TSTP Solution File: SEU154+1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SEU154+1 : 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 : 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 : Wed Aug 31 18:32:11 EDT 2022
% Result : Theorem 1.45s 0.57s
% Output : Refutation 1.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 57 ( 16 unt; 0 def)
% Number of atoms : 225 ( 57 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 275 ( 107 ~; 94 |; 57 &)
% ( 10 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 123 ( 107 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f147,plain,
$false,
inference(subsumption_resolution,[],[f144,f58]) ).
fof(f58,plain,
~ in(sK1,sK0),
inference(cnf_transformation,[],[f34]) ).
fof(f34,plain,
( ~ disjoint(singleton(sK1),sK0)
& ~ in(sK1,sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f32,f33]) ).
fof(f33,plain,
( ? [X0,X1] :
( ~ disjoint(singleton(X1),X0)
& ~ in(X1,X0) )
=> ( ~ disjoint(singleton(sK1),sK0)
& ~ in(sK1,sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f32,plain,
? [X0,X1] :
( ~ disjoint(singleton(X1),X0)
& ~ in(X1,X0) ),
inference(rectify,[],[f27]) ).
fof(f27,plain,
? [X1,X0] :
( ~ disjoint(singleton(X0),X1)
& ~ in(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,negated_conjecture,
~ ! [X1,X0] :
( ~ in(X0,X1)
=> disjoint(singleton(X0),X1) ),
inference(negated_conjecture,[],[f13]) ).
fof(f13,conjecture,
! [X1,X0] :
( ~ in(X0,X1)
=> disjoint(singleton(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_1) ).
fof(f144,plain,
in(sK1,sK0),
inference(backward_demodulation,[],[f136,f139]) ).
fof(f139,plain,
sK1 = sK5(empty_set,set_intersection2(sK0,singleton(sK1))),
inference(resolution,[],[f135,f85]) ).
fof(f85,plain,
! [X3,X1] :
( ~ in(X3,singleton(X1))
| X1 = X3 ),
inference(equality_resolution,[],[f64]) ).
fof(f64,plain,
! [X3,X0,X1] :
( X1 = X3
| ~ in(X3,X0)
| singleton(X1) != X0 ),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0,X1] :
( ( singleton(X1) = X0
| ( ( ~ in(sK4(X0,X1),X0)
| sK4(X0,X1) != X1 )
& ( in(sK4(X0,X1),X0)
| sK4(X0,X1) = X1 ) ) )
& ( ! [X3] :
( ( X1 = X3
| ~ in(X3,X0) )
& ( in(X3,X0)
| X1 != X3 ) )
| singleton(X1) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f40,f41]) ).
fof(f41,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X0)
| X1 != X2 )
& ( in(X2,X0)
| X1 = X2 ) )
=> ( ( ~ in(sK4(X0,X1),X0)
| sK4(X0,X1) != X1 )
& ( in(sK4(X0,X1),X0)
| sK4(X0,X1) = X1 ) ) ),
introduced(choice_axiom,[]) ).
fof(f40,plain,
! [X0,X1] :
( ( singleton(X1) = X0
| ? [X2] :
( ( ~ in(X2,X0)
| X1 != X2 )
& ( in(X2,X0)
| X1 = X2 ) ) )
& ( ! [X3] :
( ( X1 = X3
| ~ in(X3,X0) )
& ( in(X3,X0)
| X1 != X3 ) )
| singleton(X1) != X0 ) ),
inference(rectify,[],[f39]) ).
fof(f39,plain,
! [X1,X0] :
( ( singleton(X0) = X1
| ? [X2] :
( ( ~ in(X2,X1)
| X0 != X2 )
& ( in(X2,X1)
| X0 = X2 ) ) )
& ( ! [X2] :
( ( X0 = X2
| ~ in(X2,X1) )
& ( in(X2,X1)
| X0 != X2 ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X1,X0] :
( singleton(X0) = X1
<=> ! [X2] :
( X0 = X2
<=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f135,plain,
in(sK5(empty_set,set_intersection2(sK0,singleton(sK1))),singleton(sK1)),
inference(resolution,[],[f133,f91]) ).
fof(f91,plain,
! [X2,X3,X1] :
( ~ in(X3,set_intersection2(X1,X2))
| in(X3,X2) ),
inference(equality_resolution,[],[f83]) ).
fof(f83,plain,
! [X2,X3,X0,X1] :
( in(X3,X2)
| ~ in(X3,X0)
| set_intersection2(X1,X2) != X0 ),
inference(cnf_transformation,[],[f55]) ).
fof(f55,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(sK6(X0,X1,X2),X0)
| ~ in(sK6(X0,X1,X2),X1)
| ~ in(sK6(X0,X1,X2),X2) )
& ( in(sK6(X0,X1,X2),X0)
| ( in(sK6(X0,X1,X2),X1)
& in(sK6(X0,X1,X2),X2) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f53,f54]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ? [X4] :
( ( ~ in(X4,X0)
| ~ in(X4,X1)
| ~ in(X4,X2) )
& ( in(X4,X0)
| ( in(X4,X1)
& in(X4,X2) ) ) )
=> ( ( ~ in(sK6(X0,X1,X2),X0)
| ~ in(sK6(X0,X1,X2),X1)
| ~ in(sK6(X0,X1,X2),X2) )
& ( in(sK6(X0,X1,X2),X0)
| ( in(sK6(X0,X1,X2),X1)
& in(sK6(X0,X1,X2),X2) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f53,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,[],[f52]) ).
fof(f52,plain,
! [X2,X0,X1] :
( ( ! [X3] :
( ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) ) )
| set_intersection2(X0,X1) != X2 )
& ( set_intersection2(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( in(X3,X2)
| ( in(X3,X0)
& in(X3,X1) ) ) ) ) ),
inference(flattening,[],[f51]) ).
fof(f51,plain,
! [X2,X0,X1] :
( ( ! [X3] :
( ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) ) )
| set_intersection2(X0,X1) != X2 )
& ( set_intersection2(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( in(X3,X2)
| ( in(X3,X0)
& in(X3,X1) ) ) ) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X2,X0,X1] :
( ! [X3] :
( ( in(X3,X0)
& in(X3,X1) )
<=> in(X3,X2) )
<=> set_intersection2(X0,X1) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f133,plain,
in(sK5(empty_set,set_intersection2(sK0,singleton(sK1))),set_intersection2(sK0,singleton(sK1))),
inference(resolution,[],[f129,f69]) ).
fof(f69,plain,
! [X0,X1] :
( subset(X1,X0)
| in(sK5(X0,X1),X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0,X1] :
( ( ! [X2] :
( ~ in(X2,X1)
| in(X2,X0) )
| ~ subset(X1,X0) )
& ( subset(X1,X0)
| ( in(sK5(X0,X1),X1)
& ~ in(sK5(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f44,f45]) ).
fof(f45,plain,
! [X0,X1] :
( ? [X3] :
( in(X3,X1)
& ~ in(X3,X0) )
=> ( in(sK5(X0,X1),X1)
& ~ in(sK5(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f44,plain,
! [X0,X1] :
( ( ! [X2] :
( ~ in(X2,X1)
| in(X2,X0) )
| ~ subset(X1,X0) )
& ( subset(X1,X0)
| ? [X3] :
( in(X3,X1)
& ~ in(X3,X0) ) ) ),
inference(rectify,[],[f43]) ).
fof(f43,plain,
! [X1,X0] :
( ( ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) )
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) ) ) ),
inference(nnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X1,X0] :
( ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) )
<=> subset(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> in(X2,X1) )
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f129,plain,
~ subset(set_intersection2(sK0,singleton(sK1)),empty_set),
inference(forward_demodulation,[],[f128,f67]) ).
fof(f67,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1] : 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/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f128,plain,
~ subset(set_intersection2(singleton(sK1),sK0),empty_set),
inference(subsumption_resolution,[],[f119,f74]) ).
fof(f74,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(f119,plain,
( ~ subset(empty_set,set_intersection2(singleton(sK1),sK0))
| ~ subset(set_intersection2(singleton(sK1),sK0),empty_set) ),
inference(extensionality_resolution,[],[f73,f95]) ).
fof(f95,plain,
empty_set != set_intersection2(singleton(sK1),sK0),
inference(resolution,[],[f77,f59]) ).
fof(f59,plain,
~ disjoint(singleton(sK1),sK0),
inference(cnf_transformation,[],[f34]) ).
fof(f77,plain,
! [X0,X1] :
( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set ),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0,X1] :
( ( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) )
& ( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set ) ),
inference(rectify,[],[f49]) ).
fof(f49,plain,
! [X1,X0] :
( ( set_intersection2(X1,X0) = empty_set
| ~ disjoint(X1,X0) )
& ( disjoint(X1,X0)
| set_intersection2(X1,X0) != empty_set ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X1,X0] :
( set_intersection2(X1,X0) = empty_set
<=> disjoint(X1,X0) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X1,X0] :
( set_intersection2(X0,X1) = empty_set
<=> disjoint(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(f73,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f47]) ).
fof(f47,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X1,X0] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f136,plain,
in(sK5(empty_set,set_intersection2(sK0,singleton(sK1))),sK0),
inference(resolution,[],[f133,f90]) ).
fof(f90,plain,
! [X2,X3,X1] :
( ~ in(X3,set_intersection2(X1,X2))
| in(X3,X1) ),
inference(equality_resolution,[],[f84]) ).
fof(f84,plain,
! [X2,X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| set_intersection2(X1,X2) != X0 ),
inference(cnf_transformation,[],[f55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU154+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % 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 : n008.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 14:45:40 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.45/0.54 % (24969)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 1.45/0.54 % (24968)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.45/0.54 TRYING [1]
% 1.45/0.54 % (24970)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.45/0.54 % (24978)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)
% 1.45/0.55 % (24969)Instruction limit reached!
% 1.45/0.55 % (24969)------------------------------
% 1.45/0.55 % (24969)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.45/0.55 % (24985)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 1.45/0.55 % (24977)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 1.45/0.55 % (24984)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 1.45/0.55 TRYING [2]
% 1.45/0.55 TRYING [3]
% 1.45/0.55 % (24976)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 1.45/0.55 % (24970)Instruction limit reached!
% 1.45/0.55 % (24970)------------------------------
% 1.45/0.55 % (24970)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.45/0.55 % (24970)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.45/0.55 % (24970)Termination reason: Unknown
% 1.45/0.55 % (24970)Termination phase: Saturation
% 1.45/0.55
% 1.45/0.55 % (24970)Memory used [KB]: 895
% 1.45/0.55 % (24970)Time elapsed: 0.005 s
% 1.45/0.55 % (24970)Instructions burned: 3 (million)
% 1.45/0.55 % (24970)------------------------------
% 1.45/0.55 % (24970)------------------------------
% 1.45/0.56 % (24969)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.45/0.56 % (24969)Termination reason: Unknown
% 1.45/0.56 % (24969)Termination phase: Saturation
% 1.45/0.56
% 1.45/0.56 % (24969)Memory used [KB]: 5500
% 1.45/0.56 % (24969)Time elapsed: 0.133 s
% 1.45/0.56 % (24969)Instructions burned: 7 (million)
% 1.45/0.56 % (24969)------------------------------
% 1.45/0.56 % (24969)------------------------------
% 1.45/0.56 % (24986)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 1.45/0.56 % (24984)First to succeed.
% 1.45/0.56 TRYING [4]
% 1.45/0.57 % (24984)Refutation found. Thanks to Tanya!
% 1.45/0.57 % SZS status Theorem for theBenchmark
% 1.45/0.57 % SZS output start Proof for theBenchmark
% See solution above
% 1.45/0.57 % (24984)------------------------------
% 1.45/0.57 % (24984)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.45/0.57 % (24984)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.45/0.57 % (24984)Termination reason: Refutation
% 1.45/0.57
% 1.45/0.57 % (24984)Memory used [KB]: 1023
% 1.45/0.57 % (24984)Time elapsed: 0.135 s
% 1.45/0.57 % (24984)Instructions burned: 5 (million)
% 1.45/0.57 % (24984)------------------------------
% 1.45/0.57 % (24984)------------------------------
% 1.45/0.57 % (24961)Success in time 0.22 s
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