%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET879+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 : 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 12:42:13 PM UTC 2026
% Result : Theorem 3.48s 1.46s
% Output : Refutation 3.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 5 unt; 0 def)
% Number of atoms : 85 ( 57 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 98 ( 41 ~; 39 |; 12 &)
% ( 5 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 41 ( 35 !; 6 ?)
% 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] :
( set_difference(singleton(X0),X1) = singleton(X0)
<=> ~ in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l34_zfmisc_1) ).
fof(f6,conjecture,
! [X0,X1] :
( set_difference(singleton(X0),singleton(X1)) = singleton(X0)
<=> X0 != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_zfmisc_1) ).
fof(f7,negated_conjecture,
~ ! [X0,X1] :
( set_difference(singleton(X0),singleton(X1)) = singleton(X0)
<=> X0 != X1 ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,plain,
? [X0,X1] :
( set_difference(singleton(X0),singleton(X1)) = singleton(X0)
<~> X0 != X1 ),
inference(ennf_transformation,[],[f7]) ).
fof(f10,plain,
? [X0,X1] :
( ( X0 = X1
| singleton(X0) != set_difference(singleton(X0),singleton(X1)) )
& ( X0 != X1
| set_difference(singleton(X0),singleton(X1)) = singleton(X0) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f11,plain,
( ( sK0 = sK1
| singleton(sK0) != set_difference(singleton(sK0),singleton(sK1)) )
& ( sK0 != sK1
| singleton(sK0) = set_difference(singleton(sK0),singleton(sK1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f10]) ).
fof(f12,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(f13,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,[],[f12]) ).
fof(f14,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))],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ( set_difference(singleton(X0),X1) = singleton(X0)
| in(X0,X1) )
& ( ~ in(X0,X1)
| singleton(X0) != set_difference(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f16,plain,
( sK0 != sK1
| singleton(sK0) = set_difference(singleton(sK0),singleton(sK1)) ),
inference(cnf_transformation,[],[f11]) ).
fof(f17,plain,
( singleton(sK0) != set_difference(singleton(sK0),singleton(sK1))
| sK0 = sK1 ),
inference(cnf_transformation,[],[f11]) ).
fof(f18,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f14]) ).
fof(f19,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f14]) ).
fof(f22,plain,
! [X0,X1] :
( singleton(X0) != set_difference(singleton(X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f23,plain,
! [X0,X1] :
( singleton(X0) = set_difference(singleton(X0),X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f25,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f19]) ).
fof(f26,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f25]) ).
fof(f27,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f18]) ).
fof(f31,plain,
( singleton(sK0) != singleton(sK0)
| sK0 = sK1
| in(sK0,singleton(sK1)) ),
inference(superposition,[],[f17,f23]) ).
fof(f33,plain,
( sK0 = sK1
| in(sK0,singleton(sK1)) ),
inference(trivial_inequality_removal,[],[f31]) ).
fof(f34,plain,
sK0 = sK1,
inference(forward_subsumption_resolution,[],[f33,f27]) ).
fof(f35,plain,
( sK1 != sK1
| singleton(sK1) = set_difference(singleton(sK1),singleton(sK1)) ),
inference(superposition,[],[f16,f34]) ).
fof(f36,plain,
singleton(sK1) = set_difference(singleton(sK1),singleton(sK1)),
inference(trivial_inequality_removal,[],[f35]) ).
fof(f37,plain,
( singleton(sK1) != singleton(sK1)
| ~ in(sK1,singleton(sK1)) ),
inference(superposition,[],[f22,f36]) ).
fof(f38,plain,
~ in(sK1,singleton(sK1)),
inference(trivial_inequality_removal,[],[f37]) ).
fof(f39,plain,
$false,
inference(forward_subsumption_resolution,[],[f38,f26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET879+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n005.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Mon Sep 28 03:05:19 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 3.48/1.46 % (393985)Detected formulas, will run a generic FOF schedule.
% 3.48/1.46 % (393990)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=3095741270:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.48/1.46 % (393994)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3332823754:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.48/1.46 % (393993)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3473769247:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.48/1.46 % (393996)dis-21_1_sil=8000:lcm=predicate:random_seed=290489321: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)
% 3.48/1.46 % (393991)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=358523835:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.48/1.46 % (393992)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=3282635647:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.48/1.46 % (393994)First to succeed.
% 3.48/1.46 % (393993)Also succeeded, but the first one will report.
% 3.48/1.46 % (393994)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-393985"
% 3.48/1.46 % (393995)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2244663501:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.48/1.46 % (393995)Also succeeded, but the first one will report.
% 3.48/1.46 % (393996)Instruction limit reached!
% 3.48/1.46 % (393996)------------------------------
% 3.48/1.46 % (393996)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.46 % (393996)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.46 % (393996)CaDiCaL version: 2.1.3
% 3.48/1.46 % (393996)Termination reason: Instruction limit
% 3.48/1.46 % (393996)Termination phase: Saturation
% 3.48/1.46 % (393996)Time elapsed: 0.059 s
% 3.48/1.46 % (393996)Peak memory usage: 88 MB
% 3.48/1.46 % (393996)Instructions burned: 129 (million)
% 3.48/1.46 % (394004)lrs+10_1_sil=8000:sp=occurrence:random_seed=1384155778:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.48/1.46 % (394004)Also succeeded, but the first one will report.
% 3.48/1.46 % (393994)Refutation found. Thanks to Tanya!
% 3.48/1.46 % SZS status Theorem for theBenchmark
% 3.48/1.46 % SZS output start Proof for theBenchmark
% See solution above
% 3.48/1.46 % (393994)------------------------------
% 3.48/1.46 % (393994)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.46 % (393994)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.46 % (393994)CaDiCaL version: 2.1.3
% 3.48/1.46 % (393994)Termination reason: Refutation
% 3.48/1.46 % (393994)Time elapsed: 0.002 s
% 3.48/1.46 % (393994)Peak memory usage: 88 MB
% 3.48/1.46 % (393994)Instructions burned: 2 (million)
% 3.48/1.46 % (393994)------------------------------
% 3.48/1.46 % (393994)------------------------------
% 3.48/1.46 % (393985)Success in time 0.408 s
% 3.48/1.46 % Vampire exiting
%------------------------------------------------------------------------------