%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU130+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 12:47:20 PM UTC 2026
% Result : Theorem 2.76s 1.29s
% Output : Refutation 3.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 61 ( 12 unt; 5 def)
% Number of atoms : 193 ( 22 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 216 ( 84 ~; 85 |; 34 &)
% ( 10 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 77 ( 0 sgn 70 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f5,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& in(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f13,axiom,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
fof(f14,conjecture,
! [X0,X1] :
( subset(X0,X1)
=> set_intersection2(X0,X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(f15,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,X1)
=> set_intersection2(X0,X1) = X0 ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f23,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f24,plain,
? [X0,X1] :
( set_intersection2(X0,X1) != X0
& subset(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f28,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f29,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f28]) ).
fof(f30,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f31,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f30]) ).
fof(f32,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK0(X0,X1),X1)
& in(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f31]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(flattening,[],[f33]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(rectify,[],[f34]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ( ( ~ in(sK1(X0,X1,X2),X0)
| ~ in(sK1(X0,X1,X2),X1)
| ~ in(sK1(X0,X1,X2),X2) )
& ( ( in(sK1(X0,X1,X2),X0)
& in(sK1(X0,X1,X2),X1) )
| in(sK1(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f35]) ).
fof(f39,plain,
( sK4 != set_intersection2(sK4,sK5)
& subset(sK4,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X0,sK4),skolemize(X1,sK5)],[f24]) ).
fof(f44,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f45,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f46,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f47,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f50,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f36]) ).
fof(f59,plain,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
inference(cnf_transformation,[],[f13]) ).
fof(f60,plain,
subset(sK4,sK5),
inference(cnf_transformation,[],[f39]) ).
fof(f61,plain,
sK4 != set_intersection2(sK4,sK5),
inference(cnf_transformation,[],[f39]) ).
fof(f68,plain,
! [X0,X1,X4] :
( in(X4,set_intersection2(X0,X1))
| ~ in(X4,X0)
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f50]) ).
fof(f71,definition,
! [X0,X1] :
( sQ6_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ6_eqProxy])],[equality_proxy_definition]) ).
fof(f73,plain,
! [X0,X1] :
( sQ6_eqProxy(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(equality_proxy_replacement,[],[f44,f71]) ).
fof(f78,plain,
~ sQ6_eqProxy(sK4,set_intersection2(sK4,sK5)),
inference(equality_proxy_replacement,[],[f61,f71]) ).
fof(f99,plain,
! [X0] :
( in(X0,sK5)
| ~ in(X0,sK4) ),
inference(resolution,[],[f45,f60]) ).
fof(f104,plain,
( ~ subset(sK4,set_intersection2(sK4,sK5))
| ~ subset(set_intersection2(sK4,sK5),sK4) ),
inference(resolution,[],[f73,f78]) ).
fof(f107,definition,
( spl7_3
<=> subset(sK4,set_intersection2(sK4,sK5)) ),
introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition]) ).
fof(f108,plain,
( ~ subset(sK4,set_intersection2(sK4,sK5))
| spl7_3 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f110,definition,
( spl7_4
<=> subset(set_intersection2(sK4,sK5),sK4) ),
introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition]) ).
fof(f111,plain,
( ~ subset(set_intersection2(sK4,sK5),sK4)
| spl7_4 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f113,plain,
( ~ spl7_4
| ~ spl7_3 ),
inference(avatar_split_clause,[],[f104,f107,f110]) ).
fof(f114,plain,
( ~ in(sK0(sK4,set_intersection2(sK4,sK5)),set_intersection2(sK4,sK5))
| spl7_3 ),
inference(resolution,[],[f108,f47]) ).
fof(f115,plain,
( in(sK0(sK4,set_intersection2(sK4,sK5)),sK4)
| spl7_3 ),
inference(resolution,[],[f108,f46]) ).
fof(f126,plain,
( ~ in(sK0(sK4,set_intersection2(sK4,sK5)),sK4)
| ~ in(sK0(sK4,set_intersection2(sK4,sK5)),sK5)
| spl7_3 ),
inference(resolution,[],[f68,f114]) ).
fof(f128,definition,
( spl7_5
<=> in(sK0(sK4,set_intersection2(sK4,sK5)),sK5) ),
introduced(definition,[new_symbols(definition,[spl7_5])],[avatar_definition]) ).
fof(f129,plain,
( ~ in(sK0(sK4,set_intersection2(sK4,sK5)),sK5)
| spl7_5 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f131,definition,
( spl7_6
<=> in(sK0(sK4,set_intersection2(sK4,sK5)),sK4) ),
introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition]) ).
fof(f132,plain,
( ~ in(sK0(sK4,set_intersection2(sK4,sK5)),sK4)
| spl7_6 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f133,plain,
( ~ spl7_5
| ~ spl7_6
| spl7_3 ),
inference(avatar_split_clause,[],[f126,f107,f131,f128]) ).
fof(f134,plain,
( ~ in(sK0(sK4,set_intersection2(sK4,sK5)),sK4)
| spl7_5 ),
inference(resolution,[],[f129,f99]) ).
fof(f135,plain,
( ~ spl7_6
| spl7_5 ),
inference(avatar_split_clause,[],[f134,f128,f131]) ).
fof(f136,plain,
( $false
| spl7_3
| spl7_6 ),
inference(resolution,[],[f132,f115]) ).
fof(f137,plain,
( spl7_3
| spl7_6 ),
inference(avatar_contradiction_clause,[],[f136]) ).
fof(f138,plain,
( $false
| spl7_4 ),
inference(resolution,[],[f111,f59]) ).
fof(f141,plain,
spl7_4,
inference(avatar_contradiction_clause,[],[f138]) ).
cnf(s4,plain,
( ~ spl7_3
| ~ spl7_4 ),
inference(sat_conversion,[],[f113]) ).
cnf(s5,plain,
( spl7_3
| ~ spl7_5
| ~ spl7_6 ),
inference(sat_conversion,[],[f133]) ).
cnf(s6,plain,
( spl7_5
| ~ spl7_6 ),
inference(sat_conversion,[],[f135]) ).
cnf(s7,plain,
( spl7_3
| spl7_6 ),
inference(sat_conversion,[],[f137]) ).
cnf(s8,plain,
spl7_4,
inference(sat_conversion,[],[f141]) ).
cnf(s9,plain,
~ spl7_3,
inference(rat,[],[s4,s8]) ).
cnf(s10,plain,
spl7_6,
inference(rat,[],[s7,s9]) ).
cnf(s11,plain,
~ spl7_5,
inference(rat,[],[s5,s10,s9]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s6,s10,s11]) ).
fof(f142,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU130+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n015.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 03:43:01 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.76/1.29 % (2235692)Detected formulas, will run a generic FOF schedule.
% 2.76/1.29 % (2235700)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=229057180:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.76/1.29 % (2235700)Refutation not found, incomplete strategy
% 2.76/1.29 % (2235700)------------------------------
% 2.76/1.29 % (2235700)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.76/1.29 % (2235700)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/1.29 % (2235700)CaDiCaL version: 2.1.3
% 2.76/1.29 % (2235700)Termination reason: Refutation not found, incomplete strategy
% 2.76/1.29 % (2235700)Time elapsed: 0.001 s
% 2.76/1.29 % (2235700)Peak memory usage: 88 MB
% 2.76/1.29 % (2235697)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=2362225040:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.76/1.29 % (2235698)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=1641200808:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.76/1.29 % (2235699)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=1677335713:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.76/1.29 % (2235701)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=280004124:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.76/1.29 % (2235703)dis-21_1_sil=8000:lcm=predicate:random_seed=3767052781: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)
% 2.76/1.29 % (2235702)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=815348567:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.76/1.29 % (2235701)Refutation not found, incomplete strategy
% 2.76/1.29 % (2235701)------------------------------
% 2.76/1.29 % (2235701)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.76/1.29 % (2235701)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/1.29 % (2235701)CaDiCaL version: 2.1.3
% 2.76/1.29 % (2235701)Termination reason: Refutation not found, incomplete strategy
% 2.76/1.29 % (2235701)Time elapsed: 0.002 s
% 2.76/1.29 % (2235701)Peak memory usage: 88 MB
% 2.76/1.29 % (2235701)Instructions burned: 1 (million)
% 2.76/1.29 % (2235703)First to succeed.
% 2.76/1.29 % (2235703)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2235692"
% 2.76/1.29 % (2235702)Instruction limit reached!
% 2.76/1.29 % (2235702)------------------------------
% 2.76/1.29 % (2235702)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.76/1.29 % (2235702)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/1.29 % (2235702)CaDiCaL version: 2.1.3
% 2.76/1.29 % (2235702)Termination reason: Instruction limit
% 2.76/1.29 % (2235702)Termination phase: Saturation
% 2.76/1.29 % (2235702)Time elapsed: 0.096 s
% 2.76/1.29 % (2235702)Peak memory usage: 89 MB
% 2.76/1.29 % (2235702)Instructions burned: 140 (million)
% 2.76/1.29 % (2235700)------------------------------
% 2.76/1.29 % (2235700)------------------------------
% 2.76/1.29 % (2235701)------------------------------
% 2.76/1.29 % (2235701)------------------------------
% 2.76/1.29 % (2235711)lrs+10_1_sil=8000:sp=occurrence:random_seed=238589566:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.76/1.29 % (2235712)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1181974634:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.76/1.29 % (2235703)Refutation found. Thanks to Tanya!
% 2.76/1.29 % SZS status Theorem for theBenchmark
% 2.76/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 3.65/1.49 % (2235703)------------------------------
% 3.65/1.49 % (2235703)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.49 % (2235703)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.49 % (2235703)CaDiCaL version: 2.1.3
% 3.65/1.49 % (2235703)Termination reason: Refutation
% 3.65/1.49 % (2235703)Time elapsed: 0.004 s
% 3.65/1.49 % (2235703)Peak memory usage: 89 MB
% 3.65/1.49 % (2235703)Instructions burned: 3 (million)
% 3.65/1.49 % (2235703)------------------------------
% 3.65/1.49 % (2235703)------------------------------
% 3.65/1.49 % (2235692)Success in time 0.435 s
% 3.65/1.49 % Vampire exiting
%------------------------------------------------------------------------------