TSTP Solution File: SEU147+3 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SEU147+3 : TPTP v8.1.0. Bugfixed v4.0.0.
% 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 : n008.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 18:26:54 EDT 2022
% Result : Theorem 0.19s 0.50s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 54 ( 17 unt; 0 def)
% Number of atoms : 176 ( 66 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 197 ( 75 ~; 85 |; 26 &)
% ( 5 <=>; 5 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 86 ( 77 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f130,plain,
$false,
inference(subsumption_resolution,[],[f129,f70]) ).
fof(f70,plain,
in(empty_set,sF5),
inference(resolution,[],[f66,f47]) ).
fof(f47,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f12]) ).
fof(f12,plain,
! [X1] : subset(X1,X1),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X1,X0] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f66,plain,
! [X0] :
( ~ subset(X0,empty_set)
| in(X0,sF5) ),
inference(superposition,[],[f51,f56]) ).
fof(f56,plain,
powerset(empty_set) = sF5,
introduced(function_definition,[]) ).
fof(f51,plain,
! [X2,X0] :
( in(X2,powerset(X0))
| ~ subset(X2,X0) ),
inference(equality_resolution,[],[f40]) ).
fof(f40,plain,
! [X2,X0,X1] :
( in(X2,X1)
| ~ subset(X2,X0)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] :
( ( ! [X2] :
( ( in(X2,X1)
| ~ subset(X2,X0) )
& ( subset(X2,X0)
| ~ in(X2,X1) ) )
| powerset(X0) != X1 )
& ( powerset(X0) = X1
| ( ( ~ subset(sK1(X0,X1),X0)
| ~ in(sK1(X0,X1),X1) )
& ( subset(sK1(X0,X1),X0)
| in(sK1(X0,X1),X1) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f22,f23]) ).
fof(f23,plain,
! [X0,X1] :
( ? [X3] :
( ( ~ subset(X3,X0)
| ~ in(X3,X1) )
& ( subset(X3,X0)
| in(X3,X1) ) )
=> ( ( ~ subset(sK1(X0,X1),X0)
| ~ in(sK1(X0,X1),X1) )
& ( subset(sK1(X0,X1),X0)
| in(sK1(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f22,plain,
! [X0,X1] :
( ( ! [X2] :
( ( in(X2,X1)
| ~ subset(X2,X0) )
& ( subset(X2,X0)
| ~ in(X2,X1) ) )
| powerset(X0) != X1 )
& ( powerset(X0) = X1
| ? [X3] :
( ( ~ subset(X3,X0)
| ~ in(X3,X1) )
& ( subset(X3,X0)
| in(X3,X1) ) ) ) ),
inference(rectify,[],[f21]) ).
fof(f21,plain,
! [X0,X1] :
( ( ! [X2] :
( ( in(X2,X1)
| ~ subset(X2,X0) )
& ( subset(X2,X0)
| ~ in(X2,X1) ) )
| powerset(X0) != X1 )
& ( powerset(X0) = X1
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) ) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) )
<=> powerset(X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f129,plain,
~ in(empty_set,sF5),
inference(subsumption_resolution,[],[f128,f59]) ).
fof(f59,plain,
in(empty_set,sF6),
inference(superposition,[],[f54,f57]) ).
fof(f57,plain,
singleton(empty_set) = sF6,
introduced(function_definition,[]) ).
fof(f54,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f53]) ).
fof(f53,plain,
! [X3,X0] :
( in(X3,X0)
| singleton(X3) != X0 ),
inference(equality_resolution,[],[f43]) ).
fof(f43,plain,
! [X3,X0,X1] :
( in(X3,X0)
| X1 != X3
| singleton(X1) != X0 ),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0,X1] :
( ( singleton(X1) = X0
| ( ( sK2(X0,X1) != X1
| ~ in(sK2(X0,X1),X0) )
& ( sK2(X0,X1) = X1
| in(sK2(X0,X1),X0) ) ) )
& ( ! [X3] :
( ( in(X3,X0)
| X1 != X3 )
& ( X1 = X3
| ~ in(X3,X0) ) )
| singleton(X1) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f26,f27]) ).
fof(f27,plain,
! [X0,X1] :
( ? [X2] :
( ( X1 != X2
| ~ in(X2,X0) )
& ( X1 = X2
| in(X2,X0) ) )
=> ( ( sK2(X0,X1) != X1
| ~ in(sK2(X0,X1),X0) )
& ( sK2(X0,X1) = X1
| in(sK2(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f26,plain,
! [X0,X1] :
( ( singleton(X1) = X0
| ? [X2] :
( ( X1 != X2
| ~ in(X2,X0) )
& ( X1 = X2
| in(X2,X0) ) ) )
& ( ! [X3] :
( ( in(X3,X0)
| X1 != X3 )
& ( X1 = X3
| ~ in(X3,X0) ) )
| singleton(X1) != X0 ) ),
inference(rectify,[],[f25]) ).
fof(f25,plain,
! [X1,X0] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X1,X0] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f128,plain,
( ~ in(empty_set,sF6)
| ~ in(empty_set,sF5) ),
inference(subsumption_resolution,[],[f126,f58]) ).
fof(f58,plain,
sF6 != sF5,
inference(definition_folding,[],[f49,f57,f56]) ).
fof(f49,plain,
powerset(empty_set) != singleton(empty_set),
inference(cnf_transformation,[],[f13]) ).
fof(f13,plain,
powerset(empty_set) != singleton(empty_set),
inference(flattening,[],[f9]) ).
fof(f9,negated_conjecture,
powerset(empty_set) != singleton(empty_set),
inference(negated_conjecture,[],[f8]) ).
fof(f8,conjecture,
powerset(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).
fof(f126,plain,
( sF6 = sF5
| ~ in(empty_set,sF5)
| ~ in(empty_set,sF6) ),
inference(superposition,[],[f36,f123]) ).
fof(f123,plain,
empty_set = sK0(sF5,sF6),
inference(subsumption_resolution,[],[f120,f58]) ).
fof(f120,plain,
( sF6 = sF5
| empty_set = sK0(sF5,sF6) ),
inference(duplicate_literal_removal,[],[f118]) ).
fof(f118,plain,
( empty_set = sK0(sF5,sF6)
| sF6 = sF5
| empty_set = sK0(sF5,sF6) ),
inference(resolution,[],[f97,f73]) ).
fof(f73,plain,
! [X1] :
( ~ in(X1,sF5)
| empty_set = X1 ),
inference(resolution,[],[f68,f48]) ).
fof(f48,plain,
! [X0] :
( ~ subset(X0,empty_set)
| empty_set = X0 ),
inference(cnf_transformation,[],[f15]) ).
fof(f15,plain,
! [X0] :
( ~ subset(X0,empty_set)
| empty_set = X0 ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] :
( subset(X0,empty_set)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(f68,plain,
! [X0] :
( subset(X0,empty_set)
| ~ in(X0,sF5) ),
inference(superposition,[],[f52,f56]) ).
fof(f52,plain,
! [X2,X0] :
( ~ in(X2,powerset(X0))
| subset(X2,X0) ),
inference(equality_resolution,[],[f39]) ).
fof(f39,plain,
! [X2,X0,X1] :
( subset(X2,X0)
| ~ in(X2,X1)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f24]) ).
fof(f97,plain,
! [X7] :
( in(sK0(X7,sF6),X7)
| sF6 = X7
| empty_set = sK0(X7,sF6) ),
inference(resolution,[],[f35,f79]) ).
fof(f79,plain,
! [X0] :
( ~ in(X0,sF6)
| empty_set = X0 ),
inference(superposition,[],[f55,f57]) ).
fof(f55,plain,
! [X3,X1] :
( ~ in(X3,singleton(X1))
| X1 = X3 ),
inference(equality_resolution,[],[f42]) ).
fof(f42,plain,
! [X3,X0,X1] :
( X1 = X3
| ~ in(X3,X0)
| singleton(X1) != X0 ),
inference(cnf_transformation,[],[f28]) ).
fof(f35,plain,
! [X0,X1] :
( in(sK0(X0,X1),X1)
| X0 = X1
| in(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( ( ( ~ in(sK0(X0,X1),X1)
| ~ in(sK0(X0,X1),X0) )
& ( in(sK0(X0,X1),X1)
| in(sK0(X0,X1),X0) ) )
| X0 = X1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f18,f19]) ).
fof(f19,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) )
=> ( ( ~ in(sK0(X0,X1),X1)
| ~ in(sK0(X0,X1),X0) )
& ( in(sK0(X0,X1),X1)
| in(sK0(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) )
| X0 = X1 ),
inference(nnf_transformation,[],[f16]) ).
fof(f16,plain,
! [X0,X1] :
( ? [X2] :
( in(X2,X0)
<~> in(X2,X1) )
| X0 = X1 ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X1,X0] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
fof(f36,plain,
! [X0,X1] :
( ~ in(sK0(X0,X1),X1)
| X0 = X1
| ~ in(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SEU147+3 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.11/0.12 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 30 14:49:25 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.49 % (32718)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)
% 0.19/0.50 % (32711)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.19/0.50 % (32714)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.50 % (32714)Refutation not found, incomplete strategy% (32714)------------------------------
% 0.19/0.50 % (32714)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50 % (32714)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50 % (32714)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.50
% 0.19/0.50 % (32714)Memory used [KB]: 5884
% 0.19/0.50 % (32714)Time elapsed: 0.104 s
% 0.19/0.50 % (32714)Instructions burned: 2 (million)
% 0.19/0.50 % (32714)------------------------------
% 0.19/0.50 % (32714)------------------------------
% 0.19/0.50 % (32726)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)
% 0.19/0.50 % (32724)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.50 % (32733)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.19/0.50 % (32711)First to succeed.
% 0.19/0.50 % (32720)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.19/0.50 % (32713)dis+1002_1:1_aac=none:bd=off:sac=on:sos=on:spb=units:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.50 % (32711)Refutation found. Thanks to Tanya!
% 0.19/0.50 % SZS status Theorem for theBenchmark
% 0.19/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.51 % (32711)------------------------------
% 0.19/0.51 % (32711)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51 % (32711)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51 % (32711)Termination reason: Refutation
% 0.19/0.51
% 0.19/0.51 % (32711)Memory used [KB]: 6012
% 0.19/0.51 % (32711)Time elapsed: 0.103 s
% 0.19/0.51 % (32711)Instructions burned: 5 (million)
% 0.19/0.51 % (32711)------------------------------
% 0.19/0.51 % (32711)------------------------------
% 0.19/0.51 % (32710)Success in time 0.164 s
%------------------------------------------------------------------------------