%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU159+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n004.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 12:52:09 PM UTC 2026
% Result : Theorem 0.11s 0.43s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 73 ( 7 unt; 5 def)
% Number of atoms : 244 ( 62 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 274 ( 103 ~; 123 |; 35 &)
% ( 11 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 91 ( 0 sgn 77 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1,X2] :
( X2 = unordered_pair(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( X3 = X0
| X3 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f7,conjecture,
! [X0,X1,X2] :
( subset(unordered_pair(X0,X1),X2)
<=> ( in(X0,X2)
& in(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_zfmisc_1) ).
fof(f8,negated_conjecture,
~ ! [X0,X1,X2] :
( subset(unordered_pair(X0,X1),X2)
<=> ( in(X0,X2)
& in(X1,X2) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f11,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f12,plain,
? [X0,X1,X2] :
( subset(unordered_pair(X0,X1),X2)
<~> ( in(X0,X2)
& in(X1,X2) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X3 = X0
| X3 = X1
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X0 != X3
& X1 != X3 ) )
& ( X3 = X0
| X3 = X1
| ~ in(X3,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X3 = X0
| X3 = X1
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X0 != X3
& X1 != X3 ) )
& ( X3 = X0
| X3 = X1
| ~ in(X3,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X3 = X0
| X3 = X1
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X0 != X4
& X1 != X4 ) )
& ( X0 = X4
| X1 = X4
| ~ in(X4,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(rectify,[],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ( ( ( sK0(X0,X1,X2) != X0
& sK0(X0,X1,X2) != X1 )
| ~ in(sK0(X0,X1,X2),X2) )
& ( sK0(X0,X1,X2) = X0
| sK0(X0,X1,X2) = X1
| in(sK0(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X0 != X4
& X1 != X4 ) )
& ( X0 = X4
| X1 = X4
| ~ in(X4,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f15]) ).
fof(f17,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,[],[f11]) ).
fof(f18,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,[],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK1(X0,X1),X1)
& in(sK1(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f18]) ).
fof(f20,plain,
? [X0,X1,X2] :
( ( ~ in(X0,X2)
| ~ in(X1,X2)
| ~ subset(unordered_pair(X0,X1),X2) )
& ( ( in(X0,X2)
& in(X1,X2) )
| subset(unordered_pair(X0,X1),X2) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f21,plain,
? [X0,X1,X2] :
( ( ~ in(X0,X2)
| ~ in(X1,X2)
| ~ subset(unordered_pair(X0,X1),X2) )
& ( ( in(X0,X2)
& in(X1,X2) )
| subset(unordered_pair(X0,X1),X2) ) ),
inference(flattening,[],[f20]) ).
fof(f22,plain,
( ( ~ in(sK2,sK4)
| ~ in(sK3,sK4)
| ~ subset(unordered_pair(sK2,sK3),sK4) )
& ( ( in(sK2,sK4)
& in(sK3,sK4) )
| subset(unordered_pair(sK2,sK3),sK4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f21]) ).
fof(f25,plain,
! [X2,X0,X1,X4] :
( X0 = X4
| X1 = X4
| ~ in(X4,X2)
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f16]) ).
fof(f26,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X1 != X4
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f16]) ).
fof(f27,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X0 != X4
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f16]) ).
fof(f31,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f32,plain,
! [X0,X1] :
( in(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f33,plain,
! [X0,X1] :
( ~ in(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f35,plain,
( in(sK3,sK4)
| subset(unordered_pair(sK2,sK3),sK4) ),
inference(cnf_transformation,[],[f22]) ).
fof(f36,plain,
( in(sK2,sK4)
| subset(unordered_pair(sK2,sK3),sK4) ),
inference(cnf_transformation,[],[f22]) ).
fof(f37,plain,
( ~ in(sK2,sK4)
| ~ in(sK3,sK4)
| ~ subset(unordered_pair(sK2,sK3),sK4) ),
inference(cnf_transformation,[],[f22]) ).
fof(f38,plain,
! [X2,X1,X4] :
( in(X4,X2)
| unordered_pair(X4,X1) != X2 ),
inference(equality_resolution,[],[f27]) ).
fof(f39,plain,
! [X1,X4] : in(X4,unordered_pair(X4,X1)),
inference(equality_resolution,[],[f38]) ).
fof(f40,plain,
! [X2,X0,X4] :
( in(X4,X2)
| unordered_pair(X0,X4) != X2 ),
inference(equality_resolution,[],[f26]) ).
fof(f41,plain,
! [X0,X4] : in(X4,unordered_pair(X0,X4)),
inference(equality_resolution,[],[f40]) ).
fof(f42,plain,
! [X0,X1,X4] :
( ~ in(X4,unordered_pair(X0,X1))
| X1 = X4
| X0 = X4 ),
inference(equality_resolution,[],[f25]) ).
fof(f44,definition,
( spl5_1
<=> subset(unordered_pair(sK2,sK3),sK4) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f45,plain,
( ~ subset(unordered_pair(sK2,sK3),sK4)
| spl5_1 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f46,plain,
( subset(unordered_pair(sK2,sK3),sK4)
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f48,definition,
( spl5_2
<=> in(sK3,sK4) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f50,plain,
( in(sK3,sK4)
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f51,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f35,f48,f44]) ).
fof(f53,definition,
( spl5_3
<=> in(sK2,sK4) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
fof(f55,plain,
( in(sK2,sK4)
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f56,plain,
( spl5_1
| spl5_3 ),
inference(avatar_split_clause,[],[f36,f53,f44]) ).
fof(f57,plain,
( ~ spl5_1
| ~ spl5_2
| ~ spl5_3 ),
inference(avatar_split_clause,[],[f37,f53,f48,f44]) ).
fof(f76,plain,
! [X2,X0,X1] :
( subset(unordered_pair(X1,X0),X2)
| sK1(unordered_pair(X1,X0),X2) = X1
| sK1(unordered_pair(X1,X0),X2) = X0 ),
inference(resolution,[],[f42,f32]) ).
fof(f86,definition,
( spl5_4
<=> sK3 = sK1(unordered_pair(sK2,sK3),sK4) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
fof(f88,plain,
( sK3 = sK1(unordered_pair(sK2,sK3),sK4)
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f90,definition,
( spl5_5
<=> sK2 = sK1(unordered_pair(sK2,sK3),sK4) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
fof(f92,plain,
( sK2 = sK1(unordered_pair(sK2,sK3),sK4)
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f94,plain,
( ! [X0] :
( ~ in(X0,unordered_pair(sK2,sK3))
| in(X0,sK4) )
| ~ spl5_1 ),
inference(resolution,[],[f46,f31]) ).
fof(f95,plain,
( in(sK2,sK4)
| ~ spl5_1 ),
inference(resolution,[],[f94,f39]) ).
fof(f96,plain,
( in(sK3,sK4)
| ~ spl5_1 ),
inference(resolution,[],[f94,f41]) ).
fof(f101,plain,
( spl5_3
| ~ spl5_1 ),
inference(avatar_split_clause,[],[f95,f44,f53]) ).
fof(f102,plain,
( spl5_2
| ~ spl5_1 ),
inference(avatar_split_clause,[],[f96,f44,f48]) ).
fof(f105,plain,
( sK2 = sK1(unordered_pair(sK2,sK3),sK4)
| sK3 = sK1(unordered_pair(sK2,sK3),sK4)
| spl5_1 ),
inference(resolution,[],[f45,f76]) ).
fof(f106,plain,
( spl5_4
| spl5_5
| spl5_1 ),
inference(avatar_split_clause,[],[f105,f44,f90,f86]) ).
fof(f108,plain,
( ~ in(sK3,sK4)
| subset(unordered_pair(sK2,sK3),sK4)
| ~ spl5_4 ),
inference(superposition,[],[f33,f88]) ).
fof(f110,plain,
( subset(unordered_pair(sK2,sK3),sK4)
| ~ spl5_2
| ~ spl5_4 ),
inference(forward_subsumption_resolution,[],[f108,f50]) ).
fof(f111,plain,
( $false
| spl5_1
| ~ spl5_2
| ~ spl5_4 ),
inference(forward_subsumption_resolution,[],[f110,f45]) ).
fof(f112,plain,
( spl5_1
| ~ spl5_2
| ~ spl5_4 ),
inference(avatar_contradiction_clause,[],[f111]) ).
fof(f165,plain,
( ~ in(sK2,sK4)
| subset(unordered_pair(sK2,sK3),sK4)
| ~ spl5_5 ),
inference(superposition,[],[f33,f92]) ).
fof(f167,plain,
( subset(unordered_pair(sK2,sK3),sK4)
| ~ spl5_3
| ~ spl5_5 ),
inference(forward_subsumption_resolution,[],[f165,f55]) ).
fof(f168,plain,
( $false
| spl5_1
| ~ spl5_3
| ~ spl5_5 ),
inference(forward_subsumption_resolution,[],[f167,f45]) ).
fof(f169,plain,
( spl5_1
| ~ spl5_3
| ~ spl5_5 ),
inference(avatar_contradiction_clause,[],[f168]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f51]) ).
cnf(s2,plain,
( spl5_1
| spl5_3 ),
inference(sat_conversion,[],[f56]) ).
cnf(s3,plain,
( ~ spl5_1
| ~ spl5_2
| ~ spl5_3 ),
inference(sat_conversion,[],[f57]) ).
cnf(s6,plain,
( ~ spl5_1
| spl5_3 ),
inference(sat_conversion,[],[f101]) ).
cnf(s7,plain,
( ~ spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f102]) ).
cnf(s8,plain,
( spl5_1
| spl5_4
| spl5_5 ),
inference(sat_conversion,[],[f106]) ).
cnf(s9,plain,
( spl5_1
| ~ spl5_2
| ~ spl5_4 ),
inference(sat_conversion,[],[f112]) ).
cnf(s10,plain,
( spl5_1
| ~ spl5_3
| ~ spl5_5 ),
inference(sat_conversion,[],[f169]) ).
cnf(s11,plain,
spl5_1,
inference(rat,[],[s8,s9,s10,s1,s2]) ).
cnf(s12,plain,
spl5_2,
inference(rat,[],[s7,s11]) ).
cnf(s13,plain,
spl5_3,
inference(rat,[],[s6,s11]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s3,s13,s12,s11]) ).
fof(f170,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU159+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n004.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 03:48:07 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 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
% 0.11/0.43 % (4130106)Will run a generic schedule for satisfiability detection.
% 0.11/0.43 % (4130120)dis+10_1_sil=32000:sp=arity:random_seed=298442257:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.11/0.43 % (4130120) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4130106-4130120"...
% 0.11/0.43 % (4130120)...printing done.
% 0.11/0.43 % (4130118)% WARNING: option uhcvi not known.
% 0.11/0.43 % (4130120)Refutation found. Thanks to Tanya!
% 0.11/0.43 % SZS status Theorem for theBenchmark
% 0.11/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.43 % (4130120)------------------------------
% 0.11/0.43 % (4130120)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.43 % (4130120)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.43 % (4130120)CaDiCaL version: 2.1.3
% 0.11/0.43 % (4130120)Termination reason: Refutation
% 0.11/0.43 % (4130120)Time elapsed: 0.004 s
% 0.11/0.43 % (4130120)Peak memory usage: 12 MB
% 0.11/0.43 % (4130120)Instructions burned: 9 (million)
% 0.11/0.43 % (4130106)Success in time 0.019 s
% 0.11/0.43 % Vampire exiting
%------------------------------------------------------------------------------