%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET175+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 12:40:24 PM UTC 2026
% Result : Theorem 2.09s 0.89s
% Output : Refutation 2.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 61 ( 13 unt; 5 def)
% Number of atoms : 157 ( 12 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 159 ( 63 ~; 65 |; 20 &)
% ( 10 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 66 ( 0 sgn 62 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X0)
| member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(f2,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X0)
& member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(f6,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f9,conjecture,
! [X0,X1] : union(X0,intersection(X0,X1)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_absorbtion_for_union) ).
fof(f10,negated_conjecture,
~ ! [X0,X1] : union(X0,intersection(X0,X1)) = X0,
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f12,plain,
? [X0,X1] : union(X0,intersection(X0,X1)) != X0,
inference(ennf_transformation,[],[f10]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X0)
& ~ member(X2,X1) ) )
& ( member(X2,X0)
| member(X2,X1)
| ~ member(X2,union(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X0)
& ~ member(X2,X1) ) )
& ( member(X2,X0)
| member(X2,X1)
| ~ member(X2,union(X0,X1)) ) ),
inference(flattening,[],[f13]) ).
fof(f15,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,[],[f2]) ).
fof(f16,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,[],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f18,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f17]) ).
fof(f19,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,[],[f11]) ).
fof(f20,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,[],[f19]) ).
fof(f21,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))],[f20]) ).
fof(f25,plain,
sK2 != union(sK2,intersection(sK2,sK3)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f12]) ).
fof(f26,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f28,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f30,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f34,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f38,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f21]) ).
fof(f39,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f45,plain,
sK2 != union(sK2,intersection(sK2,sK3)),
inference(cnf_transformation,[],[f25]) ).
fof(f50,definition,
! [X0,X1] :
( sQ4_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ4_eqProxy])],[equality_proxy_definition]) ).
fof(f51,plain,
! [X0,X1] :
( sQ4_eqProxy(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(equality_proxy_replacement,[],[f34,f50]) ).
fof(f56,plain,
~ sQ4_eqProxy(sK2,union(sK2,intersection(sK2,sK3))),
inference(equality_proxy_replacement,[],[f45,f50]) ).
fof(f64,plain,
( ~ subset(sK2,union(sK2,intersection(sK2,sK3)))
| ~ subset(union(sK2,intersection(sK2,sK3)),sK2) ),
inference(resolution,[],[f51,f56]) ).
fof(f67,definition,
( spl5_1
<=> subset(sK2,union(sK2,intersection(sK2,sK3))) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f68,plain,
( ~ subset(sK2,union(sK2,intersection(sK2,sK3)))
| spl5_1 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f70,definition,
( spl5_2
<=> subset(union(sK2,intersection(sK2,sK3)),sK2) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f71,plain,
( ~ subset(union(sK2,intersection(sK2,sK3)),sK2)
| spl5_2 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f73,plain,
( ~ spl5_2
| ~ spl5_1 ),
inference(avatar_split_clause,[],[f64,f67,f70]) ).
fof(f76,plain,
( ~ member(sK0(sK2,union(sK2,intersection(sK2,sK3))),union(sK2,intersection(sK2,sK3)))
| spl5_1 ),
inference(resolution,[],[f68,f39]) ).
fof(f77,plain,
( member(sK0(sK2,union(sK2,intersection(sK2,sK3))),sK2)
| spl5_1 ),
inference(resolution,[],[f68,f38]) ).
fof(f78,plain,
( ~ member(sK0(sK2,union(sK2,intersection(sK2,sK3))),sK2)
| spl5_1 ),
inference(resolution,[],[f76,f28]) ).
fof(f80,plain,
( $false
| spl5_1 ),
inference(resolution,[],[f78,f77]) ).
fof(f81,plain,
spl5_1,
inference(avatar_contradiction_clause,[],[f80]) ).
fof(f82,plain,
( ~ member(sK0(union(sK2,intersection(sK2,sK3)),sK2),sK2)
| spl5_2 ),
inference(resolution,[],[f71,f39]) ).
fof(f83,plain,
( member(sK0(union(sK2,intersection(sK2,sK3)),sK2),union(sK2,intersection(sK2,sK3)))
| spl5_2 ),
inference(resolution,[],[f71,f38]) ).
fof(f84,plain,
( member(sK0(union(sK2,intersection(sK2,sK3)),sK2),intersection(sK2,sK3))
| member(sK0(union(sK2,intersection(sK2,sK3)),sK2),sK2)
| spl5_2 ),
inference(resolution,[],[f83,f26]) ).
fof(f86,definition,
( spl5_3
<=> member(sK0(union(sK2,intersection(sK2,sK3)),sK2),sK2) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
fof(f87,plain,
( member(sK0(union(sK2,intersection(sK2,sK3)),sK2),sK2)
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f89,definition,
( spl5_4
<=> member(sK0(union(sK2,intersection(sK2,sK3)),sK2),intersection(sK2,sK3)) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
fof(f90,plain,
( member(sK0(union(sK2,intersection(sK2,sK3)),sK2),intersection(sK2,sK3))
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f91,plain,
( spl5_3
| spl5_4
| spl5_2 ),
inference(avatar_split_clause,[],[f84,f70,f89,f86]) ).
fof(f92,plain,
( member(sK0(union(sK2,intersection(sK2,sK3)),sK2),sK2)
| ~ spl5_4 ),
inference(resolution,[],[f90,f30]) ).
fof(f94,plain,
( spl5_3
| ~ spl5_4 ),
inference(avatar_split_clause,[],[f92,f89,f86]) ).
fof(f95,plain,
( $false
| spl5_2
| ~ spl5_3 ),
inference(resolution,[],[f87,f82]) ).
fof(f96,plain,
( spl5_2
| ~ spl5_3 ),
inference(avatar_contradiction_clause,[],[f95]) ).
cnf(s2,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(sat_conversion,[],[f73]) ).
cnf(s3,plain,
spl5_1,
inference(sat_conversion,[],[f81]) ).
cnf(s4,plain,
( spl5_2
| spl5_3
| spl5_4 ),
inference(sat_conversion,[],[f91]) ).
cnf(s5,plain,
( spl5_3
| ~ spl5_4 ),
inference(sat_conversion,[],[f94]) ).
cnf(s6,plain,
( spl5_2
| ~ spl5_3 ),
inference(sat_conversion,[],[f96]) ).
cnf(s7,plain,
~ spl5_2,
inference(rat,[],[s2,s3]) ).
cnf(s8,plain,
~ spl5_3,
inference(rat,[],[s6,s7]) ).
cnf(s9,plain,
~ spl5_4,
inference(rat,[],[s5,s8]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s4,s7,s9,s8]) ).
fof(f97,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET175+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/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 01:00:34 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.32 Running first-order theorem proving
% 0.04/0.32 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
% 2.09/0.89 % (2916446)Detected formulas, will run a generic FOF schedule.
% 2.09/0.89 % (2916456)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2820138643:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.09/0.89 % (2916454)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1681294260:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.09/0.89 % (2916451)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=1088749794:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.09/0.89 % (2916453)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=3819089693:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.09/0.89 % (2916455)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2402908389:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.09/0.89 % (2916457)dis-21_1_sil=8000:lcm=predicate:random_seed=279130905: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)
% 2.09/0.89 % (2916452)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=1096921166:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.09/0.89 % (2916454)Refutation not found, incomplete strategy
% 2.09/0.89 % (2916454)------------------------------
% 2.09/0.89 % (2916454)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.09/0.89 % (2916454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.09/0.89 % (2916454)CaDiCaL version: 2.1.3
% 2.09/0.89 % (2916454)Termination reason: Refutation not found, incomplete strategy
% 2.09/0.89 % (2916454)Time elapsed: 0.001 s
% 2.09/0.89 % (2916454)Peak memory usage: 88 MB
% 2.09/0.89 % (2916457)First to succeed.
% 2.09/0.89 % (2916457)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2916446"
% 2.09/0.89 % (2916455)Also succeeded, but the first one will report.
% 2.09/0.89 % (2916456)Instruction limit reached!
% 2.09/0.89 % (2916456)------------------------------
% 2.09/0.89 % (2916456)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.09/0.89 % (2916456)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.09/0.89 % (2916456)CaDiCaL version: 2.1.3
% 2.09/0.89 % (2916456)Termination reason: Instruction limit
% 2.09/0.89 % (2916456)Termination phase: Saturation
% 2.09/0.89 % (2916456)Time elapsed: 0.047 s
% 2.09/0.89 % (2916456)Peak memory usage: 89 MB
% 2.09/0.89 % (2916456)Instructions burned: 141 (million)
% 2.09/0.89 % (2916465)lrs+10_1_sil=8000:sp=occurrence:random_seed=2516075185:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.09/0.89 % (2916454)------------------------------
% 2.09/0.89 % (2916454)------------------------------
% 2.09/0.89 % (2916457)Refutation found. Thanks to Tanya!
% 2.09/0.89 % SZS status Theorem for theBenchmark
% 2.09/0.89 % SZS output start Proof for theBenchmark
% See solution above
% 2.09/0.89 % (2916457)------------------------------
% 2.09/0.89 % (2916457)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.09/0.89 % (2916457)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.09/0.89 % (2916457)CaDiCaL version: 2.1.3
% 2.09/0.89 % (2916457)Termination reason: Refutation
% 2.09/0.89 % (2916457)Time elapsed: 0.002 s
% 2.09/0.89 % (2916457)Peak memory usage: 89 MB
% 2.09/0.89 % (2916457)Instructions burned: 3 (million)
% 2.09/0.89 % (2916457)------------------------------
% 2.09/0.89 % (2916457)------------------------------
% 2.09/0.89 % (2916446)Success in time 0.273 s
% 2.09/0.89 % Vampire exiting
%------------------------------------------------------------------------------