%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET025+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 12:39:39 PM UTC 2026
% Result : Theorem 0.17s 1.50s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 14 unt; 0 def)
% Number of atoms : 14 ( 5 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 18 ( 16 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair) ).
fof(f6,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set_defn) ).
fof(f7,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_defn) ).
fof(f44,conjecture,
! [X0,X1] : member(ordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_is_set) ).
fof(f45,negated_conjecture,
~ ! [X0,X1] : member(ordered_pair(X0,X1),universal_class),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f47,plain,
? [X0,X1] : ~ member(ordered_pair(X0,X1),universal_class),
inference(ennf_transformation,[],[f45]) ).
fof(f56,plain,
~ member(ordered_pair(sK0,sK1),universal_class),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f47]) ).
fof(f89,plain,
~ member(ordered_pair(sK0,sK1),universal_class),
inference(cnf_transformation,[],[f56]) ).
fof(f103,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
inference(cnf_transformation,[],[f7]) ).
fof(f116,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f129,plain,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[],[f5]) ).
fof(f157,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f103,f116,f116]) ).
fof(f159,plain,
~ member(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK1,sK1))),universal_class),
inference(definition_unfolding,[],[f89,f157]) ).
fof(f202,plain,
$false,
inference(resolution,[],[f129,f159]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET025+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n018.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 00:13:24 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/1.50 % (2874202)Detected formulas, will run a generic FOF schedule.
% 0.17/1.50 % (2874211)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1989454509:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.17/1.50 % (2874211)Refutation not found, incomplete strategy
% 0.17/1.50 % (2874211)------------------------------
% 0.17/1.50 % (2874211)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (2874211)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (2874211)CaDiCaL version: 2.1.3
% 0.17/1.50 % (2874211)Termination reason: Refutation not found, incomplete strategy
% 0.17/1.50 % (2874211)Time elapsed: 0.001 s
% 0.17/1.50 % (2874211)Peak memory usage: 87 MB
% 0.17/1.50 % (2874208)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=1858901656:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.17/1.50 % (2874207)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=3729463598:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.17/1.50 % (2874209)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=4203839944:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.17/1.50 % (2874210)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3740505711:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.17/1.50 % (2874210)Refutation not found, incomplete strategy
% 0.17/1.50 % (2874210)------------------------------
% 0.17/1.50 % (2874210)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (2874210)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (2874210)CaDiCaL version: 2.1.3
% 0.17/1.50 % (2874210)Termination reason: Refutation not found, incomplete strategy
% 0.17/1.50 % (2874210)Time elapsed: 0.001 s
% 0.17/1.50 % (2874210)Peak memory usage: 87 MB
% 0.17/1.50 % (2874213)dis-21_1_sil=8000:lcm=predicate:random_seed=2133635639: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)
% 0.17/1.50 % (2874213)First to succeed.
% 0.17/1.50 % (2874212)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=812887295:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.17/1.50 % (2874213)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2874202"
% 0.17/1.50 % (2874212)Also succeeded, but the first one will report.
% 0.17/1.50 % (2874211)------------------------------
% 0.17/1.50 % (2874211)------------------------------
% 0.17/1.50 % (2874221)lrs+10_1_sil=8000:sp=occurrence:random_seed=2080736924:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 0.17/1.50 % (2874221)Refutation not found, incomplete strategy
% 0.17/1.50 % (2874221)------------------------------
% 0.17/1.50 % (2874221)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (2874221)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (2874221)CaDiCaL version: 2.1.3
% 0.17/1.50 % (2874221)Termination reason: Refutation not found, incomplete strategy
% 0.17/1.50 % (2874221)Time elapsed: 0.001 s
% 0.17/1.50 % (2874221)Peak memory usage: 88 MB
% 0.17/1.50 % (2874210)------------------------------
% 0.17/1.50 % (2874210)------------------------------
% 0.17/1.50 % (2874213)Refutation found. Thanks to Tanya!
% 0.17/1.50 % SZS status Theorem for theBenchmark
% 0.17/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.50 % (2874213)------------------------------
% 0.17/1.50 % (2874213)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (2874213)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (2874213)CaDiCaL version: 2.1.3
% 0.17/1.50 % (2874213)Termination reason: Refutation
% 0.17/1.50 % (2874213)Time elapsed: 0.003 s
% 0.17/1.50 % (2874213)Peak memory usage: 88 MB
% 0.17/1.50 % (2874213)Instructions burned: 3 (million)
% 0.17/1.50 % (2874213)------------------------------
% 0.17/1.50 % (2874213)------------------------------
% 0.17/1.50 % (2874202)Success in time 0.44 s
% 0.17/1.50 % Vampire exiting
%------------------------------------------------------------------------------