%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET961+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n018.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 12:45:05 PM UTC 2026
% Result : Theorem 0.10s 0.45s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 93 ( 20 unt; 8 def)
% Number of atoms : 222 ( 55 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 236 ( 107 ~; 95 |; 19 &)
% ( 11 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 9 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 94 ( 0 sgn 86 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f4,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f7,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X0,X2)
& in(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(f10,conjecture,
! [X0,X1] :
( cartesian_product2(X0,X1) = cartesian_product2(X1,X0)
=> ( X0 = empty_set
| X1 = empty_set
| X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t114_zfmisc_1) ).
fof(f11,negated_conjecture,
~ ! [X0,X1] :
( cartesian_product2(X0,X1) = cartesian_product2(X1,X0)
=> ( X0 = empty_set
| X1 = empty_set
| X0 = X1 ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f12,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
fof(f14,plain,
? [X0,X1] :
( empty_set != X0
& empty_set != X1
& X0 != X1
& cartesian_product2(X0,X1) = cartesian_product2(X1,X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f15,plain,
? [X0,X1] :
( empty_set != X0
& empty_set != X1
& X0 != X1
& cartesian_product2(X0,X1) = cartesian_product2(X1,X0) ),
inference(flattening,[],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f17,plain,
! [X0] :
( ( X0 = empty_set
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f18,plain,
! [X0] :
( ( X0 = empty_set
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f17]) ).
fof(f19,plain,
! [X0] :
( ( X0 = empty_set
| in(sK0(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f18]) ).
fof(f20,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) )
& ( ( in(X0,X2)
& in(X1,X3) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f21,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) )
& ( ( in(X0,X2)
& in(X1,X3) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f20]) ).
fof(f24,plain,
( empty_set != sK3
& empty_set != sK4
& sK3 != sK4
& cartesian_product2(sK3,sK4) = cartesian_product2(sK4,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f15]) ).
fof(f25,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f26,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK5(X0,X1),X1)
| ~ in(sK5(X0,X1),X0) )
& ( in(sK5(X0,X1),X1)
| in(sK5(X0,X1),X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f25]) ).
fof(f29,plain,
! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f19]) ).
fof(f31,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f4]) ).
fof(f34,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f21]) ).
fof(f35,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f21]) ).
fof(f36,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(cnf_transformation,[],[f21]) ).
fof(f39,plain,
cartesian_product2(sK3,sK4) = cartesian_product2(sK4,sK3),
inference(cnf_transformation,[],[f24]) ).
fof(f40,plain,
sK3 != sK4,
inference(cnf_transformation,[],[f24]) ).
fof(f41,plain,
empty_set != sK4,
inference(cnf_transformation,[],[f24]) ).
fof(f42,plain,
empty_set != sK3,
inference(cnf_transformation,[],[f24]) ).
fof(f43,plain,
! [X0,X1] :
( in(sK5(X0,X1),X1)
| X0 = X1
| in(sK5(X0,X1),X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f44,plain,
! [X0,X1] :
( ~ in(sK5(X0,X1),X1)
| ~ in(sK5(X0,X1),X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f26]) ).
fof(f46,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(definition_unfolding,[],[f36,f31]) ).
fof(f47,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(definition_unfolding,[],[f35,f31]) ).
fof(f48,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(definition_unfolding,[],[f34,f31]) ).
fof(f49,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f29]) ).
fof(f72,plain,
! [X0] :
( in(sK5(X0,empty_set),X0)
| empty_set = X0 ),
inference(resolution,[],[f43,f49]) ).
fof(f85,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(sK3,sK4))
| in(X0,sK4) ),
inference(superposition,[],[f47,f39]) ).
fof(f102,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(sK3,sK4))
| in(X1,sK3) ),
inference(superposition,[],[f48,f39]) ).
fof(f130,plain,
! [X0,X1] :
( ~ in(X0,sK3)
| ~ in(X1,sK4)
| in(X1,sK3) ),
inference(resolution,[],[f46,f102]) ).
fof(f131,plain,
! [X0,X1] :
( ~ in(X0,sK3)
| ~ in(X1,sK4)
| in(X0,sK4) ),
inference(resolution,[],[f46,f85]) ).
fof(f143,definition,
( spl6_1
<=> ! [X1] : ~ in(X1,sK4) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
fof(f144,plain,
( ! [X1] : ~ in(X1,sK4)
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f146,definition,
( spl6_2
<=> ! [X0] :
( ~ in(X0,sK3)
| in(X0,sK4) ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
fof(f147,plain,
( ! [X0] :
( in(X0,sK4)
| ~ in(X0,sK3) )
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f148,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f131,f146,f143]) ).
fof(f150,definition,
( spl6_3
<=> ! [X1] :
( ~ in(X1,sK4)
| in(X1,sK3) ) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
fof(f151,plain,
( ! [X1] :
( in(X1,sK3)
| ~ in(X1,sK4) )
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f153,definition,
( spl6_4
<=> ! [X0] : ~ in(X0,sK3) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
fof(f154,plain,
( ! [X0] : ~ in(X0,sK3)
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f153]) ).
fof(f155,plain,
( spl6_3
| spl6_4 ),
inference(avatar_split_clause,[],[f130,f153,f150]) ).
fof(f159,plain,
( ! [X0] :
( ~ in(sK5(X0,sK4),sK3)
| ~ in(sK5(X0,sK4),X0)
| sK4 = X0 )
| ~ spl6_2 ),
inference(resolution,[],[f147,f44]) ).
fof(f177,definition,
( spl6_5
<=> empty_set = sK3 ),
introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition]) ).
fof(f179,plain,
( empty_set = sK3
| ~ spl6_5 ),
inference(avatar_component_clause,[],[f177]) ).
fof(f196,definition,
( spl6_8
<=> empty_set = sK4 ),
introduced(definition,[new_symbols(definition,[spl6_8])],[avatar_definition]) ).
fof(f198,plain,
( empty_set = sK4
| ~ spl6_8 ),
inference(avatar_component_clause,[],[f196]) ).
fof(f213,plain,
( ~ in(sK5(sK3,sK4),sK3)
| sK3 = sK4
| ~ spl6_2 ),
inference(factoring,[],[f159]) ).
fof(f218,definition,
( spl6_11
<=> sK3 = sK4 ),
introduced(definition,[new_symbols(definition,[spl6_11])],[avatar_definition]) ).
fof(f220,plain,
( sK3 = sK4
| ~ spl6_11 ),
inference(avatar_component_clause,[],[f218]) ).
fof(f222,definition,
( spl6_12
<=> in(sK5(sK3,sK4),sK3) ),
introduced(definition,[new_symbols(definition,[spl6_12])],[avatar_definition]) ).
fof(f224,plain,
( ~ in(sK5(sK3,sK4),sK3)
| spl6_12 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f225,plain,
( spl6_11
| ~ spl6_12
| ~ spl6_2 ),
inference(avatar_split_clause,[],[f213,f146,f222,f218]) ).
fof(f227,plain,
( ~ in(sK5(sK3,sK4),sK4)
| ~ spl6_3
| spl6_12 ),
inference(resolution,[],[f224,f151]) ).
fof(f233,plain,
( sK3 = sK4
| in(sK5(sK3,sK4),sK3)
| ~ spl6_3
| spl6_12 ),
inference(resolution,[],[f227,f43]) ).
fof(f235,plain,
( spl6_12
| spl6_11
| ~ spl6_3
| spl6_12 ),
inference(avatar_split_clause,[],[f233,f222,f150,f218,f222]) ).
fof(f238,plain,
( empty_set = sK3
| ~ spl6_4 ),
inference(resolution,[],[f154,f72]) ).
fof(f240,plain,
( spl6_5
| ~ spl6_4 ),
inference(avatar_split_clause,[],[f238,f153,f177]) ).
fof(f254,plain,
( sK3 != sK3
| ~ spl6_11 ),
inference(superposition,[],[f40,f220]) ).
fof(f272,plain,
( $false
| ~ spl6_11 ),
inference(trivial_inequality_removal,[],[f254]) ).
fof(f273,plain,
~ spl6_11,
inference(avatar_contradiction_clause,[],[f272]) ).
fof(f279,plain,
( empty_set != empty_set
| ~ spl6_5 ),
inference(superposition,[],[f42,f179]) ).
fof(f294,plain,
( $false
| ~ spl6_5 ),
inference(trivial_inequality_removal,[],[f279]) ).
fof(f295,plain,
~ spl6_5,
inference(avatar_contradiction_clause,[],[f294]) ).
fof(f298,plain,
( empty_set = sK4
| ~ spl6_1 ),
inference(resolution,[],[f144,f72]) ).
fof(f300,plain,
( spl6_8
| ~ spl6_1 ),
inference(avatar_split_clause,[],[f298,f143,f196]) ).
fof(f303,plain,
( empty_set != empty_set
| ~ spl6_8 ),
inference(superposition,[],[f41,f198]) ).
fof(f318,plain,
( $false
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f303]) ).
fof(f319,plain,
~ spl6_8,
inference(avatar_contradiction_clause,[],[f318]) ).
cnf(s1,plain,
( spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f148]) ).
cnf(s2,plain,
( spl6_3
| spl6_4 ),
inference(sat_conversion,[],[f155]) ).
cnf(s7,plain,
( ~ spl6_2
| spl6_11
| ~ spl6_12 ),
inference(sat_conversion,[],[f225]) ).
cnf(s9,plain,
( spl6_12
| spl6_11
| ~ spl6_3
| spl6_12 ),
inference(sat_conversion,[],[f235]) ).
cnf(s10,plain,
( ~ spl6_3
| spl6_11
| spl6_12 ),
inference(rat,[],[s9]) ).
cnf(s11,plain,
( ~ spl6_4
| spl6_5 ),
inference(sat_conversion,[],[f240]) ).
cnf(s13,plain,
~ spl6_11,
inference(sat_conversion,[],[f273]) ).
cnf(s16,plain,
~ spl6_5,
inference(sat_conversion,[],[f295]) ).
cnf(s17,plain,
( ~ spl6_1
| spl6_8 ),
inference(sat_conversion,[],[f300]) ).
cnf(s19,plain,
~ spl6_8,
inference(sat_conversion,[],[f319]) ).
cnf(s20,plain,
~ spl6_1,
inference(rat,[],[s17,s19]) ).
cnf(s21,plain,
~ spl6_4,
inference(rat,[],[s11,s16]) ).
cnf(s22,plain,
( ~ spl6_3
| spl6_12 ),
inference(rat,[],[s10,s13]) ).
cnf(s24,plain,
( ~ spl6_2
| ~ spl6_12 ),
inference(rat,[],[s7,s13]) ).
cnf(s29,plain,
spl6_3,
inference(rat,[],[s2,s21]) ).
cnf(s30,plain,
spl6_12,
inference(rat,[],[s22,s29]) ).
cnf(s33,plain,
~ spl6_2,
inference(rat,[],[s24,s30]) ).
cnf(s34,plain,
$false,
inference(rat,[],[s1,s33,s20]) ).
fof(f320,plain,
$false,
inference(avatar_sat_refutation,[],[s34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET961+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n018.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 03:18:39 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.39 Running first-order model finding
% 0.10/0.39 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.45 % (2965134)Will run a generic schedule for satisfiability detection.
% 0.10/0.45 % (2965139)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=741830301_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.45 % Detected minimum model sizes of [3]
% 0.10/0.45 % Detected maximum model sizes of [max]
% 0.10/0.45 % TRYING [3]
% 0.10/0.45 % TRYING [4]
% 0.10/0.45 % (2965140)% WARNING: option uhcvi not known.
% 0.10/0.45 % (2965140)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1241680797:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.45 % (2965141)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=793798234:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.45 % (2965142)dis+10_1_sil=32000:sp=arity:random_seed=4198037248:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.45 % (2965143)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2434579363:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.45 % (2965144)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2269635398:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.45 % (2965145)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=597086614:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.45 % (2965145) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2965134-2965145"...
% 0.10/0.45 % (2965142) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2965134-2965142"...
% 0.10/0.45 % (2965143) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2965134-2965143"...
% 0.10/0.45 % (2965140) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2965134-2965140"...
% 0.10/0.45 % (2965145)...printing done.
% 0.10/0.45 % (2965142)...printing done.
% 0.10/0.45 % (2965143)...printing done.
% 0.10/0.45 % (2965145)Refutation found. Thanks to Tanya!
% 0.10/0.45 % SZS status Theorem for theBenchmark
% 0.10/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.45 % (2965145)------------------------------
% 0.10/0.45 % (2965145)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.45 % (2965145)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.45 % (2965145)CaDiCaL version: 2.1.3
% 0.10/0.45 % (2965145)Termination reason: Refutation
% 0.10/0.45 % (2965145)Time elapsed: 0.009 s
% 0.10/0.45 % (2965145)Peak memory usage: 12 MB
% 0.10/0.45 % (2965145)Instructions burned: 11 (million)
% 0.10/0.45 % (2965134)Success in time 0.048 s
% 0.10/0.45 % Vampire exiting
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