%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP010+1 : 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 : n016.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 3.44s 1.43s
% Output : Refutation 3.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1
% Syntax : Number of formulae : 10 ( 3 unt; 0 def)
% Number of atoms : 21 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 25 ( 14 ~; 6 |; 2 &)
% ( 2 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 16 ( 8 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f40,conjecture,
! [X0,X1,X2,X3] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3))))
<=> ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecardinal_2ECARD__NOT__LE) ).
fof(f41,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3))))
<=> ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))) ),
inference(negated_conjecture,[status(cth)],[f40]) ).
fof(f57,plain,
? [X0,X1,X2,X3] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3))))
<~> ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))) ),
inference(ennf_transformation,[],[f41]) ).
fof(f124,plain,
? [X0,X1,X2,X3] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3))))
| p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))) )
& ( ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))) ) ),
inference(nnf_transformation,[],[f57]) ).
fof(f125,plain,
( ( p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(sK9,tyop_2Emin_2Ebool),sK11),s(tyop_2Emin_2Efun(sK10,tyop_2Emin_2Ebool),sK12))))
| p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(sK9,tyop_2Emin_2Ebool),sK11),s(tyop_2Emin_2Efun(sK10,tyop_2Emin_2Ebool),sK12)))) )
& ( ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(sK9,tyop_2Emin_2Ebool),sK11),s(tyop_2Emin_2Efun(sK10,tyop_2Emin_2Ebool),sK12))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(sK9,tyop_2Emin_2Ebool),sK11),s(tyop_2Emin_2Efun(sK10,tyop_2Emin_2Ebool),sK12)))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12]),skolemize(X0,sK9),skolemize(X1,sK10),skolemize(X2,sK11),skolemize(X3,sK12)],[f124]) ).
fof(f260,plain,
( ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(sK9,tyop_2Emin_2Ebool),sK11),s(tyop_2Emin_2Efun(sK10,tyop_2Emin_2Ebool),sK12))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(sK9,tyop_2Emin_2Ebool),sK11),s(tyop_2Emin_2Efun(sK10,tyop_2Emin_2Ebool),sK12)))) ),
inference(cnf_transformation,[],[f125]) ).
fof(f261,plain,
( p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(sK9,tyop_2Emin_2Ebool),sK11),s(tyop_2Emin_2Efun(sK10,tyop_2Emin_2Ebool),sK12))))
| p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(sK9,tyop_2Emin_2Ebool),sK11),s(tyop_2Emin_2Efun(sK10,tyop_2Emin_2Ebool),sK12)))) ),
inference(cnf_transformation,[],[f125]) ).
fof(f262,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(sK9,tyop_2Emin_2Ebool),sK11),s(tyop_2Emin_2Efun(sK10,tyop_2Emin_2Ebool),sK12)))),
inference(duplicate_literal_removal,[],[f260]) ).
fof(f263,plain,
p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(sK9,tyop_2Emin_2Ebool),sK11),s(tyop_2Emin_2Efun(sK10,tyop_2Emin_2Ebool),sK12)))),
inference(duplicate_literal_removal,[],[f261]) ).
fof(f310,plain,
$false,
inference(forward_subsumption_resolution,[],[f263,f262]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP010+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n016.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 : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 12:01:18 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 3.44/1.43 % (2502576)Detected formulas, will run a generic FOF schedule.
% 3.44/1.43 % (2502585)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=2192025886:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.44/1.43 % (2502590)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2957064883:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.44/1.43 % (2502590)First to succeed.
% 3.44/1.43 % (2502590)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2502576"
% 3.44/1.43 % (2502586)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=589462722:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.44/1.43 % (2502589)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2225770902:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.44/1.43 % (2502588)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3881049597:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.44/1.43 % (2502587)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=3424101332:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.44/1.43 % (2502589)Also succeeded, but the first one will report.
% 3.44/1.43 % (2502588)Also succeeded, but the first one will report.
% 3.44/1.43 % (2502591)dis-21_1_sil=8000:lcm=predicate:random_seed=1930846945: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)
% 3.44/1.43 % (2502591)Also succeeded, but the first one will report.
% 3.44/1.43 % (2502590)Refutation found. Thanks to Tanya!
% 3.44/1.43 % SZS status Theorem for theBenchmark
% 3.44/1.43 % SZS output start Proof for theBenchmark
% See solution above
% 3.44/1.43 % (2502590)------------------------------
% 3.44/1.43 % (2502590)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.43 % (2502590)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.43 % (2502590)CaDiCaL version: 2.1.3
% 3.44/1.43 % (2502590)Termination reason: Refutation
% 3.44/1.43 % (2502590)Time elapsed: 0.005 s
% 3.44/1.43 % (2502590)Peak memory usage: 89 MB
% 3.44/1.43 % (2502590)Instructions burned: 6 (million)
% 3.44/1.43 % (2502590)------------------------------
% 3.44/1.43 % (2502590)------------------------------
% 3.44/1.43 % (2502576)Success in time 0.395 s
% 3.44/1.43 % Vampire exiting
%------------------------------------------------------------------------------