%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET093+1 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 12:40:03 PM UTC 2026
% Result : Theorem 3.43s 1.22s
% Output : Refutation 3.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 9 unt; 0 def)
% Number of atoms : 17 ( 7 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 4 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 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 : 10 ( 9 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair) ).
fof(f6,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set_defn) ).
fof(f48,conjecture,
! [X0] :
( singleton(member_of(X0)) = X0
=> member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_2_to_singletons_are_sets) ).
fof(f49,negated_conjecture,
~ ! [X0] :
( singleton(member_of(X0)) = X0
=> member(X0,universal_class) ),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f66,plain,
? [X0] :
( ~ member(X0,universal_class)
& singleton(member_of(X0)) = X0 ),
inference(ennf_transformation,[],[f49]) ).
fof(f109,plain,
( ~ member(sK6,universal_class)
& sK6 = singleton(member_of(sK6)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X0,sK6)],[f66]) ).
fof(f121,plain,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[],[f5]) ).
fof(f122,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f201,plain,
sK6 = singleton(member_of(sK6)),
inference(cnf_transformation,[],[f109]) ).
fof(f202,plain,
~ member(sK6,universal_class),
inference(cnf_transformation,[],[f109]) ).
fof(f210,plain,
! [X0] : member(singleton(X0),universal_class),
inference(superposition,[],[f121,f122]) ).
fof(f211,plain,
member(sK6,universal_class),
inference(superposition,[],[f210,f201]) ).
fof(f212,plain,
$false,
inference(forward_subsumption_resolution,[],[f211,f202]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET093+1 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.35 % Computer : n013.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8046.5625MB
% 0.12/0.35 % OS : Linux 6.8.0-71-generic
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Mon Sep 28 00:38:50 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 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
% 3.43/1.22 % (704268)Detected formulas, will run a generic FOF schedule.
% 3.43/1.22 % (704278)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1025256837:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.43/1.22 % (704275)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=2094316605:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.43/1.22 % (704274)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=79185017:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.43/1.22 % (704276)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4263850904:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.43/1.22 % (704279)dis-21_1_sil=8000:lcm=predicate:random_seed=1222025101: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)
% 3.43/1.22 % (704277)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3536741463:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.43/1.22 % (704273)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=4141549147:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.43/1.22 % (704276)Refutation not found, incomplete strategy
% 3.43/1.22 % (704276)------------------------------
% 3.43/1.22 % (704276)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.43/1.22 % (704276)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/1.22 % (704276)CaDiCaL version: 2.1.3
% 3.43/1.22 % (704276)Termination reason: Refutation not found, incomplete strategy
% 3.43/1.22 % (704276)Time elapsed: 0.001 s
% 3.43/1.22 % (704276)Peak memory usage: 88 MB
% 3.43/1.22 % (704277)Refutation not found, incomplete strategy
% 3.43/1.22 % (704277)------------------------------
% 3.43/1.22 % (704277)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.43/1.22 % (704277)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/1.22 % (704277)CaDiCaL version: 2.1.3
% 3.43/1.22 % (704277)Termination reason: Refutation not found, incomplete strategy
% 3.43/1.22 % (704277)Time elapsed: 0.001 s
% 3.43/1.22 % (704277)Peak memory usage: 88 MB
% 3.43/1.22 % (704277)Instructions burned: 1 (million)
% 3.43/1.22 % (704278)First to succeed.
% 3.43/1.22 % (704278)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-704268"
% 3.43/1.22 % (704279)Instruction limit reached!
% 3.43/1.22 % (704279)------------------------------
% 3.43/1.22 % (704279)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.43/1.22 % (704279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/1.22 % (704279)CaDiCaL version: 2.1.3
% 3.43/1.22 % (704279)Termination reason: Instruction limit
% 3.43/1.22 % (704279)Termination phase: Saturation
% 3.43/1.22 % (704279)Time elapsed: 0.069 s
% 3.43/1.22 % (704279)Peak memory usage: 88 MB
% 3.43/1.22 % (704279)Instructions burned: 130 (million)
% 3.43/1.22 % (704287)lrs+10_1_sil=8000:sp=occurrence:random_seed=1509446758:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.43/1.22 % (704276)------------------------------
% 3.43/1.22 % (704276)------------------------------
% 3.43/1.22 % (704277)------------------------------
% 3.43/1.22 % (704277)------------------------------
% 3.43/1.22 % (704278)Refutation found. Thanks to Tanya!
% 3.43/1.22 % SZS status Theorem for theBenchmark
% 3.43/1.22 % SZS output start Proof for theBenchmark
% See solution above
% 3.43/1.22 % (704278)------------------------------
% 3.43/1.23 % (704278)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.43/1.23 % (704278)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/1.23 % (704278)CaDiCaL version: 2.1.3
% 3.43/1.23 % (704278)Termination reason: Refutation
% 3.43/1.23 % (704278)Time elapsed: 0.004 s
% 3.43/1.23 % (704278)Peak memory usage: 89 MB
% 3.43/1.23 % (704278)Instructions burned: 4 (million)
% 3.43/1.23 % (704278)------------------------------
% 3.43/1.23 % (704278)------------------------------
% 3.43/1.23 % (704268)Success in time 0.426 s
% 3.43/1.23 % Vampire exiting
%------------------------------------------------------------------------------