TSTP Solution File: SET908+1 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET908+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% Computer : n025.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 18:22:43 EDT 2022
% Result : Theorem 0.19s 0.49s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 45 ( 17 unt; 0 def)
% Number of atoms : 174 ( 63 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 208 ( 79 ~; 80 |; 38 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 103 ( 87 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f135,plain,
$false,
inference(resolution,[],[f126,f67]) ).
fof(f67,plain,
! [X2] : in(X2,singleton(X2)),
inference(equality_resolution,[],[f66]) ).
fof(f66,plain,
! [X2,X0] :
( in(X2,X0)
| singleton(X2) != X0 ),
inference(equality_resolution,[],[f46]) ).
fof(f46,plain,
! [X2,X0,X1] :
( in(X2,X0)
| X1 != X2
| singleton(X1) != X0 ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] :
( ( ! [X2] :
( ( X1 = X2
| ~ in(X2,X0) )
& ( in(X2,X0)
| X1 != X2 ) )
| singleton(X1) != X0 )
& ( singleton(X1) = X0
| ( ( ~ in(sK0(X0,X1),X0)
| sK0(X0,X1) != X1 )
& ( in(sK0(X0,X1),X0)
| sK0(X0,X1) = X1 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f22,f23]) ).
fof(f23,plain,
! [X0,X1] :
( ? [X3] :
( ( ~ in(X3,X0)
| X1 != X3 )
& ( in(X3,X0)
| X1 = X3 ) )
=> ( ( ~ in(sK0(X0,X1),X0)
| sK0(X0,X1) != X1 )
& ( in(sK0(X0,X1),X0)
| sK0(X0,X1) = X1 ) ) ),
introduced(choice_axiom,[]) ).
fof(f22,plain,
! [X0,X1] :
( ( ! [X2] :
( ( X1 = X2
| ~ in(X2,X0) )
& ( in(X2,X0)
| X1 != X2 ) )
| singleton(X1) != X0 )
& ( singleton(X1) = X0
| ? [X3] :
( ( ~ in(X3,X0)
| X1 != X3 )
& ( in(X3,X0)
| X1 = X3 ) ) ) ),
inference(rectify,[],[f21]) ).
fof(f21,plain,
! [X0,X1] :
( ( ! [X2] :
( ( X1 = X2
| ~ in(X2,X0) )
& ( in(X2,X0)
| X1 != X2 ) )
| singleton(X1) != X0 )
& ( singleton(X1) = X0
| ? [X2] :
( ( ~ in(X2,X0)
| X1 != X2 )
& ( in(X2,X0)
| X1 = X2 ) ) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f14,plain,
! [X0,X1] :
( ! [X2] :
( X1 = X2
<=> in(X2,X0) )
<=> singleton(X1) = X0 ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X1,X0] :
( ! [X2] :
( in(X2,X1)
<=> X0 = X2 )
<=> singleton(X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f126,plain,
! [X8] : ~ in(X8,singleton(sK4)),
inference(subsumption_resolution,[],[f125,f94]) ).
fof(f94,plain,
! [X8] : ~ in(X8,sK3),
inference(subsumption_resolution,[],[f93,f68]) ).
fof(f68,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f52]) ).
fof(f52,plain,
! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0] :
( ( empty_set = X0
| in(sK1(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f28,f29]) ).
fof(f29,plain,
! [X0] :
( ? [X1] : in(X1,X0)
=> in(sK1(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f28,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f27]) ).
fof(f27,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( empty_set = X0
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f93,plain,
! [X8] :
( ~ in(X8,sK3)
| in(X8,empty_set) ),
inference(superposition,[],[f70,f72]) ).
fof(f72,plain,
empty_set = set_union2(sK3,singleton(sK4)),
inference(forward_demodulation,[],[f55,f50]) ).
fof(f50,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f16]) ).
fof(f16,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X1,X0] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f55,plain,
empty_set = set_union2(singleton(sK4),sK3),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
empty_set = set_union2(singleton(sK4),sK3),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f33,f34]) ).
fof(f34,plain,
( ? [X0,X1] : empty_set = set_union2(singleton(X1),X0)
=> empty_set = set_union2(singleton(sK4),sK3) ),
introduced(choice_axiom,[]) ).
fof(f33,plain,
? [X0,X1] : empty_set = set_union2(singleton(X1),X0),
inference(rectify,[],[f18]) ).
fof(f18,plain,
? [X1,X0] : empty_set = set_union2(singleton(X0),X1),
inference(ennf_transformation,[],[f13]) ).
fof(f13,negated_conjecture,
~ ! [X0,X1] : empty_set != set_union2(singleton(X0),X1),
inference(negated_conjecture,[],[f12]) ).
fof(f12,conjecture,
! [X0,X1] : empty_set != set_union2(singleton(X0),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_zfmisc_1) ).
fof(f70,plain,
! [X2,X3,X1] :
( in(X3,set_union2(X1,X2))
| ~ in(X3,X1) ),
inference(equality_resolution,[],[f60]) ).
fof(f60,plain,
! [X2,X3,X0,X1] :
( in(X3,X0)
| ~ in(X3,X1)
| set_union2(X1,X2) != X0 ),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( in(X3,X1)
| in(X3,X2)
| ~ in(X3,X0) )
& ( in(X3,X0)
| ( ~ in(X3,X1)
& ~ in(X3,X2) ) ) )
| set_union2(X1,X2) != X0 )
& ( set_union2(X1,X2) = X0
| ( ( ~ in(sK5(X0,X1,X2),X0)
| ( ~ in(sK5(X0,X1,X2),X1)
& ~ in(sK5(X0,X1,X2),X2) ) )
& ( in(sK5(X0,X1,X2),X0)
| in(sK5(X0,X1,X2),X1)
| in(sK5(X0,X1,X2),X2) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f38,f39]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ? [X4] :
( ( ~ in(X4,X0)
| ( ~ in(X4,X1)
& ~ in(X4,X2) ) )
& ( in(X4,X0)
| in(X4,X1)
| in(X4,X2) ) )
=> ( ( ~ in(sK5(X0,X1,X2),X0)
| ( ~ in(sK5(X0,X1,X2),X1)
& ~ in(sK5(X0,X1,X2),X2) ) )
& ( in(sK5(X0,X1,X2),X0)
| in(sK5(X0,X1,X2),X1)
| in(sK5(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( in(X3,X1)
| in(X3,X2)
| ~ in(X3,X0) )
& ( in(X3,X0)
| ( ~ in(X3,X1)
& ~ in(X3,X2) ) ) )
| set_union2(X1,X2) != X0 )
& ( set_union2(X1,X2) = X0
| ? [X4] :
( ( ~ in(X4,X0)
| ( ~ in(X4,X1)
& ~ in(X4,X2) ) )
& ( in(X4,X0)
| in(X4,X1)
| in(X4,X2) ) ) ) ),
inference(rectify,[],[f37]) ).
fof(f37,plain,
! [X2,X0,X1] :
( ( ! [X3] :
( ( in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( in(X3,X2)
| ( ~ in(X3,X0)
& ~ in(X3,X1) ) ) )
| set_union2(X0,X1) != X2 )
& ( set_union2(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X2)
| ( ~ in(X3,X0)
& ~ in(X3,X1) ) )
& ( in(X3,X2)
| in(X3,X0)
| in(X3,X1) ) ) ) ),
inference(flattening,[],[f36]) ).
fof(f36,plain,
! [X2,X0,X1] :
( ( ! [X3] :
( ( in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( in(X3,X2)
| ( ~ in(X3,X0)
& ~ in(X3,X1) ) ) )
| set_union2(X0,X1) != X2 )
& ( set_union2(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,[],[f5]) ).
fof(f5,axiom,
! [X2,X0,X1] :
( ! [X3] :
( ( in(X3,X0)
| in(X3,X1) )
<=> in(X3,X2) )
<=> set_union2(X0,X1) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f125,plain,
! [X8] :
( in(X8,sK3)
| ~ in(X8,singleton(sK4)) ),
inference(superposition,[],[f71,f99]) ).
fof(f99,plain,
set_union2(sK3,singleton(sK4)) = sK3,
inference(backward_demodulation,[],[f72,f95]) ).
fof(f95,plain,
empty_set = sK3,
inference(resolution,[],[f94,f53]) ).
fof(f53,plain,
! [X0] :
( in(sK1(X0),X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f30]) ).
fof(f71,plain,
! [X2,X3,X1] :
( in(X3,set_union2(X1,X2))
| ~ in(X3,X2) ),
inference(equality_resolution,[],[f59]) ).
fof(f59,plain,
! [X2,X3,X0,X1] :
( in(X3,X0)
| ~ in(X3,X2)
| set_union2(X1,X2) != X0 ),
inference(cnf_transformation,[],[f40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET908+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34 % Computer : n025.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 14:47:44 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.48 % (18784)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.19/0.48 % (18792)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.49 % (18792)First to succeed.
% 0.19/0.49 % (18792)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 % (18792)------------------------------
% 0.19/0.49 % (18792)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.49 % (18792)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.49 % (18792)Termination reason: Refutation
% 0.19/0.49
% 0.19/0.49 % (18792)Memory used [KB]: 6012
% 0.19/0.49 % (18792)Time elapsed: 0.104 s
% 0.19/0.49 % (18792)Instructions burned: 4 (million)
% 0.19/0.49 % (18792)------------------------------
% 0.19/0.49 % (18792)------------------------------
% 0.19/0.49 % (18776)Success in time 0.147 s
%------------------------------------------------------------------------------