%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET918+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 12:42:19 PM UTC 2026
% Result : Theorem 3.59s 1.44s
% Output : Refutation 3.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 10 unt; 1 def)
% Number of atoms : 197 ( 90 equ)
% Maximal formula atoms : 14 ( 5 avg)
% Number of connectives : 255 ( 94 ~; 97 |; 58 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 91 ( 80 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f5,axiom,
! [X0,X1,X2] :
( X2 = unordered_pair(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( X3 = X0
| X3 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(f6,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(f10,conjecture,
! [X0,X1,X2] :
~ ( set_intersection2(unordered_pair(X0,X1),X2) = singleton(X0)
& in(X1,X2)
& X0 != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_zfmisc_1) ).
fof(f11,negated_conjecture,
~ ! [X0,X1,X2] :
~ ( set_intersection2(unordered_pair(X0,X1),X2) = singleton(X0)
& in(X1,X2)
& X0 != X1 ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f13,plain,
? [X0,X1,X2] :
( set_intersection2(unordered_pair(X0,X1),X2) = singleton(X0)
& in(X1,X2)
& X0 != X1 ),
inference(ennf_transformation,[],[f11]) ).
fof(f15,plain,
( singleton(sK0) = set_intersection2(unordered_pair(sK0,sK1),sK2)
& in(sK1,sK2)
& sK0 != sK1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f13]) ).
fof(f16,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(f17,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,[],[f16]) ).
fof(f18,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,[],[f17]) ).
fof(f19,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))],[f18]) ).
fof(f20,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,[],[f6]) ).
fof(f21,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,[],[f20]) ).
fof(f22,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,[],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ( ( ~ in(sK4(X0,X1,X2),X0)
| ~ in(sK4(X0,X1,X2),X1)
| ~ in(sK4(X0,X1,X2),X2) )
& ( ( in(sK4(X0,X1,X2),X0)
& in(sK4(X0,X1,X2),X1) )
| in(sK4(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,[sK4]),skolemize(X3,sK4(X0,X1,X2))],[f22]) ).
fof(f24,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,[],[f4]) ).
fof(f25,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,[],[f24]) ).
fof(f26,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ( ( sK5(X0,X1) != X0
| ~ in(sK5(X0,X1),X1) )
& ( sK5(X0,X1) = X0
| in(sK5(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f25]) ).
fof(f27,plain,
sK0 != sK1,
inference(cnf_transformation,[],[f15]) ).
fof(f28,plain,
in(sK1,sK2),
inference(cnf_transformation,[],[f15]) ).
fof(f29,plain,
singleton(sK0) = set_intersection2(unordered_pair(sK0,sK1),sK2),
inference(cnf_transformation,[],[f15]) ).
fof(f31,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X1 != X4
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f19]) ).
fof(f41,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f23]) ).
fof(f46,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f26]) ).
fof(f50,definition,
~ sP6(sK0),
introduced(definition,[new_symbols(definition,[sP6])],[inequality_splitting_name_introduction]) ).
fof(f51,plain,
sP6(sK1),
inference(inequality_splitting,[],[f27,f50]) ).
fof(f54,plain,
! [X2,X0,X4] :
( in(X4,X2)
| unordered_pair(X0,X4) != X2 ),
inference(equality_resolution,[],[f31]) ).
fof(f55,plain,
! [X0,X4] : in(X4,unordered_pair(X0,X4)),
inference(equality_resolution,[],[f54]) ).
fof(f57,plain,
! [X0,X1,X4] :
( in(X4,set_intersection2(X0,X1))
| ~ in(X4,X0)
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f41]) ).
fof(f62,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f46]) ).
fof(f66,plain,
! [X0] :
( ~ in(X0,unordered_pair(sK0,sK1))
| in(X0,singleton(sK0))
| ~ in(X0,sK2) ),
inference(superposition,[],[f57,f29]) ).
fof(f78,plain,
( in(sK1,singleton(sK0))
| ~ in(sK1,sK2) ),
inference(resolution,[],[f66,f55]) ).
fof(f83,plain,
in(sK1,singleton(sK0)),
inference(forward_subsumption_resolution,[],[f78,f28]) ).
fof(f85,plain,
sK0 = sK1,
inference(resolution,[],[f83,f62]) ).
fof(f101,plain,
sP6(sK0),
inference(superposition,[],[f51,f85]) ).
fof(f107,plain,
$false,
inference(forward_subsumption_resolution,[],[f101,f50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET918+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n003.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 03:11:42 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 3.59/1.44 % (1149556)Detected formulas, will run a generic FOF schedule.
% 3.59/1.44 % (1149561)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=58578635:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.59/1.44 % (1149563)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=2629286312:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.59/1.44 % (1149565)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2986855291:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.59/1.44 % (1149562)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=1990252362:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.59/1.44 % (1149564)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1829175357:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.59/1.44 % (1149567)dis-21_1_sil=8000:lcm=predicate:random_seed=545287094: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)
% 3.59/1.44 % (1149566)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1859910541:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.59/1.44 % (1149564)First to succeed.
% 3.59/1.44 % (1149565)Also succeeded, but the first one will report.
% 3.59/1.44 % (1149564)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1149556"
% 3.59/1.44 % (1149566)Also succeeded, but the first one will report.
% 3.59/1.44 % (1149567)Instruction limit reached!
% 3.59/1.44 % (1149567)------------------------------
% 3.59/1.44 % (1149567)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.44 % (1149567)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.44 % (1149567)CaDiCaL version: 2.1.3
% 3.59/1.44 % (1149567)Termination reason: Instruction limit
% 3.59/1.44 % (1149567)Termination phase: Saturation
% 3.59/1.44 % (1149567)Time elapsed: 0.076 s
% 3.59/1.44 % (1149567)Peak memory usage: 89 MB
% 3.59/1.44 % (1149567)Instructions burned: 129 (million)
% 3.59/1.44 % (1149575)lrs+10_1_sil=8000:sp=occurrence:random_seed=3958874179:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.59/1.44 % (1149575)Also succeeded, but the first one will report.
% 3.59/1.44 % (1149564)Refutation found. Thanks to Tanya!
% 3.59/1.44 % SZS status Theorem for theBenchmark
% 3.59/1.44 % SZS output start Proof for theBenchmark
% See solution above
% 3.59/1.44 % (1149564)------------------------------
% 3.59/1.44 % (1149564)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.44 % (1149564)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.44 % (1149564)CaDiCaL version: 2.1.3
% 3.59/1.44 % (1149564)Termination reason: Refutation
% 3.59/1.44 % (1149564)Time elapsed: 0.004 s
% 3.59/1.44 % (1149564)Peak memory usage: 88 MB
% 3.59/1.44 % (1149564)Instructions burned: 5 (million)
% 3.59/1.44 % (1149564)------------------------------
% 3.59/1.44 % (1149564)------------------------------
% 3.59/1.44 % (1149556)Success in time 0.428 s
% 3.59/1.44 % Vampire exiting
%------------------------------------------------------------------------------