%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET873+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 12:44:53 PM UTC 2026
% Result : Theorem 0.16s 0.46s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 10 unt; 0 def)
% Number of atoms : 34 ( 16 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 10 ~; 7 |; 1 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 30 ( 28 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f3,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f7,axiom,
! [X0,X1] :
( subset(set_union2(singleton(X0),X1),X1)
=> in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l21_zfmisc_1) ).
fof(f10,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f11,conjecture,
! [X0,X1] :
( set_union2(singleton(X0),singleton(X1)) = singleton(X0)
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_zfmisc_1) ).
fof(f12,negated_conjecture,
~ ! [X0,X1] :
( set_union2(singleton(X0),singleton(X1)) = singleton(X0)
=> X0 = X1 ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f14,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f10]) ).
fof(f18,plain,
! [X0,X1] :
( in(X0,X1)
| ~ subset(set_union2(singleton(X0),X1),X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f19,plain,
? [X0,X1] :
( X0 != X1
& set_union2(singleton(X0),singleton(X1)) = singleton(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f21,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f23,plain,
! [X2,X0,X1] :
( X0 = X2
| ~ in(X2,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f3]) ).
fof(f29,plain,
! [X0,X1] :
( ~ subset(set_union2(singleton(X0),X1),X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f32,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f14]) ).
fof(f33,plain,
singleton(sK3) = set_union2(singleton(sK3),singleton(sK4)),
inference(cnf_transformation,[],[f19]) ).
fof(f34,plain,
sK3 != sK4,
inference(cnf_transformation,[],[f19]) ).
fof(f35,plain,
! [X2,X0] :
( ~ in(X2,singleton(X0))
| X0 = X2 ),
inference(equality_resolution,[],[f23]) ).
fof(f59,plain,
! [X0,X1] :
( ~ subset(set_union2(X0,singleton(X1)),X0)
| in(X1,X0) ),
inference(superposition,[],[f29,f21]) ).
fof(f72,plain,
( ~ subset(singleton(sK3),singleton(sK3))
| in(sK4,singleton(sK3)) ),
inference(superposition,[],[f59,f33]) ).
fof(f76,plain,
in(sK4,singleton(sK3)),
inference(forward_subsumption_resolution,[],[f72,f32]) ).
fof(f79,plain,
sK3 = sK4,
inference(resolution,[],[f76,f35]) ).
fof(f80,plain,
$false,
inference(forward_subsumption_resolution,[],[f79,f34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET873+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n016.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 03:10:05 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.46 % (3221102)Will run a generic schedule for satisfiability detection.
% 0.16/0.46 % (3221107)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1721753573_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.46 % TRYING [1]
% 0.16/0.46 % TRYING [2]
% 0.16/0.46 % TRYING [3]
% 0.16/0.46 % TRYING [4]
% 0.16/0.46 % (3221108)% WARNING: option uhcvi not known.
% 0.16/0.46 % TRYING [5]
% 0.16/0.46 % (3221108)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1068446972:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.46 % (3221109)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1319256137:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.46 % (3221110)dis+10_1_sil=32000:sp=arity:random_seed=1586704386:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.46 % (3221111)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2978854513:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.46 % (3221113)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=37161633:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.46 % (3221112)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4129546258:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.46 % (3221110) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3221102-3221110"...
% 0.16/0.46 % (3221111) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3221102-3221111"...
% 0.16/0.46 % (3221108) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3221102-3221108"...
% 0.16/0.46 % (3221112) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3221102-3221112"...
% 0.16/0.46 % (3221113) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3221102-3221113"...
% 0.16/0.46 % (3221111)...printing done.
% 0.16/0.46 % (3221110)...printing done.
% 0.16/0.46 % (3221109) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3221102-3221109"...
% 0.16/0.46 % (3221108)...printing done.
% 0.16/0.46 % (3221112)...printing done.
% 0.16/0.46 % (3221111)Refutation found. Thanks to Tanya!
% 0.16/0.46 % SZS status Theorem for theBenchmark
% 0.16/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.47 % (3221111)------------------------------
% 0.16/0.47 % (3221111)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.47 % (3221111)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.47 % (3221111)CaDiCaL version: 2.1.3
% 0.16/0.47 % (3221111)Termination reason: Refutation
% 0.16/0.47 % (3221111)Time elapsed: 0.003 s
% 0.16/0.47 % (3221111)Peak memory usage: 12 MB
% 0.16/0.47 % (3221111)Instructions burned: 2 (million)
% 0.16/0.47 % (3221102)Success in time 0.047 s
% 0.16/0.47 % Vampire exiting
%------------------------------------------------------------------------------