%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET940+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 : 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 12:42:23 PM UTC 2026
% Result : Theorem 2.81s 1.37s
% Output : Refutation 2.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 9 ( 9 unt; 0 def)
% Number of atoms : 9 ( 8 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 : 3 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 10 ( 8 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,conjecture,
! [X0,X1] : union(unordered_pair(X0,X1)) = set_union2(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t93_zfmisc_1) ).
fof(f9,negated_conjecture,
~ ! [X0,X1] : union(unordered_pair(X0,X1)) = set_union2(X0,X1),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,axiom,
! [X0,X1] : union(unordered_pair(X0,X1)) = set_union2(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l52_zfmisc_1) ).
fof(f12,plain,
? [X0,X1] : set_union2(X0,X1) != union(unordered_pair(X0,X1)),
inference(ennf_transformation,[],[f9]) ).
fof(f13,plain,
set_union2(sK0,sK1) != union(unordered_pair(sK0,sK1)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f12]) ).
fof(f14,plain,
set_union2(sK0,sK1) != union(unordered_pair(sK0,sK1)),
inference(cnf_transformation,[],[f13]) ).
fof(f18,plain,
! [X0,X1] : set_union2(X0,X1) = union(unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f10]) ).
fof(f19,plain,
union(unordered_pair(sK0,sK1)) != union(unordered_pair(sK0,sK1)),
inference(definition_unfolding,[],[f14,f18]) ).
fof(f22,plain,
$false,
inference(trivial_inequality_removal,[],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET940+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n013.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 28 03:15:06 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 2.81/1.37 % (772818)Detected formulas, will run a generic FOF schedule.
% 2.81/1.37 % (772827)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1799821200:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.81/1.37 % (772827)First to succeed.
% 2.81/1.37 % (772827)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-772818"
% 2.81/1.37 % (772823)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=844183978:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.81/1.37 % (772824)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=4144711015:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.81/1.37 % (772829)dis-21_1_sil=8000:lcm=predicate:random_seed=4247042941: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)
% 2.81/1.37 % (772826)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=910625606:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.81/1.37 % (772825)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=3233080954:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.81/1.37 % (772828)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1739816505:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.81/1.37 % (772829)Also succeeded, but the first one will report.
% 2.81/1.37 % (772826)Also succeeded, but the first one will report.
% 2.81/1.37 % (772828)Also succeeded, but the first one will report.
% 2.81/1.37 % (772827)Refutation found. Thanks to Tanya!
% 2.81/1.37 % SZS status Theorem for theBenchmark
% 2.81/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 2.81/1.37 % (772827)------------------------------
% 2.81/1.37 % (772827)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.81/1.37 % (772827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.81/1.37 % (772827)CaDiCaL version: 2.1.3
% 2.81/1.37 % (772827)Termination reason: Refutation
% 2.81/1.37 % (772827)Time elapsed: 0.001 s
% 2.81/1.37 % (772827)Peak memory usage: 88 MB
% 2.81/1.37 % (772827)------------------------------
% 2.81/1.37 % (772827)------------------------------
% 2.81/1.37 % (772818)Success in time 0.313 s
% 2.81/1.37 % Vampire exiting
%------------------------------------------------------------------------------