TSTP Solution File: SET927+1 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET927+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 : n019.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 18:22:46 EDT 2022
% Result : Theorem 1.30s 0.54s
% Output : Refutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 78 ( 9 unt; 0 def)
% Number of atoms : 246 ( 100 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 270 ( 102 ~; 127 |; 30 &)
% ( 9 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 76 ( 64 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f261,plain,
$false,
inference(avatar_sat_refutation,[],[f55,f64,f65,f66,f177,f209,f228,f260]) ).
fof(f260,plain,
( spl8_1
| spl8_3
| ~ spl8_4 ),
inference(avatar_contradiction_clause,[],[f259]) ).
fof(f259,plain,
( $false
| spl8_1
| spl8_3
| ~ spl8_4 ),
inference(subsumption_resolution,[],[f258,f49]) ).
fof(f49,plain,
( sF6 != sF7
| spl8_1 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f48,plain,
( spl8_1
<=> sF6 = sF7 ),
introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).
fof(f258,plain,
( sF6 = sF7
| spl8_3
| ~ spl8_4 ),
inference(subsumption_resolution,[],[f253,f58]) ).
fof(f58,plain,
( ~ in(sK1,sK3)
| spl8_3 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f57,plain,
( spl8_3
<=> in(sK1,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_3])]) ).
fof(f253,plain,
( in(sK1,sK3)
| sF6 = sF7
| ~ spl8_4 ),
inference(superposition,[],[f41,f250]) ).
fof(f250,plain,
( ! [X6] :
( set_difference(sF5,X6) = sF7
| in(sK1,X6) )
| ~ spl8_4 ),
inference(forward_demodulation,[],[f247,f237]) ).
fof(f237,plain,
( singleton(sK1) = sF7
| ~ spl8_4 ),
inference(forward_demodulation,[],[f42,f63]) ).
fof(f63,plain,
( sK2 = sK1
| ~ spl8_4 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f61,plain,
( spl8_4
<=> sK2 = sK1 ),
introduced(avatar_definition,[new_symbols(naming,[spl8_4])]) ).
fof(f42,plain,
singleton(sK2) = sF7,
introduced(function_definition,[]) ).
fof(f247,plain,
( ! [X6] :
( in(sK1,X6)
| set_difference(sF5,X6) = singleton(sK1) )
| ~ spl8_4 ),
inference(superposition,[],[f39,f235]) ).
fof(f235,plain,
( sF5 = unordered_pair(sK1,sK1)
| ~ spl8_4 ),
inference(backward_demodulation,[],[f68,f63]) ).
fof(f68,plain,
sF5 = unordered_pair(sK1,sK2),
inference(backward_demodulation,[],[f40,f29]) ).
fof(f29,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f17]) ).
fof(f17,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(rectify,[],[f10]) ).
fof(f10,plain,
! [X1,X0] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(rectify,[],[f1]) ).
fof(f1,axiom,
! [X1,X0] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f40,plain,
unordered_pair(sK2,sK1) = sF5,
introduced(function_definition,[]) ).
fof(f39,plain,
! [X2,X1] :
( set_difference(unordered_pair(X2,X2),X1) = singleton(X2)
| in(X2,X1) ),
inference(equality_resolution,[],[f32]) ).
fof(f32,plain,
! [X2,X0,X1] :
( singleton(X2) = set_difference(unordered_pair(X2,X0),X1)
| in(X2,X1)
| X0 != X2 ),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ( singleton(X2) = set_difference(unordered_pair(X2,X0),X1)
| in(X2,X1)
| ( ~ in(X0,X1)
& X0 != X2 ) )
& ( ( ~ in(X2,X1)
& ( in(X0,X1)
| X0 = X2 ) )
| singleton(X2) != set_difference(unordered_pair(X2,X0),X1) ) ),
inference(rectify,[],[f19]) ).
fof(f19,plain,
! [X2,X1,X0] :
( ( singleton(X0) = set_difference(unordered_pair(X0,X2),X1)
| in(X0,X1)
| ( ~ in(X2,X1)
& X0 != X2 ) )
& ( ( ~ in(X0,X1)
& ( in(X2,X1)
| X0 = X2 ) )
| singleton(X0) != set_difference(unordered_pair(X0,X2),X1) ) ),
inference(flattening,[],[f18]) ).
fof(f18,plain,
! [X2,X1,X0] :
( ( singleton(X0) = set_difference(unordered_pair(X0,X2),X1)
| in(X0,X1)
| ( ~ in(X2,X1)
& X0 != X2 ) )
& ( ( ~ in(X0,X1)
& ( in(X2,X1)
| X0 = X2 ) )
| singleton(X0) != set_difference(unordered_pair(X0,X2),X1) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f11,plain,
! [X2,X1,X0] :
( singleton(X0) = set_difference(unordered_pair(X0,X2),X1)
<=> ( ~ in(X0,X1)
& ( in(X2,X1)
| X0 = X2 ) ) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X0,X2,X1] :
( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
<=> ( ( in(X1,X2)
| X0 = X1 )
& ~ in(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l39_zfmisc_1) ).
fof(f41,plain,
sF6 = set_difference(sF5,sK3),
introduced(function_definition,[]) ).
fof(f228,plain,
( ~ spl8_1
| spl8_3
| spl8_4 ),
inference(avatar_contradiction_clause,[],[f227]) ).
fof(f227,plain,
( $false
| ~ spl8_1
| spl8_3
| spl8_4 ),
inference(subsumption_resolution,[],[f226,f58]) ).
fof(f226,plain,
( in(sK1,sK3)
| ~ spl8_1
| spl8_4 ),
inference(trivial_inequality_removal,[],[f225]) ).
fof(f225,plain,
( sF6 != sF6
| in(sK1,sK3)
| ~ spl8_1
| spl8_4 ),
inference(superposition,[],[f220,f41]) ).
fof(f220,plain,
( ! [X4] :
( sF6 != set_difference(sF5,X4)
| in(sK1,X4) )
| ~ spl8_1
| spl8_4 ),
inference(forward_demodulation,[],[f219,f210]) ).
fof(f210,plain,
( sF6 = singleton(sK2)
| ~ spl8_1 ),
inference(forward_demodulation,[],[f42,f50]) ).
fof(f50,plain,
( sF6 = sF7
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f219,plain,
( ! [X4] :
( set_difference(sF5,X4) != singleton(sK2)
| in(sK1,X4) )
| spl8_4 ),
inference(subsumption_resolution,[],[f217,f62]) ).
fof(f62,plain,
( sK2 != sK1
| spl8_4 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f217,plain,
! [X4] :
( sK2 = sK1
| set_difference(sF5,X4) != singleton(sK2)
| in(sK1,X4) ),
inference(superposition,[],[f81,f68]) ).
fof(f81,plain,
! [X2,X0,X1] :
( singleton(X0) != set_difference(unordered_pair(X1,X0),X2)
| X0 = X1
| in(X1,X2) ),
inference(superposition,[],[f30,f29]) ).
fof(f30,plain,
! [X2,X0,X1] :
( singleton(X2) != set_difference(unordered_pair(X2,X0),X1)
| in(X0,X1)
| X0 = X2 ),
inference(cnf_transformation,[],[f20]) ).
fof(f209,plain,
( ~ spl8_2
| ~ spl8_1 ),
inference(avatar_split_clause,[],[f101,f48,f52]) ).
fof(f52,plain,
( spl8_2
<=> in(sK2,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).
fof(f101,plain,
( sF6 != sF7
| ~ in(sK2,sK3) ),
inference(superposition,[],[f79,f41]) ).
fof(f79,plain,
! [X6] :
( set_difference(sF5,X6) != sF7
| ~ in(sK2,X6) ),
inference(forward_demodulation,[],[f77,f42]) ).
fof(f77,plain,
! [X6] :
( set_difference(sF5,X6) != singleton(sK2)
| ~ in(sK2,X6) ),
inference(superposition,[],[f69,f68]) ).
fof(f69,plain,
! [X2,X0,X1] :
( singleton(X0) != set_difference(unordered_pair(X1,X0),X2)
| ~ in(X0,X2) ),
inference(superposition,[],[f31,f29]) ).
fof(f31,plain,
! [X2,X0,X1] :
( singleton(X2) != set_difference(unordered_pair(X2,X0),X1)
| ~ in(X2,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f177,plain,
( ~ spl8_3
| spl8_1
| spl8_2 ),
inference(avatar_split_clause,[],[f176,f52,f48,f57]) ).
fof(f176,plain,
( ~ in(sK1,sK3)
| spl8_1
| spl8_2 ),
inference(subsumption_resolution,[],[f175,f49]) ).
fof(f175,plain,
( ~ in(sK1,sK3)
| sF6 = sF7
| spl8_2 ),
inference(subsumption_resolution,[],[f146,f54]) ).
fof(f54,plain,
( ~ in(sK2,sK3)
| spl8_2 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f146,plain,
( in(sK2,sK3)
| ~ in(sK1,sK3)
| sF6 = sF7 ),
inference(superposition,[],[f41,f143]) ).
fof(f143,plain,
! [X6] :
( set_difference(sF5,X6) = sF7
| ~ in(sK1,X6)
| in(sK2,X6) ),
inference(forward_demodulation,[],[f134,f42]) ).
fof(f134,plain,
! [X6] :
( in(sK2,X6)
| set_difference(sF5,X6) = singleton(sK2)
| ~ in(sK1,X6) ),
inference(superposition,[],[f103,f68]) ).
fof(f103,plain,
! [X2,X0,X1] :
( singleton(X0) = set_difference(unordered_pair(X1,X0),X2)
| ~ in(X1,X2)
| in(X0,X2) ),
inference(superposition,[],[f33,f29]) ).
fof(f33,plain,
! [X2,X0,X1] :
( singleton(X2) = set_difference(unordered_pair(X2,X0),X1)
| in(X2,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f66,plain,
( ~ spl8_3
| ~ spl8_1
| spl8_2 ),
inference(avatar_split_clause,[],[f43,f52,f48,f57]) ).
fof(f43,plain,
( in(sK2,sK3)
| sF6 != sF7
| ~ in(sK1,sK3) ),
inference(definition_folding,[],[f37,f42,f41,f40]) ).
fof(f37,plain,
( set_difference(unordered_pair(sK2,sK1),sK3) != singleton(sK2)
| ~ in(sK1,sK3)
| in(sK2,sK3) ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
( ( set_difference(unordered_pair(sK2,sK1),sK3) != singleton(sK2)
| ( ~ in(sK1,sK3)
& sK2 != sK1 )
| in(sK2,sK3) )
& ( set_difference(unordered_pair(sK2,sK1),sK3) = singleton(sK2)
| ( ( in(sK1,sK3)
| sK2 = sK1 )
& ~ in(sK2,sK3) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f22,f23]) ).
fof(f23,plain,
( ? [X0,X1,X2] :
( ( singleton(X1) != set_difference(unordered_pair(X1,X0),X2)
| ( ~ in(X0,X2)
& X0 != X1 )
| in(X1,X2) )
& ( singleton(X1) = set_difference(unordered_pair(X1,X0),X2)
| ( ( in(X0,X2)
| X0 = X1 )
& ~ in(X1,X2) ) ) )
=> ( ( set_difference(unordered_pair(sK2,sK1),sK3) != singleton(sK2)
| ( ~ in(sK1,sK3)
& sK2 != sK1 )
| in(sK2,sK3) )
& ( set_difference(unordered_pair(sK2,sK1),sK3) = singleton(sK2)
| ( ( in(sK1,sK3)
| sK2 = sK1 )
& ~ in(sK2,sK3) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f22,plain,
? [X0,X1,X2] :
( ( singleton(X1) != set_difference(unordered_pair(X1,X0),X2)
| ( ~ in(X0,X2)
& X0 != X1 )
| in(X1,X2) )
& ( singleton(X1) = set_difference(unordered_pair(X1,X0),X2)
| ( ( in(X0,X2)
| X0 = X1 )
& ~ in(X1,X2) ) ) ),
inference(flattening,[],[f21]) ).
fof(f21,plain,
? [X0,X1,X2] :
( ( singleton(X1) != set_difference(unordered_pair(X1,X0),X2)
| ( ~ in(X0,X2)
& X0 != X1 )
| in(X1,X2) )
& ( singleton(X1) = set_difference(unordered_pair(X1,X0),X2)
| ( ( in(X0,X2)
| X0 = X1 )
& ~ in(X1,X2) ) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f12,plain,
? [X0,X1,X2] :
( ( ( in(X0,X2)
| X0 = X1 )
& ~ in(X1,X2) )
<~> singleton(X1) = set_difference(unordered_pair(X1,X0),X2) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,plain,
~ ! [X2,X0,X1] :
( ( ( in(X0,X2)
| X0 = X1 )
& ~ in(X1,X2) )
<=> singleton(X1) = set_difference(unordered_pair(X1,X0),X2) ),
inference(rectify,[],[f6]) ).
fof(f6,negated_conjecture,
~ ! [X1,X0,X2] :
( ( ( in(X1,X2)
| X0 = X1 )
& ~ in(X0,X2) )
<=> set_difference(unordered_pair(X0,X1),X2) = singleton(X0) ),
inference(negated_conjecture,[],[f5]) ).
fof(f5,conjecture,
! [X1,X0,X2] :
( ( ( in(X1,X2)
| X0 = X1 )
& ~ in(X0,X2) )
<=> set_difference(unordered_pair(X0,X1),X2) = singleton(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_zfmisc_1) ).
fof(f65,plain,
( ~ spl8_1
| spl8_2
| ~ spl8_4 ),
inference(avatar_split_clause,[],[f44,f61,f52,f48]) ).
fof(f44,plain,
( sK2 != sK1
| in(sK2,sK3)
| sF6 != sF7 ),
inference(definition_folding,[],[f36,f42,f41,f40]) ).
fof(f36,plain,
( set_difference(unordered_pair(sK2,sK1),sK3) != singleton(sK2)
| sK2 != sK1
| in(sK2,sK3) ),
inference(cnf_transformation,[],[f24]) ).
fof(f64,plain,
( spl8_3
| spl8_4
| spl8_1 ),
inference(avatar_split_clause,[],[f45,f48,f61,f57]) ).
fof(f45,plain,
( sF6 = sF7
| sK2 = sK1
| in(sK1,sK3) ),
inference(definition_folding,[],[f35,f42,f41,f40]) ).
fof(f35,plain,
( set_difference(unordered_pair(sK2,sK1),sK3) = singleton(sK2)
| in(sK1,sK3)
| sK2 = sK1 ),
inference(cnf_transformation,[],[f24]) ).
fof(f55,plain,
( spl8_1
| ~ spl8_2 ),
inference(avatar_split_clause,[],[f46,f52,f48]) ).
fof(f46,plain,
( ~ in(sK2,sK3)
| sF6 = sF7 ),
inference(definition_folding,[],[f34,f42,f41,f40]) ).
fof(f34,plain,
( set_difference(unordered_pair(sK2,sK1),sK3) = singleton(sK2)
| ~ in(sK2,sK3) ),
inference(cnf_transformation,[],[f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SET927+1 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.13 % 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 : n019.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 14:34:05 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.17/0.52 % (10902)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 1.30/0.53 % (10914)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 1.30/0.53 % (10910)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 1.30/0.53 % (10909)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)
% 1.30/0.53 % (10914)Refutation not found, incomplete strategy% (10914)------------------------------
% 1.30/0.53 % (10914)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.30/0.53 % (10902)First to succeed.
% 1.30/0.53 % (10914)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.30/0.53 % (10914)Termination reason: Refutation not found, incomplete strategy
% 1.30/0.53
% 1.30/0.53 % (10914)Memory used [KB]: 1407
% 1.30/0.53 % (10914)Time elapsed: 0.129 s
% 1.30/0.53 % (10914)Instructions burned: 2 (million)
% 1.30/0.53 % (10914)------------------------------
% 1.30/0.53 % (10914)------------------------------
% 1.30/0.54 % (10918)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.30/0.54 % (10917)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 1.30/0.54 % (10902)Refutation found. Thanks to Tanya!
% 1.30/0.54 % SZS status Theorem for theBenchmark
% 1.30/0.54 % SZS output start Proof for theBenchmark
% See solution above
% 1.30/0.54 % (10902)------------------------------
% 1.30/0.54 % (10902)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.30/0.54 % (10902)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.30/0.54 % (10902)Termination reason: Refutation
% 1.30/0.54
% 1.30/0.54 % (10902)Memory used [KB]: 6012
% 1.30/0.54 % (10902)Time elapsed: 0.118 s
% 1.30/0.54 % (10902)Instructions burned: 9 (million)
% 1.30/0.54 % (10902)------------------------------
% 1.30/0.54 % (10902)------------------------------
% 1.30/0.54 % (10901)Success in time 0.182 s
%------------------------------------------------------------------------------