%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET987+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 : 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 12:42:28 PM UTC 2026
% Result : Theorem 3.40s 1.43s
% Output : Refutation 3.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 9 unt; 1 def)
% Number of atoms : 27 ( 11 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 21 ( 12 ~; 3 |; 2 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 18 ( 16 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,conjecture,
! [X0,X1] :
( ~ in(X0,X1)
=> set_difference(set_union2(X1,singleton(X0)),singleton(X0)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t141_zfmisc_1) ).
fof(f9,negated_conjecture,
~ ! [X0,X1] :
( ~ in(X0,X1)
=> set_difference(set_union2(X1,singleton(X0)),singleton(X0)) = X1 ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,axiom,
! [X0,X1] : set_difference(set_union2(X0,X1),X1) = set_difference(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_xboole_1) ).
fof(f11,axiom,
! [X0,X1] :
( set_difference(X0,singleton(X1)) = X0
<=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_zfmisc_1) ).
fof(f13,plain,
! [X0,X1] :
( ~ in(X1,X0)
=> set_difference(X0,singleton(X1)) = X0 ),
inference(unused_predicate_definition_removal,[],[f11]) ).
fof(f14,plain,
? [X0,X1] :
( set_difference(set_union2(X1,singleton(X0)),singleton(X0)) != X1
& ~ in(X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f16,plain,
! [X0,X1] :
( set_difference(X0,singleton(X1)) = X0
| in(X1,X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f17,plain,
( sK1 != set_difference(set_union2(sK1,singleton(sK0)),singleton(sK0))
& ~ in(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f14]) ).
fof(f18,plain,
~ in(sK0,sK1),
inference(cnf_transformation,[],[f17]) ).
fof(f19,plain,
sK1 != set_difference(set_union2(sK1,singleton(sK0)),singleton(sK0)),
inference(cnf_transformation,[],[f17]) ).
fof(f23,plain,
! [X0,X1] :
( set_difference(X0,singleton(X1)) = X0
| in(X1,X0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f24,plain,
! [X0,X1] : set_difference(set_union2(X0,X1),X1) = set_difference(X0,X1),
inference(cnf_transformation,[],[f10]) ).
fof(f25,definition,
~ sP2(sK1),
introduced(definition,[new_symbols(definition,[sP2])],[inequality_splitting_name_introduction]) ).
fof(f26,plain,
sP2(set_difference(set_union2(sK1,singleton(sK0)),singleton(sK0))),
inference(inequality_splitting,[],[f19,f25]) ).
fof(f27,plain,
sP2(set_difference(sK1,singleton(sK0))),
inference(forward_demodulation,[],[f26,f24]) ).
fof(f28,plain,
( sP2(sK1)
| in(sK0,sK1) ),
inference(superposition,[],[f27,f23]) ).
fof(f29,plain,
in(sK0,sK1),
inference(forward_subsumption_resolution,[],[f28,f25]) ).
fof(f30,plain,
$false,
inference(forward_subsumption_resolution,[],[f29,f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET987+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 28 03:23:48 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 3.40/1.43 % (3228886)Detected formulas, will run a generic FOF schedule.
% 3.40/1.43 % (3228892)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=2086553035:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.40/1.43 % (3228896)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1998734367:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.40/1.43 % (3228895)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1192294060:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.40/1.43 % (3228894)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2120936804:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.40/1.43 % (3228894)First to succeed.
% 3.40/1.43 % (3228895)Also succeeded, but the first one will report.
% 3.40/1.43 % (3228894)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3228886"
% 3.40/1.43 % (3228896)Also succeeded, but the first one will report.
% 3.40/1.43 % (3228891)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=3880376968:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.40/1.43 % (3228893)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=2792582653:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.40/1.43 % (3228897)dis-21_1_sil=8000:lcm=predicate:random_seed=4018564640: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)
% 3.40/1.43 % (3228897)Refutation not found, incomplete strategy
% 3.40/1.43 % (3228897)------------------------------
% 3.40/1.43 % (3228897)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.43 % (3228897)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.43 % (3228897)CaDiCaL version: 2.1.3
% 3.40/1.43 % (3228897)Termination reason: Refutation not found, incomplete strategy
% 3.40/1.43 % (3228897)Time elapsed: 0.001 s
% 3.40/1.43 % (3228897)Peak memory usage: 88 MB
% 3.40/1.43 % (3228894)Refutation found. Thanks to Tanya!
% 3.40/1.43 % SZS status Theorem for theBenchmark
% 3.40/1.43 % SZS output start Proof for theBenchmark
% See solution above
% 3.40/1.43 % (3228894)------------------------------
% 3.40/1.43 % (3228894)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.43 % (3228894)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.43 % (3228894)CaDiCaL version: 2.1.3
% 3.40/1.43 % (3228894)Termination reason: Refutation
% 3.40/1.43 % (3228894)Time elapsed: 0.002 s
% 3.40/1.43 % (3228894)Peak memory usage: 88 MB
% 3.40/1.43 % (3228894)Instructions burned: 1 (million)
% 3.40/1.43 % (3228894)------------------------------
% 3.40/1.43 % (3228894)------------------------------
% 3.40/1.43 % (3228886)Success in time 0.395 s
% 3.40/1.43 % Vampire exiting
%------------------------------------------------------------------------------