%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET879+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 : n003.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 12:44:54 PM UTC 2026
% Result : Theorem 0.15s 5.47s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 39 ( 6 unt; 2 def)
% Number of atoms : 79 ( 34 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 74 ( 34 ~; 32 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 27 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f3,axiom,
! [X0,X1] :
( set_difference(singleton(X0),X1) = singleton(X0)
<=> ~ in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l34_zfmisc_1) ).
fof(f6,conjecture,
! [X0,X1] :
( set_difference(singleton(X0),singleton(X1)) = singleton(X0)
<=> X0 != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_zfmisc_1) ).
fof(f7,negated_conjecture,
~ ! [X0,X1] :
( set_difference(singleton(X0),singleton(X1)) = singleton(X0)
<=> X0 != X1 ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f9,plain,
? [X0,X1] :
( set_difference(singleton(X0),singleton(X1)) = singleton(X0)
<~> X0 != X1 ),
inference(ennf_transformation,[],[f7]) ).
fof(f11,plain,
! [X2,X0,X1] :
( X0 != X2
| in(X2,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f2]) ).
fof(f12,plain,
! [X2,X0,X1] :
( X0 = X2
| ~ in(X2,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f2]) ).
fof(f15,plain,
! [X0,X1] :
( in(X0,X1)
| singleton(X0) = set_difference(singleton(X0),X1) ),
inference(cnf_transformation,[],[f3]) ).
fof(f16,plain,
! [X0,X1] :
( ~ in(X0,X1)
| singleton(X0) != set_difference(singleton(X0),X1) ),
inference(cnf_transformation,[],[f3]) ).
fof(f19,plain,
( sK3 != sK4
| singleton(sK3) = set_difference(singleton(sK3),singleton(sK4)) ),
inference(cnf_transformation,[],[f9]) ).
fof(f20,plain,
( sK3 = sK4
| singleton(sK3) != set_difference(singleton(sK3),singleton(sK4)) ),
inference(cnf_transformation,[],[f9]) ).
fof(f21,plain,
! [X2,X0] :
( ~ in(X2,singleton(X0))
| X0 = X2 ),
inference(equality_resolution,[],[f12]) ).
fof(f22,plain,
! [X2,X1] :
( in(X2,X1)
| singleton(X2) != X1 ),
inference(equality_resolution,[],[f11]) ).
fof(f23,plain,
! [X2] : in(X2,singleton(X2)),
inference(equality_resolution,[],[f22]) ).
fof(f25,definition,
( spl5_1
<=> singleton(sK3) = set_difference(singleton(sK3),singleton(sK4)) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f26,plain,
( singleton(sK3) != set_difference(singleton(sK3),singleton(sK4))
| spl5_1 ),
inference(avatar_component_clause,[],[f25]) ).
fof(f27,plain,
( singleton(sK3) = set_difference(singleton(sK3),singleton(sK4))
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f25]) ).
fof(f29,definition,
( spl5_2
<=> sK3 = sK4 ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f30,plain,
( sK3 = sK4
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f29]) ).
fof(f31,plain,
( sK3 != sK4
| spl5_2 ),
inference(avatar_component_clause,[],[f29]) ).
fof(f32,plain,
( spl5_1
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f19,f29,f25]) ).
fof(f33,plain,
( ~ spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f20,f29,f25]) ).
fof(f37,plain,
! [X0,X1] :
( singleton(X0) = set_difference(singleton(X0),singleton(X1))
| X0 = X1 ),
inference(resolution,[],[f15,f21]) ).
fof(f38,plain,
! [X0] : singleton(X0) != set_difference(singleton(X0),singleton(X0)),
inference(resolution,[],[f16,f23]) ).
fof(f50,plain,
( singleton(sK3) != singleton(sK3)
| sK3 = sK4
| spl5_1 ),
inference(superposition,[],[f26,f37]) ).
fof(f51,plain,
( sK3 = sK4
| spl5_1 ),
inference(trivial_inequality_removal,[],[f50]) ).
fof(f52,plain,
( $false
| spl5_1
| spl5_2 ),
inference(forward_subsumption_resolution,[],[f51,f31]) ).
fof(f53,plain,
( spl5_1
| spl5_2 ),
inference(avatar_contradiction_clause,[],[f52]) ).
fof(f54,plain,
( singleton(sK3) = set_difference(singleton(sK3),singleton(sK3))
| ~ spl5_1
| ~ spl5_2 ),
inference(superposition,[],[f27,f30]) ).
fof(f55,plain,
( $false
| ~ spl5_1
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f54,f38]) ).
fof(f56,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(avatar_contradiction_clause,[],[f55]) ).
cnf(s1,plain,
( spl5_1
| ~ spl5_2 ),
inference(sat_conversion,[],[f32]) ).
cnf(s2,plain,
( ~ spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f33]) ).
cnf(s3,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f53]) ).
cnf(s4,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(sat_conversion,[],[f56]) ).
cnf(s5,plain,
spl5_1,
inference(rat,[],[s1,s3]) ).
cnf(s6,plain,
~ spl5_2,
inference(rat,[],[s4,s5]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s2,s6,s5]) ).
fof(f57,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET879+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/5.39 % Computer : n003.cluster.edu
% 0.12/5.39 % Model : x86_64 x86_64
% 0.12/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.39 % Memory : 8046.5625MB
% 0.12/5.39 % OS : Linux 6.8.0-71-generic
% 0.12/5.39 % CPULimit : 300
% 0.12/5.39 % WCLimit : 300
% 0.12/5.39 % DateTime : Mon Sep 28 03:07:47 UTC 2026
% 0.12/5.39 % CPUTime :
% 0.12/5.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.15/5.43 Running first-order model finding
% 0.15/5.43 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
% 0.15/5.47 % (1143870)Will run a generic schedule for satisfiability detection.
% 0.15/5.47 % (1143875)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3789797561_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/5.47 % TRYING [1]
% 0.15/5.47 % TRYING [2]
% 0.15/5.47 % TRYING [3]
% 0.15/5.47 % TRYING [4]
% 0.15/5.47 % TRYING [5]
% 0.15/5.47 % (1143876)% WARNING: option uhcvi not known.
% 0.15/5.47 % TRYING [6]
% 0.15/5.47 % (1143876)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=28072844:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/5.47 % (1143877)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4081499723:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/5.47 % (1143878)dis+10_1_sil=32000:sp=arity:random_seed=2487803771:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/5.47 % (1143879)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3821139789:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/5.47 % (1143880)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2310701597:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/5.47 % (1143881)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2108370820:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/5.47 % TRYING [7]
% 0.15/5.47 % (1143878) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1143870-1143878"...
% 0.15/5.47 % (1143879) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1143870-1143879"...
% 0.15/5.47 % (1143876) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1143870-1143876"...
% 0.15/5.47 % (1143880) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1143870-1143880"...
% 0.15/5.47 % (1143881) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1143870-1143881"...
% 0.15/5.47 % (1143877) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1143870-1143877"...
% 0.15/5.47 % (1143879)...printing done.
% 0.15/5.47 % (1143876)...printing done.
% 0.15/5.47 % (1143878)...printing done.
% 0.15/5.47 % (1143880)...printing done.
% 0.15/5.47 % (1143881)...printing done.
% 0.15/5.47 % (1143879)Refutation found. Thanks to Tanya!
% 0.15/5.47 % SZS status Theorem for theBenchmark
% 0.15/5.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/5.47 % (1143879)------------------------------
% 0.15/5.47 % (1143879)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/5.47 % (1143879)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/5.47 % (1143879)CaDiCaL version: 2.1.3
% 0.15/5.47 % (1143879)Termination reason: Refutation
% 0.15/5.47 % (1143879)Time elapsed: 0.003 s
% 0.15/5.47 % (1143879)Peak memory usage: 12 MB
% 0.15/5.47 % (1143879)Instructions burned: 2 (million)
% 0.15/5.47 % (1143870)Success in time 0.038 s
% 0.15/5.47 % Vampire exiting
%------------------------------------------------------------------------------