%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU307+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 12:48:16 PM UTC 2026
% Result : Theorem 2.35s 0.93s
% Output : Refutation 2.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 12 unt; 2 def)
% Number of atoms : 84 ( 22 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 77 ( 35 ~; 25 |; 6 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 40 ( 0 sgn 38 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f47,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X0))
& element(X2,powerset(X0)) )
=> subset_intersection2(X0,X1,X2) = set_intersection2(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_subset_1) ).
fof(f49,axiom,
! [X0] :
( one_sorted_str(X0)
=> element(cast_as_carrier_subset(X0),powerset(the_carrier(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_pre_topc) ).
fof(f56,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f57,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(f58,conjecture,
! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset_intersection2(the_carrier(X0),X1,cast_as_carrier_subset(X0)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_pre_topc) ).
fof(f59,negated_conjecture,
~ ! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset_intersection2(the_carrier(X0),X1,cast_as_carrier_subset(X0)) = X1 ) ),
inference(negated_conjecture,[status(cth)],[f58]) ).
fof(f60,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_intersection2(X0,X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(f113,plain,
! [X0,X1,X2] :
( subset_intersection2(X0,X1,X2) = set_intersection2(X1,X2)
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0)) ),
inference(ennf_transformation,[],[f47]) ).
fof(f114,plain,
! [X0,X1,X2] :
( subset_intersection2(X0,X1,X2) = set_intersection2(X1,X2)
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0)) ),
inference(flattening,[],[f113]) ).
fof(f115,plain,
! [X0] :
( element(cast_as_carrier_subset(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f49]) ).
fof(f118,plain,
! [X0] :
( cast_as_carrier_subset(X0) = the_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f119,plain,
? [X0] :
( ? [X1] :
( subset_intersection2(the_carrier(X0),X1,cast_as_carrier_subset(X0)) != X1
& element(X1,powerset(the_carrier(X0))) )
& one_sorted_str(X0) ),
inference(ennf_transformation,[],[f59]) ).
fof(f120,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f60]) ).
fof(f126,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f56]) ).
fof(f127,plain,
( sK6 != subset_intersection2(the_carrier(sK5),sK6,cast_as_carrier_subset(sK5))
& element(sK6,powerset(the_carrier(sK5)))
& one_sorted_str(sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X0,sK5),skolemize(X1,sK6)],[f119]) ).
fof(f214,plain,
! [X2,X0,X1] :
( subset_intersection2(X0,X1,X2) = set_intersection2(X1,X2)
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0)) ),
inference(cnf_transformation,[],[f114]) ).
fof(f215,plain,
! [X0] :
( element(cast_as_carrier_subset(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f115]) ).
fof(f218,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f126]) ).
fof(f220,plain,
! [X0] :
( cast_as_carrier_subset(X0) = the_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f118]) ).
fof(f221,plain,
one_sorted_str(sK5),
inference(cnf_transformation,[],[f127]) ).
fof(f222,plain,
element(sK6,powerset(the_carrier(sK5))),
inference(cnf_transformation,[],[f127]) ).
fof(f223,plain,
sK6 != subset_intersection2(the_carrier(sK5),sK6,cast_as_carrier_subset(sK5)),
inference(cnf_transformation,[],[f127]) ).
fof(f224,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X0,X1) = X0 ),
inference(cnf_transformation,[],[f120]) ).
fof(f234,plain,
( sK6 != subset_intersection2(the_carrier(sK5),sK6,the_carrier(sK5))
| ~ one_sorted_str(sK5) ),
inference(superposition,[],[f223,f220]) ).
fof(f235,plain,
sK6 != subset_intersection2(the_carrier(sK5),sK6,the_carrier(sK5)),
inference(forward_subsumption_resolution,[],[f234,f221]) ).
fof(f246,plain,
! [X0] :
( element(the_carrier(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0)
| ~ one_sorted_str(X0) ),
inference(superposition,[],[f215,f220]) ).
fof(f247,plain,
! [X0] :
( ~ one_sorted_str(X0)
| element(the_carrier(X0),powerset(the_carrier(X0))) ),
inference(duplicate_literal_removal,[],[f246]) ).
fof(f252,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| set_intersection2(X0,X1) = X0 ),
inference(resolution,[],[f224,f218]) ).
fof(f277,plain,
( sK6 != set_intersection2(sK6,the_carrier(sK5))
| ~ element(sK6,powerset(the_carrier(sK5)))
| ~ element(the_carrier(sK5),powerset(the_carrier(sK5))) ),
inference(superposition,[],[f235,f214]) ).
fof(f283,plain,
( sK6 != set_intersection2(sK6,the_carrier(sK5))
| ~ element(the_carrier(sK5),powerset(the_carrier(sK5))) ),
inference(forward_subsumption_resolution,[],[f277,f222]) ).
fof(f286,definition,
( spl7_1
<=> element(the_carrier(sK5),powerset(the_carrier(sK5))) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
fof(f290,definition,
( spl7_2
<=> sK6 = set_intersection2(sK6,the_carrier(sK5)) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
fof(f293,plain,
( ~ spl7_1
| ~ spl7_2 ),
inference(avatar_split_clause,[],[f283,f290,f286]) ).
fof(f579,plain,
element(the_carrier(sK5),powerset(the_carrier(sK5))),
inference(resolution,[],[f247,f221]) ).
fof(f593,plain,
sK6 = set_intersection2(sK6,the_carrier(sK5)),
inference(resolution,[],[f252,f222]) ).
fof(f611,plain,
spl7_1,
inference(avatar_split_clause,[],[f579,f286]) ).
fof(f612,plain,
spl7_2,
inference(avatar_split_clause,[],[f593,f290]) ).
cnf(s1,plain,
( ~ spl7_1
| ~ spl7_2 ),
inference(sat_conversion,[],[f293]) ).
cnf(s8,plain,
spl7_1,
inference(sat_conversion,[],[f611]) ).
cnf(s9,plain,
spl7_2,
inference(sat_conversion,[],[f612]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s1,s9,s8]) ).
fof(f613,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU307+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Mon Sep 28 04:37:34 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.33 Running first-order theorem proving
% 0.08/0.33 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
% 2.35/0.93 % (3019825)Detected formulas, will run a generic FOF schedule.
% 2.35/0.93 % (3019833)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4111827953:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.35/0.93 % (3019830)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=1101879430:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.35/0.93 % (3019834)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=236989429:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.35/0.93 % (3019831)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=573130764:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.35/0.93 % (3019835)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3239070532:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.35/0.93 % (3019836)dis-21_1_sil=8000:lcm=predicate:random_seed=243609257: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)
% 2.35/0.93 % (3019832)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=2236268982:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.35/0.93 % (3019833)Refutation not found, incomplete strategy
% 2.35/0.93 % (3019833)------------------------------
% 2.35/0.93 % (3019833)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.35/0.93 % (3019833)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.35/0.93 % (3019833)CaDiCaL version: 2.1.3
% 2.35/0.93 % (3019833)Termination reason: Refutation not found, incomplete strategy
% 2.35/0.93 % (3019833)Time elapsed: 0.001 s
% 2.35/0.93 % (3019833)Peak memory usage: 88 MB
% 2.35/0.93 % (3019833)Instructions burned: 2 (million)
% 2.35/0.93 % (3019834)Refutation not found, incomplete strategy
% 2.35/0.93 % (3019834)------------------------------
% 2.35/0.93 % (3019834)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.35/0.93 % (3019834)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.35/0.93 % (3019834)CaDiCaL version: 2.1.3
% 2.35/0.93 % (3019834)Termination reason: Refutation not found, incomplete strategy
% 2.35/0.93 % (3019834)Time elapsed: 0.004 s
% 2.35/0.93 % (3019834)Peak memory usage: 88 MB
% 2.35/0.93 % (3019834)Instructions burned: 10 (million)
% 2.35/0.93 % (3019835)First to succeed.
% 2.35/0.93 % (3019835)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3019825"
% 2.35/0.93 % (3019836)Instruction limit reached!
% 2.35/0.93 % (3019836)------------------------------
% 2.35/0.93 % (3019836)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.35/0.93 % (3019836)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.35/0.93 % (3019836)CaDiCaL version: 2.1.3
% 2.35/0.93 % (3019836)Termination reason: Instruction limit
% 2.35/0.93 % (3019836)Termination phase: Saturation
% 2.35/0.93 % (3019836)Time elapsed: 0.042 s
% 2.35/0.93 % (3019836)Peak memory usage: 89 MB
% 2.35/0.93 % (3019836)Instructions burned: 130 (million)
% 2.35/0.93 % (3019834)------------------------------
% 2.35/0.93 % (3019834)------------------------------
% 2.35/0.93 % (3019833)------------------------------
% 2.35/0.93 % (3019833)------------------------------
% 2.35/0.93 % (3019835)Refutation found. Thanks to Tanya!
% 2.35/0.93 % SZS status Theorem for theBenchmark
% 2.35/0.93 % SZS output start Proof for theBenchmark
% See solution above
% 2.35/0.93 % (3019835)------------------------------
% 2.35/0.93 % (3019835)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.35/0.93 % (3019835)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.35/0.93 % (3019835)CaDiCaL version: 2.1.3
% 2.35/0.93 % (3019835)Termination reason: Refutation
% 2.35/0.93 % (3019835)Time elapsed: 0.008 s
% 2.35/0.93 % (3019835)Peak memory usage: 89 MB
% 2.35/0.93 % (3019835)Instructions burned: 17 (million)
% 2.35/0.93 % (3019835)------------------------------
% 2.35/0.93 % (3019835)------------------------------
% 2.35/0.93 % (3019825)Success in time 0.299 s
% 2.35/0.93 % Vampire exiting
%------------------------------------------------------------------------------