TSTP Solution File: SEU135+2 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU135+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 17:55:56 EDT 2023
% Result : Theorem 82.16s 12.29s
% Output : Refutation 82.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 24
% Syntax : Number of formulae : 129 ( 52 unt; 0 def)
% Number of atoms : 369 ( 124 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 394 ( 154 ~; 158 |; 65 &)
% ( 8 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 233 (; 218 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f232654,plain,
$false,
inference(global_subsumption,[],[f101268,f232653]) ).
fof(f232653,plain,
empty_set = set_difference(sF12,sF14),
inference(forward_demodulation,[],[f232652,f202]) ).
fof(f202,plain,
set_union2(sK0,sK1) = sF12,
introduced(function_definition,[]) ).
fof(f232652,plain,
empty_set = set_difference(set_union2(sK0,sK1),sF14),
inference(forward_demodulation,[],[f232640,f152]) ).
fof(f152,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/tmp/tmp.tYjYJKEvuh/Vampire---4.8_4670',commutativity_k2_xboole_0) ).
fof(f232640,plain,
empty_set = set_difference(set_union2(sK1,sK0),sF14),
inference(trivial_inequality_removal,[],[f232514]) ).
fof(f232514,plain,
( empty_set != empty_set
| empty_set = set_difference(set_union2(sK1,sK0),sF14) ),
inference(superposition,[],[f9092,f232473]) ).
fof(f232473,plain,
empty_set = set_difference(sK1,sF14),
inference(duplicate_literal_removal,[],[f232441]) ).
fof(f232441,plain,
( empty_set = set_difference(sK1,sF14)
| empty_set = set_difference(sK1,sF14) ),
inference(resolution,[],[f200132,f867]) ).
fof(f867,plain,
! [X3,X4] :
( in(sK6(X3,X4),X3)
| empty_set = set_difference(X3,X4) ),
inference(resolution,[],[f133,f166]) ).
fof(f166,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK6(X0,X1),X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK6(X0,X1),X1)
& in(sK6(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f97,f98]) ).
fof(f98,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK6(X0,X1),X1)
& in(sK6(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f97,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,[],[f96]) ).
fof(f96,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,[],[f75]) ).
fof(f75,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.tYjYJKEvuh/Vampire---4.8_4670',d3_tarski) ).
fof(f133,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| empty_set = set_difference(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0,X1] :
( ( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| empty_set != set_difference(X0,X1) ) ),
inference(nnf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0,X1] :
( empty_set = set_difference(X0,X1)
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.tYjYJKEvuh/Vampire---4.8_4670',l32_xboole_1) ).
fof(f200132,plain,
! [X12] :
( ~ in(sK6(X12,sF14),sK1)
| empty_set = set_difference(X12,sF14) ),
inference(global_subsumption,[],[f10079,f200119]) ).
fof(f200119,plain,
! [X12] :
( empty_set = set_difference(X12,sF14)
| in(sK6(X12,sF14),sK0)
| ~ in(sK6(X12,sF14),sK1) ),
inference(resolution,[],[f10146,f8949]) ).
fof(f8949,plain,
! [X3] :
( in(X3,sF13)
| in(X3,sK0)
| ~ in(X3,sK1) ),
inference(superposition,[],[f193,f203]) ).
fof(f203,plain,
set_difference(sK1,sK0) = sF13,
introduced(function_definition,[]) ).
fof(f193,plain,
! [X0,X1,X4] :
( in(X4,set_difference(X0,X1))
| in(X4,X1)
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f172]) ).
fof(f172,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| in(X4,X1)
| ~ in(X4,X0)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ( ( in(sK7(X0,X1,X2),X1)
| ~ in(sK7(X0,X1,X2),X0)
| ~ in(sK7(X0,X1,X2),X2) )
& ( ( ~ in(sK7(X0,X1,X2),X1)
& in(sK7(X0,X1,X2),X0) )
| in(sK7(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| in(X4,X1)
| ~ in(X4,X0) )
& ( ( ~ in(X4,X1)
& in(X4,X0) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f102,f103]) ).
fof(f103,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) )
=> ( ( in(sK7(X0,X1,X2),X1)
| ~ in(sK7(X0,X1,X2),X0)
| ~ in(sK7(X0,X1,X2),X2) )
& ( ( ~ in(sK7(X0,X1,X2),X1)
& in(sK7(X0,X1,X2),X0) )
| in(sK7(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f102,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| in(X4,X1)
| ~ in(X4,X0) )
& ( ( ~ in(X4,X1)
& in(X4,X0) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(rectify,[],[f101]) ).
fof(f101,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(flattening,[],[f100]) ).
fof(f100,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1,X2] :
( set_difference(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tYjYJKEvuh/Vampire---4.8_4670',d4_xboole_0) ).
fof(f10146,plain,
! [X19] :
( ~ in(sK6(X19,sF14),sF13)
| empty_set = set_difference(X19,sF14) ),
inference(resolution,[],[f6105,f868]) ).
fof(f868,plain,
! [X6,X5] :
( ~ in(sK6(X5,X6),X6)
| empty_set = set_difference(X5,X6) ),
inference(resolution,[],[f133,f167]) ).
fof(f167,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK6(X0,X1),X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f6105,plain,
! [X3] :
( in(X3,sF14)
| ~ in(X3,sF13) ),
inference(global_subsumption,[],[f1225]) ).
fof(f1225,plain,
! [X4] :
( in(X4,sF14)
| ~ in(X4,sF13) ),
inference(superposition,[],[f200,f1146]) ).
fof(f1146,plain,
sF13 = set_intersection2(sF13,sF14),
inference(superposition,[],[f674,f204]) ).
fof(f204,plain,
set_union2(sK0,sF13) = sF14,
introduced(function_definition,[]) ).
fof(f674,plain,
! [X10,X11] : set_intersection2(X10,set_union2(X11,X10)) = X10,
inference(superposition,[],[f473,f152]) ).
fof(f473,plain,
! [X8,X7] : set_intersection2(X7,set_union2(X7,X8)) = X7,
inference(resolution,[],[f131,f122]) ).
fof(f122,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f47]) ).
fof(f47,axiom,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
file('/export/starexec/sandbox/tmp/tmp.tYjYJKEvuh/Vampire---4.8_4670',t7_xboole_1) ).
fof(f131,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X0,X1) = X0 ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_intersection2(X0,X1) = X0 ),
file('/export/starexec/sandbox/tmp/tmp.tYjYJKEvuh/Vampire---4.8_4670',t28_xboole_1) ).
fof(f200,plain,
! [X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,set_intersection2(X0,X1)) ),
inference(equality_resolution,[],[f183]) ).
fof(f183,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f114]) ).
fof(f114,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ( ( ~ in(sK9(X0,X1,X2),X1)
| ~ in(sK9(X0,X1,X2),X0)
| ~ in(sK9(X0,X1,X2),X2) )
& ( ( in(sK9(X0,X1,X2),X1)
& in(sK9(X0,X1,X2),X0) )
| in(sK9(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X1)
| ~ in(X4,X0) )
& ( ( in(X4,X1)
& in(X4,X0) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f112,f113]) ).
fof(f113,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) )
=> ( ( ~ in(sK9(X0,X1,X2),X1)
| ~ in(sK9(X0,X1,X2),X0)
| ~ in(sK9(X0,X1,X2),X2) )
& ( ( in(sK9(X0,X1,X2),X1)
& in(sK9(X0,X1,X2),X0) )
| in(sK9(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f112,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X1)
| ~ in(X4,X0) )
& ( ( in(X4,X1)
& in(X4,X0) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(rectify,[],[f111]) ).
fof(f111,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( ( in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(flattening,[],[f110]) ).
fof(f110,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( ( in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1,X2] :
( set_intersection2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tYjYJKEvuh/Vampire---4.8_4670',d3_xboole_0) ).
fof(f10079,plain,
! [X19] :
( ~ in(sK6(X19,sF14),sK0)
| empty_set = set_difference(X19,sF14) ),
inference(resolution,[],[f711,f868]) ).
fof(f711,plain,
! [X4] :
( in(X4,sF14)
| ~ in(X4,sK0) ),
inference(superposition,[],[f200,f680]) ).
fof(f680,plain,
sK0 = set_intersection2(sK0,sF14),
inference(superposition,[],[f473,f204]) ).
fof(f9092,plain,
! [X10] :
( empty_set != set_difference(X10,sF14)
| empty_set = set_difference(set_union2(X10,sK0),sF14) ),
inference(trivial_inequality_removal,[],[f9087]) ).
fof(f9087,plain,
! [X10] :
( empty_set != empty_set
| empty_set != set_difference(X10,sF14)
| empty_set = set_difference(set_union2(X10,sK0),sF14) ),
inference(superposition,[],[f223,f241]) ).
fof(f241,plain,
empty_set = set_difference(sK0,sF14),
inference(forward_literal_rewriting,[],[f232,f133]) ).
fof(f232,plain,
subset(sK0,sF14),
inference(superposition,[],[f122,f204]) ).
fof(f223,plain,
! [X2,X0,X1] :
( empty_set != set_difference(X2,X1)
| empty_set != set_difference(X0,X1)
| empty_set = set_difference(set_union2(X0,X2),X1) ),
inference(forward_literal_rewriting,[],[f222,f132]) ).
fof(f132,plain,
! [X0,X1] :
( empty_set != set_difference(X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f222,plain,
! [X2,X0,X1] :
( empty_set != set_difference(X2,X1)
| empty_set = set_difference(set_union2(X0,X2),X1)
| ~ subset(X0,X1) ),
inference(forward_literal_rewriting,[],[f221,f132]) ).
fof(f221,plain,
! [X2,X0,X1] :
( empty_set = set_difference(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(forward_literal_rewriting,[],[f140,f133]) ).
fof(f140,plain,
! [X2,X0,X1] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1,X2] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(flattening,[],[f67]) ).
fof(f67,plain,
! [X0,X1,X2] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,axiom,
! [X0,X1,X2] :
( ( subset(X2,X1)
& subset(X0,X1) )
=> subset(set_union2(X0,X2),X1) ),
file('/export/starexec/sandbox/tmp/tmp.tYjYJKEvuh/Vampire---4.8_4670',t8_xboole_1) ).
fof(f101268,plain,
empty_set != set_difference(sF12,sF14),
inference(global_subsumption,[],[f205,f101210]) ).
fof(f101210,plain,
( empty_set != set_difference(sF12,sF14)
| sF12 = sF14 ),
inference(superposition,[],[f268,f101100]) ).
fof(f101100,plain,
sF14 = set_intersection2(sF12,sF14),
inference(trivial_inequality_removal,[],[f101032]) ).
fof(f101032,plain,
( empty_set != empty_set
| sF14 = set_intersection2(sF12,sF14) ),
inference(superposition,[],[f10167,f100900]) ).
fof(f100900,plain,
empty_set = set_difference(sF14,set_intersection2(sF12,sF14)),
inference(superposition,[],[f35060,f151]) ).
fof(f151,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(rectify,[],[f19]) ).
fof(f19,axiom,
! [X0,X1] : set_intersection2(X0,X0) = X0,
file('/export/starexec/sandbox/tmp/tmp.tYjYJKEvuh/Vampire---4.8_4670',idempotence_k3_xboole_0) ).
fof(f35060,plain,
! [X9] : empty_set = set_difference(set_intersection2(sF14,X9),set_intersection2(sF12,X9)),
inference(trivial_inequality_removal,[],[f35027]) ).
fof(f35027,plain,
! [X9] :
( empty_set != empty_set
| empty_set = set_difference(set_intersection2(sF14,X9),set_intersection2(sF12,X9)) ),
inference(superposition,[],[f214,f35007]) ).
fof(f35007,plain,
empty_set = set_difference(sF14,sF12),
inference(forward_demodulation,[],[f35006,f204]) ).
fof(f35006,plain,
empty_set = set_difference(set_union2(sK0,sF13),sF12),
inference(forward_demodulation,[],[f34968,f152]) ).
fof(f34968,plain,
empty_set = set_difference(set_union2(sF13,sK0),sF12),
inference(trivial_inequality_removal,[],[f34967]) ).
fof(f34967,plain,
( empty_set != empty_set
| empty_set = set_difference(set_union2(sF13,sK0),sF12) ),
inference(superposition,[],[f3331,f13144]) ).
fof(f13144,plain,
empty_set = set_difference(sF13,sF12),
inference(forward_demodulation,[],[f13099,f144]) ).
fof(f144,plain,
! [X0] : set_difference(X0,empty_set) = X0,
inference(cnf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0] : set_difference(X0,empty_set) = X0,
file('/export/starexec/sandbox/tmp/tmp.tYjYJKEvuh/Vampire---4.8_4670',t3_boole) ).
fof(f13099,plain,
empty_set = set_difference(set_difference(sF13,sF12),empty_set),
inference(superposition,[],[f9150,f359]) ).
fof(f359,plain,
empty_set = set_difference(sK1,sF12),
inference(superposition,[],[f243,f202]) ).
fof(f243,plain,
! [X11,X12] : empty_set = set_difference(X11,set_union2(X12,X11)),
inference(forward_literal_rewriting,[],[f239,f133]) ).
fof(f239,plain,
! [X11,X12] : subset(X11,set_union2(X12,X11)),
inference(superposition,[],[f122,f152]) ).
fof(f9150,plain,
! [X6] : empty_set = set_difference(set_difference(sF13,X6),set_difference(sK1,X6)),
inference(trivial_inequality_removal,[],[f9137]) ).
fof(f9137,plain,
! [X6] :
( empty_set != empty_set
| empty_set = set_difference(set_difference(sF13,X6),set_difference(sK1,X6)) ),
inference(superposition,[],[f212,f256]) ).
fof(f256,plain,
empty_set = set_difference(sF13,sK1),
inference(forward_literal_rewriting,[],[f248,f133]) ).
fof(f248,plain,
subset(sF13,sK1),
inference(superposition,[],[f123,f203]) ).
fof(f123,plain,
! [X0,X1] : subset(set_difference(X0,X1),X0),
inference(cnf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0,X1] : subset(set_difference(X0,X1),X0),
file('/export/starexec/sandbox/tmp/tmp.tYjYJKEvuh/Vampire---4.8_4670',t36_xboole_1) ).
fof(f212,plain,
! [X2,X0,X1] :
( empty_set != set_difference(X0,X1)
| empty_set = set_difference(set_difference(X0,X2),set_difference(X1,X2)) ),
inference(forward_literal_rewriting,[],[f211,f132]) ).
fof(f211,plain,
! [X2,X0,X1] :
( empty_set = set_difference(set_difference(X0,X2),set_difference(X1,X2))
| ~ subset(X0,X1) ),
inference(forward_literal_rewriting,[],[f136,f133]) ).
fof(f136,plain,
! [X2,X0,X1] :
( subset(set_difference(X0,X2),set_difference(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0,X1,X2] :
( subset(set_difference(X0,X2),set_difference(X1,X2))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset(set_difference(X0,X2),set_difference(X1,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.tYjYJKEvuh/Vampire---4.8_4670',t33_xboole_1) ).
fof(f3331,plain,
! [X33] :
( empty_set != set_difference(X33,sF12)
| empty_set = set_difference(set_union2(X33,sK0),sF12) ),
inference(trivial_inequality_removal,[],[f3326]) ).
fof(f3326,plain,
! [X33] :
( empty_set != empty_set
| empty_set != set_difference(X33,sF12)
| empty_set = set_difference(set_union2(X33,sK0),sF12) ),
inference(superposition,[],[f223,f242]) ).
fof(f242,plain,
empty_set = set_difference(sK0,sF12),
inference(forward_literal_rewriting,[],[f233,f133]) ).
fof(f233,plain,
subset(sK0,sF12),
inference(superposition,[],[f122,f202]) ).
fof(f214,plain,
! [X2,X0,X1] :
( empty_set != set_difference(X0,X1)
| empty_set = set_difference(set_intersection2(X0,X2),set_intersection2(X1,X2)) ),
inference(forward_literal_rewriting,[],[f213,f132]) ).
fof(f213,plain,
! [X2,X0,X1] :
( empty_set = set_difference(set_intersection2(X0,X2),set_intersection2(X1,X2))
| ~ subset(X0,X1) ),
inference(forward_literal_rewriting,[],[f137,f133]) ).
fof(f137,plain,
! [X2,X0,X1] :
( subset(set_intersection2(X0,X2),set_intersection2(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0,X1,X2] :
( subset(set_intersection2(X0,X2),set_intersection2(X1,X2))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset(set_intersection2(X0,X2),set_intersection2(X1,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.tYjYJKEvuh/Vampire---4.8_4670',t26_xboole_1) ).
fof(f10167,plain,
! [X12,X13] :
( empty_set != set_difference(X12,set_intersection2(X13,X12))
| set_intersection2(X13,X12) = X12 ),
inference(superposition,[],[f268,f153]) ).
fof(f153,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox/tmp/tmp.tYjYJKEvuh/Vampire---4.8_4670',commutativity_k3_xboole_0) ).
fof(f268,plain,
! [X3,X4] :
( empty_set != set_difference(X3,set_intersection2(X3,X4))
| set_intersection2(X3,X4) = X3 ),
inference(forward_literal_rewriting,[],[f258,f132]) ).
fof(f258,plain,
! [X3,X4] :
( set_intersection2(X3,X4) = X3
| ~ subset(X3,set_intersection2(X3,X4)) ),
inference(resolution,[],[f124,f162]) ).
fof(f162,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f93]) ).
fof(f93,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.tYjYJKEvuh/Vampire---4.8_4670',d10_xboole_0) ).
fof(f124,plain,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
inference(cnf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
file('/export/starexec/sandbox/tmp/tmp.tYjYJKEvuh/Vampire---4.8_4670',t17_xboole_1) ).
fof(f205,plain,
sF12 != sF14,
inference(definition_folding,[],[f119,f204,f203,f202]) ).
fof(f119,plain,
set_union2(sK0,sK1) != set_union2(sK0,set_difference(sK1,sK0)),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
set_union2(sK0,sK1) != set_union2(sK0,set_difference(sK1,sK0)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f55,f78]) ).
fof(f78,plain,
( ? [X0,X1] : set_union2(X0,X1) != set_union2(X0,set_difference(X1,X0))
=> set_union2(sK0,sK1) != set_union2(sK0,set_difference(sK1,sK0)) ),
introduced(choice_axiom,[]) ).
fof(f55,plain,
? [X0,X1] : set_union2(X0,X1) != set_union2(X0,set_difference(X1,X0)),
inference(ennf_transformation,[],[f39]) ).
fof(f39,negated_conjecture,
~ ! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0)),
inference(negated_conjecture,[],[f38]) ).
fof(f38,conjecture,
! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0)),
file('/export/starexec/sandbox/tmp/tmp.tYjYJKEvuh/Vampire---4.8_4670',t39_xboole_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15 % Problem : SEU135+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.17 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.18/0.39 % Computer : n019.cluster.edu
% 0.18/0.39 % Model : x86_64 x86_64
% 0.18/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.39 % Memory : 8042.1875MB
% 0.18/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.39 % CPULimit : 300
% 0.18/0.39 % WCLimit : 300
% 0.18/0.39 % DateTime : Wed Aug 23 19:31:43 EDT 2023
% 0.18/0.39 % CPUTime :
% 0.18/0.39 This is a FOF_THM_RFO_SEQ problem
% 0.18/0.39 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.tYjYJKEvuh/Vampire---4.8_4670
% 0.18/0.39 % (4818)Running in auto input_syntax mode. Trying TPTP
% 0.18/0.45 % (4830)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_413 on Vampire---4 for (413ds/0Mi)
% 0.18/0.45 % (4827)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_424 on Vampire---4 for (424ds/0Mi)
% 0.18/0.45 % (4824)lrs-3_8_anc=none:bce=on:cond=on:drc=off:flr=on:fsd=off:fsr=off:fde=unused:gsp=on:gs=on:gsaa=full_model:lcm=predicate:lma=on:nm=16:sos=all:sp=weighted_frequency:tgt=ground:urr=ec_only:stl=188_482 on Vampire---4 for (482ds/0Mi)
% 0.18/0.45 % (4823)dis-11_4:1_aac=none:add=off:afr=on:anc=none:bd=preordered:bs=on:bsr=on:drc=off:fsr=off:fde=none:gsp=on:irw=on:lcm=reverse:lma=on:nm=0:nwc=1.7:nicw=on:sas=z3:sims=off:sos=all:sac=on:sp=weighted_frequency:tgt=full_602 on Vampire---4 for (602ds/0Mi)
% 0.18/0.45 % (4833)ott+11_14_av=off:bs=on:bsr=on:cond=on:flr=on:fsd=off:fde=unused:gsp=on:nm=4:nwc=1.5:tgt=full_386 on Vampire---4 for (386ds/0Mi)
% 0.18/0.46 % (4821)dis+1010_4:1_anc=none:bd=off:drc=off:flr=on:fsr=off:nm=4:nwc=1.1:nicw=on:sas=z3_680 on Vampire---4 for (680ds/0Mi)
% 0.18/0.46 % (4820)lrs+10_11_cond=on:drc=off:flr=on:fsr=off:gsp=on:gs=on:gsem=off:lma=on:msp=off:nm=4:nwc=1.5:nicw=on:sas=z3:sims=off:sp=scramble:stl=188_730 on Vampire---4 for (730ds/0Mi)
% 82.16/12.20 % (4824)First to succeed.
% 82.16/12.29 % (4824)Refutation found. Thanks to Tanya!
% 82.16/12.29 % SZS status Theorem for Vampire---4
% 82.16/12.29 % SZS output start Proof for Vampire---4
% See solution above
% 82.16/12.29 % (4824)------------------------------
% 82.16/12.29 % (4824)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 82.16/12.29 % (4824)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 82.16/12.29 % (4824)Termination reason: Refutation
% 82.16/12.29
% 82.16/12.29 % (4824)Memory used [KB]: 330186
% 82.16/12.29 % (4824)Time elapsed: 11.809 s
% 82.16/12.29 % (4824)------------------------------
% 82.16/12.29 % (4824)------------------------------
% 82.16/12.29 % (4818)Success in time 11.815 s
% 82.16/12.29 % Vampire---4.8 exiting
%------------------------------------------------------------------------------