%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU128+2 : 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 : n001.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 12:47:19 PM UTC 2026
% Result : Theorem 3.67s 1.42s
% Output : Refutation 3.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 44 ( 11 unt; 2 def)
% Number of atoms : 150 ( 10 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 170 ( 64 ~; 62 |; 35 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 68 ( 0 sgn 57 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f8,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(f24,conjecture,
! [X0,X1,X2] :
( ( subset(X0,X1)
& subset(X0,X2) )
=> subset(X0,set_intersection2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_xboole_1) ).
fof(f25,negated_conjecture,
~ ! [X0,X1,X2] :
( ( subset(X0,X1)
& subset(X0,X2) )
=> subset(X0,set_intersection2(X1,X2)) ),
inference(negated_conjecture,[status(cth)],[f24]) ).
fof(f44,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f49,plain,
? [X0,X1,X2] :
( ~ subset(X0,set_intersection2(X1,X2))
& subset(X0,X1)
& subset(X0,X2) ),
inference(ennf_transformation,[],[f25]) ).
fof(f50,plain,
? [X0,X1,X2] :
( ~ subset(X0,set_intersection2(X1,X2))
& subset(X0,X1)
& subset(X0,X2) ),
inference(flattening,[],[f49]) ).
fof(f70,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,[],[f44]) ).
fof(f71,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,[],[f70]) ).
fof(f72,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK2(X0,X1),X1)
& in(sK2(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f71]) ).
fof(f73,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,[],[f8]) ).
fof(f74,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,[],[f73]) ).
fof(f75,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,[],[f74]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ( ( ~ in(sK3(X0,X1,X2),X0)
| ~ in(sK3(X0,X1,X2),X1)
| ~ in(sK3(X0,X1,X2),X2) )
& ( ( in(sK3(X0,X1,X2),X0)
& in(sK3(X0,X1,X2),X1) )
| in(sK3(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,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f75]) ).
fof(f80,plain,
( ~ subset(sK6,set_intersection2(sK7,sK8))
& subset(sK6,sK7)
& subset(sK6,sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X0,sK6),skolemize(X1,sK7),skolemize(X2,sK8)],[f50]) ).
fof(f97,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f98,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f99,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f102,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f76]) ).
fof(f119,plain,
subset(sK6,sK8),
inference(cnf_transformation,[],[f80]) ).
fof(f120,plain,
subset(sK6,sK7),
inference(cnf_transformation,[],[f80]) ).
fof(f121,plain,
~ subset(sK6,set_intersection2(sK7,sK8)),
inference(cnf_transformation,[],[f80]) ).
fof(f143,plain,
! [X0,X1,X4] :
( in(X4,set_intersection2(X0,X1))
| ~ in(X4,X0)
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f102]) ).
fof(f175,plain,
in(sK2(sK6,set_intersection2(sK7,sK8)),sK6),
inference(resolution,[],[f98,f121]) ).
fof(f176,plain,
~ in(sK2(sK6,set_intersection2(sK7,sK8)),set_intersection2(sK7,sK8)),
inference(resolution,[],[f99,f121]) ).
fof(f225,plain,
! [X0] :
( in(X0,sK8)
| ~ in(X0,sK6) ),
inference(resolution,[],[f97,f119]) ).
fof(f226,plain,
! [X0] :
( in(X0,sK7)
| ~ in(X0,sK6) ),
inference(resolution,[],[f97,f120]) ).
fof(f247,plain,
( ~ in(sK2(sK6,set_intersection2(sK7,sK8)),sK7)
| ~ in(sK2(sK6,set_intersection2(sK7,sK8)),sK8) ),
inference(resolution,[],[f143,f176]) ).
fof(f250,definition,
( spl12_3
<=> in(sK2(sK6,set_intersection2(sK7,sK8)),sK8) ),
introduced(definition,[new_symbols(definition,[spl12_3])],[avatar_definition]) ).
fof(f251,plain,
( ~ in(sK2(sK6,set_intersection2(sK7,sK8)),sK8)
| spl12_3 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f253,definition,
( spl12_4
<=> in(sK2(sK6,set_intersection2(sK7,sK8)),sK7) ),
introduced(definition,[new_symbols(definition,[spl12_4])],[avatar_definition]) ).
fof(f254,plain,
( ~ in(sK2(sK6,set_intersection2(sK7,sK8)),sK7)
| spl12_4 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f255,plain,
( ~ spl12_3
| ~ spl12_4 ),
inference(avatar_split_clause,[],[f247,f253,f250]) ).
fof(f256,plain,
( ~ in(sK2(sK6,set_intersection2(sK7,sK8)),sK6)
| spl12_3 ),
inference(resolution,[],[f251,f225]) ).
fof(f257,plain,
( $false
| spl12_3 ),
inference(resolution,[],[f256,f175]) ).
fof(f258,plain,
spl12_3,
inference(avatar_contradiction_clause,[],[f257]) ).
fof(f263,plain,
( ~ in(sK2(sK6,set_intersection2(sK7,sK8)),sK6)
| spl12_4 ),
inference(resolution,[],[f226,f254]) ).
fof(f264,plain,
( $false
| spl12_4 ),
inference(resolution,[],[f263,f175]) ).
fof(f265,plain,
spl12_4,
inference(avatar_contradiction_clause,[],[f264]) ).
cnf(s3,plain,
( ~ spl12_3
| ~ spl12_4 ),
inference(sat_conversion,[],[f255]) ).
cnf(s4,plain,
spl12_3,
inference(sat_conversion,[],[f258]) ).
cnf(s5,plain,
spl12_4,
inference(sat_conversion,[],[f265]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s3,s5,s4]) ).
fof(f266,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU128+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n001.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Mon Sep 28 03:45:32 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 3.67/1.42 % (4188144)Detected formulas, will run a generic FOF schedule.
% 3.67/1.42 % (4188153)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=65259210:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.67/1.42 % (4188151)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=2319675976:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.67/1.42 % (4188154)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2476581165:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.67/1.42 % (4188150)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=1291173406:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.67/1.42 % (4188155)dis-21_1_sil=8000:lcm=predicate:random_seed=1662600567: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)
% 3.67/1.42 % (4188149)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=2015045902:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.67/1.42 % (4188152)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=280217279:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.67/1.42 % (4188155)First to succeed.
% 3.67/1.42 % (4188155)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4188144"
% 3.67/1.42 % (4188153)Instruction limit reached!
% 3.67/1.42 % (4188153)------------------------------
% 3.67/1.42 % (4188153)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.42 % (4188153)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.42 % (4188153)CaDiCaL version: 2.1.3
% 3.67/1.42 % (4188153)Termination reason: Instruction limit
% 3.67/1.42 % (4188153)Termination phase: Saturation
% 3.67/1.42 % (4188153)Time elapsed: 0.041 s
% 3.67/1.42 % (4188153)Peak memory usage: 89 MB
% 3.67/1.42 % (4188153)Instructions burned: 120 (million)
% 3.67/1.42 % (4188152)Instruction limit reached!
% 3.67/1.42 % (4188152)------------------------------
% 3.67/1.42 % (4188152)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.42 % (4188152)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.42 % (4188152)CaDiCaL version: 2.1.3
% 3.67/1.42 % (4188152)Termination reason: Instruction limit
% 3.67/1.42 % (4188152)Termination phase: Saturation
% 3.67/1.42 % (4188152)Time elapsed: 0.074 s
% 3.67/1.42 % (4188152)Peak memory usage: 89 MB
% 3.67/1.42 % (4188152)Instructions burned: 109 (million)
% 3.67/1.42 % (4188154)Instruction limit reached!
% 3.67/1.42 % (4188154)------------------------------
% 3.67/1.42 % (4188154)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.42 % (4188154)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.42 % (4188154)CaDiCaL version: 2.1.3
% 3.67/1.42 % (4188154)Termination reason: Instruction limit
% 3.67/1.42 % (4188154)Termination phase: Saturation
% 3.67/1.42 % (4188154)Time elapsed: 0.095 s
% 3.67/1.42 % (4188154)Peak memory usage: 89 MB
% 3.67/1.42 % (4188154)Instructions burned: 140 (million)
% 3.67/1.42 % (4188163)lrs+10_1_sil=8000:sp=occurrence:random_seed=3068440735:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.67/1.42 % (4188163)Instruction limit reached!
% 3.67/1.42 % (4188163)------------------------------
% 3.67/1.42 % (4188163)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.42 % (4188163)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.42 % (4188163)CaDiCaL version: 2.1.3
% 3.67/1.42 % (4188163)Termination reason: Instruction limit
% 3.67/1.42 % (4188163)Termination phase: Saturation
% 3.67/1.42 % (4188163)Time elapsed: 0.091 s
% 3.67/1.42 % (4188163)Peak memory usage: 91 MB
% 3.67/1.42 % (4188163)Instructions burned: 288 (million)
% 3.67/1.42 % (4188164)lrs+10_1_sil=32000:urr=on:br=off:random_seed=407578488:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.67/1.42 % (4188165)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1028940607:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.67/1.42 % (4188155)Refutation found. Thanks to Tanya!
% 3.67/1.42 % SZS status Theorem for theBenchmark
% 3.67/1.42 % SZS output start Proof for theBenchmark
% See solution above
% 3.67/1.42 % (4188155)------------------------------
% 3.67/1.42 % (4188155)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.42 % (4188155)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.42 % (4188155)CaDiCaL version: 2.1.3
% 3.67/1.42 % (4188155)Termination reason: Refutation
% 3.67/1.42 % (4188155)Time elapsed: 0.005 s
% 3.67/1.42 % (4188155)Peak memory usage: 89 MB
% 3.67/1.42 % (4188155)Instructions burned: 5 (million)
% 3.67/1.42 % (4188155)------------------------------
% 3.67/1.42 % (4188155)------------------------------
% 3.67/1.42 % (4188144)Success in time 0.44 s
% 3.67/1.42 % Vampire exiting
%------------------------------------------------------------------------------