%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU153+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 12:47:27 PM UTC 2026
% Result : Theorem 2.76s 1.33s
% Output : Refutation 2.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 6 unt; 0 def)
% Number of atoms : 152 ( 45 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 194 ( 76 ~; 74 |; 38 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 82 ( 73 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f4,axiom,
! [X0] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f5,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& in(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f6,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_intersection2(X0,X1) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(f12,conjecture,
! [X0,X1] :
~ ( disjoint(singleton(X0),X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l25_zfmisc_1) ).
fof(f13,negated_conjecture,
~ ! [X0,X1] :
~ ( disjoint(singleton(X0),X1)
& in(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f18,plain,
? [X0,X1] :
( disjoint(singleton(X0),X1)
& in(X0,X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f21,plain,
( disjoint(singleton(sK0),sK1)
& in(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f18]) ).
fof(f22,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X2 = X0
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f23,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ( ( sK2(X0,X1) != X0
| ~ in(sK2(X0,X1),X1) )
& ( sK2(X0,X1) = X0
| in(sK2(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f23]) ).
fof(f25,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set )
& ( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f26,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(f27,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,[],[f26]) ).
fof(f28,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,[],[f27]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ( ( ~ in(sK3(X0,X1,X2),X0)
| ~ in(sK3(X0,X1,X2),X1)
| ~ in(sK3(X0,X1,X2),X2) )
& ( ( in(sK3(X0,X1,X2),X0)
& in(sK3(X0,X1,X2),X1) )
| in(sK3(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,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f28]) ).
fof(f30,plain,
! [X0] :
( ( X0 = empty_set
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f31,plain,
! [X0] :
( ( X0 = empty_set
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f30]) ).
fof(f32,plain,
! [X0] :
( ( X0 = empty_set
| in(sK4(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X1,sK4(X0))],[f31]) ).
fof(f35,plain,
in(sK0,sK1),
inference(cnf_transformation,[],[f21]) ).
fof(f36,plain,
disjoint(singleton(sK0),sK1),
inference(cnf_transformation,[],[f21]) ).
fof(f39,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f24]) ).
fof(f43,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f48,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f29]) ).
fof(f54,plain,
! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f32]) ).
fof(f58,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f39]) ).
fof(f59,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f58]) ).
fof(f61,plain,
! [X0,X1,X4] :
( in(X4,set_intersection2(X0,X1))
| ~ in(X4,X0)
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f48]) ).
fof(f64,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f54]) ).
fof(f112,plain,
! [X2,X0,X1] :
( in(X0,empty_set)
| ~ in(X0,X1)
| ~ in(X0,X2)
| ~ disjoint(X1,X2) ),
inference(superposition,[],[f61,f43]) ).
fof(f116,plain,
! [X2,X0,X1] :
( ~ disjoint(X1,X2)
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(forward_subsumption_resolution,[],[f112,f64]) ).
fof(f150,plain,
! [X0] :
( ~ in(X0,singleton(sK0))
| ~ in(X0,sK1) ),
inference(resolution,[],[f116,f36]) ).
fof(f157,plain,
~ in(sK0,sK1),
inference(resolution,[],[f150,f59]) ).
fof(f162,plain,
$false,
inference(forward_subsumption_resolution,[],[f157,f35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU153+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n016.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 28 03:51:03 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 2.76/1.33 % (3240333)Detected formulas, will run a generic FOF schedule.
% 2.76/1.33 % (3240342)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4222947217:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.76/1.33 % (3240342)First to succeed.
% 2.76/1.33 % (3240342)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3240333"
% 2.76/1.33 % (3240341)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=851217315:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.76/1.33 % (3240339)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=1351176453:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.76/1.33 % (3240338)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=327640746:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.76/1.33 % (3240340)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=3498845502:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.76/1.33 % (3240341)Refutation not found, incomplete strategy
% 2.76/1.33 % (3240341)------------------------------
% 2.76/1.33 % (3240341)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.76/1.33 % (3240341)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/1.33 % (3240341)CaDiCaL version: 2.1.3
% 2.76/1.33 % (3240341)Termination reason: Refutation not found, incomplete strategy
% 2.76/1.33 % (3240341)Time elapsed: 0.002 s
% 2.76/1.33 % (3240341)Peak memory usage: 88 MB
% 2.76/1.33 % (3240344)dis-21_1_sil=8000:lcm=predicate:random_seed=3850296974: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)
% 2.76/1.33 % (3240343)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1850861851:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.76/1.33 % (3240343)Also succeeded, but the first one will report.
% 2.76/1.33 % (3240344)Instruction limit reached!
% 2.76/1.33 % (3240344)------------------------------
% 2.76/1.33 % (3240344)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.76/1.33 % (3240344)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/1.33 % (3240344)CaDiCaL version: 2.1.3
% 2.76/1.33 % (3240344)Termination reason: Instruction limit
% 2.76/1.33 % (3240344)Termination phase: Saturation
% 2.76/1.33 % (3240344)Time elapsed: 0.072 s
% 2.76/1.33 % (3240344)Peak memory usage: 88 MB
% 2.76/1.33 % (3240344)Instructions burned: 129 (million)
% 2.76/1.33 % (3240342)Refutation found. Thanks to Tanya!
% 2.76/1.33 % SZS status Theorem for theBenchmark
% 2.76/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 2.76/1.33 % (3240342)------------------------------
% 2.76/1.33 % (3240342)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.76/1.33 % (3240342)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/1.33 % (3240342)CaDiCaL version: 2.1.3
% 2.76/1.33 % (3240342)Termination reason: Refutation
% 2.76/1.33 % (3240342)Time elapsed: 0.003 s
% 2.76/1.33 % (3240342)Peak memory usage: 88 MB
% 2.76/1.33 % (3240342)Instructions burned: 5 (million)
% 2.76/1.33 % (3240342)------------------------------
% 2.76/1.33 % (3240342)------------------------------
% 2.76/1.33 % (3240333)Success in time 0.306 s
% 2.76/1.33 % Vampire exiting
%------------------------------------------------------------------------------