%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU325+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n011.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 12:52:53 PM UTC 2026
% Result : Theorem 0.18s 0.46s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 61 ( 24 unt; 0 def)
% Number of atoms : 132 ( 28 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 120 ( 49 ~; 35 |; 21 &)
% ( 4 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-2 aty)
% Number of variables : 68 ( 61 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [X0] :
( one_sorted_str(X0)
=> cast_as_carrier_subset(X0) = the_carrier(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_pre_topc) ).
fof(f18,axiom,
! [X0,X1] :
( X1 = union(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X2,X3)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
fof(f19,axiom,
! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
=> ( is_a_cover_of_carrier(X0,X1)
<=> cast_as_carrier_subset(X0) = union_of_subsets(the_carrier(X0),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_pre_topc) ).
fof(f29,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f30,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ~ empty(the_carrier(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f33,axiom,
( empty(empty_set)
& v1_membered(empty_set)
& v2_membered(empty_set)
& v3_membered(empty_set)
& v4_membered(empty_set)
& v5_membered(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_membered) ).
fof(f36,axiom,
! [X0] :
? [X1] :
( element(X1,powerset(X0))
& empty(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f39,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> union_of_subsets(X0,X1) = union(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
fof(f42,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( empty(X1)
| in(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f46,conjecture,
! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ! [X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
=> ~ ( is_a_cover_of_carrier(X0,X1)
& X1 = empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_tops_2) ).
fof(f47,negated_conjecture,
~ ! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ! [X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
=> ~ ( is_a_cover_of_carrier(X0,X1)
& X1 = empty_set ) ) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f48,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f49,axiom,
! [X0,X1] :
~ ( in(X0,X1)
& empty(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f79,plain,
! [X0] :
( cast_as_carrier_subset(X0) = the_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f80,plain,
! [X0] :
( ! [X1] :
( ( is_a_cover_of_carrier(X0,X1)
<=> cast_as_carrier_subset(X0) = union_of_subsets(the_carrier(X0),X1) )
| ~ element(X1,powerset(powerset(the_carrier(X0)))) )
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f83,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f84,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f83]) ).
fof(f90,plain,
! [X0,X1] :
( union_of_subsets(X0,X1) = union(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f39]) ).
fof(f92,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f42]) ).
fof(f93,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f92]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( is_a_cover_of_carrier(X0,X1)
& X1 = empty_set
& element(X1,powerset(powerset(the_carrier(X0)))) )
& ~ empty_carrier(X0)
& one_sorted_str(X0) ),
inference(ennf_transformation,[],[f47]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( is_a_cover_of_carrier(X0,X1)
& X1 = empty_set
& element(X1,powerset(powerset(the_carrier(X0)))) )
& ~ empty_carrier(X0)
& one_sorted_str(X0) ),
inference(flattening,[],[f98]) ).
fof(f100,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(ennf_transformation,[],[f48]) ).
fof(f101,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(ennf_transformation,[],[f49]) ).
fof(f128,plain,
! [X0] :
( ~ one_sorted_str(X0)
| cast_as_carrier_subset(X0) = the_carrier(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f132,plain,
! [X2,X0,X1] :
( in(sK1(X0,X2),X0)
| ~ in(X2,X1)
| union(X0) != X1 ),
inference(cnf_transformation,[],[f18]) ).
fof(f136,plain,
! [X0,X1] :
( ~ is_a_cover_of_carrier(X0,X1)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| cast_as_carrier_subset(X0) = union_of_subsets(the_carrier(X0),X1)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f140,plain,
! [X0] : element(sK4(X0),X0),
inference(cnf_transformation,[],[f29]) ).
fof(f141,plain,
! [X0] :
( empty_carrier(X0)
| ~ one_sorted_str(X0)
| ~ empty(the_carrier(X0)) ),
inference(cnf_transformation,[],[f84]) ).
fof(f149,plain,
empty(empty_set),
inference(cnf_transformation,[],[f33]) ).
fof(f158,plain,
! [X0] : empty(sK7(X0)),
inference(cnf_transformation,[],[f36]) ).
fof(f159,plain,
! [X0] : element(sK7(X0),powerset(X0)),
inference(cnf_transformation,[],[f36]) ).
fof(f164,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| union_of_subsets(X0,X1) = union(X1) ),
inference(cnf_transformation,[],[f90]) ).
fof(f167,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f93]) ).
fof(f171,plain,
element(sK11,powerset(powerset(the_carrier(sK10)))),
inference(cnf_transformation,[],[f99]) ).
fof(f172,plain,
empty_set = sK11,
inference(cnf_transformation,[],[f99]) ).
fof(f173,plain,
is_a_cover_of_carrier(sK10,sK11),
inference(cnf_transformation,[],[f99]) ).
fof(f174,plain,
one_sorted_str(sK10),
inference(cnf_transformation,[],[f99]) ).
fof(f175,plain,
~ empty_carrier(sK10),
inference(cnf_transformation,[],[f99]) ).
fof(f176,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f100]) ).
fof(f177,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f101]) ).
fof(f179,plain,
empty(sK11),
inference(definition_unfolding,[],[f149,f172]) ).
fof(f185,plain,
! [X0] :
( ~ empty(X0)
| sK11 = X0 ),
inference(definition_unfolding,[],[f176,f172]) ).
fof(f188,plain,
! [X2,X0] :
( in(sK1(X0,X2),X0)
| ~ in(X2,union(X0)) ),
inference(equality_resolution,[],[f132]) ).
fof(f190,plain,
! [X0] : sK7(X0) = sK11,
inference(resolution,[],[f158,f185]) ).
fof(f192,plain,
! [X0] : element(sK11,powerset(X0)),
inference(superposition,[],[f159,f190]) ).
fof(f193,plain,
! [X0] : ~ in(X0,sK11),
inference(resolution,[],[f177,f179]) ).
fof(f196,plain,
the_carrier(sK10) = cast_as_carrier_subset(sK10),
inference(resolution,[],[f128,f174]) ).
fof(f199,plain,
( ~ one_sorted_str(sK10)
| ~ empty(the_carrier(sK10)) ),
inference(resolution,[],[f141,f175]) ).
fof(f202,plain,
~ empty(the_carrier(sK10)),
inference(forward_subsumption_resolution,[],[f199,f174]) ).
fof(f241,plain,
! [X0] :
( ~ element(X0,the_carrier(sK10))
| in(X0,the_carrier(sK10)) ),
inference(resolution,[],[f167,f202]) ).
fof(f247,plain,
in(sK4(the_carrier(sK10)),the_carrier(sK10)),
inference(resolution,[],[f241,f140]) ).
fof(f255,plain,
! [X0] : ~ in(X0,union(sK11)),
inference(resolution,[],[f188,f193]) ).
fof(f308,plain,
! [X0] : union(sK11) = union_of_subsets(X0,sK11),
inference(resolution,[],[f164,f192]) ).
fof(f348,plain,
( ~ element(sK11,powerset(powerset(the_carrier(sK10))))
| cast_as_carrier_subset(sK10) = union_of_subsets(the_carrier(sK10),sK11)
| ~ one_sorted_str(sK10) ),
inference(resolution,[],[f136,f173]) ).
fof(f349,plain,
( cast_as_carrier_subset(sK10) = union_of_subsets(the_carrier(sK10),sK11)
| ~ one_sorted_str(sK10) ),
inference(forward_subsumption_resolution,[],[f348,f171]) ).
fof(f350,plain,
cast_as_carrier_subset(sK10) = union_of_subsets(the_carrier(sK10),sK11),
inference(forward_subsumption_resolution,[],[f349,f174]) ).
fof(f351,plain,
cast_as_carrier_subset(sK10) = union(sK11),
inference(forward_demodulation,[],[f350,f308]) ).
fof(f352,plain,
the_carrier(sK10) = union(sK11),
inference(forward_demodulation,[],[f351,f196]) ).
fof(f356,plain,
! [X0] : ~ in(X0,the_carrier(sK10)),
inference(superposition,[],[f255,f352]) ).
fof(f398,plain,
$false,
inference(resolution,[],[f356,f247]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU325+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n011.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 04:43:16 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 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
% 0.18/0.46 % (3021699)Will run a generic schedule for satisfiability detection.
% 0.18/0.46 % (3021708)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3144256135:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.46 % (3021705)% WARNING: option uhcvi not known.
% 0.18/0.46 % (3021708) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3021699-3021708"...
% 0.18/0.46 % (3021708)...printing done.
% 0.18/0.46 % (3021708)Refutation found. Thanks to Tanya!
% 0.18/0.46 % SZS status Theorem for theBenchmark
% 0.18/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.46 % (3021708)------------------------------
% 0.18/0.46 % (3021708)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.46 % (3021708)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.46 % (3021708)CaDiCaL version: 2.1.3
% 0.18/0.46 % (3021708)Termination reason: Refutation
% 0.18/0.46 % (3021708)Time elapsed: 0.005 s
% 0.18/0.46 % (3021708)Peak memory usage: 12 MB
% 0.18/0.46 % (3021708)Instructions burned: 12 (million)
% 0.18/0.46 % (3021699)Success in time 0.037 s
% 0.18/0.46 % Vampire exiting
%------------------------------------------------------------------------------