%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET921+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 : n002.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 3.42s 1.37s
% Output : Refutation 3.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 64 ( 6 unt; 3 def)
% Number of atoms : 233 ( 53 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 280 ( 111 ~; 120 |; 39 &)
% ( 9 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 85 ( 0 sgn 71 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f3,axiom,
! [X0,X1,X2] :
( X2 = set_difference(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& ~ in(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f6,conjecture,
! [X0,X1,X2] :
( in(X0,set_difference(X1,singleton(X2)))
<=> ( in(X0,X1)
& X0 != X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_zfmisc_1) ).
fof(f7,negated_conjecture,
~ ! [X0,X1,X2] :
( in(X0,set_difference(X1,singleton(X2)))
<=> ( in(X0,X1)
& X0 != X2 ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f9,plain,
? [X0,X1,X2] :
( in(X0,set_difference(X1,singleton(X2)))
<~> ( in(X0,X1)
& X0 != X2 ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f10,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,[],[f2]) ).
fof(f11,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,[],[f10]) ).
fof(f12,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ( ( sK0(X0,X1) != X0
| ~ in(sK0(X0,X1),X1) )
& ( sK0(X0,X1) = X0
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f11]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(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_difference(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(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_difference(X0,X1) != X2 ) ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(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_difference(X0,X1) != X2 ) ),
inference(rectify,[],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(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_difference(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f15]) ).
fof(f19,plain,
? [X0,X1,X2] :
( ( ~ in(X0,X1)
| X0 = X2
| ~ in(X0,set_difference(X1,singleton(X2))) )
& ( ( in(X0,X1)
& X0 != X2 )
| in(X0,set_difference(X1,singleton(X2))) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f20,plain,
? [X0,X1,X2] :
( ( ~ in(X0,X1)
| X0 = X2
| ~ in(X0,set_difference(X1,singleton(X2))) )
& ( ( in(X0,X1)
& X0 != X2 )
| in(X0,set_difference(X1,singleton(X2))) ) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
( ( ~ in(sK4,sK5)
| sK4 = sK6
| ~ in(sK4,set_difference(sK5,singleton(sK6))) )
& ( ( in(sK4,sK5)
& sK4 != sK6 )
| in(sK4,set_difference(sK5,singleton(sK6))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6)],[f20]) ).
fof(f23,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f12]) ).
fof(f24,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f12]) ).
fof(f27,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f16]) ).
fof(f28,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f16]) ).
fof(f29,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| in(X4,X1)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f16]) ).
fof(f35,plain,
( sK4 != sK6
| in(sK4,set_difference(sK5,singleton(sK6))) ),
inference(cnf_transformation,[],[f21]) ).
fof(f36,plain,
( in(sK4,sK5)
| in(sK4,set_difference(sK5,singleton(sK6))) ),
inference(cnf_transformation,[],[f21]) ).
fof(f37,plain,
( ~ in(sK4,sK5)
| sK4 = sK6
| ~ in(sK4,set_difference(sK5,singleton(sK6))) ),
inference(cnf_transformation,[],[f21]) ).
fof(f38,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f24]) ).
fof(f39,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f38]) ).
fof(f40,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f23]) ).
fof(f41,plain,
! [X0,X1,X4] :
( ~ in(X4,X0)
| in(X4,set_difference(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f29]) ).
fof(f42,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f28]) ).
fof(f43,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f27]) ).
fof(f45,definition,
( spl7_1
<=> in(sK4,set_difference(sK5,singleton(sK6))) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
fof(f46,plain,
( ~ in(sK4,set_difference(sK5,singleton(sK6)))
| spl7_1 ),
inference(avatar_component_clause,[],[f45]) ).
fof(f47,plain,
( in(sK4,set_difference(sK5,singleton(sK6)))
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f45]) ).
fof(f49,definition,
( spl7_2
<=> sK4 = sK6 ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
fof(f50,plain,
( sK4 = sK6
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f51,plain,
( sK4 != sK6
| spl7_2 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f52,plain,
( spl7_1
| ~ spl7_2 ),
inference(avatar_split_clause,[],[f35,f49,f45]) ).
fof(f54,definition,
( spl7_3
<=> in(sK4,sK5) ),
introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition]) ).
fof(f55,plain,
( ~ in(sK4,sK5)
| spl7_3 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f56,plain,
( in(sK4,sK5)
| ~ spl7_3 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f57,plain,
( spl7_1
| spl7_3 ),
inference(avatar_split_clause,[],[f36,f54,f45]) ).
fof(f58,plain,
( ~ spl7_1
| spl7_2
| ~ spl7_3 ),
inference(avatar_split_clause,[],[f37,f54,f49,f45]) ).
fof(f63,plain,
( ! [X0] :
( in(sK4,set_difference(sK5,X0))
| in(sK4,X0) )
| ~ spl7_3 ),
inference(resolution,[],[f41,f56]) ).
fof(f65,plain,
( in(sK4,singleton(sK6))
| spl7_1
| ~ spl7_3 ),
inference(resolution,[],[f63,f46]) ).
fof(f70,plain,
( sK4 = sK6
| spl7_1
| ~ spl7_3 ),
inference(resolution,[],[f65,f40]) ).
fof(f73,plain,
( $false
| spl7_1
| spl7_2
| ~ spl7_3 ),
inference(forward_subsumption_resolution,[],[f70,f51]) ).
fof(f74,plain,
( spl7_1
| spl7_2
| ~ spl7_3 ),
inference(avatar_contradiction_clause,[],[f73]) ).
fof(f75,plain,
( in(sK4,set_difference(sK5,singleton(sK4)))
| ~ spl7_1
| ~ spl7_2 ),
inference(forward_demodulation,[],[f47,f50]) ).
fof(f76,plain,
( ~ in(sK4,singleton(sK4))
| ~ spl7_1
| ~ spl7_2 ),
inference(resolution,[],[f75,f43]) ).
fof(f80,plain,
( $false
| ~ spl7_1
| ~ spl7_2 ),
inference(forward_subsumption_resolution,[],[f76,f39]) ).
fof(f81,plain,
( ~ spl7_1
| ~ spl7_2 ),
inference(avatar_contradiction_clause,[],[f80]) ).
fof(f83,plain,
( in(sK4,sK5)
| ~ spl7_1 ),
inference(resolution,[],[f47,f42]) ).
fof(f86,plain,
( $false
| ~ spl7_1
| spl7_3 ),
inference(forward_subsumption_resolution,[],[f83,f55]) ).
fof(f87,plain,
( ~ spl7_1
| spl7_3 ),
inference(avatar_contradiction_clause,[],[f86]) ).
cnf(s1,plain,
( spl7_1
| ~ spl7_2 ),
inference(sat_conversion,[],[f52]) ).
cnf(s2,plain,
( spl7_1
| spl7_3 ),
inference(sat_conversion,[],[f57]) ).
cnf(s3,plain,
( ~ spl7_1
| spl7_2
| ~ spl7_3 ),
inference(sat_conversion,[],[f58]) ).
cnf(s4,plain,
( spl7_1
| spl7_2
| ~ spl7_3 ),
inference(sat_conversion,[],[f74]) ).
cnf(s5,plain,
( ~ spl7_1
| ~ spl7_2 ),
inference(sat_conversion,[],[f81]) ).
cnf(s6,plain,
( ~ spl7_1
| spl7_3 ),
inference(sat_conversion,[],[f87]) ).
cnf(s7,plain,
spl7_1,
inference(rat,[],[s4,s1,s2]) ).
cnf(s8,plain,
spl7_3,
inference(rat,[],[s6,s7]) ).
cnf(s9,plain,
~ spl7_2,
inference(rat,[],[s5,s7]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s3,s8,s9,s7]) ).
fof(f88,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET921+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n002.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 03:12:52 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 3.42/1.37 % (4117450)Detected formulas, will run a generic FOF schedule.
% 3.42/1.37 % (4117457)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=348616721:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.42/1.37 % (4117460)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=576970409:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.42/1.37 % (4117455)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=3004051949:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.42/1.37 % (4117456)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=4253662991:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.42/1.37 % (4117460)First to succeed.
% 3.42/1.37 % (4117460)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4117450"
% 3.42/1.37 % (4117459)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2002272282:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.42/1.37 % (4117461)dis-21_1_sil=8000:lcm=predicate:random_seed=1921008316: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)
% 3.42/1.37 % (4117458)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2108824070:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.42/1.37 % (4117459)Also succeeded, but the first one will report.
% 3.42/1.37 % (4117458)Also succeeded, but the first one will report.
% 3.42/1.37 % (4117461)Instruction limit reached!
% 3.42/1.37 % (4117461)------------------------------
% 3.42/1.37 % (4117461)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.42/1.37 % (4117461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.42/1.37 % (4117461)CaDiCaL version: 2.1.3
% 3.42/1.37 % (4117461)Termination reason: Instruction limit
% 3.42/1.37 % (4117461)Termination phase: Saturation
% 3.42/1.37 % (4117461)Time elapsed: 0.078 s
% 3.42/1.37 % (4117461)Peak memory usage: 89 MB
% 3.42/1.37 % (4117461)Instructions burned: 130 (million)
% 3.42/1.37 % (4117469)lrs+10_1_sil=8000:sp=occurrence:random_seed=1107581024:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.42/1.37 % (4117469)Also succeeded, but the first one will report.
% 3.42/1.37 % (4117460)Refutation found. Thanks to Tanya!
% 3.42/1.37 % SZS status Theorem for theBenchmark
% 3.42/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 3.42/1.37 % (4117460)------------------------------
% 3.42/1.37 % (4117460)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.42/1.37 % (4117460)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.42/1.37 % (4117460)CaDiCaL version: 2.1.3
% 3.42/1.37 % (4117460)Termination reason: Refutation
% 3.42/1.37 % (4117460)Time elapsed: 0.005 s
% 3.42/1.37 % (4117460)Peak memory usage: 90 MB
% 3.42/1.37 % (4117460)Instructions burned: 4 (million)
% 3.42/1.37 % (4117460)------------------------------
% 3.42/1.37 % (4117460)------------------------------
% 3.42/1.37 % (4117450)Success in time 0.42 s
% 3.42/1.37 % Vampire exiting
%------------------------------------------------------------------------------