TSTP Solution File: SET942+1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SET942+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_sat --cores 0 -t %d %s
% Computer : n022.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 18:26:09 EDT 2022
% Result : Theorem 0.19s 0.46s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 47 ( 7 unt; 0 def)
% Number of atoms : 170 ( 13 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 196 ( 73 ~; 69 |; 37 &)
% ( 7 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 110 ( 90 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f99,plain,
$false,
inference(subsumption_resolution,[],[f98,f54]) ).
fof(f54,plain,
~ subset(sF8,sF9),
inference(definition_folding,[],[f48,f53,f52]) ).
fof(f52,plain,
union(sK7) = sF8,
introduced(function_definition,[]) ).
fof(f53,plain,
union(sK6) = sF9,
introduced(function_definition,[]) ).
fof(f48,plain,
~ subset(union(sK7),union(sK6)),
inference(cnf_transformation,[],[f33]) ).
fof(f33,plain,
( ~ subset(union(sK7),union(sK6))
& subset(sK7,sK6) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f14,f32]) ).
fof(f32,plain,
( ? [X0,X1] :
( ~ subset(union(X1),union(X0))
& subset(X1,X0) )
=> ( ~ subset(union(sK7),union(sK6))
& subset(sK7,sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f14,plain,
? [X0,X1] :
( ~ subset(union(X1),union(X0))
& subset(X1,X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,plain,
~ ! [X1,X0] :
( subset(X1,X0)
=> subset(union(X1),union(X0)) ),
inference(rectify,[],[f8]) ).
fof(f8,negated_conjecture,
~ ! [X1,X0] :
( subset(X0,X1)
=> subset(union(X0),union(X1)) ),
inference(negated_conjecture,[],[f7]) ).
fof(f7,conjecture,
! [X1,X0] :
( subset(X0,X1)
=> subset(union(X0),union(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t95_zfmisc_1) ).
fof(f98,plain,
subset(sF8,sF9),
inference(duplicate_literal_removal,[],[f95]) ).
fof(f95,plain,
( subset(sF8,sF9)
| subset(sF8,sF9) ),
inference(resolution,[],[f93,f36]) ).
fof(f36,plain,
! [X0,X1] :
( ~ in(sK0(X0,X1),X0)
| subset(X1,X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( ( ! [X2] :
( in(X2,X0)
| ~ in(X2,X1) )
| ~ subset(X1,X0) )
& ( subset(X1,X0)
| ( ~ in(sK0(X0,X1),X0)
& in(sK0(X0,X1),X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f18,f19]) ).
fof(f19,plain,
! [X0,X1] :
( ? [X3] :
( ~ in(X3,X0)
& in(X3,X1) )
=> ( ~ in(sK0(X0,X1),X0)
& in(sK0(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
! [X0,X1] :
( ( ! [X2] :
( in(X2,X0)
| ~ in(X2,X1) )
| ~ subset(X1,X0) )
& ( subset(X1,X0)
| ? [X3] :
( ~ in(X3,X0)
& in(X3,X1) ) ) ),
inference(rectify,[],[f17]) ).
fof(f17,plain,
! [X0,X1] :
( ( ! [X2] :
( in(X2,X0)
| ~ in(X2,X1) )
| ~ subset(X1,X0) )
& ( subset(X1,X0)
| ? [X2] :
( ~ in(X2,X0)
& in(X2,X1) ) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f13,plain,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
| ~ in(X2,X1) )
<=> subset(X1,X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,plain,
! [X0,X1] :
( ! [X2] :
( in(X2,X1)
=> in(X2,X0) )
<=> subset(X1,X0) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X1,X0] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f93,plain,
! [X0] :
( in(sK0(X0,sF8),sF9)
| subset(sF8,X0) ),
inference(resolution,[],[f92,f35]) ).
fof(f35,plain,
! [X0,X1] :
( in(sK0(X0,X1),X1)
| subset(X1,X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f92,plain,
! [X4] :
( ~ in(X4,sF8)
| in(X4,sF9) ),
inference(duplicate_literal_removal,[],[f91]) ).
fof(f91,plain,
! [X4] :
( in(X4,sF9)
| ~ in(X4,sF8)
| ~ in(X4,sF8) ),
inference(forward_demodulation,[],[f90,f52]) ).
fof(f90,plain,
! [X4] :
( ~ in(X4,union(sK7))
| ~ in(X4,sF8)
| in(X4,sF9) ),
inference(resolution,[],[f85,f51]) ).
fof(f51,plain,
! [X2,X1] :
( in(X2,sK2(X1,X2))
| ~ in(X2,union(X1)) ),
inference(equality_resolution,[],[f42]) ).
fof(f42,plain,
! [X2,X0,X1] :
( in(X2,sK2(X1,X2))
| ~ in(X2,X0)
| union(X1) != X0 ),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0,X1] :
( ( ! [X2] :
( ( in(X2,X0)
| ! [X3] :
( ~ in(X3,X1)
| ~ in(X2,X3) ) )
& ( ( in(sK2(X1,X2),X1)
& in(X2,sK2(X1,X2)) )
| ~ in(X2,X0) ) )
| union(X1) != X0 )
& ( union(X1) = X0
| ( ( ! [X6] :
( ~ in(X6,X1)
| ~ in(sK3(X0,X1),X6) )
| ~ in(sK3(X0,X1),X0) )
& ( ( in(sK4(X0,X1),X1)
& in(sK3(X0,X1),sK4(X0,X1)) )
| in(sK3(X0,X1),X0) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f24,f27,f26,f25]) ).
fof(f25,plain,
! [X1,X2] :
( ? [X4] :
( in(X4,X1)
& in(X2,X4) )
=> ( in(sK2(X1,X2),X1)
& in(X2,sK2(X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f26,plain,
! [X0,X1] :
( ? [X5] :
( ( ! [X6] :
( ~ in(X6,X1)
| ~ in(X5,X6) )
| ~ in(X5,X0) )
& ( ? [X7] :
( in(X7,X1)
& in(X5,X7) )
| in(X5,X0) ) )
=> ( ( ! [X6] :
( ~ in(X6,X1)
| ~ in(sK3(X0,X1),X6) )
| ~ in(sK3(X0,X1),X0) )
& ( ? [X7] :
( in(X7,X1)
& in(sK3(X0,X1),X7) )
| in(sK3(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
! [X0,X1] :
( ? [X7] :
( in(X7,X1)
& in(sK3(X0,X1),X7) )
=> ( in(sK4(X0,X1),X1)
& in(sK3(X0,X1),sK4(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f24,plain,
! [X0,X1] :
( ( ! [X2] :
( ( in(X2,X0)
| ! [X3] :
( ~ in(X3,X1)
| ~ in(X2,X3) ) )
& ( ? [X4] :
( in(X4,X1)
& in(X2,X4) )
| ~ in(X2,X0) ) )
| union(X1) != X0 )
& ( union(X1) = X0
| ? [X5] :
( ( ! [X6] :
( ~ in(X6,X1)
| ~ in(X5,X6) )
| ~ in(X5,X0) )
& ( ? [X7] :
( in(X7,X1)
& in(X5,X7) )
| in(X5,X0) ) ) ) ),
inference(rectify,[],[f23]) ).
fof(f23,plain,
! [X0,X1] :
( ( ! [X2] :
( ( in(X2,X0)
| ! [X3] :
( ~ in(X3,X1)
| ~ in(X2,X3) ) )
& ( ? [X3] :
( in(X3,X1)
& in(X2,X3) )
| ~ in(X2,X0) ) )
| union(X1) != X0 )
& ( union(X1) = X0
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,X1)
| ~ in(X2,X3) )
| ~ in(X2,X0) )
& ( ? [X3] :
( in(X3,X1)
& in(X2,X3) )
| in(X2,X0) ) ) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f9,plain,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> ? [X3] :
( in(X3,X1)
& in(X2,X3) ) )
<=> union(X1) = X0 ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X1,X0] :
( union(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X2,X3)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
fof(f85,plain,
! [X8,X9] :
( ~ in(X8,sK2(sK7,X9))
| in(X8,sF9)
| ~ in(X9,sF8) ),
inference(forward_demodulation,[],[f82,f53]) ).
fof(f82,plain,
! [X8,X9] :
( ~ in(X9,sF8)
| in(X8,union(sK6))
| ~ in(X8,sK2(sK7,X9)) ),
inference(resolution,[],[f49,f66]) ).
fof(f66,plain,
! [X2] :
( in(sK2(sK7,X2),sK6)
| ~ in(X2,sF8) ),
inference(forward_demodulation,[],[f65,f52]) ).
fof(f65,plain,
! [X2] :
( in(sK2(sK7,X2),sK6)
| ~ in(X2,union(sK7)) ),
inference(resolution,[],[f50,f58]) ).
fof(f58,plain,
! [X0] :
( ~ in(X0,sK7)
| in(X0,sK6) ),
inference(resolution,[],[f37,f47]) ).
fof(f47,plain,
subset(sK7,sK6),
inference(cnf_transformation,[],[f33]) ).
fof(f37,plain,
! [X2,X0,X1] :
( ~ subset(X1,X0)
| in(X2,X0)
| ~ in(X2,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f50,plain,
! [X2,X1] :
( in(sK2(X1,X2),X1)
| ~ in(X2,union(X1)) ),
inference(equality_resolution,[],[f43]) ).
fof(f43,plain,
! [X2,X0,X1] :
( in(sK2(X1,X2),X1)
| ~ in(X2,X0)
| union(X1) != X0 ),
inference(cnf_transformation,[],[f28]) ).
fof(f49,plain,
! [X2,X3,X1] :
( ~ in(X3,X1)
| ~ in(X2,X3)
| in(X2,union(X1)) ),
inference(equality_resolution,[],[f44]) ).
fof(f44,plain,
! [X2,X3,X0,X1] :
( in(X2,X0)
| ~ in(X3,X1)
| ~ in(X2,X3)
| union(X1) != X0 ),
inference(cnf_transformation,[],[f28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET942+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % 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 : n022.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 14:32:56 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.44 % (21775)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/101Mi)
% 0.19/0.44 % (21783)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/176Mi)
% 0.19/0.46 % (21775)First to succeed.
% 0.19/0.46 % (21775)Refutation found. Thanks to Tanya!
% 0.19/0.46 % SZS status Theorem for theBenchmark
% 0.19/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.46 % (21775)------------------------------
% 0.19/0.46 % (21775)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.46 % (21775)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.46 % (21775)Termination reason: Refutation
% 0.19/0.46
% 0.19/0.46 % (21775)Memory used [KB]: 5500
% 0.19/0.46 % (21775)Time elapsed: 0.064 s
% 0.19/0.46 % (21775)Instructions burned: 4 (million)
% 0.19/0.46 % (21775)------------------------------
% 0.19/0.46 % (21775)------------------------------
% 0.19/0.46 % (21762)Success in time 0.117 s
%------------------------------------------------------------------------------