%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET909+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 : n005.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 12:42:17 PM UTC 2026
% Result : Theorem 2.52s 1.32s
% Output : Refutation 2.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 9 unt; 0 def)
% Number of atoms : 157 ( 69 equ)
% Maximal formula atoms : 14 ( 5 avg)
% Number of connectives : 205 ( 77 ~; 80 |; 43 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 86 ( 75 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f5,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(f6,axiom,
! [X0,X1,X2] :
( X2 = set_union2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
| in(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f13,conjecture,
! [X0,X1,X2] : set_union2(unordered_pair(X0,X1),X2) != empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_zfmisc_1) ).
fof(f14,negated_conjecture,
~ ! [X0,X1,X2] : set_union2(unordered_pair(X0,X1),X2) != empty_set,
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f16,plain,
? [X0,X1,X2] : empty_set = set_union2(unordered_pair(X0,X1),X2),
inference(ennf_transformation,[],[f14]) ).
fof(f20,plain,
empty_set = set_union2(unordered_pair(sK0,sK1),sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f16]) ).
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) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X0 != X3
& X1 != X3 ) )
& ( X3 = X0
| X3 = X1
| ~ in(X3,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f22,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,[],[f21]) ).
fof(f23,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,[],[f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ( ( ( sK3(X0,X1,X2) != X0
& sK3(X0,X1,X2) != X1 )
| ~ in(sK3(X0,X1,X2),X2) )
& ( sK3(X0,X1,X2) = X0
| sK3(X0,X1,X2) = X1
| in(sK3(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,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f23]) ).
fof(f25,plain,
! [X0] :
( ( X0 = empty_set
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f26,plain,
! [X0] :
( ( X0 = empty_set
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f25]) ).
fof(f27,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))],[f26]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(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_union2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(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_union2(X0,X1) != X2 ) ),
inference(flattening,[],[f28]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(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_union2(X0,X1) != X2 ) ),
inference(rectify,[],[f29]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ( ( ( ~ in(sK5(X0,X1,X2),X0)
& ~ in(sK5(X0,X1,X2),X1) )
| ~ in(sK5(X0,X1,X2),X2) )
& ( in(sK5(X0,X1,X2),X0)
| in(sK5(X0,X1,X2),X1)
| in(sK5(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X3,sK5(X0,X1,X2))],[f30]) ).
fof(f34,plain,
empty_set = set_union2(unordered_pair(sK0,sK1),sK2),
inference(cnf_transformation,[],[f20]) ).
fof(f36,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X1 != X4
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f24]) ).
fof(f45,plain,
! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f27]) ).
fof(f49,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f31]) ).
fof(f60,plain,
! [X2,X0,X4] :
( in(X4,X2)
| unordered_pair(X0,X4) != X2 ),
inference(equality_resolution,[],[f36]) ).
fof(f61,plain,
! [X0,X4] : in(X4,unordered_pair(X0,X4)),
inference(equality_resolution,[],[f60]) ).
fof(f63,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f45]) ).
fof(f64,plain,
! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f49]) ).
fof(f100,plain,
! [X0] :
( in(X0,empty_set)
| ~ in(X0,unordered_pair(sK0,sK1)) ),
inference(superposition,[],[f64,f34]) ).
fof(f106,plain,
! [X0] : ~ in(X0,unordered_pair(sK0,sK1)),
inference(forward_subsumption_resolution,[],[f100,f63]) ).
fof(f121,plain,
$false,
inference(resolution,[],[f106,f61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET909+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n005.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 03:09:02 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 2.52/1.32 % (395211)Detected formulas, will run a generic FOF schedule.
% 2.52/1.32 % (395220)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=694531745:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.52/1.32 % (395220)First to succeed.
% 2.52/1.32 % (395220)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-395211"
% 2.52/1.32 % (395216)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=3201177530:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.52/1.32 % (395219)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1690085832:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.52/1.32 % (395222)dis-21_1_sil=8000:lcm=predicate:random_seed=1447789623: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)
% 2.52/1.32 % (395217)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=1763779373:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.52/1.32 % (395218)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=2728461834:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.52/1.32 % (395221)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2593530591:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.52/1.32 % (395219)Refutation not found, incomplete strategy
% 2.52/1.32 % (395219)------------------------------
% 2.52/1.32 % (395219)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.52/1.32 % (395219)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/1.32 % (395219)CaDiCaL version: 2.1.3
% 2.52/1.32 % (395219)Termination reason: Refutation not found, incomplete strategy
% 2.52/1.32 % (395219)Time elapsed: 0.001 s
% 2.52/1.32 % (395219)Peak memory usage: 88 MB
% 2.52/1.32 % (395221)Also succeeded, but the first one will report.
% 2.52/1.32 % (395222)Instruction limit reached!
% 2.52/1.32 % (395222)------------------------------
% 2.52/1.32 % (395222)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.52/1.32 % (395222)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/1.32 % (395222)CaDiCaL version: 2.1.3
% 2.52/1.32 % (395222)Termination reason: Instruction limit
% 2.52/1.32 % (395222)Termination phase: Saturation
% 2.52/1.32 % (395222)Time elapsed: 0.076 s
% 2.52/1.32 % (395222)Peak memory usage: 89 MB
% 2.52/1.32 % (395222)Instructions burned: 130 (million)
% 2.52/1.32 % (395220)Refutation found. Thanks to Tanya!
% 2.52/1.32 % SZS status Theorem for theBenchmark
% 2.52/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 2.52/1.33 % (395220)------------------------------
% 2.52/1.33 % (395220)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.52/1.33 % (395220)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/1.33 % (395220)CaDiCaL version: 2.1.3
% 2.52/1.33 % (395220)Termination reason: Refutation
% 2.52/1.33 % (395220)Time elapsed: 0.002 s
% 2.52/1.33 % (395220)Peak memory usage: 88 MB
% 2.52/1.33 % (395220)Instructions burned: 4 (million)
% 2.52/1.33 % (395220)------------------------------
% 2.52/1.33 % (395220)------------------------------
% 2.52/1.33 % (395211)Success in time 0.283 s
% 2.52/1.33 % Vampire exiting
%------------------------------------------------------------------------------