TSTP Solution File: SEU119+2 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SEU119+2 : TPTP v8.1.0. Released v3.3.0.
% 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 : n016.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 18:31:59 EDT 2022
% Result : Theorem 1.63s 0.59s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of formulae : 72 ( 6 unt; 0 def)
% Number of atoms : 264 ( 40 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 324 ( 132 ~; 116 |; 62 &)
% ( 10 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 125 ( 104 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f233,plain,
$false,
inference(avatar_sat_refutation,[],[f78,f83,f88,f89,f201,f208,f232]) ).
fof(f232,plain,
( spl7_3
| ~ spl7_1 ),
inference(avatar_split_clause,[],[f231,f71,f80]) ).
fof(f80,plain,
( spl7_3
<=> ! [X3] :
( ~ in(X3,sK2)
| ~ in(X3,sK3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_3])]) ).
fof(f71,plain,
( spl7_1
<=> disjoint(sK2,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_1])]) ).
fof(f231,plain,
( ! [X2] :
( ~ in(X2,sK3)
| ~ in(X2,sK2) )
| ~ spl7_1 ),
inference(subsumption_resolution,[],[f224,f69]) ).
fof(f69,plain,
! [X1] : ~ in(X1,empty_set),
inference(equality_resolution,[],[f64]) ).
fof(f64,plain,
! [X0,X1] :
( ~ in(X1,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0] :
( ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 )
& ( empty_set = X0
| in(sK5(X0),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f38,f39]) ).
fof(f39,plain,
! [X0] :
( ? [X2] : in(X2,X0)
=> in(sK5(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f38,plain,
! [X0] :
( ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 )
& ( empty_set = X0
| ? [X2] : in(X2,X0) ) ),
inference(rectify,[],[f37]) ).
fof(f37,plain,
! [X0] :
( ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 )
& ( empty_set = X0
| ? [X1] : in(X1,X0) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( ! [X1] : ~ in(X1,X0)
<=> empty_set = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f224,plain,
( ! [X2] :
( ~ in(X2,sK3)
| ~ in(X2,sK2)
| in(X2,empty_set) )
| ~ spl7_1 ),
inference(superposition,[],[f68,f202]) ).
fof(f202,plain,
( empty_set = set_intersection2(sK2,sK3)
| ~ spl7_1 ),
inference(resolution,[],[f72,f43]) ).
fof(f43,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| set_intersection2(X0,X1) = empty_set ),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set )
& ( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_intersection2(X0,X1) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(f72,plain,
( disjoint(sK2,sK3)
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f68,plain,
! [X2,X3,X1] :
( in(X3,set_intersection2(X1,X2))
| ~ in(X3,X1)
| ~ in(X3,X2) ),
inference(equality_resolution,[],[f52]) ).
fof(f52,plain,
! [X2,X3,X0,X1] :
( in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2)
| set_intersection2(X1,X2) != X0 ),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( ( in(X3,X1)
& in(X3,X2) )
| ~ in(X3,X0) )
& ( in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) ) )
| set_intersection2(X1,X2) != X0 )
& ( set_intersection2(X1,X2) = X0
| ( ( ~ in(sK1(X0,X1,X2),X0)
| ~ in(sK1(X0,X1,X2),X1)
| ~ in(sK1(X0,X1,X2),X2) )
& ( in(sK1(X0,X1,X2),X0)
| ( in(sK1(X0,X1,X2),X1)
& in(sK1(X0,X1,X2),X2) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f29,f30]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ? [X4] :
( ( ~ in(X4,X0)
| ~ in(X4,X1)
| ~ in(X4,X2) )
& ( in(X4,X0)
| ( in(X4,X1)
& in(X4,X2) ) ) )
=> ( ( ~ in(sK1(X0,X1,X2),X0)
| ~ in(sK1(X0,X1,X2),X1)
| ~ in(sK1(X0,X1,X2),X2) )
& ( in(sK1(X0,X1,X2),X0)
| ( in(sK1(X0,X1,X2),X1)
& in(sK1(X0,X1,X2),X2) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( ( in(X3,X1)
& in(X3,X2) )
| ~ in(X3,X0) )
& ( in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) ) )
| set_intersection2(X1,X2) != X0 )
& ( set_intersection2(X1,X2) = X0
| ? [X4] :
( ( ~ in(X4,X0)
| ~ in(X4,X1)
| ~ in(X4,X2) )
& ( in(X4,X0)
| ( in(X4,X1)
& in(X4,X2) ) ) ) ) ),
inference(rectify,[],[f28]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( ( in(X3,X1)
& in(X3,X2) )
| ~ in(X3,X0) )
& ( in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) ) )
| set_intersection2(X1,X2) != X0 )
& ( set_intersection2(X1,X2) = X0
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( in(X3,X0)
| ( in(X3,X1)
& in(X3,X2) ) ) ) ) ),
inference(flattening,[],[f27]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( ( in(X3,X1)
& in(X3,X2) )
| ~ in(X3,X0) )
& ( in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) ) )
| set_intersection2(X1,X2) != X0 )
& ( set_intersection2(X1,X2) = X0
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( in(X3,X0)
| ( in(X3,X1)
& in(X3,X2) ) ) ) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ! [X3] :
( ( in(X3,X1)
& in(X3,X2) )
<=> in(X3,X0) )
<=> set_intersection2(X1,X2) = X0 ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X2,X0,X1] :
( set_intersection2(X0,X1) = X2
<=> ! [X3] :
( ( in(X3,X0)
& in(X3,X1) )
<=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f208,plain,
( ~ spl7_2
| ~ spl7_3
| ~ spl7_4 ),
inference(avatar_contradiction_clause,[],[f207]) ).
fof(f207,plain,
( $false
| ~ spl7_2
| ~ spl7_3
| ~ spl7_4 ),
inference(subsumption_resolution,[],[f205,f77]) ).
fof(f77,plain,
( in(sK4,sK2)
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f75,plain,
( spl7_2
<=> in(sK4,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_2])]) ).
fof(f205,plain,
( ~ in(sK4,sK2)
| ~ spl7_3
| ~ spl7_4 ),
inference(resolution,[],[f87,f81]) ).
fof(f81,plain,
( ! [X3] :
( ~ in(X3,sK3)
| ~ in(X3,sK2) )
| ~ spl7_3 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f87,plain,
( in(sK4,sK3)
| ~ spl7_4 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f85,plain,
( spl7_4
<=> in(sK4,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_4])]) ).
fof(f201,plain,
( spl7_1
| ~ spl7_3 ),
inference(avatar_contradiction_clause,[],[f200]) ).
fof(f200,plain,
( $false
| spl7_1
| ~ spl7_3 ),
inference(subsumption_resolution,[],[f199,f73]) ).
fof(f73,plain,
( ~ disjoint(sK2,sK3)
| spl7_1 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f199,plain,
( disjoint(sK2,sK3)
| ~ spl7_3 ),
inference(trivial_inequality_removal,[],[f194]) ).
fof(f194,plain,
( disjoint(sK2,sK3)
| empty_set != empty_set
| ~ spl7_3 ),
inference(superposition,[],[f104,f184]) ).
fof(f184,plain,
( empty_set = set_intersection2(sK3,sK2)
| ~ spl7_3 ),
inference(duplicate_literal_removal,[],[f179]) ).
fof(f179,plain,
( empty_set = set_intersection2(sK3,sK2)
| empty_set = set_intersection2(sK3,sK2)
| ~ spl7_3 ),
inference(resolution,[],[f130,f112]) ).
fof(f112,plain,
! [X0,X1] :
( in(sK5(set_intersection2(X0,X1)),X1)
| set_intersection2(X0,X1) = empty_set ),
inference(resolution,[],[f67,f63]) ).
fof(f63,plain,
! [X0] :
( in(sK5(X0),X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f40]) ).
fof(f67,plain,
! [X2,X3,X1] :
( ~ in(X3,set_intersection2(X1,X2))
| in(X3,X2) ),
inference(equality_resolution,[],[f53]) ).
fof(f53,plain,
! [X2,X3,X0,X1] :
( in(X3,X2)
| ~ in(X3,X0)
| set_intersection2(X1,X2) != X0 ),
inference(cnf_transformation,[],[f31]) ).
fof(f130,plain,
( ! [X9] :
( ~ in(sK5(set_intersection2(sK3,X9)),sK2)
| empty_set = set_intersection2(sK3,X9) )
| ~ spl7_3 ),
inference(resolution,[],[f108,f81]) ).
fof(f108,plain,
! [X0,X1] :
( in(sK5(set_intersection2(X0,X1)),X0)
| set_intersection2(X0,X1) = empty_set ),
inference(resolution,[],[f66,f63]) ).
fof(f66,plain,
! [X2,X3,X1] :
( ~ in(X3,set_intersection2(X1,X2))
| in(X3,X1) ),
inference(equality_resolution,[],[f54]) ).
fof(f54,plain,
! [X2,X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| set_intersection2(X1,X2) != X0 ),
inference(cnf_transformation,[],[f31]) ).
fof(f104,plain,
! [X3,X4] :
( empty_set != set_intersection2(X4,X3)
| disjoint(X3,X4) ),
inference(superposition,[],[f44,f45]) ).
fof(f45,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(rectify,[],[f18]) ).
fof(f18,plain,
! [X1,X0] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X1,X0] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f44,plain,
! [X0,X1] :
( set_intersection2(X0,X1) != empty_set
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f89,plain,
( spl7_4
| ~ spl7_1 ),
inference(avatar_split_clause,[],[f56,f71,f85]) ).
fof(f56,plain,
( ~ disjoint(sK2,sK3)
| in(sK4,sK3) ),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
( ( disjoint(sK2,sK3)
& in(sK4,sK2)
& in(sK4,sK3) )
| ( ! [X3] :
( ~ in(X3,sK3)
| ~ in(X3,sK2) )
& ~ disjoint(sK2,sK3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f33,f35,f34]) ).
fof(f34,plain,
( ? [X0,X1] :
( ( disjoint(X0,X1)
& ? [X2] :
( in(X2,X0)
& in(X2,X1) ) )
| ( ! [X3] :
( ~ in(X3,X1)
| ~ in(X3,X0) )
& ~ disjoint(X0,X1) ) )
=> ( ( disjoint(sK2,sK3)
& ? [X2] :
( in(X2,sK2)
& in(X2,sK3) ) )
| ( ! [X3] :
( ~ in(X3,sK3)
| ~ in(X3,sK2) )
& ~ disjoint(sK2,sK3) ) ) ),
introduced(choice_axiom,[]) ).
fof(f35,plain,
( ? [X2] :
( in(X2,sK2)
& in(X2,sK3) )
=> ( in(sK4,sK2)
& in(sK4,sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f33,plain,
? [X0,X1] :
( ( disjoint(X0,X1)
& ? [X2] :
( in(X2,X0)
& in(X2,X1) ) )
| ( ! [X3] :
( ~ in(X3,X1)
| ~ in(X3,X0) )
& ~ disjoint(X0,X1) ) ),
inference(rectify,[],[f20]) ).
fof(f20,plain,
? [X0,X1] :
( ( disjoint(X0,X1)
& ? [X3] :
( in(X3,X0)
& in(X3,X1) ) )
| ( ! [X2] :
( ~ in(X2,X1)
| ~ in(X2,X0) )
& ~ disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,plain,
~ ! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X3] :
( in(X3,X0)
& in(X3,X1) ) )
& ~ ( ~ disjoint(X0,X1)
& ! [X2] :
~ ( in(X2,X1)
& in(X2,X0) ) ) ),
inference(rectify,[],[f14]) ).
fof(f14,negated_conjecture,
~ ! [X0,X1] :
( ~ ( ~ disjoint(X0,X1)
& ! [X2] :
~ ( in(X2,X1)
& in(X2,X0) ) )
& ~ ( disjoint(X0,X1)
& ? [X2] :
( in(X2,X1)
& in(X2,X0) ) ) ),
inference(negated_conjecture,[],[f13]) ).
fof(f13,conjecture,
! [X0,X1] :
( ~ ( ~ disjoint(X0,X1)
& ! [X2] :
~ ( in(X2,X1)
& in(X2,X0) ) )
& ~ ( disjoint(X0,X1)
& ? [X2] :
( in(X2,X1)
& in(X2,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_0) ).
fof(f88,plain,
( spl7_4
| spl7_3 ),
inference(avatar_split_clause,[],[f57,f80,f85]) ).
fof(f57,plain,
! [X3] :
( ~ in(X3,sK3)
| in(sK4,sK3)
| ~ in(X3,sK2) ),
inference(cnf_transformation,[],[f36]) ).
fof(f83,plain,
( spl7_3
| spl7_1 ),
inference(avatar_split_clause,[],[f61,f71,f80]) ).
fof(f61,plain,
! [X3] :
( disjoint(sK2,sK3)
| ~ in(X3,sK2)
| ~ in(X3,sK3) ),
inference(cnf_transformation,[],[f36]) ).
fof(f78,plain,
( ~ spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f58,f75,f71]) ).
fof(f58,plain,
( in(sK4,sK2)
| ~ disjoint(sK2,sK3) ),
inference(cnf_transformation,[],[f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU119+2 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 30 15:02:01 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.57 % (8721)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.57 % (8716)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.58 % (8724)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.63/0.58 % (8708)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 1.63/0.58 % (8732)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 1.63/0.58 % (8710)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 1.63/0.58 % (8721)First to succeed.
% 1.63/0.58 % (8713)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 1.63/0.59 % (8716)Instruction limit reached!
% 1.63/0.59 % (8716)------------------------------
% 1.63/0.59 % (8716)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.63/0.59 % (8716)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.63/0.59 % (8716)Termination reason: Unknown
% 1.63/0.59 % (8716)Termination phase: Saturation
% 1.63/0.59
% 1.63/0.59 % (8716)Memory used [KB]: 5373
% 1.63/0.59 % (8716)Time elapsed: 0.005 s
% 1.63/0.59 % (8716)Instructions burned: 2 (million)
% 1.63/0.59 % (8716)------------------------------
% 1.63/0.59 % (8716)------------------------------
% 1.63/0.59 % (8721)Refutation found. Thanks to Tanya!
% 1.63/0.59 % SZS status Theorem for theBenchmark
% 1.63/0.59 % SZS output start Proof for theBenchmark
% See solution above
% 1.63/0.59 % (8721)------------------------------
% 1.63/0.59 % (8721)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.63/0.59 % (8721)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.63/0.59 % (8721)Termination reason: Refutation
% 1.63/0.59
% 1.63/0.59 % (8721)Memory used [KB]: 5500
% 1.63/0.59 % (8721)Time elapsed: 0.157 s
% 1.63/0.59 % (8721)Instructions burned: 7 (million)
% 1.63/0.59 % (8721)------------------------------
% 1.63/0.59 % (8721)------------------------------
% 1.63/0.59 % (8707)Success in time 0.239 s
%------------------------------------------------------------------------------