TSTP Solution File: SEU212+3 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU212+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n020.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 : Tue Apr 30 15:24:08 EDT 2024
% Result : Theorem 0.17s 0.41s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 7
% Syntax : Number of formulae : 49 ( 7 unt; 0 def)
% Number of atoms : 223 ( 53 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 277 ( 103 ~; 102 |; 48 &)
% ( 12 <=>; 10 =>; 0 <=; 2 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 98 ( 70 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f740,plain,
$false,
inference(resolution,[],[f736,f715]) ).
fof(f715,plain,
~ in(sK0,relation_dom(sK2)),
inference(resolution,[],[f713,f92]) ).
fof(f92,plain,
relation(sK2),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
( ( sK1 != apply(sK2,sK0)
| ~ in(sK0,relation_dom(sK2))
| ~ in(ordered_pair(sK0,sK1),sK2) )
& ( ( sK1 = apply(sK2,sK0)
& in(sK0,relation_dom(sK2)) )
| in(ordered_pair(sK0,sK1),sK2) )
& function(sK2)
& relation(sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f64,f65]) ).
fof(f65,plain,
( ? [X0,X1,X2] :
( ( apply(X2,X0) != X1
| ~ in(X0,relation_dom(X2))
| ~ in(ordered_pair(X0,X1),X2) )
& ( ( apply(X2,X0) = X1
& in(X0,relation_dom(X2)) )
| in(ordered_pair(X0,X1),X2) )
& function(X2)
& relation(X2) )
=> ( ( sK1 != apply(sK2,sK0)
| ~ in(sK0,relation_dom(sK2))
| ~ in(ordered_pair(sK0,sK1),sK2) )
& ( ( sK1 = apply(sK2,sK0)
& in(sK0,relation_dom(sK2)) )
| in(ordered_pair(sK0,sK1),sK2) )
& function(sK2)
& relation(sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f64,plain,
? [X0,X1,X2] :
( ( apply(X2,X0) != X1
| ~ in(X0,relation_dom(X2))
| ~ in(ordered_pair(X0,X1),X2) )
& ( ( apply(X2,X0) = X1
& in(X0,relation_dom(X2)) )
| in(ordered_pair(X0,X1),X2) )
& function(X2)
& relation(X2) ),
inference(flattening,[],[f63]) ).
fof(f63,plain,
? [X0,X1,X2] :
( ( apply(X2,X0) != X1
| ~ in(X0,relation_dom(X2))
| ~ in(ordered_pair(X0,X1),X2) )
& ( ( apply(X2,X0) = X1
& in(X0,relation_dom(X2)) )
| in(ordered_pair(X0,X1),X2) )
& function(X2)
& relation(X2) ),
inference(nnf_transformation,[],[f42]) ).
fof(f42,plain,
? [X0,X1,X2] :
( ( in(ordered_pair(X0,X1),X2)
<~> ( apply(X2,X0) = X1
& in(X0,relation_dom(X2)) ) )
& function(X2)
& relation(X2) ),
inference(flattening,[],[f41]) ).
fof(f41,plain,
? [X0,X1,X2] :
( ( in(ordered_pair(X0,X1),X2)
<~> ( apply(X2,X0) = X1
& in(X0,relation_dom(X2)) ) )
& function(X2)
& relation(X2) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,negated_conjecture,
~ ! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(ordered_pair(X0,X1),X2)
<=> ( apply(X2,X0) = X1
& in(X0,relation_dom(X2)) ) ) ),
inference(negated_conjecture,[],[f35]) ).
fof(f35,conjecture,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(ordered_pair(X0,X1),X2)
<=> ( apply(X2,X0) = X1
& in(X0,relation_dom(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_funct_1) ).
fof(f713,plain,
( ~ relation(sK2)
| ~ in(sK0,relation_dom(sK2)) ),
inference(resolution,[],[f712,f93]) ).
fof(f93,plain,
function(sK2),
inference(cnf_transformation,[],[f66]) ).
fof(f712,plain,
( ~ function(sK2)
| ~ in(sK0,relation_dom(sK2))
| ~ relation(sK2) ),
inference(duplicate_literal_removal,[],[f705]) ).
fof(f705,plain,
( ~ in(sK0,relation_dom(sK2))
| ~ function(sK2)
| ~ relation(sK2)
| ~ in(sK0,relation_dom(sK2)) ),
inference(resolution,[],[f682,f681]) ).
fof(f681,plain,
( ~ in(ordered_pair(sK0,sK1),sK2)
| ~ in(sK0,relation_dom(sK2)) ),
inference(trivial_inequality_removal,[],[f680]) ).
fof(f680,plain,
( sK1 != sK1
| ~ in(sK0,relation_dom(sK2))
| ~ in(ordered_pair(sK0,sK1),sK2) ),
inference(backward_demodulation,[],[f96,f679]) ).
fof(f679,plain,
sK1 = apply(sK2,sK0),
inference(duplicate_literal_removal,[],[f674]) ).
fof(f674,plain,
( sK1 = apply(sK2,sK0)
| sK1 = apply(sK2,sK0) ),
inference(resolution,[],[f672,f95]) ).
fof(f95,plain,
( in(ordered_pair(sK0,sK1),sK2)
| sK1 = apply(sK2,sK0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f672,plain,
! [X0] :
( ~ in(ordered_pair(sK0,X0),sK2)
| sK1 = apply(sK2,sK0) ),
inference(resolution,[],[f670,f92]) ).
fof(f670,plain,
! [X0] :
( ~ relation(sK2)
| ~ in(ordered_pair(sK0,X0),sK2)
| sK1 = apply(sK2,sK0) ),
inference(resolution,[],[f667,f145]) ).
fof(f145,plain,
! [X0,X6,X5] :
( in(X5,relation_dom(X0))
| ~ in(ordered_pair(X5,X6),X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f107]) ).
fof(f107,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X5,X6),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ( ( ! [X3] : ~ in(ordered_pair(sK4(X0,X1),X3),X0)
| ~ in(sK4(X0,X1),X1) )
& ( in(ordered_pair(sK4(X0,X1),sK5(X0,X1)),X0)
| in(sK4(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK6(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f70,f73,f72,f71]) ).
fof(f71,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) )
=> ( ( ! [X3] : ~ in(ordered_pair(sK4(X0,X1),X3),X0)
| ~ in(sK4(X0,X1),X1) )
& ( ? [X4] : in(ordered_pair(sK4(X0,X1),X4),X0)
| in(sK4(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f72,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(sK4(X0,X1),X4),X0)
=> in(ordered_pair(sK4(X0,X1),sK5(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f73,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X5,X7),X0)
=> in(ordered_pair(X5,sK6(X0,X5)),X0) ),
introduced(choice_axiom,[]) ).
fof(f70,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( ? [X7] : in(ordered_pair(X5,X7),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f69]) ).
fof(f69,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0] :
( ! [X1] :
( relation_dom(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation_dom(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f667,plain,
( ~ in(sK0,relation_dom(sK2))
| sK1 = apply(sK2,sK0) ),
inference(duplicate_literal_removal,[],[f659]) ).
fof(f659,plain,
( sK1 = apply(sK2,sK0)
| ~ in(sK0,relation_dom(sK2))
| sK1 = apply(sK2,sK0) ),
inference(resolution,[],[f657,f95]) ).
fof(f657,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,X1),sK2)
| apply(sK2,X0) = X1
| ~ in(X0,relation_dom(sK2)) ),
inference(resolution,[],[f550,f92]) ).
fof(f550,plain,
! [X0,X1] :
( ~ relation(sK2)
| ~ in(X0,relation_dom(sK2))
| apply(sK2,X0) = X1
| ~ in(ordered_pair(X0,X1),sK2) ),
inference(resolution,[],[f117,f93]) ).
fof(f117,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(X1,relation_dom(X0))
| apply(X0,X1) = X2
| ~ relation(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0] :
( ! [X1,X2] :
( ( ( ( apply(X0,X1) = X2
| empty_set != X2 )
& ( empty_set = X2
| apply(X0,X1) != X2 ) )
| in(X1,relation_dom(X0)) )
& ( ( ( apply(X0,X1) = X2
| ~ in(ordered_pair(X1,X2),X0) )
& ( in(ordered_pair(X1,X2),X0)
| apply(X0,X1) != X2 ) )
| ~ in(X1,relation_dom(X0)) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(nnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0] :
( ! [X1,X2] :
( ( ( apply(X0,X1) = X2
<=> empty_set = X2 )
| in(X1,relation_dom(X0)) )
& ( ( apply(X0,X1) = X2
<=> in(ordered_pair(X1,X2),X0) )
| ~ in(X1,relation_dom(X0)) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f51]) ).
fof(f51,plain,
! [X0] :
( ! [X1,X2] :
( ( ( apply(X0,X1) = X2
<=> empty_set = X2 )
| in(X1,relation_dom(X0)) )
& ( ( apply(X0,X1) = X2
<=> in(ordered_pair(X1,X2),X0) )
| ~ in(X1,relation_dom(X0)) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( ( ~ in(X1,relation_dom(X0))
=> ( apply(X0,X1) = X2
<=> empty_set = X2 ) )
& ( in(X1,relation_dom(X0))
=> ( apply(X0,X1) = X2
<=> in(ordered_pair(X1,X2),X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).
fof(f96,plain,
( sK1 != apply(sK2,sK0)
| ~ in(sK0,relation_dom(sK2))
| ~ in(ordered_pair(sK0,sK1),sK2) ),
inference(cnf_transformation,[],[f66]) ).
fof(f682,plain,
( in(ordered_pair(sK0,sK1),sK2)
| ~ in(sK0,relation_dom(sK2))
| ~ function(sK2)
| ~ relation(sK2) ),
inference(superposition,[],[f149,f679]) ).
fof(f149,plain,
! [X0,X1] :
( in(ordered_pair(X1,apply(X0,X1)),X0)
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f116]) ).
fof(f116,plain,
! [X2,X0,X1] :
( in(ordered_pair(X1,X2),X0)
| apply(X0,X1) != X2
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f736,plain,
in(sK0,relation_dom(sK2)),
inference(resolution,[],[f723,f94]) ).
fof(f94,plain,
( in(ordered_pair(sK0,sK1),sK2)
| in(sK0,relation_dom(sK2)) ),
inference(cnf_transformation,[],[f66]) ).
fof(f723,plain,
! [X0] : ~ in(ordered_pair(sK0,X0),sK2),
inference(resolution,[],[f719,f92]) ).
fof(f719,plain,
! [X0] :
( ~ relation(sK2)
| ~ in(ordered_pair(sK0,X0),sK2) ),
inference(resolution,[],[f715,f145]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU212+3 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.33 % Computer : n020.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Apr 29 20:34:47 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.33 % (3770)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.36 % (3774)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.11/0.36 % (3776)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.11/0.36 TRYING [1]
% 0.17/0.36 % (3773)WARNING: value z3 for option sas not known
% 0.17/0.36 % (3775)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.17/0.36 % (3772)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.17/0.36 TRYING [2]
% 0.17/0.36 % (3773)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.17/0.37 TRYING [3]
% 0.17/0.38 % (3771)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.17/0.38 TRYING [4]
% 0.17/0.39 TRYING [1]
% 0.17/0.39 TRYING [2]
% 0.17/0.39 % (3777)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.17/0.39 TRYING [3]
% 0.17/0.39 TRYING [4]
% 0.17/0.40 % (3776)First to succeed.
% 0.17/0.40 TRYING [1]
% 0.17/0.40 TRYING [2]
% 0.17/0.41 % (3776)Refutation found. Thanks to Tanya!
% 0.17/0.41 % SZS status Theorem for theBenchmark
% 0.17/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.41 % (3776)------------------------------
% 0.17/0.41 % (3776)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.17/0.41 % (3776)Termination reason: Refutation
% 0.17/0.41
% 0.17/0.41 % (3776)Memory used [KB]: 1140
% 0.17/0.41 % (3776)Time elapsed: 0.049 s
% 0.17/0.41 % (3776)Instructions burned: 40 (million)
% 0.17/0.41 % (3776)------------------------------
% 0.17/0.41 % (3776)------------------------------
% 0.17/0.41 % (3770)Success in time 0.076 s
%------------------------------------------------------------------------------