11
% 1.78/1.11 ------ Preprocessing... pe_s pe:1:0s pe:2:0s pe_e pe_s pe_e
% 1.78/1.11
% 1.78/1.11 ------ Preprocessing...------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 1.78/1.11 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.78/1.11 ------ Proving...
% 1.78/1.11 ------ Problem Properties
% 1.78/1.11
% 1.78/1.11
% 1.78/1.11 clauses 7
% 1.78/1.11 conjectures 1
% 1.78/1.11 EPR 3
% 1.78/1.11 Horn 7
% 1.78/1.11 unary 3
% 1.78/1.11 binary 3
% 1.78/1.11 lits 12
% 1.78/1.11 lits eq 0
% 1.78/1.11 fd_pure 0
% 1.78/1.11 fd_pseudo 0
% 1.78/1.11 fd_cond 0
% 1.78/1.11 fd_pseudo_cond 0
% 1.78/1.11 AC symbols 0
% 1.78/1.11
% 1.78/1.11 ------ Schedule dynamic 5 is on
% 1.78/1.11
% 1.78/1.11 ------ no equalities: superposition off
% 1.78/1.11
% 1.78/1.11 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.78/1.11
% 1.78/1.11
% 1.78/1.11 ------
% 1.78/1.11 Current options:
% 1.78/1.11 ------
% 1.78/1.11
% 1.78/1.11
% 1.78/1.11
% 1.78/1.11
% 1.78/1.11 ------ Proving...
% 1.78/1.11
% 1.78/1.11
% 1.78/1.11 % SZS status Theorem for theBenchmark.p
% 1.78/1.11
% 1.78/1.11 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.78/1.11
% 1.78/1.11
%------------------------------------------------------------------------------