TSTP Solution File: SET949+1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---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_sat --cores 0 -t %d %s
% Computer : n011.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 18:26:10 EDT 2022
% Result : Theorem 0.20s 0.52s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 33 ( 13 unt; 0 def)
% Number of atoms : 133 ( 55 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 158 ( 58 ~; 45 |; 47 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 131 ( 99 !; 32 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f153,plain,
$false,
inference(subsumption_resolution,[],[f146,f73]) ).
fof(f73,plain,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,X1)) != sK1,
inference(superposition,[],[f45,f34]) ).
fof(f34,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f12]) ).
fof(f12,plain,
! [X0,X1] : 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(f45,plain,
! [X3,X4] : unordered_pair(unordered_pair(X3,X4),singleton(X3)) != sK1,
inference(definition_unfolding,[],[f33,f29]) ).
fof(f29,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f33,plain,
! [X3,X4] : ordered_pair(X3,X4) != sK1,
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
( ! [X3,X4] : ordered_pair(X3,X4) != sK1
& in(sK1,cartesian_product2(sK2,sK3)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f17,f18]) ).
fof(f18,plain,
( ? [X0,X1,X2] :
( ! [X3,X4] : ordered_pair(X3,X4) != X0
& in(X0,cartesian_product2(X1,X2)) )
=> ( ! [X4,X3] : ordered_pair(X3,X4) != sK1
& in(sK1,cartesian_product2(sK2,sK3)) ) ),
introduced(choice_axiom,[]) ).
fof(f17,plain,
? [X0,X1,X2] :
( ! [X3,X4] : ordered_pair(X3,X4) != X0
& in(X0,cartesian_product2(X1,X2)) ),
inference(rectify,[],[f14]) ).
fof(f14,plain,
? [X1,X0,X2] :
( ! [X3,X4] : ordered_pair(X3,X4) != X1
& in(X1,cartesian_product2(X0,X2)) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,plain,
~ ! [X1,X2,X0] :
~ ( ! [X3,X4] : ordered_pair(X3,X4) != X1
& in(X1,cartesian_product2(X0,X2)) ),
inference(rectify,[],[f9]) ).
fof(f9,negated_conjecture,
~ ! [X1,X0,X2] :
~ ( ! [X3,X4] : ordered_pair(X3,X4) != X0
& in(X0,cartesian_product2(X1,X2)) ),
inference(negated_conjecture,[],[f8]) ).
fof(f8,conjecture,
! [X1,X0,X2] :
~ ( ! [X3,X4] : ordered_pair(X3,X4) != X0
& in(X0,cartesian_product2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t102_zfmisc_1) ).
fof(f146,plain,
sK1 = unordered_pair(singleton(sK7(sK2,sK3,sK1)),unordered_pair(sK7(sK2,sK3,sK1),sK8(sK2,sK3,sK1))),
inference(resolution,[],[f140,f57]) ).
fof(f57,plain,
in(sK1,sF10),
inference(definition_folding,[],[f32,f56]) ).
fof(f56,plain,
sF10 = cartesian_product2(sK2,sK3),
introduced(function_definition,[]) ).
fof(f32,plain,
in(sK1,cartesian_product2(sK2,sK3)),
inference(cnf_transformation,[],[f19]) ).
fof(f140,plain,
! [X0] :
( ~ in(X0,sF10)
| unordered_pair(singleton(sK7(sK2,sK3,X0)),unordered_pair(sK7(sK2,sK3,X0),sK8(sK2,sK3,X0))) = X0 ),
inference(forward_demodulation,[],[f132,f34]) ).
fof(f132,plain,
! [X0] :
( unordered_pair(unordered_pair(sK7(sK2,sK3,X0),sK8(sK2,sK3,X0)),singleton(sK7(sK2,sK3,X0))) = X0
| ~ in(X0,sF10) ),
inference(superposition,[],[f51,f56]) ).
fof(f51,plain,
! [X0,X1,X8] :
( ~ in(X8,cartesian_product2(X0,X1))
| unordered_pair(unordered_pair(sK7(X0,X1,X8),sK8(X0,X1,X8)),singleton(sK7(X0,X1,X8))) = X8 ),
inference(equality_resolution,[],[f48]) ).
fof(f48,plain,
! [X2,X0,X1,X8] :
( unordered_pair(unordered_pair(sK7(X0,X1,X8),sK8(X0,X1,X8)),singleton(sK7(X0,X1,X8))) = X8
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(definition_unfolding,[],[f38,f29]) ).
fof(f38,plain,
! [X2,X0,X1,X8] :
( ordered_pair(sK7(X0,X1,X8),sK8(X0,X1,X8)) = X8
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) = X2
| ( ( ~ in(sK4(X0,X1,X2),X2)
| ! [X4,X5] :
( ordered_pair(X4,X5) != sK4(X0,X1,X2)
| ~ in(X5,X1)
| ~ in(X4,X0) ) )
& ( in(sK4(X0,X1,X2),X2)
| ( ordered_pair(sK5(X0,X1,X2),sK6(X0,X1,X2)) = sK4(X0,X1,X2)
& in(sK6(X0,X1,X2),X1)
& in(sK5(X0,X1,X2),X0) ) ) ) )
& ( ! [X8] :
( ( ( ordered_pair(sK7(X0,X1,X8),sK8(X0,X1,X8)) = X8
& in(sK8(X0,X1,X8),X1)
& in(sK7(X0,X1,X8),X0) )
| ~ in(X8,X2) )
& ( in(X8,X2)
| ! [X11,X12] :
( ordered_pair(X11,X12) != X8
| ~ in(X12,X1)
| ~ in(X11,X0) ) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8])],[f21,f24,f23,f22]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X2)
| ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) ) )
& ( in(X3,X2)
| ? [X6,X7] :
( ordered_pair(X6,X7) = X3
& in(X7,X1)
& in(X6,X0) ) ) )
=> ( ( ~ in(sK4(X0,X1,X2),X2)
| ! [X5,X4] :
( ordered_pair(X4,X5) != sK4(X0,X1,X2)
| ~ in(X5,X1)
| ~ in(X4,X0) ) )
& ( in(sK4(X0,X1,X2),X2)
| ? [X7,X6] :
( ordered_pair(X6,X7) = sK4(X0,X1,X2)
& in(X7,X1)
& in(X6,X0) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ? [X7,X6] :
( ordered_pair(X6,X7) = sK4(X0,X1,X2)
& in(X7,X1)
& in(X6,X0) )
=> ( ordered_pair(sK5(X0,X1,X2),sK6(X0,X1,X2)) = sK4(X0,X1,X2)
& in(sK6(X0,X1,X2),X1)
& in(sK5(X0,X1,X2),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f24,plain,
! [X0,X1,X8] :
( ? [X9,X10] :
( ordered_pair(X9,X10) = X8
& in(X10,X1)
& in(X9,X0) )
=> ( ordered_pair(sK7(X0,X1,X8),sK8(X0,X1,X8)) = X8
& in(sK8(X0,X1,X8),X1)
& in(sK7(X0,X1,X8),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X2)
| ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) ) )
& ( in(X3,X2)
| ? [X6,X7] :
( ordered_pair(X6,X7) = X3
& in(X7,X1)
& in(X6,X0) ) ) ) )
& ( ! [X8] :
( ( ? [X9,X10] :
( ordered_pair(X9,X10) = X8
& in(X10,X1)
& in(X9,X0) )
| ~ in(X8,X2) )
& ( in(X8,X2)
| ! [X11,X12] :
( ordered_pair(X11,X12) != X8
| ~ in(X12,X1)
| ~ in(X11,X0) ) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(rectify,[],[f20]) ).
fof(f20,plain,
! [X2,X1,X0] :
( ( cartesian_product2(X2,X1) = X0
| ? [X3] :
( ( ~ in(X3,X0)
| ! [X5,X4] :
( ordered_pair(X5,X4) != X3
| ~ in(X4,X1)
| ~ in(X5,X2) ) )
& ( in(X3,X0)
| ? [X5,X4] :
( ordered_pair(X5,X4) = X3
& in(X4,X1)
& in(X5,X2) ) ) ) )
& ( ! [X3] :
( ( ? [X5,X4] :
( ordered_pair(X5,X4) = X3
& in(X4,X1)
& in(X5,X2) )
| ~ in(X3,X0) )
& ( in(X3,X0)
| ! [X5,X4] :
( ordered_pair(X5,X4) != X3
| ~ in(X4,X1)
| ~ in(X5,X2) ) ) )
| cartesian_product2(X2,X1) != X0 ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f10,plain,
! [X2,X1,X0] :
( cartesian_product2(X2,X1) = X0
<=> ! [X3] :
( ? [X5,X4] :
( ordered_pair(X5,X4) = X3
& in(X4,X1)
& in(X5,X2) )
<=> in(X3,X0) ) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X2,X1,X0] :
( ! [X3] :
( in(X3,X2)
<=> ? [X5,X4] :
( in(X5,X1)
& in(X4,X0)
& ordered_pair(X4,X5) = X3 ) )
<=> cartesian_product2(X0,X1) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET949+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_sat --cores 0 -t %d %s
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 30 14:29:10 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.49 % (8627)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.50 % (8645)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)
% 0.20/0.50 % (8635)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.20/0.51 % (8635)First to succeed.
% 0.20/0.52 % (8635)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 % (8635)------------------------------
% 0.20/0.52 % (8635)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52 % (8635)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52 % (8635)Termination reason: Refutation
% 0.20/0.52
% 0.20/0.52 % (8635)Memory used [KB]: 5500
% 0.20/0.52 % (8635)Time elapsed: 0.106 s
% 0.20/0.52 % (8635)Instructions burned: 9 (million)
% 0.20/0.52 % (8635)------------------------------
% 0.20/0.52 % (8635)------------------------------
% 0.20/0.52 % (8619)Success in time 0.164 s
%------------------------------------------------------------------------------