%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SET914^7 : TPTP v9.2.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.23ome12TTm true
% Computer : n003.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 Oct 2 04:53:08 PM UTC 2025
% Result : Theorem 38.35s 5.55s
% Output : Refutation 38.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 39
% Syntax : Number of formulae : 71 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 452 ( 21 equ; 57 cnn)
% Maximal formula atoms : 48 ( 6 avg)
% Number of connectives : 1181 ( 122 ~; 81 |; 0 &; 849 @)
% ( 0 <=>; 71 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 9 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 14 usr; 4 con; 0-3 aty)
% ( 58 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 201 ( 128 ^; 73 !; 0 ?; 201 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf(empty_set_type,type,
empty_set: mu ).
thf(mforall_ind_type,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(set_intersection2_type,type,
set_intersection2: mu > mu > mu ).
thf(mnot_type,type,
mnot: ( $i > $o ) > $i > $o ).
thf(mor_type,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(unordered_pair_type,type,
unordered_pair: mu > mu > mu ).
thf(mimplies_type,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(disjoint_type,type,
disjoint: mu > mu > $i > $o ).
thf(exists_in_world_type,type,
exists_in_world: mu > $i > $o ).
thf(qmltpeq_type,type,
qmltpeq: mu > mu > $i > $o ).
thf(mequiv_type,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mand_type,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(in_type,type,
in: mu > mu > $i > $o ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf(mvalid,axiom,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ) ).
thf('0',plain,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ),
inference(simplify_rw_rule,[status(thm)],[mvalid]) ).
thf('1',plain,
( mvalid
= ( ^ [V_1: $i > $o] :
! [X4: $i] : ( V_1 @ X4 ) ) ),
define([status(thm)]) ).
thf(mforall_ind,axiom,
( mforall_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
! [X: mu] :
( ( exists_in_world @ X @ W )
=> ( Phi @ X @ W ) ) ) ) ).
thf('2',plain,
( mforall_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
! [X: mu] :
( ( exists_in_world @ X @ W )
=> ( Phi @ X @ W ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mforall_ind]) ).
thf('3',plain,
( mforall_ind
= ( ^ [V_1: mu > $i > $o,V_2: $i] :
! [X4: mu] :
( ( exists_in_world @ X4 @ V_2 )
=> ( V_1 @ X4 @ V_2 ) ) ) ),
define([status(thm)]) ).
thf(reflexivity,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( qmltpeq @ X @ X ) ) ) ).
thf(zf_stmt_0,axiom,
! [X4: $i,X6: mu] :
( ( exists_in_world @ X6 @ X4 )
=> ( qmltpeq @ X6 @ X6 @ X4 ) ) ).
thf(zip_derived_cl7,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( qmltpeq @ Y1 @ Y1 @ Y0 ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(existence_of_unordered_pair_ax,axiom,
! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( unordered_pair @ V2 @ V1 ) @ V ) ).
thf(zip_derived_cl6,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: mu] :
( !!
@ ^ [Y2: mu] : ( exists_in_world @ ( unordered_pair @ Y1 @ Y2 ) @ Y0 ) ) ) ),
inference(cnf,[status(esa)],[existence_of_unordered_pair_ax]) ).
thf(zip_derived_cl88,plain,
! [X2: $i] :
( !!
@ ^ [Y0: mu] :
( !!
@ ^ [Y1: mu] : ( exists_in_world @ ( unordered_pair @ Y0 @ Y1 ) @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl89,plain,
! [X2: $i,X4: mu] :
( !!
@ ^ [Y0: mu] : ( exists_in_world @ ( unordered_pair @ X4 @ Y0 ) @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl88]) ).
thf(zip_derived_cl90,plain,
! [X2: $i,X4: mu,X6: mu] : ( exists_in_world @ ( unordered_pair @ X4 @ X6 ) @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl89]) ).
thf(zip_derived_cl7_001,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( qmltpeq @ Y1 @ Y1 @ Y0 ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl95,plain,
! [X2: $i] :
( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ( qmltpeq @ Y0 @ Y0 @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl96,plain,
! [X2: $i,X4: mu] :
( ( exists_in_world @ X4 @ X2 )
=> ( qmltpeq @ X4 @ X4 @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl95]) ).
thf(zip_derived_cl97,plain,
! [X2: $i,X4: mu] :
( ~ ( exists_in_world @ X4 @ X2 )
| ( qmltpeq @ X4 @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl96]) ).
thf(zip_derived_cl102,plain,
! [X0: $i,X1: mu,X2: mu] : ( qmltpeq @ ( unordered_pair @ X2 @ X1 ) @ ( unordered_pair @ X2 @ X1 ) @ X0 ),
inference('sup-',[status(thm)],[zip_derived_cl90,zip_derived_cl97]) ).
thf(mequiv,axiom,
( mequiv
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ) ).
thf(mimplies,axiom,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ) ).
thf(mor,axiom,
( mor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
| ( Psi @ W ) ) ) ) ).
thf('4',plain,
( mor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
| ( Psi @ W ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mor]) ).
thf('5',plain,
( mor
= ( ^ [V_1: $i > $o,V_2: $i > $o,V_3: $i] :
( ( V_1 @ V_3 )
| ( V_2 @ V_3 ) ) ) ),
define([status(thm)]) ).
thf(mnot,axiom,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ) ).
thf('6',plain,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ),
inference(simplify_rw_rule,[status(thm)],[mnot]) ).
thf('7',plain,
( mnot
= ( ^ [V_1: $i > $o,V_2: $i] :
~ ( V_1 @ V_2 ) ) ),
define([status(thm)]) ).
thf('8',plain,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
inference(simplify_rw_rule,[status(thm)],[mimplies,'5','7']) ).
thf('9',plain,
( mimplies
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mor @ ( mnot @ V_1 ) @ V_2 ) ) ),
define([status(thm)]) ).
thf(mand,axiom,
( mand
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ) ).
thf('10',plain,
( mand
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mand,'5','7']) ).
thf('11',plain,
( mand
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mnot @ ( mor @ ( mnot @ V_1 ) @ ( mnot @ V_2 ) ) ) ) ),
define([status(thm)]) ).
thf('12',plain,
( mequiv
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mequiv,'9','11','5','7']) ).
thf('13',plain,
( mequiv
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mand @ ( mimplies @ V_1 @ V_2 ) @ ( mimplies @ V_2 @ V_1 ) ) ) ),
define([status(thm)]) ).
thf(d2_tarski,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] :
( mequiv @ ( qmltpeq @ C @ ( unordered_pair @ A @ B ) )
@ ( mforall_ind
@ ^ [D: mu] : ( mequiv @ ( in @ D @ C ) @ ( mor @ ( qmltpeq @ D @ A ) @ ( qmltpeq @ D @ B ) ) ) ) ) ) ) ) ) ).
thf(zf_stmt_1,axiom,
! [X4: $i,X6: mu] :
( ( exists_in_world @ X6 @ X4 )
=> ! [X8: mu] :
( ( exists_in_world @ X8 @ X4 )
=> ! [X10: mu] :
( ( exists_in_world @ X10 @ X4 )
=> ~ ( ~ ( ( qmltpeq @ X10 @ ( unordered_pair @ X6 @ X8 ) @ X4 )
| ~ ! [X14: mu] :
( ( exists_in_world @ X14 @ X4 )
=> ~ ( ~ ( ( in @ X14 @ X10 @ X4 )
| ~ ( ( qmltpeq @ X14 @ X8 @ X4 )
| ( qmltpeq @ X14 @ X6 @ X4 ) ) )
| ~ ( ( qmltpeq @ X14 @ X8 @ X4 )
| ( qmltpeq @ X14 @ X6 @ X4 )
| ~ ( in @ X14 @ X10 @ X4 ) ) ) ) )
| ~ ( ! [X12: mu] :
( ( exists_in_world @ X12 @ X4 )
=> ~ ( ~ ( ( in @ X12 @ X10 @ X4 )
| ~ ( ( qmltpeq @ X12 @ X8 @ X4 )
| ( qmltpeq @ X12 @ X6 @ X4 ) ) )
| ~ ( ( qmltpeq @ X12 @ X8 @ X4 )
| ( qmltpeq @ X12 @ X6 @ X4 )
| ~ ( in @ X12 @ X10 @ X4 ) ) ) )
| ~ ( qmltpeq @ X10 @ ( unordered_pair @ X6 @ X8 ) @ X4 ) ) ) ) ) ) ).
thf(zip_derived_cl23,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y0 )
=> ( (~)
@ ( ( (~)
@ ( ( qmltpeq @ Y3 @ ( unordered_pair @ Y1 @ Y2 ) @ Y0 )
| ( (~)
@ ( !!
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y0 )
=> ( (~)
@ ( ( (~)
@ ( ( in @ Y4 @ Y3 @ Y0 )
| ( (~)
@ ( ( qmltpeq @ Y4 @ Y2 @ Y0 )
| ( qmltpeq @ Y4 @ Y1 @ Y0 ) ) ) ) )
| ( (~)
@ ( ( qmltpeq @ Y4 @ Y2 @ Y0 )
| ( qmltpeq @ Y4 @ Y1 @ Y0 )
| ( (~) @ ( in @ Y4 @ Y3 @ Y0 ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( ( !!
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y0 )
=> ( (~)
@ ( ( (~)
@ ( ( in @ Y4 @ Y3 @ Y0 )
| ( (~)
@ ( ( qmltpeq @ Y4 @ Y2 @ Y0 )
| ( qmltpeq @ Y4 @ Y1 @ Y0 ) ) ) ) )
| ( (~)
@ ( ( qmltpeq @ Y4 @ Y2 @ Y0 )
| ( qmltpeq @ Y4 @ Y1 @ Y0 )
| ( (~) @ ( in @ Y4 @ Y3 @ Y0 ) ) ) ) ) ) ) )
| ( (~) @ ( qmltpeq @ Y3 @ ( unordered_pair @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(d3_xboole_0,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] :
( mequiv @ ( qmltpeq @ C @ ( set_intersection2 @ A @ B ) )
@ ( mforall_ind
@ ^ [D: mu] : ( mequiv @ ( in @ D @ C ) @ ( mand @ ( in @ D @ A ) @ ( in @ D @ B ) ) ) ) ) ) ) ) ) ).
thf(zf_stmt_2,axiom,
! [X4: $i,X6: mu] :
( ( exists_in_world @ X6 @ X4 )
=> ! [X8: mu] :
( ( exists_in_world @ X8 @ X4 )
=> ! [X10: mu] :
( ( exists_in_world @ X10 @ X4 )
=> ~ ( ~ ( ( qmltpeq @ X10 @ ( set_intersection2 @ X6 @ X8 ) @ X4 )
| ~ ! [X14: mu] :
( ( exists_in_world @ X14 @ X4 )
=> ~ ( ~ ( ( in @ X14 @ X10 @ X4 )
| ~ ( in @ X14 @ X6 @ X4 )
| ~ ( in @ X14 @ X8 @ X4 ) )
| ~ ( ~ ( ~ ( in @ X14 @ X8 @ X4 )
| ~ ( in @ X14 @ X6 @ X4 ) )
| ~ ( in @ X14 @ X10 @ X4 ) ) ) ) )
| ~ ( ! [X12: mu] :
( ( exists_in_world @ X12 @ X4 )
=> ~ ( ~ ( ( in @ X12 @ X10 @ X4 )
| ~ ( in @ X12 @ X6 @ X4 )
| ~ ( in @ X12 @ X8 @ X4 ) )
| ~ ( ~ ( ~ ( in @ X12 @ X8 @ X4 )
| ~ ( in @ X12 @ X6 @ X4 ) )
| ~ ( in @ X12 @ X10 @ X4 ) ) ) )
| ~ ( qmltpeq @ X10 @ ( set_intersection2 @ X6 @ X8 ) @ X4 ) ) ) ) ) ) ).
thf(zip_derived_cl24,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y0 )
=> ( (~)
@ ( ( (~)
@ ( ( qmltpeq @ Y3 @ ( set_intersection2 @ Y1 @ Y2 ) @ Y0 )
| ( (~)
@ ( !!
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y0 )
=> ( (~)
@ ( ( (~)
@ ( ( in @ Y4 @ Y3 @ Y0 )
| ( (~) @ ( in @ Y4 @ Y1 @ Y0 ) )
| ( (~) @ ( in @ Y4 @ Y2 @ Y0 ) ) ) )
| ( (~)
@ ( ( (~)
@ ( ( (~) @ ( in @ Y4 @ Y2 @ Y0 ) )
| ( (~) @ ( in @ Y4 @ Y1 @ Y0 ) ) ) )
| ( (~) @ ( in @ Y4 @ Y3 @ Y0 ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( ( !!
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y0 )
=> ( (~)
@ ( ( (~)
@ ( ( in @ Y4 @ Y3 @ Y0 )
| ( (~) @ ( in @ Y4 @ Y1 @ Y0 ) )
| ( (~) @ ( in @ Y4 @ Y2 @ Y0 ) ) ) )
| ( (~)
@ ( ( (~)
@ ( ( (~) @ ( in @ Y4 @ Y2 @ Y0 ) )
| ( (~) @ ( in @ Y4 @ Y1 @ Y0 ) ) ) )
| ( (~) @ ( in @ Y4 @ Y3 @ Y0 ) ) ) ) ) ) ) )
| ( (~) @ ( qmltpeq @ Y3 @ ( set_intersection2 @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_2]) ).
thf(commutativity_k3_xboole_0,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( qmltpeq @ ( set_intersection2 @ A @ B ) @ ( set_intersection2 @ B @ A ) ) ) ) ) ).
thf(zf_stmt_3,axiom,
! [X4: $i,X6: mu] :
( ( exists_in_world @ X6 @ X4 )
=> ! [X8: mu] :
( ( exists_in_world @ X8 @ X4 )
=> ( qmltpeq @ ( set_intersection2 @ X6 @ X8 ) @ ( set_intersection2 @ X8 @ X6 ) @ X4 ) ) ) ).
thf(zip_derived_cl21,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( qmltpeq @ ( set_intersection2 @ Y1 @ Y2 ) @ ( set_intersection2 @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_3]) ).
thf(d1_xboole_0,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mequiv @ ( qmltpeq @ A @ empty_set )
@ ( mforall_ind
@ ^ [B: mu] : ( mnot @ ( in @ B @ A ) ) ) ) ) ) ).
thf(zf_stmt_4,axiom,
! [X4: $i,X6: mu] :
( ( exists_in_world @ X6 @ X4 )
=> ~ ( ~ ( ( qmltpeq @ X6 @ empty_set @ X4 )
| ~ ! [X10: mu] :
( ( exists_in_world @ X10 @ X4 )
=> ~ ( in @ X10 @ X6 @ X4 ) ) )
| ~ ( ! [X8: mu] :
( ( exists_in_world @ X8 @ X4 )
=> ~ ( in @ X8 @ X6 @ X4 ) )
| ~ ( qmltpeq @ X6 @ empty_set @ X4 ) ) ) ) ).
thf(zip_derived_cl22,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( (~)
@ ( ( (~)
@ ( ( qmltpeq @ Y1 @ empty_set @ Y0 )
| ( (~)
@ ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( (~) @ ( in @ Y2 @ Y1 @ Y0 ) ) ) ) ) ) )
| ( (~)
@ ( ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( (~) @ ( in @ Y2 @ Y1 @ Y0 ) ) ) )
| ( (~) @ ( qmltpeq @ Y1 @ empty_set @ Y0 ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(transitivity,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] :
( mforall_ind
@ ^ [Y: mu] :
( mforall_ind
@ ^ [Z: mu] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ).
thf(zf_stmt_5,axiom,
! [X4: $i,X6: mu] :
( ( exists_in_world @ X6 @ X4 )
=> ! [X8: mu] :
( ( exists_in_world @ X8 @ X4 )
=> ! [X10: mu] :
( ( exists_in_world @ X10 @ X4 )
=> ( ( qmltpeq @ X6 @ X10 @ X4 )
| ~ ( qmltpeq @ X6 @ X8 @ X4 )
| ~ ( qmltpeq @ X8 @ X10 @ X4 ) ) ) ) ) ).
thf(zip_derived_cl9,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y0 )
=> ( ( qmltpeq @ Y1 @ Y3 @ Y0 )
| ( (~) @ ( qmltpeq @ Y1 @ Y2 @ Y0 ) )
| ( (~) @ ( qmltpeq @ Y2 @ Y3 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_5]) ).
thf(existence_of_empty_set_ax,axiom,
! [V: $i] : ( exists_in_world @ empty_set @ V ) ).
thf(zip_derived_cl4,plain,
( !!
@ ^ [Y0: $i] : ( exists_in_world @ empty_set @ Y0 ) ),
inference(cnf,[status(esa)],[existence_of_empty_set_ax]) ).
thf(zip_derived_cl6_002,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: mu] :
( !!
@ ^ [Y2: mu] : ( exists_in_world @ ( unordered_pair @ Y1 @ Y2 ) @ Y0 ) ) ) ),
inference(cnf,[status(esa)],[existence_of_unordered_pair_ax]) ).
thf(in_substitution_2,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( in @ C @ A ) ) @ ( in @ C @ B ) ) ) ) ) ) ).
thf(zf_stmt_6,axiom,
! [X4: $i,X6: mu] :
( ( exists_in_world @ X6 @ X4 )
=> ! [X8: mu] :
( ( exists_in_world @ X8 @ X4 )
=> ! [X10: mu] :
( ( exists_in_world @ X10 @ X4 )
=> ( ( in @ X10 @ X8 @ X4 )
| ~ ( qmltpeq @ X6 @ X8 @ X4 )
| ~ ( in @ X10 @ X6 @ X4 ) ) ) ) ) ).
thf(zip_derived_cl18,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y2 @ Y0 )
| ( (~) @ ( qmltpeq @ Y1 @ Y2 @ Y0 ) )
| ( (~) @ ( in @ Y3 @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_6]) ).
thf(existence_of_set_intersection2_ax,axiom,
! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( set_intersection2 @ V2 @ V1 ) @ V ) ).
thf(zip_derived_cl5,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: mu] :
( !!
@ ^ [Y2: mu] : ( exists_in_world @ ( set_intersection2 @ Y1 @ Y2 ) @ Y0 ) ) ) ),
inference(cnf,[status(esa)],[existence_of_set_intersection2_ax]) ).
thf(d7_xboole_0,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mequiv @ ( disjoint @ A @ B ) @ ( qmltpeq @ ( set_intersection2 @ A @ B ) @ empty_set ) ) ) ) ) ).
thf(zf_stmt_7,axiom,
! [X4: $i,X6: mu] :
( ( exists_in_world @ X6 @ X4 )
=> ! [X8: mu] :
( ( exists_in_world @ X8 @ X4 )
=> ~ ( ~ ( ( disjoint @ X6 @ X8 @ X4 )
| ~ ( qmltpeq @ ( set_intersection2 @ X6 @ X8 ) @ empty_set @ X4 ) )
| ~ ( ( qmltpeq @ ( set_intersection2 @ X6 @ X8 ) @ empty_set @ X4 )
| ~ ( disjoint @ X6 @ X8 @ X4 ) ) ) ) ) ).
thf(zip_derived_cl25,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( (~)
@ ( ( (~)
@ ( ( disjoint @ Y1 @ Y2 @ Y0 )
| ( (~) @ ( qmltpeq @ ( set_intersection2 @ Y1 @ Y2 ) @ empty_set @ Y0 ) ) ) )
| ( (~)
@ ( ( qmltpeq @ ( set_intersection2 @ Y1 @ Y2 ) @ empty_set @ Y0 )
| ( (~) @ ( disjoint @ Y1 @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_7]) ).
thf(idempotence_k3_xboole_0,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( qmltpeq @ ( set_intersection2 @ A @ A ) @ A ) ) ) ) ).
thf(zf_stmt_8,axiom,
! [X4: $i,X6: mu] :
( ( exists_in_world @ X6 @ X4 )
=> ! [X8: mu] :
( ( exists_in_world @ X8 @ X4 )
=> ( qmltpeq @ ( set_intersection2 @ X6 @ X6 ) @ X6 @ X4 ) ) ) ).
thf(zip_derived_cl27,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( qmltpeq @ ( set_intersection2 @ Y1 @ Y1 ) @ Y1 @ Y0 ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_8]) ).
thf(symmetry,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] :
( mforall_ind
@ ^ [Y: mu] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) ) ).
thf(zf_stmt_9,axiom,
! [X4: $i,X6: mu] :
( ( exists_in_world @ X6 @ X4 )
=> ! [X8: mu] :
( ( exists_in_world @ X8 @ X4 )
=> ( ( qmltpeq @ X8 @ X6 @ X4 )
| ~ ( qmltpeq @ X6 @ X8 @ X4 ) ) ) ) ).
thf(zip_derived_cl8,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( ( qmltpeq @ Y2 @ Y1 @ Y0 )
| ( (~) @ ( qmltpeq @ Y1 @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_9]) ).
thf(t55_zfmisc_1,conjecture,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mnot @ ( mand @ ( disjoint @ ( unordered_pair @ A @ B ) @ C ) @ ( in @ A @ C ) ) ) ) ) ) ) ).
thf(zf_stmt_10,conjecture,
! [X4: $i,X6: mu] :
( ( exists_in_world @ X6 @ X4 )
=> ! [X8: mu] :
( ( exists_in_world @ X8 @ X4 )
=> ! [X10: mu] :
( ( exists_in_world @ X10 @ X4 )
=> ( ~ ( in @ X6 @ X10 @ X4 )
| ~ ( disjoint @ ( unordered_pair @ X6 @ X8 ) @ X10 @ X4 ) ) ) ) ) ).
thf(zf_stmt_11,negated_conjecture,
~ ! [X4: $i,X6: mu] :
( ( exists_in_world @ X6 @ X4 )
=> ! [X8: mu] :
( ( exists_in_world @ X8 @ X4 )
=> ! [X10: mu] :
( ( exists_in_world @ X10 @ X4 )
=> ( ~ ( in @ X6 @ X10 @ X4 )
| ~ ( disjoint @ ( unordered_pair @ X6 @ X8 ) @ X10 @ X4 ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_10]) ).
thf(zip_derived_cl31,plain,
~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y0 )
=> ( ( (~) @ ( in @ Y1 @ Y3 @ Y0 ) )
| ( (~) @ ( disjoint @ ( unordered_pair @ Y1 @ Y2 ) @ Y3 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_11]) ).
thf(zip_derived_cl2402,plain,
$false,
inference(eprover,[status(thm)],[zip_derived_cl7,zip_derived_cl102,zip_derived_cl23,zip_derived_cl24,zip_derived_cl21,zip_derived_cl22,zip_derived_cl9,zip_derived_cl4,zip_derived_cl6,zip_derived_cl18,zip_derived_cl5,zip_derived_cl25,zip_derived_cl27,zip_derived_cl8,zip_derived_cl31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14 % Problem : SET914^7 : TPTP v9.2.0. Released v5.5.0.
% 0.12/0.15 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.23ome12TTm true
% 0.15/0.36 % Computer : n003.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Wed Oct 1 12:52:53 EDT 2025
% 0.15/0.37 % CPUTime :
% 0.15/0.37 % Running portfolio for 300 s
% 0.15/0.37 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.37 % Number of cores: 8
% 0.15/0.37 % Python version: Python 3.6.8
% 0.15/0.37 % Running in HO mode
% 0.58/0.68 % Total configuration time : 828
% 0.58/0.68 % Estimated wc time : 1656
% 0.58/0.68 % Estimated cpu time (8 cpus) : 207.0
% 0.60/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.60/0.75 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.60/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.60/0.77 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.61/0.79 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.61/0.80 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.61/0.81 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.61/0.81 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.62/0.87 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 38.35/5.55 % Solved by lams/15_e_short1.sh.
% 38.35/5.55 % done 723 iterations in 4.725s
% 38.35/5.55 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 38.35/5.55 % SZS output start Refutation
% See solution above
% 38.35/5.55
% 38.35/5.55
% 38.35/5.56 % Terminating...
% 38.35/5.63 % Runner terminated.
% 38.35/5.63 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------