TSTP Solution File: SEU355+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU355+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n002.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 : Sun May 5 09:36:13 EDT 2024
% Result : Theorem 0.15s 0.38s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 15
% Syntax : Number of formulae : 59 ( 15 unt; 0 def)
% Number of atoms : 213 ( 4 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 253 ( 99 ~; 83 |; 43 &)
% ( 10 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 139 ( 125 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f188,plain,
$false,
inference(unit_resulting_resolution,[],[f172,f156,f157,f83]) ).
fof(f83,plain,
! [X2,X0,X1] :
( ~ sP3(X0,X1,X2)
| ~ sP2(X2,X1,X0)
| relstr_element_smaller(X1,X0,X2) ),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ( ( relstr_element_smaller(X1,X0,X2)
| ~ sP2(X2,X1,X0) )
& ( sP2(X2,X1,X0)
| ~ relstr_element_smaller(X1,X0,X2) ) )
| ~ sP3(X0,X1,X2) ),
inference(rectify,[],[f55]) ).
fof(f55,plain,
! [X1,X0,X2] :
( ( ( relstr_element_smaller(X0,X1,X2)
| ~ sP2(X2,X0,X1) )
& ( sP2(X2,X0,X1)
| ~ relstr_element_smaller(X0,X1,X2) ) )
| ~ sP3(X1,X0,X2) ),
inference(nnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X1,X0,X2] :
( ( relstr_element_smaller(X0,X1,X2)
<=> sP2(X2,X0,X1) )
| ~ sP3(X1,X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f157,plain,
! [X0] : sP3(X0,sK4,sK5),
inference(unit_resulting_resolution,[],[f71,f72,f88]) ).
fof(f88,plain,
! [X2,X0,X1] :
( ~ element(X2,the_carrier(X0))
| sP3(X1,X0,X2)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0] :
( ! [X1,X2] :
( sP3(X1,X0,X2)
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(definition_folding,[],[f32,f44,f43]) ).
fof(f43,plain,
! [X2,X0,X1] :
( sP2(X2,X0,X1)
<=> ! [X3] :
( related(X0,X2,X3)
| ~ in(X3,X1)
| ~ element(X3,the_carrier(X0)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f32,plain,
! [X0] :
( ! [X1,X2] :
( ( relstr_element_smaller(X0,X1,X2)
<=> ! [X3] :
( related(X0,X2,X3)
| ~ in(X3,X1)
| ~ element(X3,the_carrier(X0)) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(flattening,[],[f31]) ).
fof(f31,plain,
! [X0] :
( ! [X1,X2] :
( ( relstr_element_smaller(X0,X1,X2)
<=> ! [X3] :
( related(X0,X2,X3)
| ~ in(X3,X1)
| ~ element(X3,the_carrier(X0)) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( rel_str(X0)
=> ! [X1,X2] :
( element(X2,the_carrier(X0))
=> ( relstr_element_smaller(X0,X1,X2)
<=> ! [X3] :
( element(X3,the_carrier(X0))
=> ( in(X3,X1)
=> related(X0,X2,X3) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_lattice3) ).
fof(f72,plain,
element(sK5,the_carrier(sK4)),
inference(cnf_transformation,[],[f48]) ).
fof(f48,plain,
( ( ~ relstr_element_smaller(sK4,empty_set,sK5)
| ~ relstr_set_smaller(sK4,empty_set,sK5) )
& element(sK5,the_carrier(sK4))
& rel_str(sK4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f28,f47,f46]) ).
fof(f46,plain,
( ? [X0] :
( ? [X1] :
( ( ~ relstr_element_smaller(X0,empty_set,X1)
| ~ relstr_set_smaller(X0,empty_set,X1) )
& element(X1,the_carrier(X0)) )
& rel_str(X0) )
=> ( ? [X1] :
( ( ~ relstr_element_smaller(sK4,empty_set,X1)
| ~ relstr_set_smaller(sK4,empty_set,X1) )
& element(X1,the_carrier(sK4)) )
& rel_str(sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f47,plain,
( ? [X1] :
( ( ~ relstr_element_smaller(sK4,empty_set,X1)
| ~ relstr_set_smaller(sK4,empty_set,X1) )
& element(X1,the_carrier(sK4)) )
=> ( ( ~ relstr_element_smaller(sK4,empty_set,sK5)
| ~ relstr_set_smaller(sK4,empty_set,sK5) )
& element(sK5,the_carrier(sK4)) ) ),
introduced(choice_axiom,[]) ).
fof(f28,plain,
? [X0] :
( ? [X1] :
( ( ~ relstr_element_smaller(X0,empty_set,X1)
| ~ relstr_set_smaller(X0,empty_set,X1) )
& element(X1,the_carrier(X0)) )
& rel_str(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,negated_conjecture,
~ ! [X0] :
( rel_str(X0)
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ( relstr_element_smaller(X0,empty_set,X1)
& relstr_set_smaller(X0,empty_set,X1) ) ) ),
inference(negated_conjecture,[],[f20]) ).
fof(f20,conjecture,
! [X0] :
( rel_str(X0)
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ( relstr_element_smaller(X0,empty_set,X1)
& relstr_set_smaller(X0,empty_set,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_yellow_0) ).
fof(f71,plain,
rel_str(sK4),
inference(cnf_transformation,[],[f48]) ).
fof(f156,plain,
! [X0,X1] : sP2(X0,X1,empty_set),
inference(unit_resulting_resolution,[],[f107,f86]) ).
fof(f86,plain,
! [X2,X0,X1] :
( sP2(X0,X1,X2)
| in(sK7(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ( ~ related(X1,X0,sK7(X0,X1,X2))
& in(sK7(X0,X1,X2),X2)
& element(sK7(X0,X1,X2),the_carrier(X1)) ) )
& ( ! [X4] :
( related(X1,X0,X4)
| ~ in(X4,X2)
| ~ element(X4,the_carrier(X1)) )
| ~ sP2(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f58,f59]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ related(X1,X0,X3)
& in(X3,X2)
& element(X3,the_carrier(X1)) )
=> ( ~ related(X1,X0,sK7(X0,X1,X2))
& in(sK7(X0,X1,X2),X2)
& element(sK7(X0,X1,X2),the_carrier(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ? [X3] :
( ~ related(X1,X0,X3)
& in(X3,X2)
& element(X3,the_carrier(X1)) ) )
& ( ! [X4] :
( related(X1,X0,X4)
| ~ in(X4,X2)
| ~ element(X4,the_carrier(X1)) )
| ~ sP2(X0,X1,X2) ) ),
inference(rectify,[],[f57]) ).
fof(f57,plain,
! [X2,X0,X1] :
( ( sP2(X2,X0,X1)
| ? [X3] :
( ~ related(X0,X2,X3)
& in(X3,X1)
& element(X3,the_carrier(X0)) ) )
& ( ! [X3] :
( related(X0,X2,X3)
| ~ in(X3,X1)
| ~ element(X3,the_carrier(X0)) )
| ~ sP2(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f43]) ).
fof(f107,plain,
! [X0] : ~ in(X0,empty_set),
inference(forward_demodulation,[],[f106,f101]) ).
fof(f101,plain,
empty_set = sK11,
inference(unit_resulting_resolution,[],[f98,f89]) ).
fof(f89,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f98,plain,
empty(sK11),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
empty(sK11),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f15,f67]) ).
fof(f67,plain,
( ? [X0] : empty(X0)
=> empty(sK11) ),
introduced(choice_axiom,[]) ).
fof(f15,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f106,plain,
! [X0] : ~ in(X0,sK11),
inference(unit_resulting_resolution,[],[f98,f95]) ).
fof(f95,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f172,plain,
~ relstr_element_smaller(sK4,empty_set,sK5),
inference(unit_resulting_resolution,[],[f166,f73]) ).
fof(f73,plain,
( ~ relstr_set_smaller(sK4,empty_set,sK5)
| ~ relstr_element_smaller(sK4,empty_set,sK5) ),
inference(cnf_transformation,[],[f48]) ).
fof(f166,plain,
relstr_set_smaller(sK4,empty_set,sK5),
inference(unit_resulting_resolution,[],[f146,f147,f76]) ).
fof(f76,plain,
! [X2,X0,X1] :
( ~ sP1(X0,X1,X2)
| ~ sP0(X2,X1,X0)
| relstr_set_smaller(X1,X0,X2) ),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ( ( relstr_set_smaller(X1,X0,X2)
| ~ sP0(X2,X1,X0) )
& ( sP0(X2,X1,X0)
| ~ relstr_set_smaller(X1,X0,X2) ) )
| ~ sP1(X0,X1,X2) ),
inference(rectify,[],[f49]) ).
fof(f49,plain,
! [X1,X0,X2] :
( ( ( relstr_set_smaller(X0,X1,X2)
| ~ sP0(X2,X0,X1) )
& ( sP0(X2,X0,X1)
| ~ relstr_set_smaller(X0,X1,X2) ) )
| ~ sP1(X1,X0,X2) ),
inference(nnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X1,X0,X2] :
( ( relstr_set_smaller(X0,X1,X2)
<=> sP0(X2,X0,X1) )
| ~ sP1(X1,X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f147,plain,
! [X0] : sP1(X0,sK4,sK5),
inference(unit_resulting_resolution,[],[f71,f72,f81]) ).
fof(f81,plain,
! [X2,X0,X1] :
( ~ element(X2,the_carrier(X0))
| sP1(X1,X0,X2)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0] :
( ! [X1,X2] :
( sP1(X1,X0,X2)
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(definition_folding,[],[f30,f41,f40]) ).
fof(f40,plain,
! [X2,X0,X1] :
( sP0(X2,X0,X1)
<=> ! [X3] :
( related(X0,X3,X2)
| ~ in(X3,X1)
| ~ element(X3,the_carrier(X0)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f30,plain,
! [X0] :
( ! [X1,X2] :
( ( relstr_set_smaller(X0,X1,X2)
<=> ! [X3] :
( related(X0,X3,X2)
| ~ in(X3,X1)
| ~ element(X3,the_carrier(X0)) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(flattening,[],[f29]) ).
fof(f29,plain,
! [X0] :
( ! [X1,X2] :
( ( relstr_set_smaller(X0,X1,X2)
<=> ! [X3] :
( related(X0,X3,X2)
| ~ in(X3,X1)
| ~ element(X3,the_carrier(X0)) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( rel_str(X0)
=> ! [X1,X2] :
( element(X2,the_carrier(X0))
=> ( relstr_set_smaller(X0,X1,X2)
<=> ! [X3] :
( element(X3,the_carrier(X0))
=> ( in(X3,X1)
=> related(X0,X3,X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_lattice3) ).
fof(f146,plain,
! [X0,X1] : sP0(X0,X1,empty_set),
inference(unit_resulting_resolution,[],[f107,f79]) ).
fof(f79,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(sK6(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( ~ related(X1,sK6(X0,X1,X2),X0)
& in(sK6(X0,X1,X2),X2)
& element(sK6(X0,X1,X2),the_carrier(X1)) ) )
& ( ! [X4] :
( related(X1,X4,X0)
| ~ in(X4,X2)
| ~ element(X4,the_carrier(X1)) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f52,f53]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ related(X1,X3,X0)
& in(X3,X2)
& element(X3,the_carrier(X1)) )
=> ( ~ related(X1,sK6(X0,X1,X2),X0)
& in(sK6(X0,X1,X2),X2)
& element(sK6(X0,X1,X2),the_carrier(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3] :
( ~ related(X1,X3,X0)
& in(X3,X2)
& element(X3,the_carrier(X1)) ) )
& ( ! [X4] :
( related(X1,X4,X0)
| ~ in(X4,X2)
| ~ element(X4,the_carrier(X1)) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f51]) ).
fof(f51,plain,
! [X2,X0,X1] :
( ( sP0(X2,X0,X1)
| ? [X3] :
( ~ related(X0,X3,X2)
& in(X3,X1)
& element(X3,the_carrier(X0)) ) )
& ( ! [X3] :
( related(X0,X3,X2)
| ~ in(X3,X1)
| ~ element(X3,the_carrier(X0)) )
| ~ sP0(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU355+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n002.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 3 11:32:42 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (14656)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37 % (14659)WARNING: value z3 for option sas not known
% 0.15/0.38 % (14660)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (14658)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (14657)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (14659)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)
% 0.15/0.38 % (14661)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)
% 0.15/0.38 % (14662)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)
% 0.15/0.38 % (14663)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)
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.15/0.38 % (14663)First to succeed.
% 0.15/0.38 TRYING [3]
% 0.15/0.38 % (14659)Also succeeded, but the first one will report.
% 0.15/0.38 % (14662)Also succeeded, but the first one will report.
% 0.15/0.38 % (14663)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-14656"
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.15/0.38 % (14663)Refutation found. Thanks to Tanya!
% 0.15/0.38 % SZS status Theorem for theBenchmark
% 0.15/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.38 % (14663)------------------------------
% 0.15/0.38 % (14663)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.38 % (14663)Termination reason: Refutation
% 0.15/0.38
% 0.15/0.38 % (14663)Memory used [KB]: 843
% 0.15/0.38 % (14663)Time elapsed: 0.007 s
% 0.15/0.38 % (14663)Instructions burned: 8 (million)
% 0.15/0.38 % (14656)Success in time 0.022 s
%------------------------------------------------------------------------------