TSTP Solution File: SET975+1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SET975+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 : n003.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 18:26:14 EDT 2022
% Result : Theorem 0.20s 0.50s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of formulae : 73 ( 13 unt; 0 def)
% Number of atoms : 156 ( 34 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 146 ( 63 ~; 66 |; 5 &)
% ( 11 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 91 ( 87 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f473,plain,
$false,
inference(avatar_sat_refutation,[],[f60,f61,f63,f124,f214,f217,f470,f472]) ).
fof(f472,plain,
spl12_12,
inference(avatar_contradiction_clause,[],[f471]) ).
fof(f471,plain,
( $false
| spl12_12 ),
inference(resolution,[],[f435,f65]) ).
fof(f65,plain,
in(sK1,sF8),
inference(superposition,[],[f38,f41]) ).
fof(f41,plain,
singleton(sK1) = sF8,
introduced(function_definition,[]) ).
fof(f38,plain,
! [X2] : in(X2,singleton(X2)),
inference(equality_resolution,[],[f37]) ).
fof(f37,plain,
! [X2,X1] :
( in(X2,X1)
| singleton(X2) != X1 ),
inference(equality_resolution,[],[f26]) ).
fof(f26,plain,
! [X2,X0,X1] :
( in(X2,X1)
| X0 != X2
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X1,X0] :
( singleton(X0) = X1
<=> ! [X2] :
( X0 = X2
<=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f435,plain,
( ~ in(sK1,sF8)
| spl12_12 ),
inference(avatar_component_clause,[],[f433]) ).
fof(f433,plain,
( spl12_12
<=> in(sK1,sF8) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_12])]) ).
fof(f470,plain,
( ~ spl12_2
| spl12_3
| ~ spl12_12
| ~ spl12_1 ),
inference(avatar_split_clause,[],[f467,f49,f433,f57,f53]) ).
fof(f53,plain,
( spl12_2
<=> in(sK3,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_2])]) ).
fof(f57,plain,
( spl12_3
<=> in(sF9,sF11) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_3])]) ).
fof(f49,plain,
( spl12_1
<=> sK2 = sK1 ),
introduced(avatar_definition,[new_symbols(naming,[spl12_1])]) ).
fof(f467,plain,
( ~ in(sK1,sF8)
| in(sF9,sF11)
| ~ in(sK3,sK4)
| ~ spl12_1 ),
inference(superposition,[],[f457,f228]) ).
fof(f228,plain,
( cartesian_product2(sF8,sK4) = sF11
| ~ spl12_1 ),
inference(superposition,[],[f44,f227]) ).
fof(f227,plain,
( sF10 = sF8
| ~ spl12_1 ),
inference(forward_demodulation,[],[f218,f41]) ).
fof(f218,plain,
( sF10 = singleton(sK1)
| ~ spl12_1 ),
inference(superposition,[],[f43,f50]) ).
fof(f50,plain,
( sK2 = sK1
| ~ spl12_1 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f43,plain,
sF10 = singleton(sK2),
introduced(function_definition,[]) ).
fof(f44,plain,
cartesian_product2(sF10,sK4) = sF11,
introduced(function_definition,[]) ).
fof(f457,plain,
! [X0,X1] :
( in(sF9,cartesian_product2(X0,X1))
| ~ in(sK3,X1)
| ~ in(sK1,X0) ),
inference(forward_demodulation,[],[f456,f42]) ).
fof(f42,plain,
sF9 = unordered_pair(sF7,sF8),
introduced(function_definition,[]) ).
fof(f456,plain,
! [X0,X1] :
( ~ in(sK3,X1)
| ~ in(sK1,X0)
| in(unordered_pair(sF7,sF8),cartesian_product2(X0,X1)) ),
inference(forward_demodulation,[],[f455,f41]) ).
fof(f455,plain,
! [X0,X1] :
( ~ in(sK3,X1)
| in(unordered_pair(sF7,singleton(sK1)),cartesian_product2(X0,X1))
| ~ in(sK1,X0) ),
inference(forward_demodulation,[],[f449,f15]) ).
fof(f15,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[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(f449,plain,
! [X0,X1] :
( in(unordered_pair(singleton(sK1),sF7),cartesian_product2(X0,X1))
| ~ in(sK1,X0)
| ~ in(sK3,X1) ),
inference(superposition,[],[f62,f40]) ).
fof(f40,plain,
sF7 = unordered_pair(sK1,sK3),
introduced(function_definition,[]) ).
fof(f62,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(forward_demodulation,[],[f34,f15]) ).
fof(f34,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(definition_unfolding,[],[f22,f23]) ).
fof(f23,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(f22,plain,
! [X2,X3,X0,X1] :
( ~ in(X0,X2)
| ~ in(X1,X3)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X3,X0,X2,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(f217,plain,
( spl12_1
| ~ spl12_10 ),
inference(avatar_split_clause,[],[f215,f211,f49]) ).
fof(f211,plain,
( spl12_10
<=> in(sK1,sF10) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_10])]) ).
fof(f215,plain,
( sK2 = sK1
| ~ spl12_10 ),
inference(resolution,[],[f213,f75]) ).
fof(f75,plain,
! [X1] :
( ~ in(X1,sF10)
| sK2 = X1 ),
inference(superposition,[],[f39,f43]) ).
fof(f39,plain,
! [X2,X0] :
( ~ in(X2,singleton(X0))
| X0 = X2 ),
inference(equality_resolution,[],[f25]) ).
fof(f25,plain,
! [X2,X0,X1] :
( ~ in(X2,X1)
| X0 = X2
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f3]) ).
fof(f213,plain,
( in(sK1,sF10)
| ~ spl12_10 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f214,plain,
( ~ spl12_3
| spl12_10 ),
inference(avatar_split_clause,[],[f209,f211,f57]) ).
fof(f209,plain,
( in(sK1,sF10)
| ~ in(sF9,sF11) ),
inference(superposition,[],[f206,f44]) ).
fof(f206,plain,
! [X0,X1] :
( ~ in(sF9,cartesian_product2(X0,X1))
| in(sK1,X0) ),
inference(forward_demodulation,[],[f205,f42]) ).
fof(f205,plain,
! [X0,X1] :
( in(sK1,X0)
| ~ in(unordered_pair(sF7,sF8),cartesian_product2(X0,X1)) ),
inference(forward_demodulation,[],[f193,f41]) ).
fof(f193,plain,
! [X0,X1] :
( in(sK1,X0)
| ~ in(unordered_pair(sF7,singleton(sK1)),cartesian_product2(X0,X1)) ),
inference(superposition,[],[f36,f40]) ).
fof(f36,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(definition_unfolding,[],[f20,f23]) ).
fof(f20,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f6]) ).
fof(f124,plain,
( spl12_2
| ~ spl12_3 ),
inference(avatar_split_clause,[],[f123,f57,f53]) ).
fof(f123,plain,
( ~ in(sF9,sF11)
| in(sK3,sK4) ),
inference(superposition,[],[f118,f44]) ).
fof(f118,plain,
! [X0,X1] :
( ~ in(sF9,cartesian_product2(X0,X1))
| in(sK3,X1) ),
inference(forward_demodulation,[],[f117,f42]) ).
fof(f117,plain,
! [X0,X1] :
( in(sK3,X1)
| ~ in(unordered_pair(sF7,sF8),cartesian_product2(X0,X1)) ),
inference(forward_demodulation,[],[f107,f41]) ).
fof(f107,plain,
! [X0,X1] :
( in(sK3,X1)
| ~ in(unordered_pair(sF7,singleton(sK1)),cartesian_product2(X0,X1)) ),
inference(superposition,[],[f35,f40]) ).
fof(f35,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(definition_unfolding,[],[f21,f23]) ).
fof(f21,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f6]) ).
fof(f63,plain,
( spl12_1
| spl12_3 ),
inference(avatar_split_clause,[],[f46,f57,f49]) ).
fof(f46,plain,
( in(sF9,sF11)
| sK2 = sK1 ),
inference(definition_folding,[],[f31,f44,f43,f42,f41,f40]) ).
fof(f31,plain,
( sK2 = sK1
| in(unordered_pair(unordered_pair(sK1,sK3),singleton(sK1)),cartesian_product2(singleton(sK2),sK4)) ),
inference(definition_unfolding,[],[f17,f23]) ).
fof(f17,plain,
( sK2 = sK1
| in(ordered_pair(sK1,sK3),cartesian_product2(singleton(sK2),sK4)) ),
inference(cnf_transformation,[],[f13]) ).
fof(f13,plain,
? [X3,X1,X0,X2] :
( in(ordered_pair(X3,X0),cartesian_product2(singleton(X1),X2))
<~> ( in(X0,X2)
& X1 = X3 ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,plain,
~ ! [X1,X2,X0,X3] :
( ( in(X0,X2)
& X1 = X3 )
<=> in(ordered_pair(X3,X0),cartesian_product2(singleton(X1),X2)) ),
inference(rectify,[],[f10]) ).
fof(f10,negated_conjecture,
~ ! [X1,X2,X3,X0] :
( in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3))
<=> ( in(X1,X3)
& X0 = X2 ) ),
inference(negated_conjecture,[],[f9]) ).
fof(f9,conjecture,
! [X1,X2,X3,X0] :
( in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3))
<=> ( in(X1,X3)
& X0 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t128_zfmisc_1) ).
fof(f61,plain,
( spl12_2
| spl12_3 ),
inference(avatar_split_clause,[],[f45,f57,f53]) ).
fof(f45,plain,
( in(sF9,sF11)
| in(sK3,sK4) ),
inference(definition_folding,[],[f30,f44,f43,f42,f41,f40]) ).
fof(f30,plain,
( in(sK3,sK4)
| in(unordered_pair(unordered_pair(sK1,sK3),singleton(sK1)),cartesian_product2(singleton(sK2),sK4)) ),
inference(definition_unfolding,[],[f18,f23]) ).
fof(f18,plain,
( in(sK3,sK4)
| in(ordered_pair(sK1,sK3),cartesian_product2(singleton(sK2),sK4)) ),
inference(cnf_transformation,[],[f13]) ).
fof(f60,plain,
( ~ spl12_1
| ~ spl12_2
| ~ spl12_3 ),
inference(avatar_split_clause,[],[f47,f57,f53,f49]) ).
fof(f47,plain,
( ~ in(sF9,sF11)
| ~ in(sK3,sK4)
| sK2 != sK1 ),
inference(definition_folding,[],[f32,f44,f43,f42,f41,f40]) ).
fof(f32,plain,
( sK2 != sK1
| ~ in(sK3,sK4)
| ~ in(unordered_pair(unordered_pair(sK1,sK3),singleton(sK1)),cartesian_product2(singleton(sK2),sK4)) ),
inference(definition_unfolding,[],[f16,f23]) ).
fof(f16,plain,
( sK2 != sK1
| ~ in(sK3,sK4)
| ~ in(ordered_pair(sK1,sK3),cartesian_product2(singleton(sK2),sK4)) ),
inference(cnf_transformation,[],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET975+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
% 0.12/0.34 % Computer : n003.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 14:33:22 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.45 % (5292)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.46 % (5289)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)
% 0.20/0.47 TRYING [1]
% 0.20/0.48 TRYING [2]
% 0.20/0.48 TRYING [3]
% 0.20/0.48 TRYING [4]
% 0.20/0.49 % (5309)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)
% 0.20/0.49 % (5314)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.20/0.50 % (5298)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.50 % (5310)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.20/0.50 % (5289)First to succeed.
% 0.20/0.50 % (5289)Refutation found. Thanks to Tanya!
% 0.20/0.50 % SZS status Theorem for theBenchmark
% 0.20/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.50 % (5289)------------------------------
% 0.20/0.50 % (5289)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.50 % (5289)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.50 % (5289)Termination reason: Refutation
% 0.20/0.50
% 0.20/0.50 % (5289)Memory used [KB]: 5628
% 0.20/0.50 % (5289)Time elapsed: 0.098 s
% 0.20/0.50 % (5289)Instructions burned: 13 (million)
% 0.20/0.50 % (5289)------------------------------
% 0.20/0.50 % (5289)------------------------------
% 0.20/0.50 % (5281)Success in time 0.152 s
%------------------------------------------------------------------------------