%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET976+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 : n007.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 12:45:07 PM UTC 2026
% Result : Theorem 0.15s 0.45s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 75 ( 10 unt; 3 def)
% Number of atoms : 208 ( 47 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 222 ( 89 ~; 101 |; 23 &)
% ( 8 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 101 ( 0 sgn 87 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f3,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f4,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f6,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X0,X2)
& in(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(f9,conjecture,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3)))
<=> ( in(X0,X2)
& X1 = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t129_zfmisc_1) ).
fof(f10,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3)))
<=> ( in(X0,X2)
& X1 = X3 ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f12,plain,
? [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3)))
<~> ( in(X0,X2)
& X1 = X3 ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f13,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X2 = X0
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f14,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ( ( sK0(X0,X1) != X0
| ~ in(sK0(X0,X1),X1) )
& ( sK0(X0,X1) = X0
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f14]) ).
fof(f16,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,[],[f6]) ).
fof(f17,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,[],[f16]) ).
fof(f20,plain,
? [X0,X1,X2,X3] :
( ( ~ in(X0,X2)
| X1 != X3
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3))) )
& ( ( in(X0,X2)
& X1 = X3 )
| in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3))) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f21,plain,
? [X0,X1,X2,X3] :
( ( ~ in(X0,X2)
| X1 != X3
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3))) )
& ( ( in(X0,X2)
& X1 = X3 )
| in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3))) ) ),
inference(flattening,[],[f20]) ).
fof(f22,plain,
( ( ~ in(sK3,sK5)
| sK4 != sK6
| ~ in(ordered_pair(sK3,sK4),cartesian_product2(sK5,singleton(sK6))) )
& ( ( in(sK3,sK5)
& sK4 = sK6 )
| in(ordered_pair(sK3,sK4),cartesian_product2(sK5,singleton(sK6))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5),skolemize(X3,sK6)],[f21]) ).
fof(f24,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f25,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f15]) ).
fof(f26,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f15]) ).
fof(f29,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f4]) ).
fof(f31,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f17]) ).
fof(f32,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f17]) ).
fof(f33,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(cnf_transformation,[],[f17]) ).
fof(f36,plain,
( sK4 = sK6
| in(ordered_pair(sK3,sK4),cartesian_product2(sK5,singleton(sK6))) ),
inference(cnf_transformation,[],[f22]) ).
fof(f37,plain,
( in(sK3,sK5)
| in(ordered_pair(sK3,sK4),cartesian_product2(sK5,singleton(sK6))) ),
inference(cnf_transformation,[],[f22]) ).
fof(f38,plain,
( ~ in(sK3,sK5)
| sK4 != sK6
| ~ in(ordered_pair(sK3,sK4),cartesian_product2(sK5,singleton(sK6))) ),
inference(cnf_transformation,[],[f22]) ).
fof(f40,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,[],[f33,f29]) ).
fof(f41,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f32,f29]) ).
fof(f42,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f31,f29]) ).
fof(f43,plain,
( ~ in(sK3,sK5)
| sK4 != sK6
| ~ in(unordered_pair(unordered_pair(sK3,sK4),singleton(sK3)),cartesian_product2(sK5,singleton(sK6))) ),
inference(definition_unfolding,[],[f38,f29]) ).
fof(f44,plain,
( in(sK3,sK5)
| in(unordered_pair(unordered_pair(sK3,sK4),singleton(sK3)),cartesian_product2(sK5,singleton(sK6))) ),
inference(definition_unfolding,[],[f37,f29]) ).
fof(f45,plain,
( sK4 = sK6
| in(unordered_pair(unordered_pair(sK3,sK4),singleton(sK3)),cartesian_product2(sK5,singleton(sK6))) ),
inference(definition_unfolding,[],[f36,f29]) ).
fof(f46,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f26]) ).
fof(f47,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f46]) ).
fof(f48,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f25]) ).
fof(f50,definition,
( spl7_1
<=> in(unordered_pair(unordered_pair(sK3,sK4),singleton(sK3)),cartesian_product2(sK5,singleton(sK6))) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
fof(f51,plain,
( ~ in(unordered_pair(unordered_pair(sK3,sK4),singleton(sK3)),cartesian_product2(sK5,singleton(sK6)))
| spl7_1 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f52,plain,
( in(unordered_pair(unordered_pair(sK3,sK4),singleton(sK3)),cartesian_product2(sK5,singleton(sK6)))
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f54,definition,
( spl7_2
<=> in(sK3,sK5) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
fof(f56,plain,
( in(sK3,sK5)
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f57,plain,
( spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f44,f54,f50]) ).
fof(f59,definition,
( spl7_3
<=> sK4 = sK6 ),
introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition]) ).
fof(f60,plain,
( sK4 = sK6
| ~ spl7_3 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f61,plain,
( sK4 != sK6
| spl7_3 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f62,plain,
( ~ spl7_1
| ~ spl7_3
| ~ spl7_2 ),
inference(avatar_split_clause,[],[f43,f54,f59,f50]) ).
fof(f73,plain,
( in(unordered_pair(singleton(sK3),unordered_pair(sK3,sK4)),cartesian_product2(sK5,singleton(sK6)))
| ~ spl7_1 ),
inference(superposition,[],[f52,f24]) ).
fof(f406,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(forward_demodulation,[],[f41,f24]) ).
fof(f407,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(forward_demodulation,[],[f42,f24]) ).
fof(f414,plain,
( in(sK3,sK5)
| ~ spl7_1 ),
inference(resolution,[],[f406,f73]) ).
fof(f421,plain,
( spl7_2
| ~ spl7_1 ),
inference(avatar_split_clause,[],[f414,f50,f54]) ).
fof(f436,plain,
( in(sK4,singleton(sK6))
| ~ spl7_1 ),
inference(resolution,[],[f407,f73]) ).
fof(f439,plain,
( sK4 = sK6
| ~ spl7_1 ),
inference(resolution,[],[f436,f48]) ).
fof(f441,plain,
( $false
| ~ spl7_1
| spl7_3 ),
inference(forward_subsumption_resolution,[],[f439,f61]) ).
fof(f442,plain,
( ~ spl7_1
| spl7_3 ),
inference(avatar_contradiction_clause,[],[f441]) ).
fof(f443,plain,
( ~ in(unordered_pair(singleton(sK3),unordered_pair(sK3,sK4)),cartesian_product2(sK5,singleton(sK6)))
| spl7_1 ),
inference(forward_demodulation,[],[f51,f24]) ).
fof(f444,plain,
( in(unordered_pair(unordered_pair(sK3,sK4),singleton(sK3)),cartesian_product2(sK5,singleton(sK6)))
| spl7_3 ),
inference(forward_subsumption_resolution,[],[f45,f61]) ).
fof(f445,plain,
( in(unordered_pair(singleton(sK3),unordered_pair(sK3,sK4)),cartesian_product2(sK5,singleton(sK6)))
| spl7_3 ),
inference(forward_demodulation,[],[f444,f24]) ).
fof(f449,plain,
( $false
| spl7_1
| spl7_3 ),
inference(forward_subsumption_resolution,[],[f443,f445]) ).
fof(f450,plain,
( spl7_1
| spl7_3 ),
inference(avatar_contradiction_clause,[],[f449]) ).
fof(f555,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(forward_demodulation,[],[f40,f24]) ).
fof(f581,plain,
( ~ in(sK3,sK5)
| ~ in(sK4,singleton(sK6))
| spl7_1 ),
inference(resolution,[],[f555,f443]) ).
fof(f587,plain,
( ~ in(sK4,singleton(sK6))
| spl7_1
| ~ spl7_2 ),
inference(forward_subsumption_resolution,[],[f581,f56]) ).
fof(f590,plain,
( ~ in(sK4,singleton(sK4))
| spl7_1
| ~ spl7_2
| ~ spl7_3 ),
inference(forward_demodulation,[],[f587,f60]) ).
fof(f591,plain,
( $false
| spl7_1
| ~ spl7_2
| ~ spl7_3 ),
inference(forward_subsumption_resolution,[],[f590,f47]) ).
fof(f592,plain,
( spl7_1
| ~ spl7_2
| ~ spl7_3 ),
inference(avatar_contradiction_clause,[],[f591]) ).
cnf(s17,plain,
( spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f57]) ).
cnf(s20,plain,
( ~ spl7_1
| ~ spl7_2
| ~ spl7_3 ),
inference(sat_conversion,[],[f62]) ).
cnf(s260,plain,
( ~ spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f421]) ).
cnf(s278,plain,
( ~ spl7_1
| spl7_3 ),
inference(sat_conversion,[],[f442]) ).
cnf(s285,plain,
( spl7_1
| spl7_3 ),
inference(sat_conversion,[],[f450]) ).
cnf(s405,plain,
( spl7_1
| ~ spl7_2
| ~ spl7_3 ),
inference(sat_conversion,[],[f592]) ).
cnf(s408,plain,
spl7_1,
inference(rat,[],[s405,s17,s285]) ).
cnf(s409,plain,
spl7_3,
inference(rat,[],[s278,s408]) ).
cnf(s410,plain,
spl7_2,
inference(rat,[],[s260,s408]) ).
cnf(s411,plain,
$false,
inference(rat,[],[s20,s409,s410,s408]) ).
fof(f593,plain,
$false,
inference(avatar_sat_refutation,[],[s411]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET976+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n007.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 03:15:56 UTC 2026
% 0.15/0.38 % CPUTime :
% 0.15/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.15/0.41 Running first-order model finding
% 0.15/0.41 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
% 0.15/0.45 % (1995007)Will run a generic schedule for satisfiability detection.
% 0.15/0.45 % (1995014)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3029743696:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.45 % (1995013)% WARNING: option uhcvi not known.
% 0.15/0.45 % (1995014) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1995007-1995014"...
% 0.15/0.45 % (1995013)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2656830766:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.45 % (1995017)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3126505606:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.45 % (1995015)dis+10_1_sil=32000:sp=arity:random_seed=1036450956:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.45 % (1995016)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1798556192:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.45 % (1995018)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=452414154:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.45 % (1995014)...printing done.
% 0.15/0.45 % (1995014)Refutation found. Thanks to Tanya!
% 0.15/0.45 % SZS status Theorem for theBenchmark
% 0.15/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.45 % (1995014)------------------------------
% 0.15/0.45 % (1995014)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.45 % (1995014)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.45 % (1995014)CaDiCaL version: 2.1.3
% 0.15/0.45 % (1995014)Termination reason: Refutation
% 0.15/0.45 % (1995014)Time elapsed: 0.007 s
% 0.15/0.45 % (1995014)Peak memory usage: 12 MB
% 0.15/0.45 % (1995014)Instructions burned: 18 (million)
% 0.15/0.45 % (1995007)Success in time 0.035 s
% 0.15/0.45 % Vampire exiting
%------------------------------------------------------------------------------