%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET579+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 : n007.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 12:41:12 PM UTC 2026
% Result : Theorem 1.10s 1.14s
% Output : Refutation 2.64s
% 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 : 223 ( 87 ~; 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,difference(X0,X1))
<=> ( member(X2,X0)
& ~ member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
fof(f2,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(f3,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f5,conjecture,
! [X0,X1,X2] :
( ! [X3] :
( member(X3,X0)
<=> ( member(X3,X1)
& ~ member(X3,X2) ) )
=> X0 = difference(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th20) ).
fof(f6,negated_conjecture,
~ ! [X0,X1,X2] :
( ! [X3] :
( member(X3,X0)
<=> ( member(X3,X1)
& ~ member(X3,X2) ) )
=> X0 = difference(X1,X2) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f7,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f8,plain,
? [X0,X1,X2] :
( difference(X1,X2) != X0
& ! [X3] :
( member(X3,X0)
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f9,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| ~ member(X2,X0)
| member(X2,X1) )
& ( ( member(X2,X0)
& ~ member(X2,X1) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f10,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| ~ member(X2,X0)
| member(X2,X1) )
& ( ( member(X2,X0)
& ~ member(X2,X1) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(flattening,[],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f12,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f11]) ).
fof(f13,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,[],[f7]) ).
fof(f14,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,[],[f13]) ).
fof(f15,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))],[f14]) ).
fof(f16,plain,
? [X0,X1,X2] :
( difference(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,[],[f8]) ).
fof(f17,plain,
? [X0,X1,X2] :
( difference(X1,X2) != X0
& ! [X3] :
( ( member(X3,X0)
| ~ member(X3,X1)
| member(X3,X2) )
& ( ( member(X3,X1)
& ~ member(X3,X2) )
| ~ member(X3,X0) ) ) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
( sK1 != difference(sK2,sK3)
& ! [X3] :
( ( member(X3,sK1)
| ~ member(X3,sK2)
| member(X3,sK3) )
& ( ( member(X3,sK2)
& ~ member(X3,sK3) )
| ~ member(X3,sK1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f17]) ).
fof(f19,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f10]) ).
fof(f20,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f10]) ).
fof(f21,plain,
! [X2,X0,X1] :
( member(X2,difference(X0,X1))
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f10]) ).
fof(f24,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f26,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f27,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f29,plain,
! [X3] :
( ~ member(X3,sK3)
| ~ member(X3,sK1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f30,plain,
! [X3] :
( member(X3,sK2)
| ~ member(X3,sK1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f31,plain,
! [X3] :
( member(X3,sK3)
| ~ member(X3,sK2)
| member(X3,sK1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f32,plain,
sK1 != difference(sK2,sK3),
inference(cnf_transformation,[],[f18]) ).
fof(f35,definition,
! [X0,X1] :
( sQ4_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ4_eqProxy])],[equality_proxy_definition]) ).
fof(f36,plain,
! [X0,X1] :
( sQ4_eqProxy(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(equality_proxy_replacement,[],[f24,f35]) ).
fof(f37,plain,
~ sQ4_eqProxy(sK1,difference(sK2,sK3)),
inference(equality_proxy_replacement,[],[f32,f35]) ).
fof(f46,plain,
( ~ subset(sK1,difference(sK2,sK3))
| ~ subset(difference(sK2,sK3),sK1) ),
inference(resolution,[],[f36,f37]) ).
fof(f49,definition,
( spl5_1
<=> subset(sK1,difference(sK2,sK3)) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f50,plain,
( ~ subset(sK1,difference(sK2,sK3))
| spl5_1 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f52,definition,
( spl5_2
<=> subset(difference(sK2,sK3),sK1) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f53,plain,
( ~ subset(difference(sK2,sK3),sK1)
| spl5_2 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f55,plain,
( ~ spl5_2
| ~ spl5_1 ),
inference(avatar_split_clause,[],[f46,f49,f52]) ).
fof(f56,plain,
( ~ member(sK0(sK1,difference(sK2,sK3)),difference(sK2,sK3))
| spl5_1 ),
inference(resolution,[],[f50,f27]) ).
fof(f57,plain,
( member(sK0(sK1,difference(sK2,sK3)),sK1)
| spl5_1 ),
inference(resolution,[],[f50,f26]) ).
fof(f60,plain,
( ~ member(sK0(sK1,difference(sK2,sK3)),sK2)
| member(sK0(sK1,difference(sK2,sK3)),sK3)
| spl5_1 ),
inference(resolution,[],[f56,f21]) ).
fof(f62,definition,
( spl5_3
<=> member(sK0(sK1,difference(sK2,sK3)),sK3) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
fof(f63,plain,
( member(sK0(sK1,difference(sK2,sK3)),sK3)
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f65,definition,
( spl5_4
<=> member(sK0(sK1,difference(sK2,sK3)),sK2) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
fof(f66,plain,
( ~ member(sK0(sK1,difference(sK2,sK3)),sK2)
| spl5_4 ),
inference(avatar_component_clause,[],[f65]) ).
fof(f67,plain,
( spl5_3
| ~ spl5_4
| spl5_1 ),
inference(avatar_split_clause,[],[f60,f49,f65,f62]) ).
fof(f68,plain,
( ~ member(sK0(sK1,difference(sK2,sK3)),sK1)
| spl5_4 ),
inference(resolution,[],[f66,f30]) ).
fof(f69,plain,
( $false
| spl5_1
| spl5_4 ),
inference(resolution,[],[f68,f57]) ).
fof(f70,plain,
( spl5_1
| spl5_4 ),
inference(avatar_contradiction_clause,[],[f69]) ).
fof(f71,plain,
( ~ member(sK0(sK1,difference(sK2,sK3)),sK1)
| ~ spl5_3 ),
inference(resolution,[],[f63,f29]) ).
fof(f72,plain,
( $false
| spl5_1
| ~ spl5_3 ),
inference(resolution,[],[f71,f57]) ).
fof(f73,plain,
( spl5_1
| ~ spl5_3 ),
inference(avatar_contradiction_clause,[],[f72]) ).
fof(f74,plain,
( ~ member(sK0(difference(sK2,sK3),sK1),sK1)
| spl5_2 ),
inference(resolution,[],[f53,f27]) ).
fof(f75,plain,
( member(sK0(difference(sK2,sK3),sK1),difference(sK2,sK3))
| spl5_2 ),
inference(resolution,[],[f53,f26]) ).
fof(f76,plain,
( member(sK0(difference(sK2,sK3),sK1),sK2)
| spl5_2 ),
inference(resolution,[],[f75,f20]) ).
fof(f77,plain,
( ~ member(sK0(difference(sK2,sK3),sK1),sK3)
| spl5_2 ),
inference(resolution,[],[f75,f19]) ).
fof(f78,plain,
( ~ member(sK0(difference(sK2,sK3),sK1),sK2)
| member(sK0(difference(sK2,sK3),sK1),sK1)
| spl5_2 ),
inference(resolution,[],[f77,f31]) ).
fof(f80,definition,
( spl5_5
<=> member(sK0(difference(sK2,sK3),sK1),sK1) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
fof(f81,plain,
( member(sK0(difference(sK2,sK3),sK1),sK1)
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f83,definition,
( spl5_6
<=> member(sK0(difference(sK2,sK3),sK1),sK2) ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
fof(f84,plain,
( ~ member(sK0(difference(sK2,sK3),sK1),sK2)
| spl5_6 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f85,plain,
( spl5_5
| ~ spl5_6
| spl5_2 ),
inference(avatar_split_clause,[],[f78,f52,f83,f80]) ).
fof(f86,plain,
( $false
| spl5_2
| spl5_6 ),
inference(resolution,[],[f84,f76]) ).
fof(f88,plain,
( spl5_2
| spl5_6 ),
inference(avatar_contradiction_clause,[],[f86]) ).
fof(f89,plain,
( $false
| spl5_2
| ~ spl5_5 ),
inference(resolution,[],[f81,f74]) ).
fof(f90,plain,
( spl5_2
| ~ spl5_5 ),
inference(avatar_contradiction_clause,[],[f89]) ).
cnf(s2,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(sat_conversion,[],[f55]) ).
cnf(s3,plain,
( spl5_1
| spl5_3
| ~ spl5_4 ),
inference(sat_conversion,[],[f67]) ).
cnf(s4,plain,
( spl5_1
| spl5_4 ),
inference(sat_conversion,[],[f70]) ).
cnf(s5,plain,
( spl5_1
| ~ spl5_3 ),
inference(sat_conversion,[],[f73]) ).
cnf(s6,plain,
( spl5_2
| spl5_5
| ~ spl5_6 ),
inference(sat_conversion,[],[f85]) ).
cnf(s7,plain,
( spl5_2
| spl5_6 ),
inference(sat_conversion,[],[f88]) ).
cnf(s8,plain,
( spl5_2
| ~ spl5_5 ),
inference(sat_conversion,[],[f90]) ).
cnf(s9,plain,
spl5_1,
inference(rat,[],[s3,s4,s5]) ).
cnf(s10,plain,
~ spl5_2,
inference(rat,[],[s2,s9]) ).
cnf(s11,plain,
~ spl5_5,
inference(rat,[],[s8,s10]) ).
cnf(s12,plain,
spl5_6,
inference(rat,[],[s7,s10]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s6,s11,s12,s10]) ).
fof(f91,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET579+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n007.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 02:10:40 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
% 1.10/1.14 % (1962423)Detected formulas, will run a generic FOF schedule.
% 1.10/1.14 % (1962481)dis-21_1_sil=8000:lcm=predicate:random_seed=2626296156: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)
% 1.10/1.14 % (1962481)First to succeed.
% 1.10/1.14 % (1962481)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1962423"
% 1.10/1.14 % (1962478)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3969916345:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.10/1.14 % (1962475)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=3694552576:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.10/1.14 % (1962476)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=1450105846:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.10/1.14 % (1962479)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3779212122:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.10/1.14 % (1962477)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=3668339164:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.10/1.14 % (1962480)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=850410304:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.10/1.14 % (1962478)Refutation not found, incomplete strategy
% 1.10/1.14 % (1962478)------------------------------
% 1.10/1.14 % (1962478)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.10/1.14 % (1962478)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.10/1.14 % (1962478)CaDiCaL version: 2.1.3
% 1.10/1.14 % (1962478)Termination reason: Refutation not found, incomplete strategy
% 1.10/1.14 % (1962478)Time elapsed: 0.002 s
% 1.10/1.14 % (1962478)Peak memory usage: 88 MB
% 1.10/1.14 % (1962478)Instructions burned: 1 (million)
% 1.10/1.14 % (1962479)Also succeeded, but the first one will report.
% 1.10/1.14 % (1962480)Instruction limit reached!
% 1.10/1.14 % (1962480)------------------------------
% 1.10/1.14 % (1962480)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.10/1.14 % (1962480)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.10/1.14 % (1962480)CaDiCaL version: 2.1.3
% 1.10/1.14 % (1962480)Termination reason: Instruction limit
% 1.10/1.14 % (1962480)Termination phase: Saturation
% 1.10/1.14 % (1962480)Time elapsed: 0.096 s
% 1.10/1.14 % (1962480)Peak memory usage: 89 MB
% 1.10/1.14 % (1962480)Instructions burned: 140 (million)
% 1.10/1.14 % (1962481)Refutation found. Thanks to Tanya!
% 1.10/1.14 % SZS status Theorem for theBenchmark
% 1.10/1.14 % SZS output start Proof for theBenchmark
% See solution above
% 2.64/1.33 % (1962481)------------------------------
% 2.64/1.33 % (1962481)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/1.33 % (1962481)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/1.33 % (1962481)CaDiCaL version: 2.1.3
% 2.64/1.33 % (1962481)Termination reason: Refutation
% 2.64/1.33 % (1962481)Time elapsed: 0.002 s
% 2.64/1.33 % (1962481)Peak memory usage: 89 MB
% 2.64/1.33 % (1962481)Instructions burned: 3 (million)
% 2.64/1.33 % (1962481)------------------------------
% 2.64/1.33 % (1962481)------------------------------
% 2.64/1.33 % (1962423)Success in time 0.281 s
% 2.64/1.33 % Vampire exiting
%------------------------------------------------------------------------------