TSTP Solution File: SET949+1 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET949+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 : n007.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 18:22:50 EDT 2022
% Result : Theorem 0.20s 0.52s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 35 ( 16 unt; 0 def)
% Number of atoms : 134 ( 58 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 158 ( 59 ~; 45 |; 46 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 138 ( 109 !; 29 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f131,plain,
$false,
inference(trivial_inequality_removal,[],[f118]) ).
fof(f118,plain,
sK2 != sK2,
inference(superposition,[],[f102,f89]) ).
fof(f89,plain,
unordered_pair(singleton(sK5(sK0,sK1,sK2)),unordered_pair(sK4(sK0,sK1,sK2),sK5(sK0,sK1,sK2))) = sK2,
inference(resolution,[],[f60,f32]) ).
fof(f32,plain,
in(sK2,cartesian_product2(sK1,sK0)),
inference(cnf_transformation,[],[f18]) ).
fof(f18,plain,
( in(sK2,cartesian_product2(sK1,sK0))
& ! [X3,X4] : sK2 != ordered_pair(X4,X3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f15,f17]) ).
fof(f17,plain,
( ? [X0,X1,X2] :
( in(X2,cartesian_product2(X1,X0))
& ! [X3,X4] : ordered_pair(X4,X3) != X2 )
=> ( in(sK2,cartesian_product2(sK1,sK0))
& ! [X4,X3] : sK2 != ordered_pair(X4,X3) ) ),
introduced(choice_axiom,[]) ).
fof(f15,plain,
? [X0,X1,X2] :
( in(X2,cartesian_product2(X1,X0))
& ! [X3,X4] : ordered_pair(X4,X3) != X2 ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,plain,
~ ! [X0,X1,X2] :
~ ( in(X2,cartesian_product2(X1,X0))
& ! [X3,X4] : ordered_pair(X4,X3) != X2 ),
inference(rectify,[],[f9]) ).
fof(f9,negated_conjecture,
~ ! [X2,X1,X0] :
~ ( ! [X4,X3] : ordered_pair(X3,X4) != X0
& in(X0,cartesian_product2(X1,X2)) ),
inference(negated_conjecture,[],[f8]) ).
fof(f8,conjecture,
! [X2,X1,X0] :
~ ( ! [X4,X3] : ordered_pair(X3,X4) != X0
& in(X0,cartesian_product2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t102_zfmisc_1) ).
fof(f60,plain,
! [X2,X3,X0] :
( ~ in(X3,cartesian_product2(X2,X0))
| unordered_pair(singleton(sK5(X0,X2,X3)),unordered_pair(sK4(X0,X2,X3),sK5(X0,X2,X3))) = X3 ),
inference(forward_demodulation,[],[f58,f36]) ).
fof(f36,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(rectify,[],[f12]) ).
fof(f12,plain,
! [X1,X0] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X1,X0] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f58,plain,
! [X2,X3,X0] :
( unordered_pair(singleton(sK5(X0,X2,X3)),unordered_pair(sK5(X0,X2,X3),sK4(X0,X2,X3))) = X3
| ~ in(X3,cartesian_product2(X2,X0)) ),
inference(backward_demodulation,[],[f55,f36]) ).
fof(f55,plain,
! [X2,X3,X0] :
( unordered_pair(unordered_pair(sK5(X0,X2,X3),sK4(X0,X2,X3)),singleton(sK5(X0,X2,X3))) = X3
| ~ in(X3,cartesian_product2(X2,X0)) ),
inference(equality_resolution,[],[f50]) ).
fof(f50,plain,
! [X2,X3,X0,X1] :
( unordered_pair(unordered_pair(sK5(X0,X2,X3),sK4(X0,X2,X3)),singleton(sK5(X0,X2,X3))) = X3
| ~ in(X3,X1)
| cartesian_product2(X2,X0) != X1 ),
inference(definition_unfolding,[],[f43,f34]) ).
fof(f34,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f21]) ).
fof(f21,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(rectify,[],[f14]) ).
fof(f14,plain,
! [X1,X0] : unordered_pair(unordered_pair(X1,X0),singleton(X1)) = ordered_pair(X1,X0),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X1,X0] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f43,plain,
! [X2,X3,X0,X1] :
( ordered_pair(sK5(X0,X2,X3),sK4(X0,X2,X3)) = X3
| ~ in(X3,X1)
| cartesian_product2(X2,X0) != X1 ),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( in(X3,X1)
| ! [X4,X5] :
( ordered_pair(X5,X4) != X3
| ~ in(X4,X0)
| ~ in(X5,X2) ) )
& ( ( ordered_pair(sK5(X0,X2,X3),sK4(X0,X2,X3)) = X3
& in(sK4(X0,X2,X3),X0)
& in(sK5(X0,X2,X3),X2) )
| ~ in(X3,X1) ) )
| cartesian_product2(X2,X0) != X1 )
& ( cartesian_product2(X2,X0) = X1
| ( ( ! [X9,X10] :
( ordered_pair(X10,X9) != sK6(X0,X1,X2)
| ~ in(X9,X0)
| ~ in(X10,X2) )
| ~ in(sK6(X0,X1,X2),X1) )
& ( ( sK6(X0,X1,X2) = ordered_pair(sK8(X0,X1,X2),sK7(X0,X1,X2))
& in(sK7(X0,X1,X2),X0)
& in(sK8(X0,X1,X2),X2) )
| in(sK6(X0,X1,X2),X1) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8])],[f24,f27,f26,f25]) ).
fof(f25,plain,
! [X0,X2,X3] :
( ? [X6,X7] :
( ordered_pair(X7,X6) = X3
& in(X6,X0)
& in(X7,X2) )
=> ( ordered_pair(sK5(X0,X2,X3),sK4(X0,X2,X3)) = X3
& in(sK4(X0,X2,X3),X0)
& in(sK5(X0,X2,X3),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ? [X8] :
( ( ! [X9,X10] :
( ordered_pair(X10,X9) != X8
| ~ in(X9,X0)
| ~ in(X10,X2) )
| ~ in(X8,X1) )
& ( ? [X11,X12] :
( ordered_pair(X12,X11) = X8
& in(X11,X0)
& in(X12,X2) )
| in(X8,X1) ) )
=> ( ( ! [X10,X9] :
( ordered_pair(X10,X9) != sK6(X0,X1,X2)
| ~ in(X9,X0)
| ~ in(X10,X2) )
| ~ in(sK6(X0,X1,X2),X1) )
& ( ? [X12,X11] :
( sK6(X0,X1,X2) = ordered_pair(X12,X11)
& in(X11,X0)
& in(X12,X2) )
| in(sK6(X0,X1,X2),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ? [X12,X11] :
( sK6(X0,X1,X2) = ordered_pair(X12,X11)
& in(X11,X0)
& in(X12,X2) )
=> ( sK6(X0,X1,X2) = ordered_pair(sK8(X0,X1,X2),sK7(X0,X1,X2))
& in(sK7(X0,X1,X2),X0)
& in(sK8(X0,X1,X2),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( in(X3,X1)
| ! [X4,X5] :
( ordered_pair(X5,X4) != X3
| ~ in(X4,X0)
| ~ in(X5,X2) ) )
& ( ? [X6,X7] :
( ordered_pair(X7,X6) = X3
& in(X6,X0)
& in(X7,X2) )
| ~ in(X3,X1) ) )
| cartesian_product2(X2,X0) != X1 )
& ( cartesian_product2(X2,X0) = X1
| ? [X8] :
( ( ! [X9,X10] :
( ordered_pair(X10,X9) != X8
| ~ in(X9,X0)
| ~ in(X10,X2) )
| ~ in(X8,X1) )
& ( ? [X11,X12] :
( ordered_pair(X12,X11) = X8
& in(X11,X0)
& in(X12,X2) )
| in(X8,X1) ) ) ) ),
inference(rectify,[],[f23]) ).
fof(f23,plain,
! [X1,X0,X2] :
( ( ! [X3] :
( ( in(X3,X0)
| ! [X5,X4] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X2) ) )
& ( ? [X5,X4] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X2) )
| ~ in(X3,X0) ) )
| cartesian_product2(X2,X1) != X0 )
& ( cartesian_product2(X2,X1) = X0
| ? [X3] :
( ( ! [X5,X4] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X2) )
| ~ in(X3,X0) )
& ( ? [X5,X4] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X2) )
| in(X3,X0) ) ) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f11,plain,
! [X1,X0,X2] :
( ! [X3] :
( in(X3,X0)
<=> ? [X5,X4] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X2) ) )
<=> cartesian_product2(X2,X1) = X0 ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X2,X1,X0] :
( cartesian_product2(X0,X1) = X2
<=> ! [X3] :
( ? [X4,X5] :
( in(X5,X1)
& ordered_pair(X4,X5) = X3
& in(X4,X0) )
<=> in(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(f102,plain,
! [X2,X3] : sK2 != unordered_pair(singleton(X3),unordered_pair(X2,X3)),
inference(superposition,[],[f71,f36]) ).
fof(f71,plain,
! [X2,X3] : unordered_pair(unordered_pair(X3,X2),singleton(X2)) != sK2,
inference(superposition,[],[f47,f36]) ).
fof(f47,plain,
! [X3,X4] : unordered_pair(unordered_pair(X4,X3),singleton(X4)) != sK2,
inference(definition_unfolding,[],[f31,f34]) ).
fof(f31,plain,
! [X3,X4] : sK2 != ordered_pair(X4,X3),
inference(cnf_transformation,[],[f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET949+1 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.13 % 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 : n007.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 14:17:01 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.51 % (8523)lrs-11_1:1_nm=0:sac=on:sd=4:ss=axioms:st=3.0:i=24:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/24Mi)
% 0.20/0.52 % (8523)First to succeed.
% 0.20/0.52 % (8501)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)
% 0.20/0.52 % (8523)Refutation found. Thanks to Tanya!
% 0.20/0.52 % SZS status Theorem for theBenchmark
% 0.20/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.52 % (8523)------------------------------
% 0.20/0.52 % (8523)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52 % (8523)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52 % (8523)Termination reason: Refutation
% 0.20/0.52
% 0.20/0.52 % (8523)Memory used [KB]: 6012
% 0.20/0.52 % (8523)Time elapsed: 0.112 s
% 0.20/0.52 % (8523)Instructions burned: 6 (million)
% 0.20/0.52 % (8523)------------------------------
% 0.20/0.52 % (8523)------------------------------
% 0.20/0.52 % (8493)Success in time 0.162 s
%------------------------------------------------------------------------------