%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET578+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 12:41:11 PM UTC 2026
% Result : Theorem 2.75s 1.28s
% Output : Refutation 3.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 77 ( 8 unt; 7 def)
% Number of atoms : 213 ( 14 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 217 ( 81 ~; 90 |; 29 &)
% ( 14 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 7 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 75 ( 0 sgn 64 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X0)
& member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
fof(f2,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f7,conjecture,
! [X0,X1,X2] :
( ! [X3] :
( member(X3,X0)
<=> ( member(X3,X1)
& member(X3,X2) ) )
=> X0 = intersection(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th19) ).
fof(f8,negated_conjecture,
~ ! [X0,X1,X2] :
( ! [X3] :
( member(X3,X0)
<=> ( member(X3,X1)
& member(X3,X2) ) )
=> X0 = intersection(X1,X2) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f10,plain,
? [X0,X1,X2] :
( intersection(X1,X2) != X0
& ! [X3] :
( member(X3,X0)
<=> ( member(X3,X1)
& member(X3,X2) ) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f11,plain,
! [X0,X1,X2] :
( ( member(X2,intersection(X0,X1))
| ~ member(X2,X0)
| ~ member(X2,X1) )
& ( ( member(X2,X0)
& member(X2,X1) )
| ~ member(X2,intersection(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f12,plain,
! [X0,X1,X2] :
( ( member(X2,intersection(X0,X1))
| ~ member(X2,X0)
| ~ member(X2,X1) )
& ( ( member(X2,X0)
& member(X2,X1) )
| ~ member(X2,intersection(X0,X1)) ) ),
inference(flattening,[],[f11]) ).
fof(f13,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f14,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f16,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f16]) ).
fof(f21,plain,
? [X0,X1,X2] :
( intersection(X1,X2) != X0
& ! [X3] :
( ( member(X3,X0)
| ~ member(X3,X1)
| ~ member(X3,X2) )
& ( ( member(X3,X1)
& member(X3,X2) )
| ~ member(X3,X0) ) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f22,plain,
? [X0,X1,X2] :
( intersection(X1,X2) != X0
& ! [X3] :
( ( member(X3,X0)
| ~ member(X3,X1)
| ~ member(X3,X2) )
& ( ( member(X3,X1)
& member(X3,X2) )
| ~ member(X3,X0) ) ) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
( sK2 != intersection(sK3,sK4)
& ! [X3] :
( ( member(X3,sK2)
| ~ member(X3,sK3)
| ~ member(X3,sK4) )
& ( ( member(X3,sK3)
& member(X3,sK4) )
| ~ member(X3,sK2) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f22]) ).
fof(f24,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f25,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f26,plain,
! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
| ~ member(X2,X0)
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f29,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f32,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f33,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f39,plain,
! [X3] :
( member(X3,sK4)
| ~ member(X3,sK2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f40,plain,
! [X3] :
( member(X3,sK3)
| ~ member(X3,sK2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f41,plain,
! [X3] :
( ~ member(X3,sK4)
| ~ member(X3,sK3)
| member(X3,sK2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f42,plain,
sK2 != intersection(sK3,sK4),
inference(cnf_transformation,[],[f23]) ).
fof(f47,definition,
! [X0,X1] :
( sQ5_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ5_eqProxy])],[equality_proxy_definition]) ).
fof(f48,plain,
! [X0,X1] :
( sQ5_eqProxy(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(equality_proxy_replacement,[],[f29,f47]) ).
fof(f52,plain,
~ sQ5_eqProxy(sK2,intersection(sK3,sK4)),
inference(equality_proxy_replacement,[],[f42,f47]) ).
fof(f61,plain,
( ~ subset(sK2,intersection(sK3,sK4))
| ~ subset(intersection(sK3,sK4),sK2) ),
inference(resolution,[],[f48,f52]) ).
fof(f64,definition,
( spl6_1
<=> subset(sK2,intersection(sK3,sK4)) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
fof(f65,plain,
( ~ subset(sK2,intersection(sK3,sK4))
| spl6_1 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f67,definition,
( spl6_2
<=> subset(intersection(sK3,sK4),sK2) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
fof(f68,plain,
( ~ subset(intersection(sK3,sK4),sK2)
| spl6_2 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f70,plain,
( ~ spl6_2
| ~ spl6_1 ),
inference(avatar_split_clause,[],[f61,f64,f67]) ).
fof(f73,plain,
( ~ member(sK0(sK2,intersection(sK3,sK4)),intersection(sK3,sK4))
| spl6_1 ),
inference(resolution,[],[f65,f33]) ).
fof(f74,plain,
( member(sK0(sK2,intersection(sK3,sK4)),sK2)
| spl6_1 ),
inference(resolution,[],[f65,f32]) ).
fof(f75,plain,
( ~ member(sK0(sK2,intersection(sK3,sK4)),sK3)
| ~ member(sK0(sK2,intersection(sK3,sK4)),sK4)
| spl6_1 ),
inference(resolution,[],[f73,f26]) ).
fof(f77,definition,
( spl6_3
<=> member(sK0(sK2,intersection(sK3,sK4)),sK4) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
fof(f78,plain,
( ~ member(sK0(sK2,intersection(sK3,sK4)),sK4)
| spl6_3 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f80,definition,
( spl6_4
<=> member(sK0(sK2,intersection(sK3,sK4)),sK3) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
fof(f81,plain,
( ~ member(sK0(sK2,intersection(sK3,sK4)),sK3)
| spl6_4 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f82,plain,
( ~ spl6_3
| ~ spl6_4
| spl6_1 ),
inference(avatar_split_clause,[],[f75,f64,f80,f77]) ).
fof(f83,plain,
( ~ member(sK0(sK2,intersection(sK3,sK4)),sK2)
| spl6_3 ),
inference(resolution,[],[f78,f39]) ).
fof(f84,plain,
( $false
| spl6_1
| spl6_3 ),
inference(resolution,[],[f83,f74]) ).
fof(f85,plain,
( spl6_1
| spl6_3 ),
inference(avatar_contradiction_clause,[],[f84]) ).
fof(f86,plain,
( ~ member(sK0(sK2,intersection(sK3,sK4)),sK2)
| spl6_4 ),
inference(resolution,[],[f81,f40]) ).
fof(f87,plain,
( $false
| spl6_1
| spl6_4 ),
inference(resolution,[],[f86,f74]) ).
fof(f88,plain,
( spl6_1
| spl6_4 ),
inference(avatar_contradiction_clause,[],[f87]) ).
fof(f89,plain,
( ~ member(sK0(intersection(sK3,sK4),sK2),sK2)
| spl6_2 ),
inference(resolution,[],[f68,f33]) ).
fof(f90,plain,
( member(sK0(intersection(sK3,sK4),sK2),intersection(sK3,sK4))
| spl6_2 ),
inference(resolution,[],[f68,f32]) ).
fof(f91,plain,
( member(sK0(intersection(sK3,sK4),sK2),sK3)
| spl6_2 ),
inference(resolution,[],[f90,f25]) ).
fof(f92,plain,
( member(sK0(intersection(sK3,sK4),sK2),sK4)
| spl6_2 ),
inference(resolution,[],[f90,f24]) ).
fof(f93,plain,
( ~ member(sK0(intersection(sK3,sK4),sK2),sK3)
| member(sK0(intersection(sK3,sK4),sK2),sK2)
| spl6_2 ),
inference(resolution,[],[f92,f41]) ).
fof(f95,definition,
( spl6_5
<=> member(sK0(intersection(sK3,sK4),sK2),sK2) ),
introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition]) ).
fof(f96,plain,
( member(sK0(intersection(sK3,sK4),sK2),sK2)
| ~ spl6_5 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f98,definition,
( spl6_6
<=> member(sK0(intersection(sK3,sK4),sK2),sK3) ),
introduced(definition,[new_symbols(definition,[spl6_6])],[avatar_definition]) ).
fof(f99,plain,
( ~ member(sK0(intersection(sK3,sK4),sK2),sK3)
| spl6_6 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f100,plain,
( spl6_5
| ~ spl6_6
| spl6_2 ),
inference(avatar_split_clause,[],[f93,f67,f98,f95]) ).
fof(f101,plain,
( $false
| spl6_2
| spl6_6 ),
inference(resolution,[],[f99,f91]) ).
fof(f103,plain,
( spl6_2
| spl6_6 ),
inference(avatar_contradiction_clause,[],[f101]) ).
fof(f104,plain,
( $false
| spl6_2
| ~ spl6_5 ),
inference(resolution,[],[f96,f89]) ).
fof(f105,plain,
( spl6_2
| ~ spl6_5 ),
inference(avatar_contradiction_clause,[],[f104]) ).
cnf(s2,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(sat_conversion,[],[f70]) ).
cnf(s3,plain,
( spl6_1
| ~ spl6_3
| ~ spl6_4 ),
inference(sat_conversion,[],[f82]) ).
cnf(s4,plain,
( spl6_1
| spl6_3 ),
inference(sat_conversion,[],[f85]) ).
cnf(s5,plain,
( spl6_1
| spl6_4 ),
inference(sat_conversion,[],[f88]) ).
cnf(s6,plain,
( spl6_2
| spl6_5
| ~ spl6_6 ),
inference(sat_conversion,[],[f100]) ).
cnf(s7,plain,
( spl6_2
| spl6_6 ),
inference(sat_conversion,[],[f103]) ).
cnf(s8,plain,
( spl6_2
| ~ spl6_5 ),
inference(sat_conversion,[],[f105]) ).
cnf(s9,plain,
spl6_1,
inference(rat,[],[s3,s4,s5]) ).
cnf(s10,plain,
~ spl6_2,
inference(rat,[],[s2,s9]) ).
cnf(s11,plain,
~ spl6_5,
inference(rat,[],[s8,s10]) ).
cnf(s12,plain,
spl6_6,
inference(rat,[],[s7,s10]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s6,s11,s12,s10]) ).
fof(f106,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET578+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n010.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 02:12:47 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.42 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
% 2.75/1.28 % (1499490)Detected formulas, will run a generic FOF schedule.
% 2.75/1.28 % (1499497)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=1898582789:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.75/1.28 % (1499498)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1138934597:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.75/1.28 % (1499496)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=1927262602:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.75/1.28 % (1499498)Refutation not found, incomplete strategy
% 2.75/1.28 % (1499498)------------------------------
% 2.75/1.28 % (1499498)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.75/1.28 % (1499498)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/1.28 % (1499498)CaDiCaL version: 2.1.3
% 2.75/1.28 % (1499498)Termination reason: Refutation not found, incomplete strategy
% 2.75/1.28 % (1499498)Time elapsed: 0.002 s
% 2.75/1.28 % (1499498)Peak memory usage: 88 MB
% 2.75/1.28 % (1499498)Instructions burned: 1 (million)
% 2.75/1.28 % (1499495)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=510167469:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.75/1.28 % (1499500)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2373367721:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.75/1.28 % (1499499)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2788853499:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.75/1.28 % (1499501)dis-21_1_sil=8000:lcm=predicate:random_seed=3634696609: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)
% 2.75/1.28 % (1499501)First to succeed.
% 2.75/1.28 % (1499501)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1499490"
% 2.75/1.28 % (1499499)Also succeeded, but the first one will report.
% 2.75/1.28 % (1499500)Instruction limit reached!
% 2.75/1.28 % (1499500)------------------------------
% 2.75/1.28 % (1499500)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.75/1.28 % (1499500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/1.28 % (1499500)CaDiCaL version: 2.1.3
% 2.75/1.28 % (1499500)Termination reason: Instruction limit
% 2.75/1.28 % (1499500)Termination phase: Saturation
% 2.75/1.28 % (1499500)Time elapsed: 0.093 s
% 2.75/1.28 % (1499500)Peak memory usage: 89 MB
% 2.75/1.28 % (1499500)Instructions burned: 140 (million)
% 2.75/1.28 % (1499498)------------------------------
% 2.75/1.28 % (1499498)------------------------------
% 2.75/1.28 % (1499509)lrs+10_1_sil=8000:sp=occurrence:random_seed=1214664746:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.75/1.28 % (1499501)Refutation found. Thanks to Tanya!
% 2.75/1.28 % SZS status Theorem for theBenchmark
% 2.75/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.42/1.37 % (1499501)------------------------------
% 3.42/1.37 % (1499501)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.42/1.37 % (1499501)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.42/1.37 % (1499501)CaDiCaL version: 2.1.3
% 3.42/1.37 % (1499501)Termination reason: Refutation
% 3.42/1.37 % (1499501)Time elapsed: 0.004 s
% 3.42/1.37 % (1499501)Peak memory usage: 89 MB
% 3.42/1.37 % (1499501)Instructions burned: 3 (million)
% 3.42/1.37 % (1499501)------------------------------
% 3.42/1.37 % (1499501)------------------------------
% 3.42/1.37 % (1499490)Success in time 0.419 s
% 3.42/1.37 % Vampire exiting
%------------------------------------------------------------------------------