%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET016-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n002.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 12:42:37 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.45s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 33 ( 14 unt; 2 def)
% Number of atoms : 53 ( 17 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 20 ~; 18 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : member(X0,singleton_set(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_1) ).
fof(f2,axiom,
! [X0,X1] :
( ~ member(X0,singleton_set(X1))
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_2) ).
fof(f3,axiom,
! [X0,X1] : member(X0,unordered_pair(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_1) ).
fof(f4,axiom,
! [X0,X1] : member(X0,unordered_pair(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_2) ).
fof(f5,axiom,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_3) ).
fof(f6,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton_set(X0),unordered_pair(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair) ).
fof(f7,axiom,
ordered_pair(m1,r1) = ordered_pair(m2,r2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_ordered_pairs) ).
fof(f8,negated_conjecture,
m1 != m2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_first_components_equal) ).
fof(f9,plain,
unordered_pair(singleton_set(m1),unordered_pair(m1,r1)) = unordered_pair(singleton_set(m2),unordered_pair(m2,r2)),
inference(definition_unfolding,[],[f7,f6,f6]) ).
fof(f15,plain,
member(singleton_set(m2),unordered_pair(singleton_set(m1),unordered_pair(m1,r1))),
inference(superposition,[],[f3,f9]) ).
fof(f16,plain,
( singleton_set(m1) = singleton_set(m2)
| unordered_pair(m1,r1) = singleton_set(m2) ),
inference(resolution,[],[f15,f5]) ).
fof(f18,definition,
( spl0_1
<=> unordered_pair(m1,r1) = singleton_set(m2) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f20,plain,
( unordered_pair(m1,r1) = singleton_set(m2)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f18]) ).
fof(f22,definition,
( spl0_2
<=> singleton_set(m1) = singleton_set(m2) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f24,plain,
( singleton_set(m1) = singleton_set(m2)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f22]) ).
fof(f25,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f16,f22,f18]) ).
fof(f29,plain,
( member(m2,singleton_set(m1))
| ~ spl0_2 ),
inference(superposition,[],[f1,f24]) ).
fof(f40,plain,
( m1 = m2
| ~ spl0_2 ),
inference(resolution,[],[f29,f2]) ).
fof(f41,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f40,f8]) ).
fof(f42,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f41]) ).
fof(f53,plain,
( member(r1,singleton_set(m2))
| ~ spl0_1 ),
inference(superposition,[],[f4,f20]) ).
fof(f54,plain,
( member(m1,singleton_set(m2))
| ~ spl0_1 ),
inference(superposition,[],[f3,f20]) ).
fof(f55,plain,
( r1 = m2
| ~ spl0_1 ),
inference(resolution,[],[f53,f2]) ).
fof(f62,plain,
( m1 != r1
| ~ spl0_1 ),
inference(superposition,[],[f8,f55]) ).
fof(f94,plain,
( member(m1,singleton_set(r1))
| ~ spl0_1 ),
inference(forward_demodulation,[],[f54,f55]) ).
fof(f107,plain,
( m1 = r1
| ~ spl0_1 ),
inference(resolution,[],[f94,f2]) ).
fof(f108,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f107,f62]) ).
fof(f109,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f108]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f25]) ).
cnf(s3,plain,
~ spl0_2,
inference(sat_conversion,[],[f42]) ).
cnf(s8,plain,
~ spl0_1,
inference(sat_conversion,[],[f109]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s1,s3,s8]) ).
fof(f110,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET016-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 % Computer : n002.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 00:08:37 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 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
% 0.11/0.45 % (4034408)Will run a generic schedule for satisfiability detection.
% 0.11/0.45 % (4034416)dis+10_1_sil=32000:sp=arity:random_seed=3076766913:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.45 % (4034416) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4034408-4034416"...
% 0.11/0.45 % (4034416)...printing done.
% 0.11/0.45 % (4034414)% WARNING: option uhcvi not known.
% 0.11/0.45 % (4034416)Refutation found. Thanks to Tanya!
% 0.11/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.45 % (4034416)------------------------------
% 0.11/0.45 % (4034416)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.45 % (4034416)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.45 % (4034416)CaDiCaL version: 2.1.3
% 0.11/0.45 % (4034416)Termination reason: Refutation
% 0.11/0.45 % (4034416)Time elapsed: 0.002 s
% 0.11/0.45 % (4034416)Peak memory usage: 12 MB
% 0.11/0.45 % (4034416)Instructions burned: 4 (million)
% 0.11/0.45 % (4034408)Success in time 0.026 s
% 0.11/0.45 % Vampire exiting
%------------------------------------------------------------------------------