TSTP Solution File: ITP010_2 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : ITP010_2 : TPTP v8.1.0. Bugfixed v7.5.0.
% 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 : n026.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 17:15:57 EDT 2022
% Result : Theorem 0.20s 0.52s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 25
% Syntax : Number of formulae : 37 ( 3 unt; 22 typ; 0 def)
% Number of atoms : 201 ( 0 equ)
% Maximal formula atoms : 12 ( 13 avg)
% Number of connectives : 83 ( 29 ~; 18 |; 24 &)
% ( 3 <=>; 8 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 7 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 : 23 ( 14 >; 9 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 6 con; 0-3 aty)
% Number of variables : 34 ( 12 !; 22 ?; 16 :)
% 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,
sK0: ( del * $i * $i ) > $i ).
tff(func_def_24,type,
sK1: del ).
tff(func_def_26,type,
sK3: del ).
tff(pred_def_1,type,
mem: ( $i * del ) > $o ).
tff(f84,plain,
$false,
inference(subsumption_resolution,[],[f82,f83]) ).
tff(f83,plain,
~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK3,sK1),sK2),sK4)),
inference(duplicate_literal_removal,[],[f79]) ).
tff(f79,plain,
( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK3,sK1),sK2),sK4))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK3,sK1),sK2),sK4)) ),
inference(cnf_transformation,[],[f71]) ).
tff(f71,plain,
( mem(sK2,arr(sK3,bool))
& ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK3,sK1),sK2),sK4))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK3,sK1),sK2),sK4)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK3,sK1),sK2),sK4))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK3,sK1),sK2),sK4)) )
& mem(sK4,arr(sK1,bool)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4])],[f68,f70,f69]) ).
tff(f69,plain,
( ? [X0: del,X1,X2: del] :
( mem(X1,arr(X2,bool))
& ? [X3] :
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(X2,X0),X1),X3))
| p(ap(ap(c_2Ecardinal_2Ecardleq(X2,X0),X1),X3)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X2,X0),X1),X3))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X2,X0),X1),X3)) )
& mem(X3,arr(X0,bool)) ) )
=> ( mem(sK2,arr(sK3,bool))
& ? [X3] :
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK3,sK1),sK2),X3))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK3,sK1),sK2),X3)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK3,sK1),sK2),X3))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK3,sK1),sK2),X3)) )
& mem(X3,arr(sK1,bool)) ) ) ),
introduced(choice_axiom,[]) ).
tff(f70,plain,
( ? [X3] :
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK3,sK1),sK2),X3))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK3,sK1),sK2),X3)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK3,sK1),sK2),X3))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK3,sK1),sK2),X3)) )
& mem(X3,arr(sK1,bool)) )
=> ( ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK3,sK1),sK2),sK4))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK3,sK1),sK2),sK4)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK3,sK1),sK2),sK4))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK3,sK1),sK2),sK4)) )
& mem(sK4,arr(sK1,bool)) ) ),
introduced(choice_axiom,[]) ).
tff(f68,plain,
? [X0: del,X1,X2: del] :
( mem(X1,arr(X2,bool))
& ? [X3] :
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(X2,X0),X1),X3))
| p(ap(ap(c_2Ecardinal_2Ecardleq(X2,X0),X1),X3)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X2,X0),X1),X3))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X2,X0),X1),X3)) )
& mem(X3,arr(X0,bool)) ) ),
inference(rectify,[],[f67]) ).
tff(f67,plain,
? [X2: del,X0,X1: del] :
( mem(X0,arr(X1,bool))
& ? [X3] :
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(X1,X2),X0),X3))
| p(ap(ap(c_2Ecardinal_2Ecardleq(X1,X2),X0),X3)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X1,X2),X0),X3))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X1,X2),X0),X3)) )
& mem(X3,arr(X2,bool)) ) ),
inference(flattening,[],[f66]) ).
tff(f66,plain,
? [X2: del,X0,X1: del] :
( mem(X0,arr(X1,bool))
& ? [X3] :
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(X1,X2),X0),X3))
| p(ap(ap(c_2Ecardinal_2Ecardleq(X1,X2),X0),X3)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X1,X2),X0),X3))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X1,X2),X0),X3)) )
& mem(X3,arr(X2,bool)) ) ),
inference(nnf_transformation,[],[f57]) ).
tff(f57,plain,
? [X2: del,X0,X1: del] :
( mem(X0,arr(X1,bool))
& ? [X3] :
( ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X1,X2),X0),X3))
<~> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X1,X2),X0),X3)) )
& mem(X3,arr(X2,bool)) ) ),
inference(ennf_transformation,[],[f49]) ).
tff(f49,plain,
~ ! [X0,X1: del,X2: del] :
( mem(X0,arr(X1,bool))
=> ! [X3] :
( mem(X3,arr(X2,bool))
=> ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X1,X2),X0),X3))
<=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X1,X2),X0),X3)) ) ) ),
inference(rectify,[],[f48]) ).
tff(f48,negated_conjecture,
~ ! [X15,X8: del,X9: del] :
( 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,
! [X15,X8: del,X9: del] :
( 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(f82,plain,
p(ap(ap(c_2Ecardinal_2Ecardleq(sK3,sK1),sK2),sK4)),
inference(duplicate_literal_removal,[],[f80]) ).
tff(f80,plain,
( p(ap(ap(c_2Ecardinal_2Ecardleq(sK3,sK1),sK2),sK4))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK3,sK1),sK2),sK4)) ),
inference(cnf_transformation,[],[f71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ITP010_2 : TPTP v8.1.0. Bugfixed v7.5.0.
% 0.07/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 29 23:44:20 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.50 % (30356)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)
% 0.20/0.51 % (30372)dis-10_3:2_amm=sco:ep=RS:fsr=off:nm=10:sd=2:sos=on:ss=axioms:st=3.0:i=11:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/11Mi)
% 0.20/0.52 % (30364)lrs+10_1:2_br=off:nm=4:ss=included:urr=on:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.52 % (30356)First to succeed.
% 0.20/0.52 % (30357)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.20/0.52 % (30356)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 % (30356)------------------------------
% 0.20/0.52 % (30356)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52 % (30356)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52 % (30356)Termination reason: Refutation
% 0.20/0.52
% 0.20/0.52 % (30356)Memory used [KB]: 6012
% 0.20/0.52 % (30356)Time elapsed: 0.004 s
% 0.20/0.52 % (30356)Instructions burned: 2 (million)
% 0.20/0.52 % (30356)------------------------------
% 0.20/0.52 % (30356)------------------------------
% 0.20/0.52 % (30350)Success in time 0.16 s
%------------------------------------------------------------------------------