%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU309+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 0.42s 0.83s
% Output : Refutation 2.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 69 ( 14 unt; 4 def)
% Number of atoms : 165 ( 34 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 177 ( 81 ~; 75 |; 7 &)
% ( 4 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 64 ( 0 sgn 62 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f22,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(f26,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X0))
& element(X2,powerset(X0)) )
=> element(subset_difference(X0,X1,X2),powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_subset_1) ).
fof(f54,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(f55,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X0))
& element(X2,powerset(X0)) )
=> subset_difference(X0,X1,X2) = set_difference(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
fof(f57,axiom,
! [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,conjecture,
! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_pre_topc) ).
fof(f60,negated_conjecture,
~ ! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1)) = X1 ) ),
inference(negated_conjecture,[status(cth)],[f59]) ).
fof(f65,axiom,
! [X0,X1] : set_difference(X0,set_difference(X0,X1)) = set_intersection2(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).
fof(f104,plain,
! [X0] :
( element(cast_as_carrier_subset(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f107,plain,
! [X0,X1,X2] :
( element(subset_difference(X0,X1,X2),powerset(X0))
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0)) ),
inference(ennf_transformation,[],[f26]) ).
fof(f108,plain,
! [X0,X1,X2] :
( element(subset_difference(X0,X1,X2),powerset(X0))
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0)) ),
inference(flattening,[],[f107]) ).
fof(f127,plain,
! [X0,X1,X2] :
( subset_intersection2(X0,X1,X2) = set_intersection2(X1,X2)
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0)) ),
inference(ennf_transformation,[],[f54]) ).
fof(f128,plain,
! [X0,X1,X2] :
( subset_intersection2(X0,X1,X2) = set_intersection2(X1,X2)
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0)) ),
inference(flattening,[],[f127]) ).
fof(f129,plain,
! [X0,X1,X2] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0)) ),
inference(ennf_transformation,[],[f55]) ).
fof(f130,plain,
! [X0,X1,X2] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0)) ),
inference(flattening,[],[f129]) ).
fof(f131,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,[],[f57]) ).
fof(f133,plain,
? [X0] :
( ? [X1] :
( subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1)) != X1
& element(X1,powerset(the_carrier(X0))) )
& one_sorted_str(X0) ),
inference(ennf_transformation,[],[f60]) ).
fof(f148,plain,
( sK6 != subset_difference(the_carrier(sK5),cast_as_carrier_subset(sK5),subset_difference(the_carrier(sK5),cast_as_carrier_subset(sK5),sK6))
& 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)],[f133]) ).
fof(f174,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f17]) ).
fof(f177,plain,
! [X0] :
( element(cast_as_carrier_subset(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f179,plain,
! [X2,X0,X1] :
( element(subset_difference(X0,X1,X2),powerset(X0))
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0)) ),
inference(cnf_transformation,[],[f108]) ).
fof(f246,plain,
! [X2,X0,X1] :
( subset_intersection2(X0,X1,X2) = set_intersection2(X1,X2)
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0)) ),
inference(cnf_transformation,[],[f128]) ).
fof(f247,plain,
! [X2,X0,X1] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0)) ),
inference(cnf_transformation,[],[f130]) ).
fof(f249,plain,
! [X0,X1] :
( ~ one_sorted_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| subset_intersection2(the_carrier(X0),X1,cast_as_carrier_subset(X0)) = X1 ),
inference(cnf_transformation,[],[f131]) ).
fof(f251,plain,
one_sorted_str(sK5),
inference(cnf_transformation,[],[f148]) ).
fof(f252,plain,
element(sK6,powerset(the_carrier(sK5))),
inference(cnf_transformation,[],[f148]) ).
fof(f253,plain,
sK6 != subset_difference(the_carrier(sK5),cast_as_carrier_subset(sK5),subset_difference(the_carrier(sK5),cast_as_carrier_subset(sK5),sK6)),
inference(cnf_transformation,[],[f148]) ).
fof(f258,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1)),
inference(cnf_transformation,[],[f65]) ).
fof(f330,plain,
! [X0] :
( subset_intersection2(the_carrier(sK5),X0,cast_as_carrier_subset(sK5)) = X0
| ~ element(X0,powerset(the_carrier(sK5))) ),
inference(resolution,[],[f249,f251]) ).
fof(f337,plain,
! [X0] :
( set_intersection2(X0,cast_as_carrier_subset(sK5)) = X0
| ~ element(X0,powerset(the_carrier(sK5)))
| ~ element(cast_as_carrier_subset(sK5),powerset(the_carrier(sK5)))
| ~ element(X0,powerset(the_carrier(sK5))) ),
inference(superposition,[],[f246,f330]) ).
fof(f344,plain,
! [X0] :
( set_intersection2(X0,cast_as_carrier_subset(sK5)) = X0
| ~ element(X0,powerset(the_carrier(sK5)))
| ~ element(cast_as_carrier_subset(sK5),powerset(the_carrier(sK5))) ),
inference(duplicate_literal_removal,[],[f337]) ).
fof(f347,definition,
( spl7_1
<=> element(cast_as_carrier_subset(sK5),powerset(the_carrier(sK5))) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
fof(f348,plain,
( element(cast_as_carrier_subset(sK5),powerset(the_carrier(sK5)))
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f347]) ).
fof(f349,plain,
( ~ element(cast_as_carrier_subset(sK5),powerset(the_carrier(sK5)))
| spl7_1 ),
inference(avatar_component_clause,[],[f347]) ).
fof(f351,definition,
( spl7_2
<=> ! [X0] :
( set_intersection2(X0,cast_as_carrier_subset(sK5)) = X0
| ~ element(X0,powerset(the_carrier(sK5))) ) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
fof(f352,plain,
( ! [X0] :
( ~ element(X0,powerset(the_carrier(sK5)))
| set_intersection2(X0,cast_as_carrier_subset(sK5)) = X0 )
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f351]) ).
fof(f354,plain,
( ~ spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f344,f351,f347]) ).
fof(f355,plain,
( ~ one_sorted_str(sK5)
| spl7_1 ),
inference(resolution,[],[f349,f177]) ).
fof(f361,plain,
( $false
| spl7_1 ),
inference(forward_subsumption_resolution,[],[f355,f251]) ).
fof(f362,plain,
spl7_1,
inference(avatar_contradiction_clause,[],[f361]) ).
fof(f364,plain,
( sK6 != set_difference(cast_as_carrier_subset(sK5),subset_difference(the_carrier(sK5),cast_as_carrier_subset(sK5),sK6))
| ~ element(cast_as_carrier_subset(sK5),powerset(the_carrier(sK5)))
| ~ element(subset_difference(the_carrier(sK5),cast_as_carrier_subset(sK5),sK6),powerset(the_carrier(sK5))) ),
inference(superposition,[],[f253,f247]) ).
fof(f384,definition,
( spl7_6
<=> element(subset_difference(the_carrier(sK5),cast_as_carrier_subset(sK5),sK6),powerset(the_carrier(sK5))) ),
introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition]) ).
fof(f386,plain,
( ~ element(subset_difference(the_carrier(sK5),cast_as_carrier_subset(sK5),sK6),powerset(the_carrier(sK5)))
| spl7_6 ),
inference(avatar_component_clause,[],[f384]) ).
fof(f388,definition,
( spl7_7
<=> sK6 = set_difference(cast_as_carrier_subset(sK5),subset_difference(the_carrier(sK5),cast_as_carrier_subset(sK5),sK6)) ),
introduced(definition,[new_symbols(definition,[spl7_7])],[avatar_definition]) ).
fof(f390,plain,
( sK6 != set_difference(cast_as_carrier_subset(sK5),subset_difference(the_carrier(sK5),cast_as_carrier_subset(sK5),sK6))
| spl7_7 ),
inference(avatar_component_clause,[],[f388]) ).
fof(f391,plain,
( ~ spl7_6
| ~ spl7_1
| ~ spl7_7 ),
inference(avatar_split_clause,[],[f364,f388,f347,f384]) ).
fof(f421,plain,
( ~ element(cast_as_carrier_subset(sK5),powerset(the_carrier(sK5)))
| ~ element(sK6,powerset(the_carrier(sK5)))
| spl7_6 ),
inference(resolution,[],[f386,f179]) ).
fof(f429,plain,
( ~ element(sK6,powerset(the_carrier(sK5)))
| ~ spl7_1
| spl7_6 ),
inference(forward_subsumption_resolution,[],[f421,f348]) ).
fof(f432,plain,
( $false
| ~ spl7_1
| spl7_6 ),
inference(forward_subsumption_resolution,[],[f429,f252]) ).
fof(f433,plain,
( ~ spl7_1
| spl7_6 ),
inference(avatar_contradiction_clause,[],[f432]) ).
fof(f442,plain,
( sK6 != set_difference(cast_as_carrier_subset(sK5),set_difference(cast_as_carrier_subset(sK5),sK6))
| ~ element(cast_as_carrier_subset(sK5),powerset(the_carrier(sK5)))
| ~ element(sK6,powerset(the_carrier(sK5)))
| spl7_7 ),
inference(superposition,[],[f390,f247]) ).
fof(f443,plain,
( sK6 != set_difference(cast_as_carrier_subset(sK5),set_difference(cast_as_carrier_subset(sK5),sK6))
| ~ element(sK6,powerset(the_carrier(sK5)))
| ~ spl7_1
| spl7_7 ),
inference(forward_subsumption_resolution,[],[f442,f348]) ).
fof(f445,plain,
( sK6 != set_difference(cast_as_carrier_subset(sK5),set_difference(cast_as_carrier_subset(sK5),sK6))
| ~ spl7_1
| spl7_7 ),
inference(forward_subsumption_resolution,[],[f443,f252]) ).
fof(f447,plain,
( sK6 != set_intersection2(cast_as_carrier_subset(sK5),sK6)
| ~ spl7_1
| spl7_7 ),
inference(forward_demodulation,[],[f445,f258]) ).
fof(f448,plain,
( sK6 != set_intersection2(sK6,cast_as_carrier_subset(sK5))
| ~ spl7_1
| spl7_7 ),
inference(forward_demodulation,[],[f447,f174]) ).
fof(f511,plain,
( sK6 = set_intersection2(sK6,cast_as_carrier_subset(sK5))
| ~ spl7_2 ),
inference(resolution,[],[f352,f252]) ).
fof(f512,plain,
( $false
| ~ spl7_1
| ~ spl7_2
| spl7_7 ),
inference(forward_subsumption_resolution,[],[f511,f448]) ).
fof(f513,plain,
( ~ spl7_1
| ~ spl7_2
| spl7_7 ),
inference(avatar_contradiction_clause,[],[f512]) ).
cnf(s2,plain,
( ~ spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f354]) ).
cnf(s3,plain,
spl7_1,
inference(sat_conversion,[],[f362]) ).
cnf(s5,plain,
( ~ spl7_1
| ~ spl7_6
| ~ spl7_7 ),
inference(sat_conversion,[],[f391]) ).
cnf(s10,plain,
( ~ spl7_1
| spl7_6 ),
inference(sat_conversion,[],[f433]) ).
cnf(s14,plain,
( ~ spl7_1
| ~ spl7_2
| spl7_7 ),
inference(sat_conversion,[],[f513]) ).
cnf(s16,plain,
spl7_6,
inference(rat,[],[s10,s3]) ).
cnf(s20,plain,
~ spl7_7,
inference(rat,[],[s5,s3,s16]) ).
cnf(s23,plain,
~ spl7_2,
inference(rat,[],[s14,s3,s20]) ).
cnf(s24,plain,
$false,
inference(rat,[],[s2,s23,s3]) ).
fof(f533,plain,
$false,
inference(avatar_sat_refutation,[],[s24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU309+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 04:37:49 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.32 Running first-order theorem proving
% 0.04/0.32 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
% 0.42/0.83 % (3020242)Detected formulas, will run a generic FOF schedule.
% 0.42/0.83 % (3020252)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4238636231:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.42/0.83 % (3020253)dis-21_1_sil=8000:lcm=predicate:random_seed=4174187937: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)
% 0.42/0.83 % (3020247)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=3485160153:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.42/0.83 % (3020251)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1455908898:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.42/0.83 % (3020248)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=1790131357:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.42/0.83 % (3020249)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=3192220812:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.42/0.83 % (3020250)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2544714137:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.42/0.83 % (3020250)Refutation not found, incomplete strategy
% 0.42/0.83 % (3020250)------------------------------
% 0.42/0.83 % (3020250)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.42/0.83 % (3020250)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.42/0.83 % (3020250)CaDiCaL version: 2.1.3
% 0.42/0.83 % (3020250)Termination reason: Refutation not found, incomplete strategy
% 0.42/0.83 % (3020250)Time elapsed: 0.002 s
% 0.42/0.83 % (3020250)Peak memory usage: 88 MB
% 0.42/0.83 % (3020250)Instructions burned: 2 (million)
% 0.42/0.83 % (3020252)First to succeed.
% 0.42/0.83 % (3020252)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3020242"
% 0.42/0.83 % (3020251)Also succeeded, but the first one will report.
% 0.42/0.83 % (3020253)Instruction limit reached!
% 0.42/0.83 % (3020253)------------------------------
% 0.42/0.83 % (3020253)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.42/0.83 % (3020253)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.42/0.83 % (3020253)CaDiCaL version: 2.1.3
% 0.42/0.83 % (3020253)Termination reason: Instruction limit
% 0.42/0.83 % (3020253)Termination phase: Saturation
% 0.42/0.83 % (3020253)Time elapsed: 0.040 s
% 0.42/0.83 % (3020253)Peak memory usage: 89 MB
% 0.42/0.83 % (3020253)Instructions burned: 131 (million)
% 0.42/0.83 % (3020250)------------------------------
% 0.42/0.83 % (3020250)------------------------------
% 0.42/0.83 % (3020252)Refutation found. Thanks to Tanya!
% 0.42/0.83 % SZS status Theorem for theBenchmark
% 0.42/0.83 % SZS output start Proof for theBenchmark
% See solution above
% 2.34/0.93 % (3020252)------------------------------
% 2.34/0.93 % (3020252)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.34/0.93 % (3020252)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.34/0.93 % (3020252)CaDiCaL version: 2.1.3
% 2.34/0.93 % (3020252)Termination reason: Refutation
% 2.34/0.93 % (3020252)Time elapsed: 0.007 s
% 2.34/0.93 % (3020252)Peak memory usage: 90 MB
% 2.34/0.93 % (3020252)Instructions burned: 15 (million)
% 2.34/0.93 % (3020252)------------------------------
% 2.34/0.93 % (3020252)------------------------------
% 2.34/0.93 % (3020242)Success in time 0.299 s
% 2.34/0.93 % Vampire exiting
%------------------------------------------------------------------------------