%------------------------------------------------------------------------------
% 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/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 5.36s 6.80s
% Output : Refutation 5.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 11 ( 3 unt; 0 def)
% Number of atoms : 49 ( 0 equ)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 54 ( 16 ~; 8 |; 19 &)
% ( 2 <=>; 8 =>; 0 <=; 1 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 20 ( 8 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f41,conjecture,
! [X0] :
( ne(X0)
=> ! [X1] :
( ne(X1)
=> ! [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)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ecardinal_2ECARD__NOT__LE) ).
fof(f42,negated_conjecture,
~ ! [X0] :
( ne(X0)
=> ! [X1] :
( ne(X1)
=> ! [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(negated_conjecture,[status(cth)],[f41]) ).
fof(f57,plain,
? [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)) )
& ne(X1) )
& ne(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f85,plain,
? [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))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) )
& mem(X3,arr(X1,bool)) )
& mem(X2,arr(X0,bool)) )
& ne(X1) )
& ne(X0) ),
inference(nnf_transformation,[],[f57]) ).
fof(f86,plain,
? [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))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) )
& mem(X3,arr(X1,bool)) )
& mem(X2,arr(X0,bool)) )
& ne(X1) )
& ne(X0) ),
inference(flattening,[],[f85]) ).
fof(f87,plain,
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,sK8),sK9),sK10))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,sK8),sK9),sK10)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,sK8),sK9),sK10))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,sK8),sK9),sK10)) )
& mem(sK10,arr(sK8,bool))
& mem(sK9,arr(sK7,bool))
& ne(sK8)
& ne(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10]),skolemize(X0,sK7),skolemize(X1,sK8),skolemize(X2,sK9),skolemize(X3,sK10)],[f86]) ).
fof(f122,plain,
( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,sK8),sK9),sK10))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,sK8),sK9),sK10)) ),
inference(cnf_transformation,[],[f87]) ).
fof(f123,plain,
( p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,sK8),sK9),sK10))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,sK8),sK9),sK10)) ),
inference(cnf_transformation,[],[f87]) ).
fof(f198,plain,
~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,sK8),sK9),sK10)),
inference(duplicate_literal_removal,[],[f122]) ).
fof(f199,plain,
p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,sK8),sK9),sK10)),
inference(duplicate_literal_removal,[],[f123]) ).
fof(f200,plain,
$false,
inference(forward_subsumption_resolution,[],[f199,f198]) ).
%------------------------------------------------------------------------------
%----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/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/5.40 % Computer : n015.cluster.edu
% 0.15/5.40 % Model : x86_64 x86_64
% 0.15/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.40 % Memory : 8046.5625MB
% 0.15/5.40 % OS : Linux 6.8.0-71-generic
% 0.15/5.40 % CPULimit : 300
% 0.15/5.40 % WCLimit : 300
% 0.15/5.40 % DateTime : Sun Sep 27 12:00:21 UTC 2026
% 0.15/5.40 % CPUTime :
% 0.15/5.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/5.44 Running first-order theorem proving
% 0.15/5.44 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.36/6.80 % (1533606)Detected formulas, will run a generic FOF schedule.
% 5.36/6.80 % (1533611)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=950553543:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.36/6.80 % (1533612)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=3697243127:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.36/6.80 % (1533615)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2957898113:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.36/6.80 % (1533614)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=628692680:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.36/6.80 % (1533613)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=529883248:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.36/6.80 % (1533617)dis-21_1_sil=8000:lcm=predicate:random_seed=1990363547: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)
% 5.36/6.80 % (1533616)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1774388704:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.36/6.80 % (1533615)First to succeed.
% 5.36/6.80 % (1533615)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1533606"
% 5.36/6.80 % (1533617)Also succeeded, but the first one will report.
% 5.36/6.80 % (1533616)Also succeeded, but the first one will report.
% 5.36/6.80 % (1533614)Also succeeded, but the first one will report.
% 5.36/6.80 % (1533611)Also succeeded, but the first one will report.
% 5.36/6.80 % (1533615)Refutation found. Thanks to Tanya!
% 5.36/6.80 % SZS status Theorem for theBenchmark
% 5.36/6.80 % SZS output start Proof for theBenchmark
% See solution above
% 5.36/6.80 % (1533615)------------------------------
% 5.36/6.80 % (1533615)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.36/6.80 % (1533615)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.36/6.80 % (1533615)CaDiCaL version: 2.1.3
% 5.36/6.80 % (1533615)Termination reason: Refutation
% 5.36/6.80 % (1533615)Time elapsed: 0.004 s
% 5.36/6.80 % (1533615)Peak memory usage: 88 MB
% 5.36/6.80 % (1533615)Instructions burned: 2 (million)
% 5.36/6.80 % (1533615)------------------------------
% 5.36/6.80 % (1533615)------------------------------
% 5.36/6.80 % (1533606)Success in time 0.668 s
% 5.36/6.80 % Vampire exiting
%------------------------------------------------------------------------------