%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET351+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n011.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 12:43:40 PM UTC 2026
% Result : Theorem 0.38s 0.46s
% Output : Refutation 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 49 ( 11 unt; 2 def)
% Number of atoms : 101 ( 5 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 87 ( 35 ~; 40 |; 3 &)
% ( 7 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn 48 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(f8,axiom,
! [X0,X1] :
( member(X0,singleton(X1))
<=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',singleton) ).
fof(f10,axiom,
! [X0,X1] :
( member(X0,sum(X1))
<=> ? [X2] :
( member(X2,X1)
& member(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',sum) ).
fof(f12,conjecture,
! [X0] : equal_set(sum(singleton(X0)),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI39) ).
fof(f13,negated_conjecture,
~ ! [X0] : equal_set(sum(singleton(X0)),X0),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ( subset(X0,X1)
& subset(X1,X0) )
=> equal_set(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f15,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f16,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f17,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(flattening,[],[f16]) ).
fof(f19,plain,
? [X0] : ~ equal_set(sum(singleton(X0)),X0),
inference(ennf_transformation,[],[f13]) ).
fof(f20,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| member(X2,X1)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f21,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f22,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f23,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f36,plain,
! [X0,X1] :
( X0 != X1
| member(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f8]) ).
fof(f37,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f8]) ).
fof(f41,plain,
! [X0,X1] :
( member(X0,sK1(X0,X1))
| ~ member(X0,sum(X1)) ),
inference(cnf_transformation,[],[f10]) ).
fof(f42,plain,
! [X0,X1] :
( member(sK1(X0,X1),X1)
| ~ member(X0,sum(X1)) ),
inference(cnf_transformation,[],[f10]) ).
fof(f43,plain,
! [X2,X0,X1] :
( ~ member(X0,X2)
| ~ member(X2,X1)
| member(X0,sum(X1)) ),
inference(cnf_transformation,[],[f10]) ).
fof(f47,plain,
~ equal_set(sum(singleton(sK3)),sK3),
inference(cnf_transformation,[],[f19]) ).
fof(f48,plain,
! [X1] : member(X1,singleton(X1)),
inference(equality_resolution,[],[f36]) ).
fof(f56,plain,
! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,X2)
| member(sK0(X2,X1),X2) ),
inference(resolution,[],[f20,f21]) ).
fof(f58,plain,
( ~ subset(sum(singleton(sK3)),sK3)
| ~ subset(sK3,sum(singleton(sK3))) ),
inference(resolution,[],[f23,f47]) ).
fof(f60,definition,
( spl4_1
<=> subset(sK3,sum(singleton(sK3))) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f62,plain,
( ~ subset(sK3,sum(singleton(sK3)))
| spl4_1 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f64,definition,
( spl4_2
<=> subset(sum(singleton(sK3)),sK3) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f66,plain,
( ~ subset(sum(singleton(sK3)),sK3)
| spl4_2 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f67,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f58,f64,f60]) ).
fof(f68,plain,
( ~ member(sK0(sK3,sum(singleton(sK3))),sum(singleton(sK3)))
| spl4_1 ),
inference(resolution,[],[f62,f22]) ).
fof(f69,plain,
( member(sK0(sK3,sum(singleton(sK3))),sK3)
| spl4_1 ),
inference(resolution,[],[f62,f21]) ).
fof(f76,plain,
! [X0,X1] :
( ~ member(X0,sum(singleton(X1)))
| sK1(X0,singleton(X1)) = X1 ),
inference(resolution,[],[f42,f37]) ).
fof(f107,plain,
( ! [X0] :
( ~ member(sK0(sK3,sum(singleton(sK3))),X0)
| ~ member(X0,singleton(sK3)) )
| spl4_1 ),
inference(resolution,[],[f43,f68]) ).
fof(f136,plain,
( ~ member(sK3,singleton(sK3))
| spl4_1 ),
inference(resolution,[],[f107,f69]) ).
fof(f145,plain,
( $false
| spl4_1 ),
inference(forward_subsumption_resolution,[],[f136,f48]) ).
fof(f146,plain,
spl4_1,
inference(avatar_contradiction_clause,[],[f145]) ).
fof(f159,plain,
( ~ member(sK0(sum(singleton(sK3)),sK3),sK3)
| spl4_2 ),
inference(resolution,[],[f66,f22]) ).
fof(f160,plain,
( member(sK0(sum(singleton(sK3)),sK3),sum(singleton(sK3)))
| spl4_2 ),
inference(resolution,[],[f66,f21]) ).
fof(f513,plain,
( ! [X0] :
( member(sK0(sum(singleton(sK3)),sK3),X0)
| member(sK0(sum(singleton(sK3)),X0),sum(singleton(sK3))) )
| spl4_2 ),
inference(resolution,[],[f56,f160]) ).
fof(f559,plain,
( sK3 = sK1(sK0(sum(singleton(sK3)),sK3),singleton(sK3))
| spl4_2 ),
inference(resolution,[],[f76,f160]) ).
fof(f566,plain,
( member(sK0(sum(singleton(sK3)),sK3),sK3)
| ~ member(sK0(sum(singleton(sK3)),sK3),sum(singleton(sK3)))
| spl4_2 ),
inference(superposition,[],[f41,f559]) ).
fof(f567,plain,
( member(sK0(sum(singleton(sK3)),sK3),sK3)
| spl4_2 ),
inference(forward_subsumption_resolution,[],[f566,f513]) ).
fof(f568,plain,
( $false
| spl4_2 ),
inference(forward_subsumption_resolution,[],[f567,f159]) ).
fof(f569,plain,
spl4_2,
inference(avatar_contradiction_clause,[],[f568]) ).
cnf(s1,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f67]) ).
cnf(s2,plain,
spl4_1,
inference(sat_conversion,[],[f146]) ).
cnf(s5,plain,
spl4_2,
inference(sat_conversion,[],[f569]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s5,s2]) ).
fof(f570,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET351+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 01:32:30 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.39 Running first-order model finding
% 0.10/0.39 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
% 0.38/0.46 % (2934715)Will run a generic schedule for satisfiability detection.
% 0.38/0.46 % (2934720)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1703581561_2999 on theBenchmark for (2999ds/0Mi)
% 0.38/0.46 % TRYING [1]
% 0.38/0.46 % TRYING [2]
% 0.38/0.46 % TRYING [3]
% 0.38/0.46 % TRYING [4]
% 0.38/0.46 % (2934721)% WARNING: option uhcvi not known.
% 0.38/0.46 % TRYING [5]
% 0.38/0.46 % (2934722)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=319612736:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.38/0.46 % (2934726)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=362894942:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.38/0.46 % (2934723)dis+10_1_sil=32000:sp=arity:random_seed=4242339104:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.38/0.46 % (2934724)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4019035343:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.38/0.46 % (2934725)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=522939176:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.38/0.46 % (2934721)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=42496956:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.38/0.46 % TRYING [6]
% 0.38/0.46 % TRYING [7]
% 0.38/0.46 % (2934724) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2934715-2934724"...
% 0.38/0.46 % (2934724)...printing done.
% 0.38/0.46 % (2934724)Refutation found. Thanks to Tanya!
% 0.38/0.46 % SZS status Theorem for theBenchmark
% 0.38/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.38/0.47 % (2934724)------------------------------
% 0.38/0.47 % (2934724)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.38/0.47 % (2934724)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.38/0.47 % (2934724)CaDiCaL version: 2.1.3
% 0.38/0.47 % (2934724)Termination reason: Refutation
% 0.38/0.47 % (2934724)Time elapsed: 0.023 s
% 0.38/0.47 % (2934724)Peak memory usage: 12 MB
% 0.38/0.47 % (2934724)Instructions burned: 33 (million)
% 0.38/0.47 % (2934715)Success in time 0.061 s
% 0.38/0.47 % Vampire exiting
%------------------------------------------------------------------------------