TSTP Solution File: SEU353+1 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SEU353+1 : TPTP v8.1.0. Released v3.3.0.
% 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 18:33:23 EDT 2022
% Result : Theorem 0.20s 0.52s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 76 ( 28 unt; 0 def)
% Number of atoms : 190 ( 41 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 189 ( 75 ~; 63 |; 35 &)
% ( 2 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-4 aty)
% Number of variables : 89 ( 81 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f483,plain,
$false,
inference(subsumption_resolution,[],[f482,f267]) ).
fof(f267,plain,
sK7 != sF19,
inference(definition_folding,[],[f221,f266,f265,f264,f264]) ).
fof(f264,plain,
sF17 = the_carrier(sK6),
introduced(function_definition,[]) ).
fof(f265,plain,
identity_on_carrier(sK6) = sF18,
introduced(function_definition,[]) ).
fof(f266,plain,
apply_as_element(sF17,sF17,sF18,sK7) = sF19,
introduced(function_definition,[]) ).
fof(f221,plain,
apply_as_element(the_carrier(sK6),the_carrier(sK6),identity_on_carrier(sK6),sK7) != sK7,
inference(cnf_transformation,[],[f140]) ).
fof(f140,plain,
( apply_as_element(the_carrier(sK6),the_carrier(sK6),identity_on_carrier(sK6),sK7) != sK7
& element(sK7,the_carrier(sK6))
& ~ empty_carrier(sK6)
& one_sorted_str(sK6) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f99,f139,f138]) ).
fof(f138,plain,
( ? [X0] :
( ? [X1] :
( apply_as_element(the_carrier(X0),the_carrier(X0),identity_on_carrier(X0),X1) != X1
& element(X1,the_carrier(X0)) )
& ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ( ? [X1] :
( apply_as_element(the_carrier(sK6),the_carrier(sK6),identity_on_carrier(sK6),X1) != X1
& element(X1,the_carrier(sK6)) )
& ~ empty_carrier(sK6)
& one_sorted_str(sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f139,plain,
( ? [X1] :
( apply_as_element(the_carrier(sK6),the_carrier(sK6),identity_on_carrier(sK6),X1) != X1
& element(X1,the_carrier(sK6)) )
=> ( apply_as_element(the_carrier(sK6),the_carrier(sK6),identity_on_carrier(sK6),sK7) != sK7
& element(sK7,the_carrier(sK6)) ) ),
introduced(choice_axiom,[]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( apply_as_element(the_carrier(X0),the_carrier(X0),identity_on_carrier(X0),X1) != X1
& element(X1,the_carrier(X0)) )
& ~ empty_carrier(X0)
& one_sorted_str(X0) ),
inference(flattening,[],[f98]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( apply_as_element(the_carrier(X0),the_carrier(X0),identity_on_carrier(X0),X1) != X1
& element(X1,the_carrier(X0)) )
& ~ empty_carrier(X0)
& one_sorted_str(X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f58,negated_conjecture,
~ ! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> apply_as_element(the_carrier(X0),the_carrier(X0),identity_on_carrier(X0),X1) = X1 ) ),
inference(negated_conjecture,[],[f57]) ).
fof(f57,conjecture,
! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> apply_as_element(the_carrier(X0),the_carrier(X0),identity_on_carrier(X0),X1) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t91_tmap_1) ).
fof(f482,plain,
sK7 = sF19,
inference(forward_demodulation,[],[f481,f344]) ).
fof(f344,plain,
apply(sF18,sK7) = sK7,
inference(forward_demodulation,[],[f343,f314]) ).
fof(f314,plain,
sF18 = identity_as_relation_of(sF17),
inference(forward_demodulation,[],[f313,f265]) ).
fof(f313,plain,
identity_on_carrier(sK6) = identity_as_relation_of(sF17),
inference(forward_demodulation,[],[f310,f264]) ).
fof(f310,plain,
identity_on_carrier(sK6) = identity_as_relation_of(the_carrier(sK6)),
inference(resolution,[],[f197,f218]) ).
fof(f218,plain,
one_sorted_str(sK6),
inference(cnf_transformation,[],[f140]) ).
fof(f197,plain,
! [X0] :
( ~ one_sorted_str(X0)
| identity_on_carrier(X0) = identity_as_relation_of(the_carrier(X0)) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0] :
( identity_on_carrier(X0) = identity_as_relation_of(the_carrier(X0))
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] :
( one_sorted_str(X0)
=> identity_on_carrier(X0) = identity_as_relation_of(the_carrier(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_grcat_1) ).
fof(f343,plain,
apply(identity_as_relation_of(sF17),sK7) = sK7,
inference(resolution,[],[f274,f307]) ).
fof(f307,plain,
in(sK7,sF17),
inference(subsumption_resolution,[],[f301,f293]) ).
fof(f293,plain,
~ empty(sF17),
inference(subsumption_resolution,[],[f292,f218]) ).
fof(f292,plain,
( ~ empty(sF17)
| ~ one_sorted_str(sK6) ),
inference(subsumption_resolution,[],[f291,f219]) ).
fof(f219,plain,
~ empty_carrier(sK6),
inference(cnf_transformation,[],[f140]) ).
fof(f291,plain,
( empty_carrier(sK6)
| ~ one_sorted_str(sK6)
| ~ empty(sF17) ),
inference(superposition,[],[f214,f264]) ).
fof(f214,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0] :
( empty_carrier(X0)
| ~ one_sorted_str(X0)
| ~ empty(the_carrier(X0)) ),
inference(flattening,[],[f85]) ).
fof(f85,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ~ empty(the_carrier(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f301,plain,
( in(sK7,sF17)
| empty(sF17) ),
inference(resolution,[],[f195,f268]) ).
fof(f268,plain,
element(sK7,sF17),
inference(definition_folding,[],[f220,f264]) ).
fof(f220,plain,
element(sK7,the_carrier(sK6)),
inference(cnf_transformation,[],[f140]) ).
fof(f195,plain,
! [X0,X1] :
( ~ element(X1,X0)
| in(X1,X0)
| empty(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0,X1] :
( empty(X0)
| in(X1,X0)
| ~ element(X1,X0) ),
inference(flattening,[],[f81]) ).
fof(f81,plain,
! [X1,X0] :
( in(X1,X0)
| empty(X0)
| ~ element(X1,X0) ),
inference(ennf_transformation,[],[f69]) ).
fof(f69,plain,
! [X1,X0] :
( element(X1,X0)
=> ( in(X1,X0)
| empty(X0) ) ),
inference(rectify,[],[f49]) ).
fof(f49,axiom,
! [X1,X0] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f274,plain,
! [X0,X1] :
( ~ in(X1,X0)
| apply(identity_as_relation_of(X0),X1) = X1 ),
inference(forward_demodulation,[],[f194,f238]) ).
fof(f238,plain,
! [X0] : identity_as_relation_of(X0) = identity_relation(X0),
inference(cnf_transformation,[],[f44]) ).
fof(f44,axiom,
! [X0] : identity_as_relation_of(X0) = identity_relation(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_partfun1) ).
fof(f194,plain,
! [X0,X1] :
( ~ in(X1,X0)
| apply(identity_relation(X0),X1) = X1 ),
inference(cnf_transformation,[],[f100]) ).
fof(f100,plain,
! [X0,X1] :
( ~ in(X1,X0)
| apply(identity_relation(X0),X1) = X1 ),
inference(ennf_transformation,[],[f50]) ).
fof(f50,axiom,
! [X1,X0] :
( in(X1,X0)
=> apply(identity_relation(X0),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_funct_1) ).
fof(f481,plain,
apply(sF18,sK7) = sF19,
inference(forward_demodulation,[],[f478,f266]) ).
fof(f478,plain,
apply(sF18,sK7) = apply_as_element(sF17,sF17,sF18,sK7),
inference(resolution,[],[f438,f268]) ).
fof(f438,plain,
! [X11] :
( ~ element(X11,sF17)
| apply(sF18,X11) = apply_as_element(sF17,sF17,sF18,X11) ),
inference(subsumption_resolution,[],[f437,f322]) ).
fof(f322,plain,
relation_of2(sF18,sF17,sF17),
inference(superposition,[],[f295,f314]) ).
fof(f295,plain,
! [X0] : relation_of2(identity_as_relation_of(X0),X0,X0),
inference(resolution,[],[f189,f251]) ).
fof(f251,plain,
! [X0] : relation_of2_as_subset(identity_as_relation_of(X0),X0,X0),
inference(cnf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( v1_partfun1(identity_as_relation_of(X0),X0,X0)
& relation_of2_as_subset(identity_as_relation_of(X0),X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_partfun1) ).
fof(f189,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| relation_of2(X0,X1,X2) ),
inference(cnf_transformation,[],[f130]) ).
fof(f130,plain,
! [X0,X1,X2] :
( ( relation_of2(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) )
& ( relation_of2_as_subset(X0,X1,X2)
| ~ relation_of2(X0,X1,X2) ) ),
inference(rectify,[],[f129]) ).
fof(f129,plain,
! [X2,X1,X0] :
( ( relation_of2(X2,X1,X0)
| ~ relation_of2_as_subset(X2,X1,X0) )
& ( relation_of2_as_subset(X2,X1,X0)
| ~ relation_of2(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X2,X1,X0] :
( relation_of2(X2,X1,X0)
<=> relation_of2_as_subset(X2,X1,X0) ),
inference(rectify,[],[f46]) ).
fof(f46,axiom,
! [X1,X0,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f437,plain,
! [X11] :
( ~ element(X11,sF17)
| ~ relation_of2(sF18,sF17,sF17)
| apply(sF18,X11) = apply_as_element(sF17,sF17,sF18,X11) ),
inference(subsumption_resolution,[],[f436,f293]) ).
fof(f436,plain,
! [X11] :
( empty(sF17)
| ~ relation_of2(sF18,sF17,sF17)
| ~ element(X11,sF17)
| apply(sF18,X11) = apply_as_element(sF17,sF17,sF18,X11) ),
inference(subsumption_resolution,[],[f434,f290]) ).
fof(f290,plain,
function(sF18),
inference(subsumption_resolution,[],[f289,f218]) ).
fof(f289,plain,
( function(sF18)
| ~ one_sorted_str(sK6) ),
inference(superposition,[],[f204,f265]) ).
fof(f204,plain,
! [X0] :
( function(identity_on_carrier(X0))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0] :
( ~ one_sorted_str(X0)
| ( quasi_total(identity_on_carrier(X0),the_carrier(X0),the_carrier(X0))
& function(identity_on_carrier(X0))
& relation_of2_as_subset(identity_on_carrier(X0),the_carrier(X0),the_carrier(X0)) ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0] :
( one_sorted_str(X0)
=> ( quasi_total(identity_on_carrier(X0),the_carrier(X0),the_carrier(X0))
& function(identity_on_carrier(X0))
& relation_of2_as_subset(identity_on_carrier(X0),the_carrier(X0),the_carrier(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_grcat_1) ).
fof(f434,plain,
! [X11] :
( ~ function(sF18)
| ~ element(X11,sF17)
| apply(sF18,X11) = apply_as_element(sF17,sF17,sF18,X11)
| empty(sF17)
| ~ relation_of2(sF18,sF17,sF17) ),
inference(resolution,[],[f253,f340]) ).
fof(f340,plain,
quasi_total(sF18,sF17,sF17),
inference(forward_demodulation,[],[f339,f264]) ).
fof(f339,plain,
quasi_total(sF18,the_carrier(sK6),the_carrier(sK6)),
inference(subsumption_resolution,[],[f337,f218]) ).
fof(f337,plain,
( quasi_total(sF18,the_carrier(sK6),the_carrier(sK6))
| ~ one_sorted_str(sK6) ),
inference(superposition,[],[f205,f265]) ).
fof(f205,plain,
! [X0] :
( quasi_total(identity_on_carrier(X0),the_carrier(X0),the_carrier(X0))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f253,plain,
! [X2,X3,X0,X1] :
( ~ quasi_total(X3,X0,X1)
| ~ element(X2,X0)
| empty(X0)
| ~ relation_of2(X3,X0,X1)
| ~ function(X3)
| apply(X3,X2) = apply_as_element(X0,X1,X3,X2) ),
inference(cnf_transformation,[],[f160]) ).
fof(f160,plain,
! [X0,X1,X2,X3] :
( ~ relation_of2(X3,X0,X1)
| apply(X3,X2) = apply_as_element(X0,X1,X3,X2)
| ~ quasi_total(X3,X0,X1)
| ~ function(X3)
| ~ element(X2,X0)
| empty(X0) ),
inference(rectify,[],[f91]) ).
fof(f91,plain,
! [X1,X3,X2,X0] :
( ~ relation_of2(X0,X1,X3)
| apply(X0,X2) = apply_as_element(X1,X3,X0,X2)
| ~ quasi_total(X0,X1,X3)
| ~ function(X0)
| ~ element(X2,X1)
| empty(X1) ),
inference(flattening,[],[f90]) ).
fof(f90,plain,
! [X2,X1,X0,X3] :
( apply(X0,X2) = apply_as_element(X1,X3,X0,X2)
| ~ relation_of2(X0,X1,X3)
| ~ quasi_total(X0,X1,X3)
| ~ function(X0)
| ~ element(X2,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f72]) ).
fof(f72,plain,
! [X2,X1,X0,X3] :
( ( relation_of2(X0,X1,X3)
& quasi_total(X0,X1,X3)
& function(X0)
& element(X2,X1)
& ~ empty(X1) )
=> apply(X0,X2) = apply_as_element(X1,X3,X0,X2) ),
inference(rectify,[],[f45]) ).
fof(f45,axiom,
! [X2,X0,X3,X1] :
( ( ~ empty(X0)
& relation_of2(X2,X0,X1)
& element(X3,X0)
& function(X2)
& quasi_total(X2,X0,X1) )
=> apply_as_element(X0,X1,X2,X3) = apply(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k8_funct_2) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU353+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.14/0.34 % Computer : n003.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 30 15:18:22 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.49 % (12781)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)
% 0.20/0.49 % (12773)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.50 % (12795)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)
% 0.20/0.51 % (12773)Instruction limit reached!
% 0.20/0.51 % (12773)------------------------------
% 0.20/0.51 % (12773)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51 % (12773)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51 % (12773)Termination reason: Unknown
% 0.20/0.51 % (12773)Termination phase: Saturation
% 0.20/0.51
% 0.20/0.51 % (12773)Memory used [KB]: 5628
% 0.20/0.51 % (12773)Time elapsed: 0.077 s
% 0.20/0.51 % (12773)Instructions burned: 7 (million)
% 0.20/0.51 % (12773)------------------------------
% 0.20/0.51 % (12773)------------------------------
% 0.20/0.51 % (12781)First to succeed.
% 0.20/0.52 % (12776)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.52 % (12781)Refutation found. Thanks to Tanya!
% 0.20/0.52 % SZS status Theorem for theBenchmark
% 0.20/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.52 % (12781)------------------------------
% 0.20/0.52 % (12781)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52 % (12781)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52 % (12781)Termination reason: Refutation
% 0.20/0.52
% 0.20/0.52 % (12781)Memory used [KB]: 1279
% 0.20/0.52 % (12781)Time elapsed: 0.071 s
% 0.20/0.52 % (12781)Instructions burned: 13 (million)
% 0.20/0.52 % (12781)------------------------------
% 0.20/0.52 % (12781)------------------------------
% 0.20/0.52 % (12762)Success in time 0.169 s
%------------------------------------------------------------------------------