%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP010+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 11:34:04 AM UTC 2026
% Result : Theorem 0.11s 0.45s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 1
% Syntax : Number of formulae : 6 ( 3 unt; 0 def)
% Number of atoms : 9 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 8 ~; 0 |; 0 &)
% ( 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 : 12 ( 8 !; 4 ?)
% 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/sandbox/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(f149,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool),sK7),s(tyop_2Emin_2Efun(sK6,tyop_2Emin_2Ebool),sK8)))),
inference(cnf_transformation,[],[f57]) ).
fof(f150,plain,
p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool),sK7),s(tyop_2Emin_2Efun(sK6,tyop_2Emin_2Ebool),sK8)))),
inference(cnf_transformation,[],[f57]) ).
fof(f152,plain,
$false,
inference(forward_subsumption_resolution,[],[f150,f149]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP010+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 12:01:17 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.45 % (2502304)Will run a generic schedule for satisfiability detection.
% 0.11/0.45 % (2502318)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=75766727:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.45 % (2502318) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2502304-2502318"...
% 0.11/0.45 % (2502315)% WARNING: option uhcvi not known.
% 0.11/0.45 % (2502318)...printing done.
% 0.11/0.45 % (2502318)Refutation found. Thanks to Tanya!
% 0.11/0.45 % SZS status Theorem for theBenchmark
% 0.11/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.45 % (2502318)------------------------------
% 0.11/0.45 % (2502318)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.45 % (2502318)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.45 % (2502318)CaDiCaL version: 2.1.3
% 0.11/0.45 % (2502318)Termination reason: Refutation
% 0.11/0.45 % (2502318)Time elapsed: 0.002 s
% 0.11/0.45 % (2502318)Peak memory usage: 12 MB
% 0.11/0.45 % (2502318)Instructions burned: 6 (million)
% 0.11/0.45 % (2502304)Success in time 0.038 s
% 0.11/0.45 % Vampire exiting
%------------------------------------------------------------------------------