%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET624+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 : n004.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 12:41:26 PM UTC 2026
% Result : Theorem 3.35s 1.24s
% Output : Refutation 3.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 78 ( 7 unt; 5 def)
% Number of atoms : 213 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 236 ( 101 ~; 108 |; 17 &)
% ( 9 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 59 ( 0 sgn 47 !; 12 ?)
% 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] :
( intersect(X0,X1)
<=> ? [X2] :
( member(X2,X0)
& member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersect_defn) ).
fof(f6,conjecture,
! [X0,X1,X2] :
( intersect(X0,union(X1,X2))
<=> ( intersect(X0,X1)
| intersect(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_intersect_with_union) ).
fof(f7,negated_conjecture,
~ ! [X0,X1,X2] :
( intersect(X0,union(X1,X2))
<=> ( intersect(X0,X1)
| intersect(X0,X2) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f9,plain,
? [X0,X1,X2] :
( intersect(X0,union(X1,X2))
<~> ( intersect(X0,X1)
| intersect(X0,X2) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f10,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(f11,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,[],[f10]) ).
fof(f12,plain,
! [X0,X1] :
( ( intersect(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| ~ member(X2,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& member(X2,X1) )
| ~ intersect(X0,X1) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f13,plain,
! [X0,X1] :
( ( intersect(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| ~ member(X2,X1) ) )
& ( ? [X3] :
( member(X3,X0)
& member(X3,X1) )
| ~ intersect(X0,X1) ) ),
inference(rectify,[],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ( intersect(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| ~ member(X2,X1) ) )
& ( ( member(sK0(X0,X1),X0)
& member(sK0(X0,X1),X1) )
| ~ intersect(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f13]) ).
fof(f18,plain,
? [X0,X1,X2] :
( ( ( ~ intersect(X0,X1)
& ~ intersect(X0,X2) )
| ~ intersect(X0,union(X1,X2)) )
& ( intersect(X0,X1)
| intersect(X0,X2)
| intersect(X0,union(X1,X2)) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f19,plain,
? [X0,X1,X2] :
( ( ( ~ intersect(X0,X1)
& ~ intersect(X0,X2) )
| ~ intersect(X0,union(X1,X2)) )
& ( intersect(X0,X1)
| intersect(X0,X2)
| intersect(X0,union(X1,X2)) ) ),
inference(flattening,[],[f18]) ).
fof(f20,plain,
( ( ( ~ intersect(sK2,sK3)
& ~ intersect(sK2,sK4) )
| ~ intersect(sK2,union(sK3,sK4)) )
& ( intersect(sK2,sK3)
| intersect(sK2,sK4)
| intersect(sK2,union(sK3,sK4)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f19]) ).
fof(f21,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) ),
inference(cnf_transformation,[],[f11]) ).
fof(f22,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f11]) ).
fof(f23,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f11]) ).
fof(f24,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f25,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f26,plain,
! [X2,X0,X1] :
( intersect(X0,X1)
| ~ member(X2,X0)
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f33,plain,
( intersect(sK2,sK3)
| intersect(sK2,sK4)
| intersect(sK2,union(sK3,sK4)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f34,plain,
( ~ intersect(sK2,sK4)
| ~ intersect(sK2,union(sK3,sK4)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f35,plain,
( ~ intersect(sK2,sK3)
| ~ intersect(sK2,union(sK3,sK4)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f45,definition,
( spl6_1
<=> intersect(sK2,union(sK3,sK4)) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
fof(f46,plain,
( intersect(sK2,union(sK3,sK4))
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f45]) ).
fof(f48,definition,
( spl6_2
<=> intersect(sK2,sK4) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
fof(f49,plain,
( intersect(sK2,sK4)
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f51,definition,
( spl6_3
<=> intersect(sK2,sK3) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
fof(f52,plain,
( intersect(sK2,sK3)
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f53,plain,
( spl6_1
| spl6_2
| spl6_3 ),
inference(avatar_split_clause,[],[f33,f51,f48,f45]) ).
fof(f54,plain,
( ~ intersect(sK2,union(sK3,sK4))
| spl6_1 ),
inference(avatar_component_clause,[],[f45]) ).
fof(f55,plain,
( ~ intersect(sK2,sK4)
| spl6_2 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f56,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(avatar_split_clause,[],[f34,f48,f45]) ).
fof(f57,plain,
( ~ intersect(sK2,sK3)
| spl6_3 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f58,plain,
( ~ spl6_1
| ~ spl6_3 ),
inference(avatar_split_clause,[],[f35,f51,f45]) ).
fof(f61,plain,
( member(sK0(sK2,sK4),sK4)
| ~ spl6_2 ),
inference(resolution,[],[f24,f49]) ).
fof(f63,plain,
( member(sK0(sK2,sK4),sK2)
| ~ spl6_2 ),
inference(resolution,[],[f25,f49]) ).
fof(f67,plain,
( ! [X0] :
( ~ member(X0,union(sK3,sK4))
| ~ member(X0,sK2) )
| spl6_1 ),
inference(resolution,[],[f26,f54]) ).
fof(f72,plain,
( ! [X0] :
( ~ member(X0,sK3)
| ~ member(X0,sK2) )
| spl6_1 ),
inference(resolution,[],[f67,f23]) ).
fof(f73,plain,
( ! [X0] :
( ~ member(X0,sK4)
| ~ member(X0,sK2) )
| spl6_1 ),
inference(resolution,[],[f67,f22]) ).
fof(f77,plain,
( ~ member(sK0(sK2,sK4),sK2)
| spl6_1
| ~ spl6_2 ),
inference(resolution,[],[f73,f61]) ).
fof(f79,plain,
( $false
| spl6_1
| ~ spl6_2 ),
inference(resolution,[],[f77,f63]) ).
fof(f80,plain,
( spl6_1
| ~ spl6_2 ),
inference(avatar_contradiction_clause,[],[f79]) ).
fof(f83,plain,
( member(sK0(sK2,sK3),sK2)
| ~ spl6_3 ),
inference(resolution,[],[f52,f25]) ).
fof(f84,plain,
( member(sK0(sK2,sK3),sK3)
| ~ spl6_3 ),
inference(resolution,[],[f52,f24]) ).
fof(f85,plain,
( ! [X0] :
( ~ member(X0,sK4)
| ~ member(X0,sK2) )
| spl6_2 ),
inference(resolution,[],[f55,f26]) ).
fof(f89,plain,
( ~ member(sK0(sK2,sK3),sK2)
| spl6_1
| ~ spl6_3 ),
inference(resolution,[],[f84,f72]) ).
fof(f91,plain,
( $false
| spl6_1
| ~ spl6_3 ),
inference(resolution,[],[f89,f83]) ).
fof(f92,plain,
( spl6_1
| ~ spl6_3 ),
inference(avatar_contradiction_clause,[],[f91]) ).
fof(f93,plain,
( ! [X0] :
( ~ member(X0,sK3)
| ~ member(X0,sK2) )
| spl6_3 ),
inference(resolution,[],[f57,f26]) ).
fof(f99,plain,
( member(sK0(sK2,union(sK3,sK4)),sK2)
| ~ spl6_1 ),
inference(resolution,[],[f46,f25]) ).
fof(f100,plain,
( member(sK0(sK2,union(sK3,sK4)),union(sK3,sK4))
| ~ spl6_1 ),
inference(resolution,[],[f46,f24]) ).
fof(f103,plain,
( member(sK0(sK2,union(sK3,sK4)),sK4)
| member(sK0(sK2,union(sK3,sK4)),sK3)
| ~ spl6_1 ),
inference(resolution,[],[f100,f21]) ).
fof(f105,definition,
( spl6_4
<=> member(sK0(sK2,union(sK3,sK4)),sK3) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
fof(f106,plain,
( member(sK0(sK2,union(sK3,sK4)),sK3)
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f108,definition,
( spl6_5
<=> member(sK0(sK2,union(sK3,sK4)),sK4) ),
introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition]) ).
fof(f109,plain,
( member(sK0(sK2,union(sK3,sK4)),sK4)
| ~ spl6_5 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f110,plain,
( spl6_4
| spl6_5
| ~ spl6_1 ),
inference(avatar_split_clause,[],[f103,f45,f108,f105]) ).
fof(f111,plain,
( ~ member(sK0(sK2,union(sK3,sK4)),sK2)
| spl6_2
| ~ spl6_5 ),
inference(resolution,[],[f109,f85]) ).
fof(f112,plain,
( $false
| ~ spl6_1
| spl6_2
| ~ spl6_5 ),
inference(resolution,[],[f111,f99]) ).
fof(f113,plain,
( ~ spl6_1
| spl6_2
| ~ spl6_5 ),
inference(avatar_contradiction_clause,[],[f112]) ).
fof(f114,plain,
( ~ member(sK0(sK2,union(sK3,sK4)),sK2)
| spl6_3
| ~ spl6_4 ),
inference(resolution,[],[f106,f93]) ).
fof(f115,plain,
( $false
| ~ spl6_1
| spl6_3
| ~ spl6_4 ),
inference(resolution,[],[f114,f99]) ).
fof(f116,plain,
( ~ spl6_1
| spl6_3
| ~ spl6_4 ),
inference(avatar_contradiction_clause,[],[f115]) ).
cnf(s1,plain,
( spl6_1
| spl6_2
| spl6_3 ),
inference(sat_conversion,[],[f53]) ).
cnf(s2,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(sat_conversion,[],[f56]) ).
cnf(s3,plain,
( ~ spl6_1
| ~ spl6_3 ),
inference(sat_conversion,[],[f58]) ).
cnf(s4,plain,
( spl6_1
| ~ spl6_2 ),
inference(sat_conversion,[],[f80]) ).
cnf(s5,plain,
( spl6_1
| ~ spl6_3 ),
inference(sat_conversion,[],[f92]) ).
cnf(s6,plain,
( ~ spl6_1
| spl6_4
| spl6_5 ),
inference(sat_conversion,[],[f110]) ).
cnf(s7,plain,
( ~ spl6_1
| spl6_2
| ~ spl6_5 ),
inference(sat_conversion,[],[f113]) ).
cnf(s8,plain,
( ~ spl6_1
| spl6_3
| ~ spl6_4 ),
inference(sat_conversion,[],[f116]) ).
cnf(s9,plain,
spl6_1,
inference(rat,[],[s1,s4,s5]) ).
cnf(s10,plain,
~ spl6_3,
inference(rat,[],[s3,s9]) ).
cnf(s11,plain,
~ spl6_2,
inference(rat,[],[s2,s9]) ).
cnf(s12,plain,
~ spl6_4,
inference(rat,[],[s8,s9,s10]) ).
cnf(s13,plain,
~ spl6_5,
inference(rat,[],[s7,s9,s11]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s6,s9,s13,s12]) ).
fof(f117,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET624+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n004.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 02:22:22 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 3.35/1.24 % (4090654)Detected formulas, will run a generic FOF schedule.
% 3.35/1.24 % (4090664)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1228562526:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.35/1.24 % (4090661)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=2535526685:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.35/1.24 % (4090662)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1278030814:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.35/1.24 % (4090663)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1124435856:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.35/1.24 % (4090659)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=774050854:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.35/1.24 % (4090665)dis-21_1_sil=8000:lcm=predicate:random_seed=158799627: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)
% 3.35/1.24 % (4090660)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=4071054152:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.35/1.24 % (4090662)Refutation not found, incomplete strategy
% 3.35/1.24 % (4090662)------------------------------
% 3.35/1.24 % (4090662)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.35/1.24 % (4090662)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/1.24 % (4090662)CaDiCaL version: 2.1.3
% 3.35/1.24 % (4090662)Termination reason: Refutation not found, incomplete strategy
% 3.35/1.24 % (4090662)Time elapsed: 0.001 s
% 3.35/1.24 % (4090662)Peak memory usage: 88 MB
% 3.35/1.24 % (4090665)First to succeed.
% 3.35/1.24 % (4090665)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4090654"
% 3.35/1.24 % (4090663)Also succeeded, but the first one will report.
% 3.35/1.24 % (4090664)Also succeeded, but the first one will report.
% 3.35/1.24 % (4090662)------------------------------
% 3.35/1.24 % (4090662)------------------------------
% 3.35/1.24 % (4090665)Refutation found. Thanks to Tanya!
% 3.35/1.24 % SZS status Theorem for theBenchmark
% 3.35/1.24 % SZS output start Proof for theBenchmark
% See solution above
% 3.35/1.24 % (4090665)------------------------------
% 3.35/1.24 % (4090665)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.35/1.24 % (4090665)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/1.24 % (4090665)CaDiCaL version: 2.1.3
% 3.35/1.24 % (4090665)Termination reason: Refutation
% 3.35/1.24 % (4090665)Time elapsed: 0.004 s
% 3.35/1.24 % (4090665)Peak memory usage: 89 MB
% 3.35/1.24 % (4090665)Instructions burned: 3 (million)
% 3.35/1.24 % (4090665)------------------------------
% 3.35/1.24 % (4090665)------------------------------
% 3.35/1.24 % (4090654)Success in time 0.418 s
% 3.35/1.24 % Vampire exiting
%------------------------------------------------------------------------------