%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU130+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 : n006.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 2.68s 1.37s
% Output : Refutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 48 ( 17 unt; 5 def)
% Number of atoms : 97 ( 12 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 86 ( 37 ~; 32 |; 8 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 38 ( 1 sgn 36 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f20,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f23,axiom,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
fof(f24,axiom,
! [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(f28,conjecture,
! [X0,X1] :
( subset(X0,X1)
=> set_intersection2(X0,X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(f29,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,X1)
=> set_intersection2(X0,X1) = X0 ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f42,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f20]) ).
fof(f51,plain,
! [X0,X1,X2] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X1)
| ~ subset(X0,X2) ),
inference(ennf_transformation,[],[f24]) ).
fof(f52,plain,
! [X0,X1,X2] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X1)
| ~ subset(X0,X2) ),
inference(flattening,[],[f51]) ).
fof(f56,plain,
? [X0,X1] :
( set_intersection2(X0,X1) != X0
& subset(X0,X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f65,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f66,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f65]) ).
fof(f84,plain,
( sK6 != set_intersection2(sK6,sK7)
& subset(sK6,sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X1,sK7)],[f56]) ).
fof(f92,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f119,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f42]) ).
fof(f122,plain,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
inference(cnf_transformation,[],[f23]) ).
fof(f123,plain,
! [X2,X0,X1] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X1)
| ~ subset(X0,X2) ),
inference(cnf_transformation,[],[f52]) ).
fof(f127,plain,
subset(sK6,sK7),
inference(cnf_transformation,[],[f84]) ).
fof(f128,plain,
sK6 != set_intersection2(sK6,sK7),
inference(cnf_transformation,[],[f84]) ).
fof(f151,definition,
! [X0,X1] :
( sQ10_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ10_eqProxy])],[equality_proxy_definition]) ).
fof(f154,plain,
! [X0,X1] :
( sQ10_eqProxy(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(equality_proxy_replacement,[],[f92,f151]) ).
fof(f168,plain,
~ sQ10_eqProxy(sK6,set_intersection2(sK6,sK7)),
inference(equality_proxy_replacement,[],[f128,f151]) ).
fof(f246,plain,
( ~ subset(sK6,set_intersection2(sK6,sK7))
| ~ subset(set_intersection2(sK6,sK7),sK6) ),
inference(resolution,[],[f154,f168]) ).
fof(f250,definition,
( spl11_5
<=> subset(sK6,set_intersection2(sK6,sK7)) ),
introduced(definition,[new_symbols(definition,[spl11_5])],[avatar_definition]) ).
fof(f251,plain,
( ~ subset(sK6,set_intersection2(sK6,sK7))
| spl11_5 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f253,definition,
( spl11_6
<=> subset(set_intersection2(sK6,sK7),sK6) ),
introduced(definition,[new_symbols(definition,[spl11_6])],[avatar_definition]) ).
fof(f254,plain,
( ~ subset(set_intersection2(sK6,sK7),sK6)
| spl11_6 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f256,plain,
( ~ spl11_6
| ~ spl11_5 ),
inference(avatar_split_clause,[],[f246,f250,f253]) ).
fof(f640,plain,
( ~ subset(sK6,sK6)
| ~ subset(sK6,sK7)
| spl11_5 ),
inference(resolution,[],[f123,f251]) ).
fof(f647,definition,
( spl11_7
<=> subset(sK6,sK7) ),
introduced(definition,[new_symbols(definition,[spl11_7])],[avatar_definition]) ).
fof(f648,plain,
( ~ subset(sK6,sK7)
| spl11_7 ),
inference(avatar_component_clause,[],[f647]) ).
fof(f650,definition,
( spl11_8
<=> subset(sK6,sK6) ),
introduced(definition,[new_symbols(definition,[spl11_8])],[avatar_definition]) ).
fof(f651,plain,
( ~ subset(sK6,sK6)
| spl11_8 ),
inference(avatar_component_clause,[],[f650]) ).
fof(f652,plain,
( ~ spl11_7
| ~ spl11_8
| spl11_5 ),
inference(avatar_split_clause,[],[f640,f250,f650,f647]) ).
fof(f657,plain,
( $false
| spl11_7 ),
inference(resolution,[],[f648,f127]) ).
fof(f661,plain,
spl11_7,
inference(avatar_contradiction_clause,[],[f657]) ).
fof(f662,plain,
( $false
| spl11_6 ),
inference(resolution,[],[f254,f122]) ).
fof(f666,plain,
spl11_6,
inference(avatar_contradiction_clause,[],[f662]) ).
fof(f667,plain,
( $false
| spl11_8 ),
inference(resolution,[],[f651,f119]) ).
fof(f671,plain,
spl11_8,
inference(avatar_contradiction_clause,[],[f667]) ).
cnf(s6,plain,
( ~ spl11_5
| ~ spl11_6 ),
inference(sat_conversion,[],[f256]) ).
cnf(s7,plain,
( spl11_5
| ~ spl11_7
| ~ spl11_8 ),
inference(sat_conversion,[],[f652]) ).
cnf(s9,plain,
spl11_7,
inference(sat_conversion,[],[f661]) ).
cnf(s10,plain,
spl11_6,
inference(sat_conversion,[],[f666]) ).
cnf(s11,plain,
spl11_8,
inference(sat_conversion,[],[f671]) ).
cnf(s14,plain,
spl11_5,
inference(rat,[],[s7,s11,s9]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s6,s10,s14]) ).
fof(f673,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU130+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n006.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 03:39:40 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 2.68/1.37 % (3554562)Detected formulas, will run a generic FOF schedule.
% 2.68/1.37 % (3554573)dis-21_1_sil=8000:lcm=predicate:random_seed=160725055: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)
% 2.68/1.37 % (3554573)First to succeed.
% 2.68/1.37 % (3554573)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3554562"
% 2.68/1.37 % (3554571)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1501465736:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.68/1.37 % (3554572)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1007080560:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.68/1.37 % (3554568)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=2056482406:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.68/1.37 % (3554569)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=2380279740:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.68/1.37 % (3554570)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=112519462:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.68/1.37 % (3554567)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=1679684129:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.68/1.37 % (3554572)Also succeeded, but the first one will report.
% 2.68/1.37 % (3554570)Also succeeded, but the first one will report.
% 2.68/1.37 % (3554571)Instruction limit reached!
% 2.68/1.37 % (3554571)------------------------------
% 2.68/1.37 % (3554571)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.37 % (3554571)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.37 % (3554571)CaDiCaL version: 2.1.3
% 2.68/1.37 % (3554571)Termination reason: Instruction limit
% 2.68/1.37 % (3554571)Termination phase: Saturation
% 2.68/1.37 % (3554571)Time elapsed: 0.075 s
% 2.68/1.37 % (3554571)Peak memory usage: 88 MB
% 2.68/1.37 % (3554571)Instructions burned: 120 (million)
% 2.68/1.37 % (3554573)Refutation found. Thanks to Tanya!
% 2.68/1.37 % SZS status Theorem for theBenchmark
% 2.68/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 2.68/1.37 % (3554573)------------------------------
% 2.68/1.37 % (3554573)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.37 % (3554573)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.37 % (3554573)CaDiCaL version: 2.1.3
% 2.68/1.37 % (3554573)Termination reason: Refutation
% 2.68/1.37 % (3554573)Time elapsed: 0.006 s
% 2.68/1.37 % (3554573)Peak memory usage: 89 MB
% 2.68/1.37 % (3554573)Instructions burned: 14 (million)
% 2.68/1.37 % (3554573)------------------------------
% 2.68/1.37 % (3554573)------------------------------
% 2.68/1.37 % (3554562)Success in time 0.297 s
% 2.68/1.37 % Vampire exiting
%------------------------------------------------------------------------------