%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET916+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 : 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 12:42:18 PM UTC 2026
% Result : Theorem 3.38s 1.37s
% Output : Refutation 3.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 48 ( 12 unt; 2 def)
% Number of atoms : 201 ( 65 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 258 ( 105 ~; 90 |; 57 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 93 ( 0 sgn 81 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2] :
( X2 = unordered_pair(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( X3 = X0
| X3 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(f5,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& in(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f10,axiom,
! [X0,X1] :
( ~ ( ~ disjoint(X0,X1)
& ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
& ~ ( ? [X2] : in(X2,set_intersection2(X0,X1))
& disjoint(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(f11,conjecture,
! [X0,X1,X2] :
~ ( ~ in(X0,X1)
& ~ in(X2,X1)
& ~ disjoint(unordered_pair(X0,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_zfmisc_1) ).
fof(f12,negated_conjecture,
~ ! [X0,X1,X2] :
~ ( ~ in(X0,X1)
& ~ in(X2,X1)
& ~ disjoint(unordered_pair(X0,X2),X1) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f14,plain,
! [X0,X1] :
( ~ ( ~ disjoint(X0,X1)
& ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X0,X1))
& disjoint(X0,X1) ) ),
inference(rectify,[],[f10]) ).
fof(f17,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| ? [X2] : in(X2,set_intersection2(X0,X1)) )
& ( ! [X3] : ~ in(X3,set_intersection2(X0,X1))
| ~ disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f18,plain,
? [X0,X1,X2] :
( ~ in(X0,X1)
& ~ in(X2,X1)
& ~ disjoint(unordered_pair(X0,X2),X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X3 = X0
| X3 = X1
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X0 != X3
& X1 != X3 ) )
& ( X3 = X0
| X3 = X1
| ~ in(X3,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X3 = X0
| X3 = X1
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X0 != X3
& X1 != X3 ) )
& ( X3 = X0
| X3 = X1
| ~ in(X3,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X3 = X0
| X3 = X1
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X0 != X4
& X1 != X4 ) )
& ( X0 = X4
| X1 = X4
| ~ in(X4,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(rectify,[],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ( ( ( sK0(X0,X1,X2) != X0
& sK0(X0,X1,X2) != X1 )
| ~ in(sK0(X0,X1,X2),X2) )
& ( sK0(X0,X1,X2) = X0
| sK0(X0,X1,X2) = X1
| in(sK0(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X0 != X4
& X1 != X4 ) )
& ( X0 = X4
| X1 = X4
| ~ in(X4,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(rectify,[],[f24]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ( ( ~ in(sK1(X0,X1,X2),X0)
| ~ in(sK1(X0,X1,X2),X1)
| ~ in(sK1(X0,X1,X2),X2) )
& ( ( in(sK1(X0,X1,X2),X0)
& in(sK1(X0,X1,X2),X1) )
| in(sK1(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f25]) ).
fof(f29,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| in(sK4(X0,X1),set_intersection2(X0,X1)) )
& ( ! [X3] : ~ in(X3,set_intersection2(X0,X1))
| ~ disjoint(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f17]) ).
fof(f30,plain,
( ~ in(sK5,sK6)
& ~ in(sK7,sK6)
& ~ disjoint(unordered_pair(sK5,sK7),sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X0,sK5),skolemize(X1,sK6),skolemize(X2,sK7)],[f18]) ).
fof(f34,plain,
! [X2,X0,X1,X4] :
( X0 = X4
| X1 = X4
| ~ in(X4,X2)
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f22]) ).
fof(f40,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f26]) ).
fof(f41,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f26]) ).
fof(f51,plain,
! [X0,X1] :
( disjoint(X0,X1)
| in(sK4(X0,X1),set_intersection2(X0,X1)) ),
inference(cnf_transformation,[],[f29]) ).
fof(f52,plain,
~ disjoint(unordered_pair(sK5,sK7),sK6),
inference(cnf_transformation,[],[f30]) ).
fof(f53,plain,
~ in(sK7,sK6),
inference(cnf_transformation,[],[f30]) ).
fof(f54,plain,
~ in(sK5,sK6),
inference(cnf_transformation,[],[f30]) ).
fof(f59,plain,
! [X0,X1,X4] :
( ~ in(X4,unordered_pair(X0,X1))
| X1 = X4
| X0 = X4 ),
inference(equality_resolution,[],[f34]) ).
fof(f61,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f41]) ).
fof(f62,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f40]) ).
fof(f76,plain,
in(sK4(unordered_pair(sK5,sK7),sK6),set_intersection2(unordered_pair(sK5,sK7),sK6)),
inference(resolution,[],[f51,f52]) ).
fof(f79,plain,
in(sK4(unordered_pair(sK5,sK7),sK6),sK6),
inference(resolution,[],[f76,f62]) ).
fof(f80,plain,
in(sK4(unordered_pair(sK5,sK7),sK6),unordered_pair(sK5,sK7)),
inference(resolution,[],[f76,f61]) ).
fof(f93,plain,
( sK7 = sK4(unordered_pair(sK5,sK7),sK6)
| sK5 = sK4(unordered_pair(sK5,sK7),sK6) ),
inference(resolution,[],[f80,f59]) ).
fof(f97,definition,
( spl8_1
<=> sK5 = sK4(unordered_pair(sK5,sK7),sK6) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
fof(f99,plain,
( sK5 = sK4(unordered_pair(sK5,sK7),sK6)
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f101,definition,
( spl8_2
<=> sK7 = sK4(unordered_pair(sK5,sK7),sK6) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
fof(f103,plain,
( sK7 = sK4(unordered_pair(sK5,sK7),sK6)
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f104,plain,
( spl8_1
| spl8_2 ),
inference(avatar_split_clause,[],[f93,f101,f97]) ).
fof(f107,plain,
( in(sK7,sK6)
| ~ spl8_2 ),
inference(superposition,[],[f79,f103]) ).
fof(f109,plain,
( $false
| ~ spl8_2 ),
inference(forward_subsumption_resolution,[],[f107,f53]) ).
fof(f110,plain,
~ spl8_2,
inference(avatar_contradiction_clause,[],[f109]) ).
fof(f118,plain,
( in(sK5,sK6)
| ~ spl8_1 ),
inference(superposition,[],[f79,f99]) ).
fof(f120,plain,
( $false
| ~ spl8_1 ),
inference(forward_subsumption_resolution,[],[f118,f54]) ).
fof(f121,plain,
~ spl8_1,
inference(avatar_contradiction_clause,[],[f120]) ).
cnf(s1,plain,
( spl8_1
| spl8_2 ),
inference(sat_conversion,[],[f104]) ).
cnf(s2,plain,
~ spl8_2,
inference(sat_conversion,[],[f110]) ).
cnf(s3,plain,
~ spl8_1,
inference(sat_conversion,[],[f121]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f122,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET916+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n007.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 03:07:41 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 3.38/1.37 % (1988441)Detected formulas, will run a generic FOF schedule.
% 3.38/1.37 % (1988450)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=376508250:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.38/1.37 % (1988450)Instruction limit reached!
% 3.38/1.37 % (1988450)------------------------------
% 3.38/1.37 % (1988450)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.37 % (1988450)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.37 % (1988450)CaDiCaL version: 2.1.3
% 3.38/1.37 % (1988450)Termination reason: Instruction limit
% 3.38/1.37 % (1988450)Termination phase: Saturation
% 3.38/1.37 % (1988450)Time elapsed: 0.036 s
% 3.38/1.37 % (1988450)Peak memory usage: 88 MB
% 3.38/1.37 % (1988450)Instructions burned: 120 (million)
% 3.38/1.37 % (1988452)dis-21_1_sil=8000:lcm=predicate:random_seed=3937055750: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)
% 3.38/1.37 % (1988449)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1256514269:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.38/1.37 % (1988446)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=2755956097:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.38/1.37 % (1988448)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=1723261289:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.38/1.37 % (1988447)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=818092386:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.38/1.37 % (1988451)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3490666051:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.38/1.37 % (1988449)Refutation not found, incomplete strategy
% 3.38/1.37 % (1988449)------------------------------
% 3.38/1.37 % (1988449)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.37 % (1988449)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.37 % (1988449)CaDiCaL version: 2.1.3
% 3.38/1.37 % (1988449)Termination reason: Refutation not found, incomplete strategy
% 3.38/1.37 % (1988449)Time elapsed: 0.001 s
% 3.38/1.37 % (1988449)Peak memory usage: 88 MB
% 3.38/1.37 % (1988449)Instructions burned: 1 (million)
% 3.38/1.37 % (1988451)First to succeed.
% 3.38/1.37 % (1988451)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1988441"
% 3.38/1.37 % (1988452)Instruction limit reached!
% 3.38/1.37 % (1988452)------------------------------
% 3.38/1.37 % (1988452)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.37 % (1988452)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.37 % (1988452)CaDiCaL version: 2.1.3
% 3.38/1.37 % (1988452)Termination reason: Instruction limit
% 3.38/1.37 % (1988452)Termination phase: Saturation
% 3.38/1.37 % (1988452)Time elapsed: 0.076 s
% 3.38/1.37 % (1988452)Peak memory usage: 89 MB
% 3.38/1.37 % (1988452)Instructions burned: 131 (million)
% 3.38/1.37 % (1988454)lrs+10_1_sil=8000:sp=occurrence:random_seed=3362063906:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.38/1.37 % (1988454)Also succeeded, but the first one will report.
% 3.38/1.37 % (1988461)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3491360446:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.38/1.37 % (1988449)------------------------------
% 3.38/1.37 % (1988449)------------------------------
% 3.38/1.37 % (1988451)Refutation found. Thanks to Tanya!
% 3.38/1.37 % SZS status Theorem for theBenchmark
% 3.38/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 3.38/1.38 % (1988451)------------------------------
% 3.38/1.38 % (1988451)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.38 % (1988451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.38 % (1988451)CaDiCaL version: 2.1.3
% 3.38/1.38 % (1988451)Termination reason: Refutation
% 3.38/1.38 % (1988451)Time elapsed: 0.005 s
% 3.38/1.38 % (1988451)Peak memory usage: 90 MB
% 3.38/1.38 % (1988451)Instructions burned: 5 (million)
% 3.38/1.38 % (1988451)------------------------------
% 3.38/1.38 % (1988451)------------------------------
% 3.38/1.38 % (1988441)Success in time 0.414 s
% 3.38/1.38 % Vampire exiting
%------------------------------------------------------------------------------