%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET636+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 12:41:29 PM UTC 2026
% Result : Theorem 2.45s 1.24s
% Output : Refutation 2.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 51 ( 10 unt; 0 def)
% Number of atoms : 152 ( 28 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 171 ( 70 ~; 69 |; 24 &)
% ( 7 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 88 ( 79 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X0)
& member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
fof(f2,axiom,
! [X0,X1] :
( intersect(X0,X1)
<=> ? [X2] :
( member(X2,X0)
& member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_defn) ).
fof(f3,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f4,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> ~ intersect(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint_defn) ).
fof(f6,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f11,axiom,
! [X0,X1] :
( X0 = X1
<=> ! [X2] :
( member(X2,X0)
<=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f12,conjecture,
! [X0,X1] :
( disjoint(X0,X1)
<=> intersection(X0,X1) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th118) ).
fof(f13,negated_conjecture,
~ ! [X0,X1] :
( disjoint(X0,X1)
<=> intersection(X0,X1) = empty_set ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
? [X0,X1] :
( disjoint(X0,X1)
<~> intersection(X0,X1) = empty_set ),
inference(ennf_transformation,[],[f13]) ).
fof(f16,plain,
? [X0,X1] :
( ( intersection(X0,X1) != empty_set
| ~ disjoint(X0,X1) )
& ( intersection(X0,X1) = empty_set
| disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f17,plain,
( ( empty_set != intersection(sK0,sK1)
| ~ disjoint(sK0,sK1) )
& ( empty_set = intersection(sK0,sK1)
| disjoint(sK0,sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) ) )
& ( ! [X2] :
( ( member(X2,X0)
| ~ member(X2,X1) )
& ( member(X2,X1)
| ~ member(X2,X0) ) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f19,plain,
! [X0,X1] :
( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) ) )
& ( ! [X3] :
( ( member(X3,X0)
| ~ member(X3,X1) )
& ( member(X3,X1)
| ~ member(X3,X0) ) )
| X0 != X1 ) ),
inference(rectify,[],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( ( X0 = X1
| ( ( ~ member(sK2(X0,X1),X1)
| ~ member(sK2(X0,X1),X0) )
& ( member(sK2(X0,X1),X1)
| member(sK2(X0,X1),X0) ) ) )
& ( ! [X3] :
( ( member(X3,X0)
| ~ member(X3,X1) )
& ( member(X3,X1)
| ~ member(X3,X0) ) )
| X0 != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( member(X2,intersection(X0,X1))
| ~ member(X2,X0)
| ~ member(X2,X1) )
& ( ( member(X2,X0)
& member(X2,X1) )
| ~ member(X2,intersection(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( member(X2,intersection(X0,X1))
| ~ member(X2,X0)
| ~ member(X2,X1) )
& ( ( member(X2,X0)
& member(X2,X1) )
| ~ member(X2,intersection(X0,X1)) ) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| intersect(X0,X1) )
& ( ~ intersect(X0,X1)
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f24,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(f25,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,[],[f24]) ).
fof(f26,plain,
! [X0,X1] :
( ( intersect(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| ~ member(X2,X1) ) )
& ( ( member(sK3(X0,X1),X0)
& member(sK3(X0,X1),X1) )
| ~ intersect(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1))],[f25]) ).
fof(f27,plain,
( empty_set = intersection(sK0,sK1)
| disjoint(sK0,sK1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f28,plain,
( empty_set != intersection(sK0,sK1)
| ~ disjoint(sK0,sK1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f31,plain,
! [X0,X1] :
( member(sK2(X0,X1),X1)
| X0 = X1
| member(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f33,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f35,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f36,plain,
! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
| ~ member(X2,X0)
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f37,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f3]) ).
fof(f38,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f39,plain,
! [X0,X1] :
( disjoint(X0,X1)
| intersect(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f41,plain,
! [X0,X1] :
( member(sK3(X0,X1),X1)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f42,plain,
! [X0,X1] :
( member(sK3(X0,X1),X0)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f43,plain,
! [X2,X0,X1] :
( intersect(X0,X1)
| ~ member(X2,X0)
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f66,plain,
! [X0] :
( member(X0,empty_set)
| ~ member(X0,sK0)
| ~ member(X0,sK1)
| disjoint(sK0,sK1) ),
inference(superposition,[],[f36,f27]) ).
fof(f69,plain,
! [X0] :
( disjoint(sK0,sK1)
| ~ member(X0,sK1)
| ~ member(X0,sK0) ),
inference(forward_subsumption_resolution,[],[f66,f37]) ).
fof(f70,plain,
! [X0] :
( ~ member(X0,sK1)
| ~ member(X0,sK0)
| ~ intersect(sK0,sK1) ),
inference(resolution,[],[f69,f38]) ).
fof(f71,plain,
! [X0] :
( ~ member(X0,sK1)
| ~ member(X0,sK0) ),
inference(forward_subsumption_resolution,[],[f70,f43]) ).
fof(f72,plain,
! [X0] :
( member(sK2(X0,empty_set),X0)
| empty_set = X0 ),
inference(resolution,[],[f31,f37]) ).
fof(f75,plain,
! [X0] :
( ~ member(sK3(X0,sK1),sK0)
| ~ intersect(X0,sK1) ),
inference(resolution,[],[f71,f41]) ).
fof(f78,plain,
( ~ intersect(sK0,sK1)
| ~ intersect(sK0,sK1) ),
inference(resolution,[],[f75,f42]) ).
fof(f79,plain,
~ intersect(sK0,sK1),
inference(duplicate_literal_removal,[],[f78]) ).
fof(f92,plain,
! [X0,X1] :
( member(sK2(intersection(X0,X1),empty_set),X0)
| intersection(X0,X1) = empty_set ),
inference(resolution,[],[f72,f35]) ).
fof(f93,plain,
! [X0,X1] :
( member(sK2(intersection(X0,X1),empty_set),X1)
| intersection(X0,X1) = empty_set ),
inference(resolution,[],[f72,f34]) ).
fof(f238,plain,
! [X0] :
( ~ member(sK2(intersection(sK1,X0),empty_set),sK0)
| empty_set = intersection(sK1,X0) ),
inference(resolution,[],[f92,f71]) ).
fof(f703,plain,
( empty_set = intersection(sK1,sK0)
| empty_set = intersection(sK1,sK0) ),
inference(resolution,[],[f238,f93]) ).
fof(f706,plain,
empty_set = intersection(sK1,sK0),
inference(duplicate_literal_removal,[],[f703]) ).
fof(f707,plain,
empty_set = intersection(sK0,sK1),
inference(forward_demodulation,[],[f706,f33]) ).
fof(f710,plain,
( empty_set != empty_set
| ~ disjoint(sK0,sK1) ),
inference(superposition,[],[f28,f707]) ).
fof(f754,plain,
~ disjoint(sK0,sK1),
inference(trivial_inequality_removal,[],[f710]) ).
fof(f760,plain,
intersect(sK0,sK1),
inference(resolution,[],[f754,f39]) ).
fof(f761,plain,
$false,
inference(forward_subsumption_resolution,[],[f760,f79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET636+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n006.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 28 02:23:11 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 2.45/1.24 % (3530665)Detected formulas, will run a generic FOF schedule.
% 2.45/1.24 % (3530674)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1594988072:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.45/1.24 % (3530674)First to succeed.
% 2.45/1.24 % (3530674)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3530665"
% 2.45/1.24 % (3530673)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=27558068:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.45/1.24 % (3530670)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=1293686199:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.45/1.24 % (3530675)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1958191032:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.45/1.24 % (3530676)dis-21_1_sil=8000:lcm=predicate:random_seed=744958650: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)
% 2.45/1.24 % (3530671)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=2164306216:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.45/1.24 % (3530672)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=744520312:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.45/1.24 % (3530675)Also succeeded, but the first one will report.
% 2.45/1.24 % (3530673)Instruction limit reached!
% 2.45/1.24 % (3530673)------------------------------
% 2.45/1.24 % (3530673)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.45/1.24 % (3530673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.45/1.24 % (3530673)CaDiCaL version: 2.1.3
% 2.45/1.24 % (3530673)Termination reason: Instruction limit
% 2.45/1.24 % (3530673)Termination phase: Saturation
% 2.45/1.24 % (3530673)Time elapsed: 0.062 s
% 2.45/1.24 % (3530673)Peak memory usage: 89 MB
% 2.45/1.24 % (3530673)Instructions burned: 110 (million)
% 2.45/1.24 % (3530676)Instruction limit reached!
% 2.45/1.24 % (3530676)------------------------------
% 2.45/1.24 % (3530676)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.45/1.24 % (3530676)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.45/1.24 % (3530676)CaDiCaL version: 2.1.3
% 2.45/1.24 % (3530676)Termination reason: Instruction limit
% 2.45/1.24 % (3530676)Termination phase: Saturation
% 2.45/1.24 % (3530676)Time elapsed: 0.071 s
% 2.45/1.24 % (3530676)Peak memory usage: 89 MB
% 2.45/1.24 % (3530676)Instructions burned: 130 (million)
% 2.45/1.24 % (3530674)Refutation found. Thanks to Tanya!
% 2.45/1.24 % SZS status Theorem for theBenchmark
% 2.45/1.24 % SZS output start Proof for theBenchmark
% See solution above
% 2.45/1.24 % (3530674)------------------------------
% 2.45/1.24 % (3530674)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.45/1.24 % (3530674)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.45/1.24 % (3530674)CaDiCaL version: 2.1.3
% 2.45/1.24 % (3530674)Termination reason: Refutation
% 2.45/1.24 % (3530674)Time elapsed: 0.009 s
% 2.45/1.24 % (3530674)Peak memory usage: 88 MB
% 2.45/1.24 % (3530674)Instructions burned: 24 (million)
% 2.45/1.24 % (3530674)------------------------------
% 2.45/1.24 % (3530674)------------------------------
% 2.45/1.24 % (3530665)Success in time 0.269 s
% 2.45/1.24 % Vampire exiting
%------------------------------------------------------------------------------