%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% 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 12:44:13 PM UTC 2026
% Result : Theorem 0.17s 0.47s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 78 ( 7 unt; 5 def)
% Number of atoms : 209 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 228 ( 97 ~; 104 |; 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 : 61 ( 0 sgn 49 !; 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,X1)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f11]) ).
fof(f23,plain,
! [X2,X0,X1] :
( ~ member(X2,X0)
| member(X2,union(X0,X1)) ),
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] :
( ~ member(X2,X0)
| intersect(X0,X1)
| ~ 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(f37,definition,
( spl5_1
<=> intersect(sK2,union(sK3,sK4)) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f38,plain,
( ~ intersect(sK2,union(sK3,sK4))
| spl5_1 ),
inference(avatar_component_clause,[],[f37]) ).
fof(f39,plain,
( intersect(sK2,union(sK3,sK4))
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f37]) ).
fof(f41,definition,
( spl5_2
<=> intersect(sK2,sK4) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f42,plain,
( ~ intersect(sK2,sK4)
| spl5_2 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f43,plain,
( intersect(sK2,sK4)
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f45,definition,
( spl5_3
<=> intersect(sK2,sK3) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
fof(f46,plain,
( ~ intersect(sK2,sK3)
| spl5_3 ),
inference(avatar_component_clause,[],[f45]) ).
fof(f47,plain,
( intersect(sK2,sK3)
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f45]) ).
fof(f48,plain,
( spl5_1
| spl5_2
| spl5_3 ),
inference(avatar_split_clause,[],[f33,f45,f41,f37]) ).
fof(f49,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f34,f41,f37]) ).
fof(f50,plain,
( ~ spl5_1
| ~ spl5_3 ),
inference(avatar_split_clause,[],[f35,f45,f37]) ).
fof(f53,plain,
( member(sK0(sK2,sK4),sK4)
| ~ spl5_2 ),
inference(resolution,[],[f24,f43]) ).
fof(f56,plain,
( ! [X0] : member(sK0(sK2,sK4),union(X0,sK4))
| ~ spl5_2 ),
inference(resolution,[],[f53,f22]) ).
fof(f57,plain,
( member(sK0(sK2,sK4),sK2)
| ~ spl5_2 ),
inference(resolution,[],[f25,f43]) ).
fof(f62,plain,
( ! [X0] :
( ~ member(sK0(sK2,sK4),X0)
| intersect(sK2,X0) )
| ~ spl5_2 ),
inference(resolution,[],[f26,f57]) ).
fof(f347,plain,
( ! [X0] : intersect(sK2,union(X0,sK4))
| ~ spl5_2 ),
inference(resolution,[],[f62,f56]) ).
fof(f368,plain,
( $false
| spl5_1
| ~ spl5_2 ),
inference(resolution,[],[f347,f38]) ).
fof(f374,plain,
( spl5_1
| ~ spl5_2 ),
inference(avatar_contradiction_clause,[],[f368]) ).
fof(f375,plain,
( member(sK0(sK2,sK3),sK2)
| ~ spl5_3 ),
inference(resolution,[],[f47,f25]) ).
fof(f376,plain,
( member(sK0(sK2,sK3),sK3)
| ~ spl5_3 ),
inference(resolution,[],[f47,f24]) ).
fof(f382,plain,
( ! [X0] :
( ~ member(sK0(sK2,sK3),X0)
| intersect(sK2,X0) )
| ~ spl5_3 ),
inference(resolution,[],[f375,f26]) ).
fof(f387,plain,
( ! [X0] : member(sK0(sK2,sK3),union(sK3,X0))
| ~ spl5_3 ),
inference(resolution,[],[f376,f23]) ).
fof(f445,plain,
( ! [X0] : intersect(sK2,union(sK3,X0))
| ~ spl5_3 ),
inference(resolution,[],[f382,f387]) ).
fof(f487,plain,
( $false
| spl5_1
| ~ spl5_3 ),
inference(resolution,[],[f445,f38]) ).
fof(f493,plain,
( spl5_1
| ~ spl5_3 ),
inference(avatar_contradiction_clause,[],[f487]) ).
fof(f494,plain,
( member(sK0(sK2,union(sK3,sK4)),sK2)
| ~ spl5_1 ),
inference(resolution,[],[f39,f25]) ).
fof(f495,plain,
( member(sK0(sK2,union(sK3,sK4)),union(sK3,sK4))
| ~ spl5_1 ),
inference(resolution,[],[f39,f24]) ).
fof(f501,plain,
( ! [X0] :
( ~ member(sK0(sK2,union(sK3,sK4)),X0)
| intersect(sK2,X0) )
| ~ spl5_1 ),
inference(resolution,[],[f494,f26]) ).
fof(f504,plain,
( member(sK0(sK2,union(sK3,sK4)),sK4)
| member(sK0(sK2,union(sK3,sK4)),sK3)
| ~ spl5_1 ),
inference(resolution,[],[f495,f21]) ).
fof(f510,definition,
( spl5_4
<=> member(sK0(sK2,union(sK3,sK4)),sK3) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
fof(f512,plain,
( member(sK0(sK2,union(sK3,sK4)),sK3)
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f510]) ).
fof(f514,definition,
( spl5_5
<=> member(sK0(sK2,union(sK3,sK4)),sK4) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
fof(f516,plain,
( member(sK0(sK2,union(sK3,sK4)),sK4)
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f514]) ).
fof(f517,plain,
( spl5_4
| spl5_5
| ~ spl5_1 ),
inference(avatar_split_clause,[],[f504,f37,f514,f510]) ).
fof(f577,plain,
( intersect(sK2,sK4)
| ~ spl5_1
| ~ spl5_5 ),
inference(resolution,[],[f501,f516]) ).
fof(f578,plain,
( $false
| ~ spl5_1
| spl5_2
| ~ spl5_5 ),
inference(forward_subsumption_resolution,[],[f577,f42]) ).
fof(f579,plain,
( ~ spl5_1
| spl5_2
| ~ spl5_5 ),
inference(avatar_contradiction_clause,[],[f578]) ).
fof(f583,plain,
( intersect(sK2,sK3)
| ~ spl5_1
| ~ spl5_4 ),
inference(resolution,[],[f512,f501]) ).
fof(f588,plain,
( $false
| ~ spl5_1
| spl5_3
| ~ spl5_4 ),
inference(forward_subsumption_resolution,[],[f583,f46]) ).
fof(f589,plain,
( ~ spl5_1
| spl5_3
| ~ spl5_4 ),
inference(avatar_contradiction_clause,[],[f588]) ).
cnf(s1,plain,
( spl5_1
| spl5_2
| spl5_3 ),
inference(sat_conversion,[],[f48]) ).
cnf(s2,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(sat_conversion,[],[f49]) ).
cnf(s3,plain,
( ~ spl5_1
| ~ spl5_3 ),
inference(sat_conversion,[],[f50]) ).
cnf(s4,plain,
( spl5_1
| ~ spl5_2 ),
inference(sat_conversion,[],[f374]) ).
cnf(s5,plain,
( spl5_1
| ~ spl5_3 ),
inference(sat_conversion,[],[f493]) ).
cnf(s6,plain,
( ~ spl5_1
| spl5_4
| spl5_5 ),
inference(sat_conversion,[],[f517]) ).
cnf(s8,plain,
( ~ spl5_1
| spl5_2
| ~ spl5_5 ),
inference(sat_conversion,[],[f579]) ).
cnf(s9,plain,
( ~ spl5_1
| spl5_3
| ~ spl5_4 ),
inference(sat_conversion,[],[f589]) ).
cnf(s10,plain,
spl5_1,
inference(rat,[],[s1,s4,s5]) ).
cnf(s11,plain,
~ spl5_3,
inference(rat,[],[s3,s10]) ).
cnf(s12,plain,
~ spl5_2,
inference(rat,[],[s2,s10]) ).
cnf(s13,plain,
~ spl5_4,
inference(rat,[],[s9,s10,s11]) ).
cnf(s14,plain,
~ spl5_5,
inference(rat,[],[s8,s10,s12]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s6,s10,s14,s13]) ).
fof(f590,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET624+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n010.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 02:22:47 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.47 % (1504323)Will run a generic schedule for satisfiability detection.
% 0.17/0.47 % (1504344)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2851322725:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.47 % (1504340)% WARNING: option uhcvi not known.
% 0.17/0.47 % (1504339)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1836365073_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.47 % (1504340)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=254073511:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.47 % (1504342)dis+10_1_sil=32000:sp=arity:random_seed=2589415293:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.47 % (1504341)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3125230682:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.47 % (1504345)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1356194044:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.47 % (1504343)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1613713434:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.47 % TRYING [1]
% 0.17/0.47 % TRYING [2]
% 0.17/0.47 % TRYING [3]
% 0.17/0.47 % (1504344) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1504323-1504344"...
% 0.17/0.47 % (1504344)...printing done.
% 0.17/0.47 % (1504344)Refutation found. Thanks to Tanya!
% 0.17/0.47 % SZS status Theorem for theBenchmark
% 0.17/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.47 % (1504344)------------------------------
% 0.17/0.47 % (1504344)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.47 % (1504344)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.47 % (1504344)CaDiCaL version: 2.1.3
% 0.17/0.47 % (1504344)Termination reason: Refutation
% 0.17/0.47 % (1504344)Time elapsed: 0.009 s
% 0.17/0.47 % (1504344)Peak memory usage: 12 MB
% 0.17/0.47 % (1504344)Instructions burned: 24 (million)
% 0.17/0.47 % (1504323)Success in time 0.041 s
% 0.17/0.47 % Vampire exiting
%------------------------------------------------------------------------------