TSTP Solution File: SET902+1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SET902+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 : n027.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 18:26:03 EDT 2022
% Result : Theorem 0.19s 0.52s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 70 ( 21 unt; 0 def)
% Number of atoms : 153 ( 91 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 157 ( 74 ~; 54 |; 21 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 39 ( 36 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f183,plain,
$false,
inference(avatar_sat_refutation,[],[f55,f64,f65,f118,f123,f147,f162,f180]) ).
fof(f180,plain,
( spl7_2
| ~ spl7_8 ),
inference(avatar_contradiction_clause,[],[f179]) ).
fof(f179,plain,
( $false
| spl7_2
| ~ spl7_8 ),
inference(trivial_inequality_removal,[],[f171]) ).
fof(f171,plain,
( sK2 != sK2
| spl7_2
| ~ spl7_8 ),
inference(superposition,[],[f66,f122]) ).
fof(f122,plain,
( sK2 = sF5
| ~ spl7_8 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f120,plain,
( spl7_8
<=> sK2 = sF5 ),
introduced(avatar_definition,[new_symbols(naming,[spl7_8])]) ).
fof(f66,plain,
( sK2 != sF5
| spl7_2 ),
inference(superposition,[],[f54,f43]) ).
fof(f43,plain,
sF5 = sF6,
inference(definition_folding,[],[f35,f42,f41]) ).
fof(f41,plain,
sF5 = set_union2(sK2,sK1),
introduced(function_definition,[]) ).
fof(f42,plain,
sF6 = singleton(sK3),
introduced(function_definition,[]) ).
fof(f35,plain,
set_union2(sK2,sK1) = singleton(sK3),
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
? [X1,X0,X2] :
( ( singleton(X2) != X0
| empty_set != X1 )
& ( singleton(X2) != X0
| singleton(X2) != X1 )
& ( singleton(X2) != X1
| empty_set != X0 )
& set_union2(X0,X1) = singleton(X2) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,plain,
~ ! [X2,X1,X0] :
~ ( ~ ( empty_set = X1
& singleton(X2) = X0 )
& ~ ( singleton(X2) = X1
& empty_set = X0 )
& ~ ( singleton(X2) = X1
& singleton(X2) = X0 )
& set_union2(X0,X1) = singleton(X2) ),
inference(rectify,[],[f12]) ).
fof(f12,negated_conjecture,
~ ! [X1,X2,X0] :
~ ( ~ ( empty_set = X1
& singleton(X0) = X2 )
& ~ ( empty_set = X2
& singleton(X0) = X1 )
& ~ ( singleton(X0) = X1
& singleton(X0) = X2 )
& singleton(X0) = set_union2(X1,X2) ),
inference(negated_conjecture,[],[f11]) ).
fof(f11,conjecture,
! [X1,X2,X0] :
~ ( ~ ( empty_set = X1
& singleton(X0) = X2 )
& ~ ( empty_set = X2
& singleton(X0) = X1 )
& ~ ( singleton(X0) = X1
& singleton(X0) = X2 )
& singleton(X0) = set_union2(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_zfmisc_1) ).
fof(f54,plain,
( sK2 != sF6
| spl7_2 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f52,plain,
( spl7_2
<=> sK2 = sF6 ),
introduced(avatar_definition,[new_symbols(naming,[spl7_2])]) ).
fof(f162,plain,
( spl7_3
| ~ spl7_7 ),
inference(avatar_contradiction_clause,[],[f161]) ).
fof(f161,plain,
( $false
| spl7_3
| ~ spl7_7 ),
inference(trivial_inequality_removal,[],[f154]) ).
fof(f154,plain,
( sK1 != sK1
| spl7_3
| ~ spl7_7 ),
inference(superposition,[],[f67,f117]) ).
fof(f117,plain,
( sK1 = sF5
| ~ spl7_7 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f115,plain,
( spl7_7
<=> sK1 = sF5 ),
introduced(avatar_definition,[new_symbols(naming,[spl7_7])]) ).
fof(f67,plain,
( sK1 != sF5
| spl7_3 ),
inference(superposition,[],[f59,f43]) ).
fof(f59,plain,
( sK1 != sF6
| spl7_3 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f57,plain,
( spl7_3
<=> sK1 = sF6 ),
introduced(avatar_definition,[new_symbols(naming,[spl7_3])]) ).
fof(f147,plain,
( ~ spl7_1
| ~ spl7_4 ),
inference(avatar_contradiction_clause,[],[f146]) ).
fof(f146,plain,
( $false
| ~ spl7_1
| ~ spl7_4 ),
inference(trivial_inequality_removal,[],[f141]) ).
fof(f141,plain,
( empty_set != empty_set
| ~ spl7_1
| ~ spl7_4 ),
inference(superposition,[],[f71,f128]) ).
fof(f128,plain,
( empty_set = sF5
| ~ spl7_1
| ~ spl7_4 ),
inference(forward_demodulation,[],[f127,f38]) ).
fof(f38,plain,
! [X1] : set_union2(X1,X1) = X1,
inference(cnf_transformation,[],[f15]) ).
fof(f15,plain,
! [X1] : set_union2(X1,X1) = X1,
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X1,X0] : set_union2(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(f127,plain,
( set_union2(empty_set,empty_set) = sF5
| ~ spl7_1
| ~ spl7_4 ),
inference(forward_demodulation,[],[f124,f62]) ).
fof(f62,plain,
( empty_set = sK2
| ~ spl7_4 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f61,plain,
( spl7_4
<=> empty_set = sK2 ),
introduced(avatar_definition,[new_symbols(naming,[spl7_4])]) ).
fof(f124,plain,
( set_union2(empty_set,sK2) = sF5
| ~ spl7_1 ),
inference(superposition,[],[f96,f49]) ).
fof(f49,plain,
( empty_set = sK1
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f48,plain,
( spl7_1
<=> empty_set = sK1 ),
introduced(avatar_definition,[new_symbols(naming,[spl7_1])]) ).
fof(f96,plain,
set_union2(sK1,sK2) = sF5,
inference(superposition,[],[f41,f27]) ).
fof(f27,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f16]) ).
fof(f16,plain,
! [X1,X0] : set_union2(X0,X1) = set_union2(X1,X0),
inference(rectify,[],[f1]) ).
fof(f1,axiom,
! [X1,X0] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f71,plain,
empty_set != sF5,
inference(superposition,[],[f69,f43]) ).
fof(f69,plain,
empty_set != sF6,
inference(superposition,[],[f26,f42]) ).
fof(f26,plain,
! [X0] : empty_set != singleton(X0),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : empty_set != singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(f123,plain,
( spl7_8
| spl7_4 ),
inference(avatar_split_clause,[],[f113,f61,f120]) ).
fof(f113,plain,
( empty_set = sK2
| sK2 = sF5 ),
inference(resolution,[],[f109,f73]) ).
fof(f73,plain,
subset(sK2,sF5),
inference(superposition,[],[f29,f41]) ).
fof(f29,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(f109,plain,
! [X0] :
( ~ subset(X0,sF5)
| sF5 = X0
| empty_set = X0 ),
inference(forward_demodulation,[],[f108,f43]) ).
fof(f108,plain,
! [X0] :
( ~ subset(X0,sF5)
| sF6 = X0
| empty_set = X0 ),
inference(forward_demodulation,[],[f107,f43]) ).
fof(f107,plain,
! [X0] :
( empty_set = X0
| ~ subset(X0,sF6)
| sF6 = X0 ),
inference(superposition,[],[f25,f42]) ).
fof(f25,plain,
! [X0,X1] :
( ~ subset(X1,singleton(X0))
| singleton(X0) = X1
| empty_set = X1 ),
inference(cnf_transformation,[],[f18]) ).
fof(f18,plain,
! [X0,X1] :
( ( empty_set = X1
| singleton(X0) = X1 )
<=> subset(X1,singleton(X0)) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X1,X0] :
( subset(X0,singleton(X1))
<=> ( singleton(X1) = X0
| empty_set = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(f118,plain,
( spl7_7
| spl7_1 ),
inference(avatar_split_clause,[],[f112,f48,f115]) ).
fof(f112,plain,
( empty_set = sK1
| sK1 = sF5 ),
inference(resolution,[],[f109,f100]) ).
fof(f100,plain,
subset(sK1,sF5),
inference(superposition,[],[f95,f41]) ).
fof(f95,plain,
! [X4,X5] : subset(X4,set_union2(X5,X4)),
inference(superposition,[],[f29,f27]) ).
fof(f65,plain,
( ~ spl7_3
| ~ spl7_2 ),
inference(avatar_split_clause,[],[f45,f52,f57]) ).
fof(f45,plain,
( sK2 != sF6
| sK1 != sF6 ),
inference(definition_folding,[],[f33,f42,f42]) ).
fof(f33,plain,
( sK1 != singleton(sK3)
| sK2 != singleton(sK3) ),
inference(cnf_transformation,[],[f19]) ).
fof(f64,plain,
( ~ spl7_3
| ~ spl7_4 ),
inference(avatar_split_clause,[],[f44,f61,f57]) ).
fof(f44,plain,
( empty_set != sK2
| sK1 != sF6 ),
inference(definition_folding,[],[f34,f42]) ).
fof(f34,plain,
( empty_set != sK2
| sK1 != singleton(sK3) ),
inference(cnf_transformation,[],[f19]) ).
fof(f55,plain,
( ~ spl7_1
| ~ spl7_2 ),
inference(avatar_split_clause,[],[f46,f52,f48]) ).
fof(f46,plain,
( sK2 != sF6
| empty_set != sK1 ),
inference(definition_folding,[],[f32,f42]) ).
fof(f32,plain,
( empty_set != sK1
| sK2 != singleton(sK3) ),
inference(cnf_transformation,[],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET902+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34 % Computer : n027.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 14:44:16 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.50 % (12925)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.50 % (12924)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.19/0.50 TRYING [1]
% 0.19/0.50 % (12927)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)
% 0.19/0.51 % (12927)First to succeed.
% 0.19/0.51 % (12947)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)
% 0.19/0.51 % (12951)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)
% 0.19/0.51 % (12926)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)
% 0.19/0.52 % (12937)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.52 % (12935)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)
% 0.19/0.52 % (12939)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.19/0.52 % (12930)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)
% 0.19/0.52 TRYING [1]
% 0.19/0.52 TRYING [2]
% 0.19/0.52 % (12932)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.52 TRYING [3]
% 0.19/0.52 TRYING [4]
% 0.19/0.52 % (12927)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 % (12927)------------------------------
% 0.19/0.52 % (12927)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52 % (12927)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52 % (12927)Termination reason: Refutation
% 0.19/0.52
% 0.19/0.52 % (12927)Memory used [KB]: 5500
% 0.19/0.52 % (12927)Time elapsed: 0.105 s
% 0.19/0.52 % (12927)Instructions burned: 3 (million)
% 0.19/0.52 % (12927)------------------------------
% 0.19/0.52 % (12927)------------------------------
% 0.19/0.52 % (12922)Success in time 0.177 s
%------------------------------------------------------------------------------