TSTP Solution File: SET662+3 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SET662+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n027.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 : Wed Aug 31 18:25:16 EDT 2022
% Result : Theorem 0.19s 0.49s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of formulae : 59 ( 11 unt; 0 def)
% Number of atoms : 226 ( 1 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 277 ( 110 ~; 98 |; 36 &)
% ( 10 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 116 ( 104 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f260,plain,
$false,
inference(subsumption_resolution,[],[f259,f120]) ).
fof(f120,plain,
~ ilf_type(empty_set,sF11),
inference(definition_folding,[],[f81,f119]) ).
fof(f119,plain,
sF11 = relation_type(sK0,sK1),
introduced(function_definition,[]) ).
fof(f81,plain,
~ ilf_type(empty_set,relation_type(sK0,sK1)),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
( ~ ilf_type(empty_set,relation_type(sK0,sK1))
& ilf_type(sK1,set_type)
& ilf_type(sK0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f38,f51,f50]) ).
fof(f50,plain,
( ? [X0] :
( ? [X1] :
( ~ ilf_type(empty_set,relation_type(X0,X1))
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) )
=> ( ? [X1] :
( ~ ilf_type(empty_set,relation_type(sK0,X1))
& ilf_type(X1,set_type) )
& ilf_type(sK0,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f51,plain,
( ? [X1] :
( ~ ilf_type(empty_set,relation_type(sK0,X1))
& ilf_type(X1,set_type) )
=> ( ~ ilf_type(empty_set,relation_type(sK0,sK1))
& ilf_type(sK1,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f38,plain,
? [X0] :
( ? [X1] :
( ~ ilf_type(empty_set,relation_type(X0,X1))
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ilf_type(empty_set,relation_type(X0,X1)) ) ),
inference(negated_conjecture,[],[f22]) ).
fof(f22,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ilf_type(empty_set,relation_type(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_25) ).
fof(f259,plain,
ilf_type(empty_set,sF11),
inference(superposition,[],[f246,f119]) ).
fof(f246,plain,
! [X6,X5] : ilf_type(empty_set,relation_type(X5,X6)),
inference(resolution,[],[f157,f218]) ).
fof(f218,plain,
! [X0] : ilf_type(empty_set,subset_type(X0)),
inference(resolution,[],[f185,f182]) ).
fof(f182,plain,
! [X0] : member(empty_set,power_set(X0)),
inference(resolution,[],[f128,f162]) ).
fof(f162,plain,
! [X0] : ~ member(X0,empty_set),
inference(subsumption_resolution,[],[f95,f103]) ).
fof(f103,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p20) ).
fof(f95,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ member(X0,empty_set) ),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0] :
( ~ member(X0,empty_set)
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ~ member(X0,empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4) ).
fof(f128,plain,
! [X0,X1] :
( member(sK6(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(subsumption_resolution,[],[f127,f103]) ).
fof(f127,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ ilf_type(X0,set_type)
| member(sK6(X0,X1),X0) ),
inference(subsumption_resolution,[],[f107,f103]) ).
fof(f107,plain,
! [X0,X1] :
( member(sK6(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| member(X0,power_set(X1))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ( member(sK6(X0,X1),X0)
& ilf_type(sK6(X0,X1),set_type)
& ~ member(sK6(X0,X1),X1) ) )
& ( ! [X3] :
( ~ member(X3,X0)
| ~ ilf_type(X3,set_type)
| member(X3,X1) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f63,f64]) ).
fof(f64,plain,
! [X0,X1] :
( ? [X2] :
( member(X2,X0)
& ilf_type(X2,set_type)
& ~ member(X2,X1) )
=> ( member(sK6(X0,X1),X0)
& ilf_type(sK6(X0,X1),set_type)
& ~ member(sK6(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f63,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ? [X2] :
( member(X2,X0)
& ilf_type(X2,set_type)
& ~ member(X2,X1) ) )
& ( ! [X3] :
( ~ member(X3,X0)
| ~ ilf_type(X3,set_type)
| member(X3,X1) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f62]) ).
fof(f62,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ? [X2] :
( member(X2,X0)
& ilf_type(X2,set_type)
& ~ member(X2,X1) ) )
& ( ! [X2] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| member(X2,X1) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0] :
( ! [X1] :
( ( member(X0,power_set(X1))
<=> ! [X2] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| member(X2,X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f33]) ).
fof(f33,plain,
! [X0] :
( ! [X1] :
( ( member(X0,power_set(X1))
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( member(X0,power_set(X1))
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12) ).
fof(f185,plain,
! [X0,X1] :
( ~ member(X0,power_set(X1))
| ilf_type(X0,subset_type(X1)) ),
inference(resolution,[],[f132,f167]) ).
fof(f167,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) ),
inference(subsumption_resolution,[],[f166,f159]) ).
fof(f159,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ~ empty(X0) ),
inference(subsumption_resolution,[],[f158,f103]) ).
fof(f158,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ member(X1,X0)
| ~ empty(X0) ),
inference(subsumption_resolution,[],[f110,f103]) ).
fof(f110,plain,
! [X0,X1] :
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ empty(X0)
| ~ member(X1,X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( ! [X1] :
( ~ ilf_type(X1,set_type)
| ~ member(X1,X0) )
| ~ empty(X0) )
& ( empty(X0)
| ( ilf_type(sK7(X0),set_type)
& member(sK7(X0),X0) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f67,f68]) ).
fof(f68,plain,
! [X0] :
( ? [X2] :
( ilf_type(X2,set_type)
& member(X2,X0) )
=> ( ilf_type(sK7(X0),set_type)
& member(sK7(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f67,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( ! [X1] :
( ~ ilf_type(X1,set_type)
| ~ member(X1,X0) )
| ~ empty(X0) )
& ( empty(X0)
| ? [X2] :
( ilf_type(X2,set_type)
& member(X2,X0) ) ) ) ),
inference(rectify,[],[f66]) ).
fof(f66,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( ! [X1] :
( ~ ilf_type(X1,set_type)
| ~ member(X1,X0) )
| ~ empty(X0) )
& ( empty(X0)
| ? [X1] :
( ilf_type(X1,set_type)
& member(X1,X0) ) ) ) ),
inference(nnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ! [X1] :
( ~ ilf_type(X1,set_type)
| ~ member(X1,X0) )
<=> empty(X0) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( empty(X0)
<=> ! [X1] :
( ilf_type(X1,set_type)
=> ~ member(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p11) ).
fof(f166,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| empty(X1)
| ~ member(X0,X1) ),
inference(subsumption_resolution,[],[f165,f103]) ).
fof(f165,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ ilf_type(X0,set_type)
| empty(X1)
| ilf_type(X0,member_type(X1)) ),
inference(subsumption_resolution,[],[f101,f103]) ).
fof(f101,plain,
! [X0,X1] :
( ~ ilf_type(X1,set_type)
| ~ member(X0,X1)
| ilf_type(X0,member_type(X1))
| ~ ilf_type(X0,set_type)
| empty(X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| empty(X1)
| ( ( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) )
& ( member(X0,X1)
| ~ ilf_type(X0,member_type(X1)) ) ) ) ),
inference(nnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| empty(X1)
| ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) ) ) ),
inference(flattening,[],[f46]) ).
fof(f46,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| empty(X1)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p14) ).
fof(f132,plain,
! [X0,X1] :
( ~ ilf_type(X1,member_type(power_set(X0)))
| ilf_type(X1,subset_type(X0)) ),
inference(subsumption_resolution,[],[f131,f103]) ).
fof(f131,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,member_type(power_set(X0))) ),
inference(subsumption_resolution,[],[f111,f103]) ).
fof(f111,plain,
! [X0,X1] :
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,member_type(power_set(X0)))
| ilf_type(X1,subset_type(X0)) ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0)) )
& ( ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,member_type(power_set(X0))) ) ) ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ilf_type(X1,member_type(power_set(X0)))
<=> ilf_type(X1,subset_type(X0)) ) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,member_type(power_set(X0)))
<=> ilf_type(X1,subset_type(X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7) ).
fof(f157,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ilf_type(X2,relation_type(X0,X1)) ),
inference(subsumption_resolution,[],[f156,f103]) ).
fof(f156,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ilf_type(X2,relation_type(X0,X1)) ),
inference(subsumption_resolution,[],[f97,f103]) ).
fof(f97,plain,
! [X2,X0,X1] :
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ilf_type(X2,relation_type(X0,X1)) ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0] :
( ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X2,subset_type(cross_product(X0,X1))) )
& ! [X3] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1)) ) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> ilf_type(X2,relation_type(X0,X1)) )
& ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ilf_type(X3,subset_type(cross_product(X0,X1))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET662+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 30 14:26:01 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.48 % (11541)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.19/0.48 % (11549)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.19/0.48 % (11549)First to succeed.
% 0.19/0.49 % (11549)Refutation found. Thanks to Tanya!
% 0.19/0.49 % SZS status Theorem for theBenchmark
% 0.19/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.49 % (11549)------------------------------
% 0.19/0.49 % (11549)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.49 % (11549)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.49 % (11549)Termination reason: Refutation
% 0.19/0.49
% 0.19/0.49 % (11549)Memory used [KB]: 1023
% 0.19/0.49 % (11549)Time elapsed: 0.079 s
% 0.19/0.49 % (11549)Instructions burned: 7 (million)
% 0.19/0.49 % (11549)------------------------------
% 0.19/0.49 % (11549)------------------------------
% 0.19/0.49 % (11521)Success in time 0.147 s
%------------------------------------------------------------------------------