%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET930+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 12:42:21 PM UTC 2026
% Result : Theorem 1.01s 1.03s
% Output : Refutation 3.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of formulae : 63 ( 18 unt; 6 def)
% Number of atoms : 159 ( 45 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 175 ( 79 ~; 62 |; 29 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn 50 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f4,axiom,
! [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
<=> ( ~ in(X0,X2)
& ( in(X1,X2)
| X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l39_zfmisc_1) ).
fof(f7,axiom,
! [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) = unordered_pair(X0,X1)
<=> ( ~ in(X0,X2)
& ~ in(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_zfmisc_1) ).
fof(f8,axiom,
! [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) = empty_set
<=> ( in(X0,X2)
& in(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_zfmisc_1) ).
fof(f9,conjecture,
! [X0,X1,X2] :
~ ( set_difference(unordered_pair(X0,X1),X2) != empty_set
& set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
& set_difference(unordered_pair(X0,X1),X2) != singleton(X1)
& set_difference(unordered_pair(X0,X1),X2) != unordered_pair(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_zfmisc_1) ).
fof(f10,negated_conjecture,
~ ! [X0,X1,X2] :
~ ( set_difference(unordered_pair(X0,X1),X2) != empty_set
& set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
& set_difference(unordered_pair(X0,X1),X2) != singleton(X1)
& set_difference(unordered_pair(X0,X1),X2) != unordered_pair(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f12,plain,
? [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) != empty_set
& set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
& set_difference(unordered_pair(X0,X1),X2) != singleton(X1)
& set_difference(unordered_pair(X0,X1),X2) != unordered_pair(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f13,plain,
( empty_set != set_difference(unordered_pair(sK0,sK1),sK2)
& set_difference(unordered_pair(sK0,sK1),sK2) != singleton(sK0)
& set_difference(unordered_pair(sK0,sK1),sK2) != singleton(sK1)
& unordered_pair(sK0,sK1) != set_difference(unordered_pair(sK0,sK1),sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f12]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( set_difference(unordered_pair(X0,X1),X2) = empty_set
| ~ in(X0,X2)
| ~ in(X1,X2) )
& ( ( in(X0,X2)
& in(X1,X2) )
| empty_set != set_difference(unordered_pair(X0,X1),X2) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ( set_difference(unordered_pair(X0,X1),X2) = empty_set
| ~ in(X0,X2)
| ~ in(X1,X2) )
& ( ( in(X0,X2)
& in(X1,X2) )
| empty_set != set_difference(unordered_pair(X0,X1),X2) ) ),
inference(flattening,[],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ( set_difference(unordered_pair(X0,X1),X2) = unordered_pair(X0,X1)
| in(X0,X2)
| in(X1,X2) )
& ( ( ~ in(X0,X2)
& ~ in(X1,X2) )
| unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ( set_difference(unordered_pair(X0,X1),X2) = unordered_pair(X0,X1)
| in(X0,X2)
| in(X1,X2) )
& ( ( ~ in(X0,X2)
& ~ in(X1,X2) )
| unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2) ) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
| in(X0,X2)
| ( ~ in(X1,X2)
& X0 != X1 ) )
& ( ( ~ in(X0,X2)
& ( in(X1,X2)
| X0 = X1 ) )
| set_difference(unordered_pair(X0,X1),X2) != singleton(X0) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
| in(X0,X2)
| ( ~ in(X1,X2)
& X0 != X1 ) )
& ( ( ~ in(X0,X2)
& ( in(X1,X2)
| X0 = X1 ) )
| set_difference(unordered_pair(X0,X1),X2) != singleton(X0) ) ),
inference(flattening,[],[f18]) ).
fof(f20,plain,
unordered_pair(sK0,sK1) != set_difference(unordered_pair(sK0,sK1),sK2),
inference(cnf_transformation,[],[f13]) ).
fof(f21,plain,
set_difference(unordered_pair(sK0,sK1),sK2) != singleton(sK1),
inference(cnf_transformation,[],[f13]) ).
fof(f22,plain,
set_difference(unordered_pair(sK0,sK1),sK2) != singleton(sK0),
inference(cnf_transformation,[],[f13]) ).
fof(f23,plain,
empty_set != set_difference(unordered_pair(sK0,sK1),sK2),
inference(cnf_transformation,[],[f13]) ).
fof(f24,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f27,plain,
! [X2,X0,X1] :
( empty_set = set_difference(unordered_pair(X0,X1),X2)
| ~ in(X0,X2)
| ~ in(X1,X2) ),
inference(cnf_transformation,[],[f15]) ).
fof(f30,plain,
! [X2,X0,X1] :
( unordered_pair(X0,X1) = set_difference(unordered_pair(X0,X1),X2)
| in(X0,X2)
| in(X1,X2) ),
inference(cnf_transformation,[],[f17]) ).
fof(f34,plain,
! [X2,X0,X1] :
( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
| in(X0,X2)
| ~ in(X1,X2) ),
inference(cnf_transformation,[],[f19]) ).
fof(f35,definition,
~ sP3(empty_set),
introduced(definition,[new_symbols(definition,[sP3])],[inequality_splitting_name_introduction]) ).
fof(f36,plain,
sP3(set_difference(unordered_pair(sK0,sK1),sK2)),
inference(inequality_splitting,[],[f23,f35]) ).
fof(f37,definition,
~ sP4(set_difference(unordered_pair(sK0,sK1),sK2)),
introduced(definition,[new_symbols(definition,[sP4])],[inequality_splitting_name_introduction]) ).
fof(f38,plain,
sP4(singleton(sK0)),
inference(inequality_splitting,[],[f22,f37]) ).
fof(f39,definition,
~ sP5(set_difference(unordered_pair(sK0,sK1),sK2)),
introduced(definition,[new_symbols(definition,[sP5])],[inequality_splitting_name_introduction]) ).
fof(f40,plain,
sP5(singleton(sK1)),
inference(inequality_splitting,[],[f21,f39]) ).
fof(f41,definition,
~ sP6(unordered_pair(sK0,sK1)),
introduced(definition,[new_symbols(definition,[sP6])],[inequality_splitting_name_introduction]) ).
fof(f42,plain,
sP6(set_difference(unordered_pair(sK0,sK1),sK2)),
inference(inequality_splitting,[],[f20,f41]) ).
fof(f52,plain,
! [X0,X1] :
( sP5(set_difference(unordered_pair(sK1,X0),X1))
| in(sK1,X1)
| ~ in(X0,X1) ),
inference(superposition,[],[f40,f34]) ).
fof(f55,plain,
( sP3(empty_set)
| ~ in(sK0,sK2)
| ~ in(sK1,sK2) ),
inference(superposition,[],[f36,f27]) ).
fof(f56,plain,
( ~ in(sK0,sK2)
| ~ in(sK1,sK2) ),
inference(forward_subsumption_resolution,[],[f55,f35]) ).
fof(f58,definition,
( spl9_1
<=> in(sK1,sK2) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
fof(f59,plain,
( ~ in(sK1,sK2)
| spl9_1 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f60,plain,
( in(sK1,sK2)
| ~ spl9_1 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f62,definition,
( spl9_2
<=> in(sK0,sK2) ),
introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition]) ).
fof(f63,plain,
( ~ in(sK0,sK2)
| spl9_2 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f64,plain,
( in(sK0,sK2)
| ~ spl9_2 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f75,plain,
( ~ spl9_1
| ~ spl9_2 ),
inference(avatar_split_clause,[],[f56,f62,f58]) ).
fof(f76,plain,
( ~ sP4(singleton(sK0))
| in(sK0,sK2)
| ~ in(sK1,sK2) ),
inference(superposition,[],[f37,f34]) ).
fof(f83,plain,
( sP6(unordered_pair(sK0,sK1))
| in(sK0,sK2)
| in(sK1,sK2) ),
inference(superposition,[],[f42,f30]) ).
fof(f141,plain,
! [X0,X1] :
( sP5(set_difference(unordered_pair(X0,sK1),X1))
| in(sK1,X1)
| ~ in(X0,X1) ),
inference(superposition,[],[f52,f24]) ).
fof(f150,plain,
( in(sK1,sK2)
| ~ in(sK0,sK2) ),
inference(resolution,[],[f141,f39]) ).
fof(f160,plain,
( ~ in(sK0,sK2)
| spl9_1 ),
inference(forward_subsumption_resolution,[],[f150,f59]) ).
fof(f161,plain,
( $false
| spl9_1
| ~ spl9_2 ),
inference(forward_subsumption_resolution,[],[f160,f64]) ).
fof(f162,plain,
( spl9_1
| ~ spl9_2 ),
inference(avatar_contradiction_clause,[],[f161]) ).
fof(f169,plain,
( in(sK0,sK2)
| in(sK1,sK2) ),
inference(forward_subsumption_resolution,[],[f83,f41]) ).
fof(f172,plain,
( in(sK1,sK2)
| spl9_2 ),
inference(forward_subsumption_resolution,[],[f169,f63]) ).
fof(f173,plain,
( $false
| spl9_1
| spl9_2 ),
inference(forward_subsumption_resolution,[],[f172,f59]) ).
fof(f174,plain,
( spl9_1
| spl9_2 ),
inference(avatar_contradiction_clause,[],[f173]) ).
fof(f175,plain,
( in(sK0,sK2)
| ~ in(sK1,sK2) ),
inference(forward_subsumption_resolution,[],[f76,f38]) ).
fof(f179,plain,
( ~ in(sK1,sK2)
| spl9_2 ),
inference(forward_subsumption_resolution,[],[f175,f63]) ).
fof(f184,plain,
( $false
| ~ spl9_1
| spl9_2 ),
inference(forward_subsumption_resolution,[],[f179,f60]) ).
fof(f185,plain,
( ~ spl9_1
| spl9_2 ),
inference(avatar_contradiction_clause,[],[f184]) ).
cnf(s3,plain,
( ~ spl9_1
| ~ spl9_2 ),
inference(sat_conversion,[],[f75]) ).
cnf(s7,plain,
( spl9_1
| ~ spl9_2 ),
inference(sat_conversion,[],[f162]) ).
cnf(s10,plain,
( spl9_1
| spl9_2 ),
inference(sat_conversion,[],[f174]) ).
cnf(s12,plain,
( ~ spl9_1
| spl9_2 ),
inference(sat_conversion,[],[f185]) ).
cnf(s13,plain,
spl9_1,
inference(rat,[],[s7,s10]) ).
cnf(s14,plain,
spl9_2,
inference(rat,[],[s12,s13]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s3,s14,s13]) ).
fof(f186,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET930+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n018.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 03:13:39 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
% 0.11/0.41 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
% 1.01/1.03 % (2962402)Detected formulas, will run a generic FOF schedule.
% 1.01/1.03 % (2962409)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=2189730471:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.01/1.03 % (2962408)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=2978439212:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.01/1.03 % (2962412)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4058247736:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.01/1.03 % (2962410)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3776642667:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.01/1.03 % (2962407)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=2510144937:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.01/1.03 % (2962411)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1252466105:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.01/1.03 % (2962413)dis-21_1_sil=8000:lcm=predicate:random_seed=3925611403: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)
% 1.01/1.03 % (2962413)Refutation not found, incomplete strategy
% 1.01/1.03 % (2962413)------------------------------
% 1.01/1.03 % (2962413)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.01/1.03 % (2962413)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.01/1.03 % (2962413)CaDiCaL version: 2.1.3
% 1.01/1.03 % (2962413)Termination reason: Refutation not found, incomplete strategy
% 1.01/1.03 % (2962413)Time elapsed: 0.002 s
% 1.01/1.03 % (2962413)Peak memory usage: 88 MB
% 1.01/1.03 % (2962413)Instructions burned: 2 (million)
% 1.01/1.03 % (2962410)First to succeed.
% 1.01/1.03 % (2962411)Also succeeded, but the first one will report.
% 1.01/1.03 % (2962410)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2962402"
% 1.01/1.03 % (2962412)Instruction limit reached!
% 1.01/1.03 % (2962412)------------------------------
% 1.01/1.03 % (2962412)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.01/1.03 % (2962412)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.01/1.03 % (2962412)CaDiCaL version: 2.1.3
% 1.01/1.03 % (2962412)Termination reason: Instruction limit
% 1.01/1.03 % (2962412)Termination phase: Saturation
% 1.01/1.03 % (2962412)Time elapsed: 0.076 s
% 1.01/1.03 % (2962412)Peak memory usage: 88 MB
% 1.01/1.03 % (2962412)Instructions burned: 140 (million)
% 1.01/1.03 % (2962413)------------------------------
% 1.01/1.03 % (2962413)------------------------------
% 1.01/1.03 % (2962410)Refutation found. Thanks to Tanya!
% 1.01/1.03 % SZS status Theorem for theBenchmark
% 1.01/1.03 % SZS output start Proof for theBenchmark
% See solution above
% 3.44/1.22 % (2962410)------------------------------
% 3.44/1.22 % (2962410)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.22 % (2962410)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.22 % (2962410)CaDiCaL version: 2.1.3
% 3.44/1.22 % (2962410)Termination reason: Refutation
% 3.44/1.22 % (2962410)Time elapsed: 0.005 s
% 3.44/1.22 % (2962410)Peak memory usage: 89 MB
% 3.44/1.22 % (2962410)Instructions burned: 5 (million)
% 3.44/1.22 % (2962410)------------------------------
% 3.44/1.22 % (2962410)------------------------------
% 3.44/1.22 % (2962402)Success in time 0.426 s
% 3.44/1.22 % Vampire exiting
%------------------------------------------------------------------------------