TSTP Solution File: SET979+1 by SnakeForV-SAT---1.0
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%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SET979+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 : n013.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 18:26:15 EDT 2022
% Result : Theorem 0.19s 0.52s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 8 unt; 0 def)
% Number of atoms : 52 ( 37 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 45 ( 22 ~; 14 |; 6 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 39 ( 30 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f93,plain,
$false,
inference(avatar_sat_refutation,[],[f55,f89,f92]) ).
fof(f92,plain,
spl5_2,
inference(avatar_contradiction_clause,[],[f91]) ).
fof(f91,plain,
( $false
| spl5_2 ),
inference(trivial_inequality_removal,[],[f90]) ).
fof(f90,plain,
( cartesian_product2(set_union2(singleton(sK1),singleton(sK2)),sK3) != cartesian_product2(set_union2(singleton(sK1),singleton(sK2)),sK3)
| spl5_2 ),
inference(superposition,[],[f54,f43]) ).
fof(f43,plain,
! [X2,X0,X1] : cartesian_product2(set_union2(X2,X0),X1) = set_union2(cartesian_product2(X2,X1),cartesian_product2(X0,X1)),
inference(cnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0,X1,X2] :
( cartesian_product2(set_union2(X2,X0),X1) = set_union2(cartesian_product2(X2,X1),cartesian_product2(X0,X1))
& set_union2(cartesian_product2(X1,X2),cartesian_product2(X1,X0)) = cartesian_product2(X1,set_union2(X2,X0)) ),
inference(rectify,[],[f16]) ).
fof(f16,plain,
! [X2,X0,X1] :
( cartesian_product2(set_union2(X1,X2),X0) = set_union2(cartesian_product2(X1,X0),cartesian_product2(X2,X0))
& set_union2(cartesian_product2(X0,X1),cartesian_product2(X0,X2)) = cartesian_product2(X0,set_union2(X1,X2)) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X2,X0,X1] :
( cartesian_product2(X2,set_union2(X0,X1)) = set_union2(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
& cartesian_product2(set_union2(X0,X1),X2) = set_union2(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t120_zfmisc_1) ).
fof(f54,plain,
( set_union2(cartesian_product2(singleton(sK1),sK3),cartesian_product2(singleton(sK2),sK3)) != cartesian_product2(set_union2(singleton(sK1),singleton(sK2)),sK3)
| spl5_2 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f52,plain,
( spl5_2
<=> set_union2(cartesian_product2(singleton(sK1),sK3),cartesian_product2(singleton(sK2),sK3)) = cartesian_product2(set_union2(singleton(sK1),singleton(sK2)),sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).
fof(f89,plain,
spl5_1,
inference(avatar_contradiction_clause,[],[f88]) ).
fof(f88,plain,
( $false
| spl5_1 ),
inference(trivial_inequality_removal,[],[f87]) ).
fof(f87,plain,
( cartesian_product2(sK3,set_union2(singleton(sK1),singleton(sK2))) != cartesian_product2(sK3,set_union2(singleton(sK1),singleton(sK2)))
| spl5_1 ),
inference(superposition,[],[f50,f42]) ).
fof(f42,plain,
! [X2,X0,X1] : set_union2(cartesian_product2(X1,X2),cartesian_product2(X1,X0)) = cartesian_product2(X1,set_union2(X2,X0)),
inference(cnf_transformation,[],[f33]) ).
fof(f50,plain,
( cartesian_product2(sK3,set_union2(singleton(sK1),singleton(sK2))) != set_union2(cartesian_product2(sK3,singleton(sK1)),cartesian_product2(sK3,singleton(sK2)))
| spl5_1 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f48,plain,
( spl5_1
<=> cartesian_product2(sK3,set_union2(singleton(sK1),singleton(sK2))) = set_union2(cartesian_product2(sK3,singleton(sK1)),cartesian_product2(sK3,singleton(sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).
fof(f55,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f46,f52,f48]) ).
fof(f46,plain,
( set_union2(cartesian_product2(singleton(sK1),sK3),cartesian_product2(singleton(sK2),sK3)) != cartesian_product2(set_union2(singleton(sK1),singleton(sK2)),sK3)
| cartesian_product2(sK3,set_union2(singleton(sK1),singleton(sK2))) != set_union2(cartesian_product2(sK3,singleton(sK1)),cartesian_product2(sK3,singleton(sK2))) ),
inference(definition_unfolding,[],[f37,f44,f44]) ).
fof(f44,plain,
! [X0,X1] : unordered_pair(X1,X0) = set_union2(singleton(X1),singleton(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f12,plain,
! [X0,X1] : unordered_pair(X1,X0) = set_union2(singleton(X1),singleton(X0)),
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X1,X0] : unordered_pair(X0,X1) = set_union2(singleton(X0),singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_enumset1) ).
fof(f37,plain,
( set_union2(cartesian_product2(sK3,singleton(sK1)),cartesian_product2(sK3,singleton(sK2))) != cartesian_product2(sK3,unordered_pair(sK1,sK2))
| set_union2(cartesian_product2(singleton(sK1),sK3),cartesian_product2(singleton(sK2),sK3)) != cartesian_product2(unordered_pair(sK1,sK2),sK3) ),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
( set_union2(cartesian_product2(sK3,singleton(sK1)),cartesian_product2(sK3,singleton(sK2))) != cartesian_product2(sK3,unordered_pair(sK1,sK2))
| set_union2(cartesian_product2(singleton(sK1),sK3),cartesian_product2(singleton(sK2),sK3)) != cartesian_product2(unordered_pair(sK1,sK2),sK3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f25,f26]) ).
fof(f26,plain,
( ? [X0,X1,X2] :
( cartesian_product2(X2,unordered_pair(X0,X1)) != set_union2(cartesian_product2(X2,singleton(X0)),cartesian_product2(X2,singleton(X1)))
| cartesian_product2(unordered_pair(X0,X1),X2) != set_union2(cartesian_product2(singleton(X0),X2),cartesian_product2(singleton(X1),X2)) )
=> ( set_union2(cartesian_product2(sK3,singleton(sK1)),cartesian_product2(sK3,singleton(sK2))) != cartesian_product2(sK3,unordered_pair(sK1,sK2))
| set_union2(cartesian_product2(singleton(sK1),sK3),cartesian_product2(singleton(sK2),sK3)) != cartesian_product2(unordered_pair(sK1,sK2),sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f25,plain,
? [X0,X1,X2] :
( cartesian_product2(X2,unordered_pair(X0,X1)) != set_union2(cartesian_product2(X2,singleton(X0)),cartesian_product2(X2,singleton(X1)))
| cartesian_product2(unordered_pair(X0,X1),X2) != set_union2(cartesian_product2(singleton(X0),X2),cartesian_product2(singleton(X1),X2)) ),
inference(rectify,[],[f18]) ).
fof(f18,plain,
? [X1,X0,X2] :
( cartesian_product2(X2,unordered_pair(X1,X0)) != set_union2(cartesian_product2(X2,singleton(X1)),cartesian_product2(X2,singleton(X0)))
| set_union2(cartesian_product2(singleton(X1),X2),cartesian_product2(singleton(X0),X2)) != cartesian_product2(unordered_pair(X1,X0),X2) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,plain,
~ ! [X2,X1,X0] :
( cartesian_product2(X2,unordered_pair(X1,X0)) = set_union2(cartesian_product2(X2,singleton(X1)),cartesian_product2(X2,singleton(X0)))
& set_union2(cartesian_product2(singleton(X1),X2),cartesian_product2(singleton(X0),X2)) = cartesian_product2(unordered_pair(X1,X0),X2) ),
inference(rectify,[],[f10]) ).
fof(f10,negated_conjecture,
~ ! [X1,X0,X2] :
( cartesian_product2(unordered_pair(X0,X1),X2) = set_union2(cartesian_product2(singleton(X0),X2),cartesian_product2(singleton(X1),X2))
& cartesian_product2(X2,unordered_pair(X0,X1)) = set_union2(cartesian_product2(X2,singleton(X0)),cartesian_product2(X2,singleton(X1))) ),
inference(negated_conjecture,[],[f9]) ).
fof(f9,conjecture,
! [X1,X0,X2] :
( cartesian_product2(unordered_pair(X0,X1),X2) = set_union2(cartesian_product2(singleton(X0),X2),cartesian_product2(singleton(X1),X2))
& cartesian_product2(X2,unordered_pair(X0,X1)) = set_union2(cartesian_product2(X2,singleton(X0)),cartesian_product2(X2,singleton(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t132_zfmisc_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET979+1 : TPTP v8.1.0. Released v3.2.0.
% 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
% 0.13/0.34 % Computer : n013.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 14:29:32 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.50 % (31651)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.51 % (31643)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.19/0.51 % (31646)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.19/0.52 % (31660)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.19/0.52 % (31644)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.52 % (31666)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.19/0.52 % (31645)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.52 % (31651)First to succeed.
% 0.19/0.52 % (31651)Refutation found. Thanks to Tanya!
% 0.19/0.52 % SZS status Theorem for theBenchmark
% 0.19/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.52 % (31651)------------------------------
% 0.19/0.52 % (31651)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52 % (31651)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52 % (31651)Termination reason: Refutation
% 0.19/0.52
% 0.19/0.52 % (31651)Memory used [KB]: 5500
% 0.19/0.52 % (31651)Time elapsed: 0.110 s
% 0.19/0.52 % (31651)Instructions burned: 2 (million)
% 0.19/0.52 % (31651)------------------------------
% 0.19/0.52 % (31651)------------------------------
% 0.19/0.52 % (31640)Success in time 0.177 s
%------------------------------------------------------------------------------