%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n020.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 11:34:05 AM UTC 2026
% Result : Theorem 0.20s 0.48s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 1
% Syntax : Number of formulae : 8 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 45 ( 0 equ)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 18 ( 9 ~; 0 |; 2 &)
% ( 2 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 28 ( 28 fml; 0 var)
% Number of types : 4 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 3 prp; 0-3 aty)
% Number of functors : 21 ( 21 usr; 6 con; 0-3 aty)
% Number of variables : 12 ( 8 !; 4 ?; 12 :)
% 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 * $i ) > $i ).
tff(func_def_25,type,
sK2: ( del * tp__o ) > $i ).
tff(func_def_26,type,
sK6: del ).
tff(func_def_27,type,
sK7: del ).
tff(pred_def_1,type,
mem: ( $i * del ) > $o ).
tff(pred_def_3,type,
sP3: ( tp__o * tp__o ) > $o ).
tff(pred_def_4,type,
sP4: ( tp__o * tp__o * tp__o ) > $o ).
tff(pred_def_5,type,
sP5: ( tp__o * 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/sandbox2/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(f78,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(f152,plain,
~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6,sK7),sK8),sK9)),
inference(cnf_transformation,[],[f78]) ).
tff(f153,plain,
p(ap(ap(c_2Ecardinal_2Ecardleq(sK6,sK7),sK8),sK9)),
inference(cnf_transformation,[],[f78]) ).
tff(f206,plain,
~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6,sK7),sK8),sK9)),
inference(consistent_polarity_flipping,[],[f153]) ).
tff(f207,plain,
p(ap(ap(c_2Ecardinal_2Ecardleq(sK6,sK7),sK8),sK9)),
inference(consistent_polarity_flipping,[],[f152]) ).
tff(f220,plain,
$false,
inference(forward_subsumption_resolution,[],[f207,f206]) ).
%------------------------------------------------------------------------------
%----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 SAT
% 0.13/0.40 % Computer : n020.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sun Sep 27 11:57:35 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.44 Running first-order model finding
% 0.13/0.44 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.48 % (3245991)Will run a generic schedule for satisfiability detection.
% 0.20/0.48 % (3245997)% WARNING: option uhcvi not known.
% 0.20/0.48 % (3245997)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4091649911:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.48 % (3245997) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3245991-3245997"...
% 0.20/0.48 % (3245997)...printing done.
% 0.20/0.48 % (3245997)Refutation found. Thanks to Tanya!
% 0.20/0.48 % SZS status Theorem for theBenchmark
% 0.20/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.48 % (3245997)------------------------------
% 0.20/0.48 % (3245997)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.48 % (3245997)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.48 % (3245997)CaDiCaL version: 2.1.3
% 0.20/0.48 % (3245997)Termination reason: Refutation
% 0.20/0.48 % (3245997)Time elapsed: 0.003 s
% 0.20/0.48 % (3245997)Peak memory usage: 11 MB
% 0.20/0.48 % (3245997)Instructions burned: 4 (million)
% 0.20/0.48 % (3245991)Success in time 0.028 s
% 0.20/0.48 % Vampire exiting
%------------------------------------------------------------------------------