%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP010_2 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:27:58 AM UTC 2026
% Result : Theorem 2.59s 6.27s
% Output : Refutation 2.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 11 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 107 ( 0 equ)
% Maximal formula atoms : 6 ( 9 avg)
% Number of connectives : 42 ( 16 ~; 8 |; 11 &)
% ( 2 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 70 ( 70 fml; 0 var)
% Number of types : 4 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 10 usr; 3 prp; 0-3 aty)
% Number of functors : 21 ( 21 usr; 6 con; 0-3 aty)
% Number of variables : 20 ( 8 !; 12 ?; 20 :)
% 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,
sK5: ( del * $i * $i ) > $i ).
tff(func_def_24,type,
sK6: ( del * $i ) > $i ).
tff(func_def_25,type,
sK7: ( del * tp__o ) > $i ).
tff(func_def_26,type,
sK8: del ).
tff(func_def_27,type,
sK9: del ).
tff(pred_def_1,type,
mem: ( $i * del ) > $o ).
tff(pred_def_3,type,
sP0: ( tp__o * 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 ) > $o ).
tff(f47,conjecture,
! [X0: del,X1: del,X2: $i] :
( mem(X2,arr(X0,bool))
=> ! [X3: $i] :
( 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)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ecardinal_2ECARD__NOT__LE) ).
tff(f48,negated_conjecture,
~ ! [X0: del,X1: del,X2: $i] :
( mem(X2,arr(X0,bool))
=> ! [X3: $i] :
( 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(negated_conjecture,[status(cth)],[f47]) ).
tff(f87,plain,
? [X0: del,X1: del,X2: $i] :
( ? [X3: $i] :
( ( ~ 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,[],[f48]) ).
tff(f137,plain,
? [X0: del,X1: del,X2: $i] :
( ? [X3: $i] :
( ( 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,[],[f87]) ).
tff(f138,plain,
? [X0: del,X1: del,X2: $i] :
( ? [X3: $i] :
( ( 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,[],[f137]) ).
tff(f139,plain,
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK8,sK9),sK10),sK11))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK8,sK9),sK10),sK11)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK8,sK9),sK10),sK11))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK8,sK9),sK10),sK11)) )
& mem(sK11,arr(sK9,bool))
& mem(sK10,arr(sK8,bool)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11]),skolemize(X0,sK8),skolemize(X1,sK9),skolemize(X2,sK10),skolemize(X3,sK11)],[f138]) ).
tff(f254,plain,
( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK8,sK9),sK10),sK11))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK8,sK9),sK10),sK11)) ),
inference(cnf_transformation,[],[f139]) ).
tff(f255,plain,
( p(ap(ap(c_2Ecardinal_2Ecardleq(sK8,sK9),sK10),sK11))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK8,sK9),sK10),sK11)) ),
inference(cnf_transformation,[],[f139]) ).
tff(f257,plain,
~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK8,sK9),sK10),sK11)),
inference(duplicate_literal_removal,[],[f254]) ).
tff(f258,plain,
p(ap(ap(c_2Ecardinal_2Ecardleq(sK8,sK9),sK10),sK11)),
inference(duplicate_literal_removal,[],[f255]) ).
tff(f260,plain,
$false,
inference(forward_subsumption_resolution,[],[f258,f257]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP010_2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/5.39 % Computer : n006.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Sun Sep 27 11:56:34 UTC 2026
% 0.11/5.40 % CPUTime :
% 0.11/5.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/5.43 Running first-order theorem proving
% 0.16/5.43 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.59/6.27 % (2844691)Detected formulas, will run a generic FOF schedule.
% 2.59/6.27 % (2844701)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=114696318:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.59/6.27 % (2844701)First to succeed.
% 2.59/6.27 % (2844701)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2844691"
% 2.59/6.27 % (2844700)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2503109886:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.59/6.27 % (2844697)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1790574780:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.59/6.27 % (2844699)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2959209373:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.59/6.27 % (2844702)dis-21_1_sil=8000:lcm=predicate:random_seed=2496174436:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.59/6.27 % (2844698)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2256365750:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.59/6.27 % (2844696)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2436607687:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.59/6.27 % (2844699)Also succeeded, but the first one will report.
% 2.59/6.27 % (2844700)Also succeeded, but the first one will report.
% 2.59/6.27 % (2844702)Also succeeded, but the first one will report.
% 2.59/6.27 % (2844701)Refutation found. Thanks to Tanya!
% 2.59/6.27 % SZS status Theorem for theBenchmark
% 2.59/6.27 % SZS output start Proof for theBenchmark
% See solution above
% 2.59/6.27 % (2844701)------------------------------
% 2.59/6.27 % (2844701)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/6.27 % (2844701)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/6.27 % (2844701)CaDiCaL version: 2.1.3
% 2.59/6.27 % (2844701)Termination reason: Refutation
% 2.59/6.27 % (2844701)Time elapsed: 0.002 s
% 2.59/6.27 % (2844701)Peak memory usage: 89 MB
% 2.59/6.27 % (2844701)Instructions burned: 5 (million)
% 2.59/6.27 % (2844701)------------------------------
% 2.59/6.27 % (2844701)------------------------------
% 2.59/6.27 % (2844691)Success in time 0.3 s
% 2.59/6.27 % Vampire exiting
%------------------------------------------------------------------------------