TSTP Solution File: ITP010_2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP010_2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n028.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 06:56:49 EDT 2024
% Result : Theorem 0.11s 0.39s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 36
% Syntax : Number of formulae : 53 ( 9 unt; 30 typ; 0 def)
% Number of atoms : 207 ( 0 equ)
% Maximal formula atoms : 12 ( 9 avg)
% Number of connectives : 80 ( 28 ~; 16 |; 21 &)
% ( 6 <=>; 8 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 132 ( 132 fml; 0 var)
% Number of types : 4 ( 2 usr)
% Number of type conns : 44 ( 22 >; 22 *; 0 +; 0 <<)
% Number of predicates : 15 ( 14 usr; 6 prp; 0-3 aty)
% Number of functors : 21 ( 21 usr; 6 con; 0-3 aty)
% Number of variables : 30 ( 12 !; 18 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
del: $tType ).
tff(type_def_6,type,
tp__o: $tType ).
tff(func_def_0,type,
bool: del ).
tff(func_def_1,type,
ind: del ).
tff(func_def_2,type,
arr: ( del * del ) > del ).
tff(func_def_4,type,
k: ( del * $i ) > $i ).
tff(func_def_5,type,
i: del > $i ).
tff(func_def_6,type,
inj__o: tp__o > $i ).
tff(func_def_7,type,
surj__o: $i > tp__o ).
tff(func_def_9,type,
fo__c_2Ebool_2ET: tp__o ).
tff(func_def_10,type,
c_2Ecardinal_2Ecardleq: ( del * del ) > $i ).
tff(func_def_12,type,
fo__c_2Ebool_2EF: tp__o ).
tff(func_def_14,type,
fo__c_2Emin_2E_3D_3D_3E: ( tp__o * tp__o ) > tp__o ).
tff(func_def_16,type,
fo__c_2Ebool_2E_5C_2F: ( tp__o * tp__o ) > tp__o ).
tff(func_def_18,type,
fo__c_2Ebool_2E_2F_5C: ( tp__o * tp__o ) > tp__o ).
tff(func_def_20,type,
fo__c_2Ebool_2E_7E: tp__o > tp__o ).
tff(func_def_21,type,
c_2Emin_2E_3D: del > $i ).
tff(func_def_22,type,
c_2Ebool_2E_21: del > $i ).
tff(func_def_23,type,
sK6: del ).
tff(func_def_24,type,
sK7: del ).
tff(func_def_27,type,
sK10: ( del * $i ) > $i ).
tff(func_def_28,type,
sK11: ( del * tp__o ) > $i ).
tff(func_def_29,type,
sK12: ( del * $i * $i ) > $i ).
tff(pred_def_1,type,
mem: ( $i * del ) > $o ).
tff(pred_def_3,type,
sP0: ( tp__o * tp__o ) > $o ).
tff(pred_def_4,type,
sP1: ( tp__o * tp__o * tp__o ) > $o ).
tff(pred_def_5,type,
sP2: ( tp__o * tp__o * tp__o ) > $o ).
tff(pred_def_6,type,
sP3: ( tp__o * tp__o * tp__o ) > $o ).
tff(pred_def_7,type,
sP4: ( tp__o * tp__o * tp__o ) > $o ).
tff(pred_def_8,type,
sP5: ( tp__o * tp__o * tp__o ) > $o ).
tff(f320,plain,
$false,
inference(avatar_sat_refutation,[],[f308,f313,f318,f319]) ).
tff(f319,plain,
spl13_3,
inference(avatar_split_clause,[],[f303,f315]) ).
tff(f315,plain,
( spl13_3
<=> p(ap(ap(c_2Ecardinal_2Ecardleq(sK6,sK7),sK8),sK9)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_3])]) ).
tff(f303,plain,
p(ap(ap(c_2Ecardinal_2Ecardleq(sK6,sK7),sK8),sK9)),
inference(duplicate_literal_removal,[],[f185]) ).
tff(f185,plain,
( p(ap(ap(c_2Ecardinal_2Ecardleq(sK6,sK7),sK8),sK9))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK6,sK7),sK8),sK9)) ),
inference(cnf_transformation,[],[f135]) ).
tff(f135,plain,
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK6,sK7),sK8),sK9))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK6,sK7),sK8),sK9)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6,sK7),sK8),sK9))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6,sK7),sK8),sK9)) )
& mem(sK9,arr(sK7,bool))
& mem(sK8,arr(sK6,bool)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9])],[f132,f134,f133]) ).
tff(f133,plain,
( ? [X0: del,X1: del,X2] :
( ? [X3] :
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
| p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) )
& mem(X3,arr(X1,bool)) )
& mem(X2,arr(X0,bool)) )
=> ( ? [X3] :
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK6,sK7),sK8),X3))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK6,sK7),sK8),X3)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6,sK7),sK8),X3))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6,sK7),sK8),X3)) )
& mem(X3,arr(sK7,bool)) )
& mem(sK8,arr(sK6,bool)) ) ),
introduced(choice_axiom,[]) ).
tff(f134,plain,
( ? [X3] :
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK6,sK7),sK8),X3))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK6,sK7),sK8),X3)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6,sK7),sK8),X3))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6,sK7),sK8),X3)) )
& mem(X3,arr(sK7,bool)) )
=> ( ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK6,sK7),sK8),sK9))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK6,sK7),sK8),sK9)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6,sK7),sK8),sK9))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6,sK7),sK8),sK9)) )
& mem(sK9,arr(sK7,bool)) ) ),
introduced(choice_axiom,[]) ).
tff(f132,plain,
? [X0: del,X1: del,X2] :
( ? [X3] :
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
| p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) )
& mem(X3,arr(X1,bool)) )
& mem(X2,arr(X0,bool)) ),
inference(flattening,[],[f131]) ).
tff(f131,plain,
? [X0: del,X1: del,X2] :
( ? [X3] :
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
| p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) )
& mem(X3,arr(X1,bool)) )
& mem(X2,arr(X0,bool)) ),
inference(nnf_transformation,[],[f99]) ).
tff(f99,plain,
? [X0: del,X1: del,X2] :
( ? [X3] :
( ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
<~> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) )
& mem(X3,arr(X1,bool)) )
& mem(X2,arr(X0,bool)) ),
inference(ennf_transformation,[],[f49]) ).
tff(f49,plain,
~ ! [X0: del,X1: del,X2] :
( mem(X2,arr(X0,bool))
=> ! [X3] :
( mem(X3,arr(X1,bool))
=> ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
<=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) ) ) ),
inference(rectify,[],[f48]) ).
tff(f48,negated_conjecture,
~ ! [X8: del,X9: del,X15] :
( mem(X15,arr(X8,bool))
=> ! [X16] :
( mem(X16,arr(X9,bool))
=> ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X8,X9),X15),X16))
<=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X8,X9),X15),X16)) ) ) ),
inference(negated_conjecture,[],[f47]) ).
tff(f47,conjecture,
! [X8: del,X9: del,X15] :
( mem(X15,arr(X8,bool))
=> ! [X16] :
( mem(X16,arr(X9,bool))
=> ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X8,X9),X15),X16))
<=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X8,X9),X15),X16)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ecardinal_2ECARD__NOT__LE) ).
tff(f318,plain,
~ spl13_3,
inference(avatar_split_clause,[],[f302,f315]) ).
tff(f302,plain,
~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6,sK7),sK8),sK9)),
inference(duplicate_literal_removal,[],[f184]) ).
tff(f184,plain,
( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6,sK7),sK8),sK9))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6,sK7),sK8),sK9)) ),
inference(cnf_transformation,[],[f135]) ).
tff(f313,plain,
spl13_2,
inference(avatar_split_clause,[],[f183,f310]) ).
tff(f310,plain,
( spl13_2
<=> mem(sK9,arr(sK7,bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_2])]) ).
tff(f183,plain,
mem(sK9,arr(sK7,bool)),
inference(cnf_transformation,[],[f135]) ).
tff(f308,plain,
spl13_1,
inference(avatar_split_clause,[],[f182,f305]) ).
tff(f305,plain,
( spl13_1
<=> mem(sK8,arr(sK6,bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_1])]) ).
tff(f182,plain,
mem(sK8,arr(sK6,bool)),
inference(cnf_transformation,[],[f135]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.14 % Problem : ITP010_2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.06/0.16 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.37 % Computer : n028.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8042.1875MB
% 0.11/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri May 3 19:04:37 EDT 2024
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % (28753)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.39 % (28756)WARNING: value z3 for option sas not known
% 0.11/0.39 % (28758)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)
% 0.11/0.39 % (28755)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.11/0.39 % (28757)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.11/0.39 % (28756)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)
% 0.11/0.39 % (28760)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)
% 0.11/0.39 % (28759)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)
% 0.11/0.39 % (28754)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.11/0.39 % (28758)First to succeed.
% 0.11/0.39 % (28760)Also succeeded, but the first one will report.
% 0.11/0.39 % (28756)Also succeeded, but the first one will report.
% 0.11/0.39 % (28759)Also succeeded, but the first one will report.
% 0.11/0.39 % (28758)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-28753"
% 0.11/0.39 % (28758)Refutation found. Thanks to Tanya!
% 0.11/0.39 % SZS status Theorem for theBenchmark
% 0.11/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.39 % (28758)------------------------------
% 0.11/0.39 % (28758)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.11/0.39 % (28758)Termination reason: Refutation
% 0.11/0.39
% 0.11/0.39 % (28758)Memory used [KB]: 954
% 0.11/0.39 % (28758)Time elapsed: 0.007 s
% 0.11/0.39 % (28758)Instructions burned: 9 (million)
% 0.11/0.39 % (28753)Success in time 0.022 s
%------------------------------------------------------------------------------