%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET891+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 : n009.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 12:42:15 PM UTC 2026
% Result : Theorem 3.36s 1.34s
% Output : Refutation 3.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 15 unt; 1 def)
% Number of atoms : 15 ( 11 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 16 ( 14 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1] : union(unordered_pair(X0,X1)) = set_union2(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l52_zfmisc_1) ).
fof(f9,conjecture,
! [X0,X1] : union(unordered_pair(singleton(X0),singleton(X1))) = unordered_pair(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_zfmisc_1) ).
fof(f10,negated_conjecture,
~ ! [X0,X1] : union(unordered_pair(singleton(X0),singleton(X1))) = unordered_pair(X0,X1),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,axiom,
! [X0,X1] : unordered_pair(X0,X1) = set_union2(singleton(X0),singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_enumset1) ).
fof(f13,plain,
? [X0,X1] : unordered_pair(X0,X1) != union(unordered_pair(singleton(X0),singleton(X1))),
inference(ennf_transformation,[],[f10]) ).
fof(f14,plain,
unordered_pair(sK0,sK1) != union(unordered_pair(singleton(sK0),singleton(sK1))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f13]) ).
fof(f15,plain,
unordered_pair(sK0,sK1) != union(unordered_pair(singleton(sK0),singleton(sK1))),
inference(cnf_transformation,[],[f14]) ).
fof(f19,plain,
! [X0,X1] : set_union2(X0,X1) = union(unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f6]) ).
fof(f20,plain,
! [X0,X1] : unordered_pair(X0,X1) = set_union2(singleton(X0),singleton(X1)),
inference(cnf_transformation,[],[f11]) ).
fof(f21,plain,
! [X0,X1] : set_union2(X0,X1) = union(set_union2(singleton(X0),singleton(X1))),
inference(definition_unfolding,[],[f19,f20]) ).
fof(f22,plain,
set_union2(singleton(sK0),singleton(sK1)) != union(set_union2(singleton(singleton(sK0)),singleton(singleton(sK1)))),
inference(definition_unfolding,[],[f15,f20,f20]) ).
fof(f24,definition,
~ sP2(set_union2(singleton(sK0),singleton(sK1))),
introduced(definition,[new_symbols(definition,[sP2])],[inequality_splitting_name_introduction]) ).
fof(f25,plain,
sP2(union(set_union2(singleton(singleton(sK0)),singleton(singleton(sK1))))),
inference(inequality_splitting,[],[f22,f24]) ).
fof(f26,plain,
sP2(set_union2(singleton(sK0),singleton(sK1))),
inference(forward_demodulation,[],[f25,f21]) ).
fof(f27,plain,
$false,
inference(forward_subsumption_resolution,[],[f26,f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET891+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 03:07:00 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 3.36/1.34 % (2624959)Detected formulas, will run a generic FOF schedule.
% 3.36/1.34 % (2624966)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=2070320557:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.36/1.34 % (2624968)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3053795911:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.36/1.34 % (2624969)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2453673556:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.36/1.34 % (2624967)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1042724850:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.36/1.34 % (2624964)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=1088680721:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.36/1.34 % (2624970)dis-21_1_sil=8000:lcm=predicate:random_seed=1726714106: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)
% 3.36/1.34 % (2624965)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=3645036862:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.36/1.34 % (2624967)First to succeed.
% 3.36/1.34 % (2624970)Also succeeded, but the first one will report.
% 3.36/1.34 % (2624968)Also succeeded, but the first one will report.
% 3.36/1.34 % (2624967)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2624959"
% 3.36/1.34 % (2624969)Also succeeded, but the first one will report.
% 3.36/1.34 % (2624967)Refutation found. Thanks to Tanya!
% 3.36/1.34 % SZS status Theorem for theBenchmark
% 3.36/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 3.36/1.35 % (2624967)------------------------------
% 3.36/1.35 % (2624967)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.36/1.35 % (2624967)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.36/1.35 % (2624967)CaDiCaL version: 2.1.3
% 3.36/1.35 % (2624967)Termination reason: Refutation
% 3.36/1.35 % (2624967)Time elapsed: 0.002 s
% 3.36/1.35 % (2624967)Peak memory usage: 88 MB
% 3.36/1.35 % (2624967)------------------------------
% 3.36/1.35 % (2624967)------------------------------
% 3.36/1.35 % (2624959)Success in time 0.404 s
% 3.36/1.35 % Vampire exiting
%------------------------------------------------------------------------------