TSTP Solution File: SEU325+2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU325+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 09:33:42 EDT 2024
% Result : Theorem 259.73s 37.63s
% Output : Refutation 259.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 17
% Syntax : Number of formulae : 73 ( 21 unt; 0 def)
% Number of atoms : 222 ( 47 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 231 ( 82 ~; 64 |; 58 &)
% ( 9 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-2 aty)
% Number of variables : 82 ( 66 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f312190,plain,
$false,
inference(resolution,[],[f227772,f2932]) ).
fof(f2932,plain,
empty(empty_set),
inference(cnf_transformation,[],[f207]) ).
fof(f207,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f227772,plain,
~ empty(empty_set),
inference(backward_demodulation,[],[f4593,f227765]) ).
fof(f227765,plain,
empty_set = the_carrier(sK164),
inference(resolution,[],[f227761,f4153]) ).
fof(f4153,plain,
! [X0] : element(empty_set,powerset(X0)),
inference(backward_demodulation,[],[f3436,f4146]) ).
fof(f4146,plain,
! [X0] : empty_set = sK378(X0),
inference(resolution,[],[f3108,f3437]) ).
fof(f3437,plain,
! [X0] : empty(sK378(X0)),
inference(cnf_transformation,[],[f2034]) ).
fof(f2034,plain,
! [X0] :
( empty(sK378(X0))
& element(sK378(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK378])],[f297,f2033]) ).
fof(f2033,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK378(X0))
& element(sK378(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f297,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f3108,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f906]) ).
fof(f906,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f511]) ).
fof(f511,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f3436,plain,
! [X0] : element(sK378(X0),powerset(X0)),
inference(cnf_transformation,[],[f2034]) ).
fof(f227761,plain,
( ~ element(empty_set,powerset(powerset(the_carrier(sK164))))
| empty_set = the_carrier(sK164) ),
inference(resolution,[],[f160114,f2388]) ).
fof(f2388,plain,
one_sorted_str(sK164),
inference(cnf_transformation,[],[f1394]) ).
fof(f1394,plain,
( empty_set = sK165
& is_a_cover_of_carrier(sK164,sK165)
& element(sK165,powerset(powerset(the_carrier(sK164))))
& one_sorted_str(sK164)
& ~ empty_carrier(sK164) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK164,sK165])],[f597,f1393,f1392]) ).
fof(f1392,plain,
( ? [X0] :
( ? [X1] :
( empty_set = X1
& is_a_cover_of_carrier(X0,X1)
& element(X1,powerset(powerset(the_carrier(X0)))) )
& one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ( ? [X1] :
( empty_set = X1
& is_a_cover_of_carrier(sK164,X1)
& element(X1,powerset(powerset(the_carrier(sK164)))) )
& one_sorted_str(sK164)
& ~ empty_carrier(sK164) ) ),
introduced(choice_axiom,[]) ).
fof(f1393,plain,
( ? [X1] :
( empty_set = X1
& is_a_cover_of_carrier(sK164,X1)
& element(X1,powerset(powerset(the_carrier(sK164)))) )
=> ( empty_set = sK165
& is_a_cover_of_carrier(sK164,sK165)
& element(sK165,powerset(powerset(the_carrier(sK164)))) ) ),
introduced(choice_axiom,[]) ).
fof(f597,plain,
? [X0] :
( ? [X1] :
( empty_set = X1
& is_a_cover_of_carrier(X0,X1)
& element(X1,powerset(powerset(the_carrier(X0)))) )
& one_sorted_str(X0)
& ~ empty_carrier(X0) ),
inference(flattening,[],[f596]) ).
fof(f596,plain,
? [X0] :
( ? [X1] :
( empty_set = X1
& is_a_cover_of_carrier(X0,X1)
& element(X1,powerset(powerset(the_carrier(X0)))) )
& one_sorted_str(X0)
& ~ empty_carrier(X0) ),
inference(ennf_transformation,[],[f499]) ).
fof(f499,negated_conjecture,
~ ! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
=> ~ ( empty_set = X1
& is_a_cover_of_carrier(X0,X1) ) ) ),
inference(negated_conjecture,[],[f498]) ).
fof(f498,conjecture,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
=> ~ ( empty_set = X1
& is_a_cover_of_carrier(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_tops_2) ).
fof(f160114,plain,
( ~ one_sorted_str(sK164)
| ~ element(empty_set,powerset(powerset(the_carrier(sK164))))
| empty_set = the_carrier(sK164) ),
inference(forward_demodulation,[],[f160113,f4412]) ).
fof(f4412,plain,
the_carrier(sK164) = cast_as_carrier_subset(sK164),
inference(resolution,[],[f2476,f2388]) ).
fof(f2476,plain,
! [X0] :
( ~ one_sorted_str(X0)
| the_carrier(X0) = cast_as_carrier_subset(X0) ),
inference(cnf_transformation,[],[f612]) ).
fof(f612,plain,
! [X0] :
( the_carrier(X0) = cast_as_carrier_subset(X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f368]) ).
fof(f368,axiom,
! [X0] :
( one_sorted_str(X0)
=> the_carrier(X0) = cast_as_carrier_subset(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_pre_topc) ).
fof(f160113,plain,
( empty_set = cast_as_carrier_subset(sK164)
| ~ element(empty_set,powerset(powerset(the_carrier(sK164))))
| ~ one_sorted_str(sK164) ),
inference(forward_demodulation,[],[f160112,f80497]) ).
fof(f80497,plain,
! [X0] : empty_set = union_of_subsets(X0,empty_set),
inference(forward_demodulation,[],[f80485,f11789]) ).
fof(f11789,plain,
empty_set = union(empty_set),
inference(resolution,[],[f7101,f2955]) ).
fof(f2955,plain,
ordinal(empty_set),
inference(cnf_transformation,[],[f214]) ).
fof(f214,axiom,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation_empty_yielding(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_ordinal1) ).
fof(f7101,plain,
( ~ ordinal(empty_set)
| empty_set = union(empty_set) ),
inference(resolution,[],[f7098,f3392]) ).
fof(f3392,plain,
! [X0] :
( ~ being_limit_ordinal(X0)
| union(X0) = X0 ),
inference(cnf_transformation,[],[f1994]) ).
fof(f1994,plain,
! [X0] :
( ( being_limit_ordinal(X0)
| union(X0) != X0 )
& ( union(X0) = X0
| ~ being_limit_ordinal(X0) ) ),
inference(nnf_transformation,[],[f103]) ).
fof(f103,axiom,
! [X0] :
( being_limit_ordinal(X0)
<=> union(X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_ordinal1) ).
fof(f7098,plain,
( being_limit_ordinal(empty_set)
| ~ ordinal(empty_set) ),
inference(resolution,[],[f2491,f4047]) ).
fof(f4047,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f3428]) ).
fof(f3428,plain,
! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f2027]) ).
fof(f2027,plain,
! [X0] :
( ( empty_set = X0
| in(sK374(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK374])],[f2025,f2026]) ).
fof(f2026,plain,
! [X0] :
( ? [X1] : in(X1,X0)
=> in(sK374(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f2025,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f2024]) ).
fof(f2024,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f68]) ).
fof(f68,axiom,
! [X0] :
( empty_set = X0
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f2491,plain,
! [X0] :
( in(sK187(X0),X0)
| being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f1473]) ).
fof(f1473,plain,
! [X0] :
( ( ( being_limit_ordinal(X0)
| ( ~ in(succ(sK187(X0)),X0)
& in(sK187(X0),X0)
& ordinal(sK187(X0)) ) )
& ( ! [X2] :
( in(succ(X2),X0)
| ~ in(X2,X0)
| ~ ordinal(X2) )
| ~ being_limit_ordinal(X0) ) )
| ~ ordinal(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK187])],[f1471,f1472]) ).
fof(f1472,plain,
! [X0] :
( ? [X1] :
( ~ in(succ(X1),X0)
& in(X1,X0)
& ordinal(X1) )
=> ( ~ in(succ(sK187(X0)),X0)
& in(sK187(X0),X0)
& ordinal(sK187(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1471,plain,
! [X0] :
( ( ( being_limit_ordinal(X0)
| ? [X1] :
( ~ in(succ(X1),X0)
& in(X1,X0)
& ordinal(X1) ) )
& ( ! [X2] :
( in(succ(X2),X0)
| ~ in(X2,X0)
| ~ ordinal(X2) )
| ~ being_limit_ordinal(X0) ) )
| ~ ordinal(X0) ),
inference(rectify,[],[f1470]) ).
fof(f1470,plain,
! [X0] :
( ( ( being_limit_ordinal(X0)
| ? [X1] :
( ~ in(succ(X1),X0)
& in(X1,X0)
& ordinal(X1) ) )
& ( ! [X1] :
( in(succ(X1),X0)
| ~ in(X1,X0)
| ~ ordinal(X1) )
| ~ being_limit_ordinal(X0) ) )
| ~ ordinal(X0) ),
inference(nnf_transformation,[],[f625]) ).
fof(f625,plain,
! [X0] :
( ( being_limit_ordinal(X0)
<=> ! [X1] :
( in(succ(X1),X0)
| ~ in(X1,X0)
| ~ ordinal(X1) ) )
| ~ ordinal(X0) ),
inference(flattening,[],[f624]) ).
fof(f624,plain,
! [X0] :
( ( being_limit_ordinal(X0)
<=> ! [X1] :
( in(succ(X1),X0)
| ~ in(X1,X0)
| ~ ordinal(X1) ) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f462]) ).
fof(f462,axiom,
! [X0] :
( ordinal(X0)
=> ( being_limit_ordinal(X0)
<=> ! [X1] :
( ordinal(X1)
=> ( in(X1,X0)
=> in(succ(X1),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_ordinal1) ).
fof(f80485,plain,
! [X0] : union(empty_set) = union_of_subsets(X0,empty_set),
inference(resolution,[],[f3588,f4153]) ).
fof(f3588,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| union_of_subsets(X0,X1) = union(X1) ),
inference(cnf_transformation,[],[f1052]) ).
fof(f1052,plain,
! [X0,X1] :
( union_of_subsets(X0,X1) = union(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f313]) ).
fof(f313,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(f160112,plain,
( cast_as_carrier_subset(sK164) = union_of_subsets(the_carrier(sK164),empty_set)
| ~ element(empty_set,powerset(powerset(the_carrier(sK164))))
| ~ one_sorted_str(sK164) ),
inference(resolution,[],[f3040,f4114]) ).
fof(f4114,plain,
is_a_cover_of_carrier(sK164,empty_set),
inference(forward_demodulation,[],[f2390,f2391]) ).
fof(f2391,plain,
empty_set = sK165,
inference(cnf_transformation,[],[f1394]) ).
fof(f2390,plain,
is_a_cover_of_carrier(sK164,sK165),
inference(cnf_transformation,[],[f1394]) ).
fof(f3040,plain,
! [X0,X1] :
( ~ is_a_cover_of_carrier(X0,X1)
| union_of_subsets(the_carrier(X0),X1) = cast_as_carrier_subset(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f1784]) ).
fof(f1784,plain,
! [X0] :
( ! [X1] :
( ( ( is_a_cover_of_carrier(X0,X1)
| union_of_subsets(the_carrier(X0),X1) != cast_as_carrier_subset(X0) )
& ( union_of_subsets(the_carrier(X0),X1) = cast_as_carrier_subset(X0)
| ~ is_a_cover_of_carrier(X0,X1) ) )
| ~ element(X1,powerset(powerset(the_carrier(X0)))) )
| ~ one_sorted_str(X0) ),
inference(nnf_transformation,[],[f885]) ).
fof(f885,plain,
! [X0] :
( ! [X1] :
( ( is_a_cover_of_carrier(X0,X1)
<=> union_of_subsets(the_carrier(X0),X1) = cast_as_carrier_subset(X0) )
| ~ element(X1,powerset(powerset(the_carrier(X0)))) )
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f113]) ).
fof(f113,axiom,
! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
=> ( is_a_cover_of_carrier(X0,X1)
<=> union_of_subsets(the_carrier(X0),X1) = cast_as_carrier_subset(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_pre_topc) ).
fof(f4593,plain,
~ empty(the_carrier(sK164)),
inference(resolution,[],[f4591,f2388]) ).
fof(f4591,plain,
( ~ one_sorted_str(sK164)
| ~ empty(the_carrier(sK164)) ),
inference(resolution,[],[f3039,f2387]) ).
fof(f2387,plain,
~ empty_carrier(sK164),
inference(cnf_transformation,[],[f1394]) ).
fof(f3039,plain,
! [X0] :
( empty_carrier(X0)
| ~ empty(the_carrier(X0))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f1783]) ).
fof(f1783,plain,
! [X0] :
( ( ( empty_carrier(X0)
| ~ empty(the_carrier(X0)) )
& ( empty(the_carrier(X0))
| ~ empty_carrier(X0) ) )
| ~ one_sorted_str(X0) ),
inference(nnf_transformation,[],[f884]) ).
fof(f884,plain,
! [X0] :
( ( empty_carrier(X0)
<=> empty(the_carrier(X0)) )
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f63]) ).
fof(f63,axiom,
! [X0] :
( one_sorted_str(X0)
=> ( empty_carrier(X0)
<=> empty(the_carrier(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_struct_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SEU325+2 : TPTP v8.1.2. Released v3.3.0.
% 0.14/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n013.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 3 11:19:34 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (27695)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.40 % (27698)WARNING: value z3 for option sas not known
% 0.21/0.40 % (27700)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.21/0.40 % (27697)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.40 % (27699)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.40 % (27701)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.21/0.40 % (27698)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.40 % (27702)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.21/0.42 % (27696)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 1.35/0.59 TRYING [1]
% 1.35/0.61 TRYING [2]
% 3.19/0.86 TRYING [3]
% 11.77/2.08 TRYING [1]
% 12.28/2.15 TRYING [2]
% 13.41/2.32 TRYING [4]
% 14.27/2.42 TRYING [3]
% 21.69/3.49 TRYING [4]
% 28.00/4.38 TRYING [1]
% 30.63/4.76 TRYING [2]
% 45.99/6.99 TRYING [5]
% 52.99/7.96 TRYING [5]
% 62.84/9.47 TRYING [3]
% 118.22/17.39 TRYING [6]
% 200.11/29.12 TRYING [4]
% 217.31/31.58 TRYING [6]
% 259.73/37.61 % (27701)First to succeed.
% 259.73/37.61 % (27701)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-27695"
% 259.73/37.63 % (27701)Refutation found. Thanks to Tanya!
% 259.73/37.63 % SZS status Theorem for theBenchmark
% 259.73/37.63 % SZS output start Proof for theBenchmark
% See solution above
% 259.73/37.63 % (27701)------------------------------
% 259.73/37.63 % (27701)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 259.73/37.63 % (27701)Termination reason: Refutation
% 259.73/37.63
% 259.73/37.63 % (27701)Memory used [KB]: 178511
% 259.73/37.63 % (27701)Time elapsed: 37.207 s
% 259.73/37.63 % (27701)Instructions burned: 68902 (million)
% 259.73/37.63 % (27695)Success in time 37.15 s
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