%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU131+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n001.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 12:52:01 PM UTC 2026
% Result : Theorem 0.17s 0.48s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 9
% Syntax : Number of formulae : 72 ( 10 unt; 2 def)
% Number of atoms : 226 ( 39 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 255 ( 101 ~; 113 |; 30 &)
% ( 8 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 101 ( 0 sgn 91 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f3,axiom,
! [X0,X1,X2] :
( X2 = set_difference(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& ~ in(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f7,conjecture,
! [X0,X1] :
( set_difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l32_xboole_1) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
( set_difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f13,axiom,
! [X0] : set_difference(X0,empty_set) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
fof(f15,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f16,axiom,
! [X0,X1] :
~ ( in(X0,X1)
& empty(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f20,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f21,plain,
? [X0,X1] :
( set_difference(X0,X1) = empty_set
<~> subset(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f23,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f24,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f26,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f20]) ).
fof(f27,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK0(X0,X1),X1)
& in(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f27]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| in(X3,X1) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| in(X3,X1) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(flattening,[],[f29]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| in(X4,X1) )
& ( ( in(X4,X0)
& ~ in(X4,X1) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(rectify,[],[f30]) ).
fof(f32,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ( ( ~ in(sK1(X0,X1,X2),X0)
| in(sK1(X0,X1,X2),X1)
| ~ in(sK1(X0,X1,X2),X2) )
& ( ( in(sK1(X0,X1,X2),X0)
& ~ in(sK1(X0,X1,X2),X1) )
| in(sK1(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| in(X4,X1) )
& ( ( in(X4,X0)
& ~ in(X4,X1) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f31]) ).
fof(f33,plain,
? [X0,X1] :
( ( ~ subset(X0,X1)
| set_difference(X0,X1) != empty_set )
& ( subset(X0,X1)
| set_difference(X0,X1) = empty_set ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f34,plain,
( ( ~ subset(sK2,sK3)
| empty_set != set_difference(sK2,sK3) )
& ( subset(sK2,sK3)
| empty_set = set_difference(sK2,sK3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f33]) ).
fof(f35,plain,
empty(sK4),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X0,sK4)],[f9]) ).
fof(f40,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f41,plain,
! [X0,X1] :
( in(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f42,plain,
! [X0,X1] :
( ~ in(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f43,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f32]) ).
fof(f45,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| in(X4,X1)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f32]) ).
fof(f46,plain,
! [X2,X0,X1] :
( ~ in(sK1(X0,X1,X2),X1)
| set_difference(X0,X1) = X2
| in(sK1(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f32]) ).
fof(f47,plain,
! [X2,X0,X1] :
( in(sK1(X0,X1,X2),X2)
| in(sK1(X0,X1,X2),X0)
| set_difference(X0,X1) = X2 ),
inference(cnf_transformation,[],[f32]) ).
fof(f50,plain,
( subset(sK2,sK3)
| empty_set = set_difference(sK2,sK3) ),
inference(cnf_transformation,[],[f34]) ).
fof(f51,plain,
( ~ subset(sK2,sK3)
| empty_set != set_difference(sK2,sK3) ),
inference(cnf_transformation,[],[f34]) ).
fof(f52,plain,
empty(sK4),
inference(cnf_transformation,[],[f35]) ).
fof(f57,plain,
! [X0] : set_difference(X0,empty_set) = X0,
inference(cnf_transformation,[],[f13]) ).
fof(f59,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f23]) ).
fof(f60,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f62,plain,
! [X0,X1,X4] :
( in(X4,set_difference(X0,X1))
| ~ in(X4,X0)
| in(X4,X1) ),
inference(equality_resolution,[],[f45]) ).
fof(f64,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f43]) ).
fof(f66,definition,
( spl7_1
<=> empty_set = set_difference(sK2,sK3) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
fof(f67,plain,
( empty_set != set_difference(sK2,sK3)
| spl7_1 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f68,plain,
( empty_set = set_difference(sK2,sK3)
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f70,definition,
( spl7_2
<=> subset(sK2,sK3) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
fof(f71,plain,
( ~ subset(sK2,sK3)
| spl7_2 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f72,plain,
( subset(sK2,sK3)
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f73,plain,
( spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f50,f70,f66]) ).
fof(f74,plain,
( ~ spl7_1
| ~ spl7_2 ),
inference(avatar_split_clause,[],[f51,f70,f66]) ).
fof(f76,plain,
empty_set = sK4,
inference(resolution,[],[f59,f52]) ).
fof(f89,plain,
! [X0,X1] :
( ~ in(X1,empty_set)
| ~ in(X1,X0) ),
inference(superposition,[],[f64,f57]) ).
fof(f159,plain,
! [X2,X0,X1] :
( in(sK1(X0,X1,X2),X0)
| set_difference(X0,X1) = X2
| ~ empty(X2) ),
inference(resolution,[],[f47,f60]) ).
fof(f298,plain,
( ! [X0] :
( in(X0,empty_set)
| ~ in(X0,sK2)
| in(X0,sK3) )
| ~ spl7_1 ),
inference(superposition,[],[f62,f68]) ).
fof(f302,plain,
( ! [X0] :
( ~ in(X0,sK2)
| in(X0,sK3) )
| ~ spl7_1 ),
inference(forward_subsumption_resolution,[],[f298,f89]) ).
fof(f304,plain,
( ! [X0] :
( in(sK0(sK2,X0),sK3)
| subset(sK2,X0) )
| ~ spl7_1 ),
inference(resolution,[],[f302,f41]) ).
fof(f409,plain,
( subset(sK2,sK3)
| subset(sK2,sK3)
| ~ spl7_1 ),
inference(resolution,[],[f304,f42]) ).
fof(f414,plain,
( subset(sK2,sK3)
| ~ spl7_1 ),
inference(duplicate_literal_removal,[],[f409]) ).
fof(f415,plain,
( $false
| ~ spl7_1
| spl7_2 ),
inference(forward_subsumption_resolution,[],[f414,f71]) ).
fof(f416,plain,
( ~ spl7_1
| spl7_2 ),
inference(avatar_contradiction_clause,[],[f415]) ).
fof(f417,plain,
( ! [X0] :
( ~ in(X0,sK2)
| in(X0,sK3) )
| ~ spl7_2 ),
inference(resolution,[],[f72,f40]) ).
fof(f422,plain,
( ! [X0,X1] :
( in(sK1(sK2,X0,X1),sK3)
| set_difference(sK2,X0) = X1
| ~ empty(X1) )
| ~ spl7_2 ),
inference(resolution,[],[f417,f159]) ).
fof(f706,plain,
( ! [X0] :
( set_difference(sK2,sK3) = X0
| ~ empty(X0)
| set_difference(sK2,sK3) = X0
| in(sK1(sK2,sK3,X0),X0) )
| ~ spl7_2 ),
inference(resolution,[],[f422,f46]) ).
fof(f717,plain,
( ! [X0] :
( set_difference(sK2,sK3) = X0
| ~ empty(X0)
| in(sK1(sK2,sK3,X0),X0) )
| ~ spl7_2 ),
inference(duplicate_literal_removal,[],[f706]) ).
fof(f720,plain,
( ! [X0] :
( ~ empty(X0)
| set_difference(sK2,sK3) = X0 )
| ~ spl7_2 ),
inference(forward_subsumption_resolution,[],[f717,f60]) ).
fof(f730,plain,
( set_difference(sK2,sK3) = sK4
| ~ spl7_2 ),
inference(resolution,[],[f720,f52]) ).
fof(f731,plain,
( empty_set = set_difference(sK2,sK3)
| ~ spl7_2 ),
inference(forward_demodulation,[],[f730,f76]) ).
fof(f734,plain,
( $false
| spl7_1
| ~ spl7_2 ),
inference(forward_subsumption_resolution,[],[f731,f67]) ).
fof(f735,plain,
( spl7_1
| ~ spl7_2 ),
inference(avatar_contradiction_clause,[],[f734]) ).
cnf(s1,plain,
( spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f73]) ).
cnf(s2,plain,
( ~ spl7_1
| ~ spl7_2 ),
inference(sat_conversion,[],[f74]) ).
cnf(s13,plain,
( ~ spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f416]) ).
cnf(s15,plain,
( spl7_1
| ~ spl7_2 ),
inference(sat_conversion,[],[f735]) ).
cnf(s16,plain,
spl7_1,
inference(rat,[],[s1,s15]) ).
cnf(s17,plain,
spl7_2,
inference(rat,[],[s13,s16]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s2,s17,s16]) ).
fof(f736,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU131+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 % Computer : n001.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Mon Sep 28 03:45:47 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.42 Running first-order model finding
% 0.13/0.42 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
% 0.17/0.48 % (4188551)Will run a generic schedule for satisfiability detection.
% 0.17/0.48 % (4188559)dis+10_1_sil=32000:sp=arity:random_seed=4169961051:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.48 % (4188557)% WARNING: option uhcvi not known.
% 0.17/0.48 % (4188556)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=945244467_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.48 % (4188557)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3761780609:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.48 % (4188561)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1347300777:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.48 % (4188558)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1539169187:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.48 % (4188560)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4173639431:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.48 % (4188562)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4187474774:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.48 % TRYING [1]
% 0.17/0.48 % TRYING [2]
% 0.17/0.48 % TRYING [3]
% 0.17/0.48 % (4188559) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4188551-4188559"...
% 0.17/0.48 % (4188559)...printing done.
% 0.17/0.48 % TRYING [4]
% 0.17/0.48 % (4188559)Refutation found. Thanks to Tanya!
% 0.17/0.48 % SZS status Theorem for theBenchmark
% 0.17/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.48 % (4188559)------------------------------
% 0.17/0.48 % (4188559)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.49 % (4188559)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.49 % (4188559)CaDiCaL version: 2.1.3
% 0.17/0.49 % (4188559)Termination reason: Refutation
% 0.17/0.49 % (4188559)Time elapsed: 0.011 s
% 0.17/0.49 % (4188559)Peak memory usage: 12 MB
% 0.17/0.49 % (4188559)Instructions burned: 27 (million)
% 0.17/0.49 % (4188551)Success in time 0.049 s
% 0.17/0.49 % Vampire exiting
%------------------------------------------------------------------------------