%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET101+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n011.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 12:43:07 PM UTC 2026
% Result : Theorem 0.11s 0.43s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 15 unt; 0 def)
% Number of atoms : 40 ( 16 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 37 ( 17 ~; 12 |; 7 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 32 ( 30 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2] :
( member(X0,unordered_pair(X1,X2))
<=> ( member(X0,universal_class)
& ( X0 = X1
| X0 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',unordered_pair_defn) ).
fof(f5,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',unordered_pair) ).
fof(f6,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',singleton_set_defn) ).
fof(f7,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',ordered_pair_defn) ).
fof(f44,conjecture,
! [X0,X1] : member(singleton(X0),ordered_pair(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_member_of_ordered_pair) ).
fof(f45,negated_conjecture,
~ ! [X0,X1] : member(singleton(X0),ordered_pair(X0,X1)),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f60,plain,
? [X0,X1] : ~ member(singleton(X0),ordered_pair(X0,X1)),
inference(ennf_transformation,[],[f45]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ( member(X0,unordered_pair(X1,X2))
| ~ member(X0,universal_class)
| ( X0 != X1
& X0 != X2 ) )
& ( ( member(X0,universal_class)
& ( X0 = X1
| X0 = X2 ) )
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ( member(X0,unordered_pair(X1,X2))
| ~ member(X0,universal_class)
| ( X0 != X1
& X0 != X2 ) )
& ( ( member(X0,universal_class)
& ( X0 = X1
| X0 = X2 ) )
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(flattening,[],[f66]) ).
fof(f103,plain,
~ member(singleton(sK6),ordered_pair(sK6,sK7)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X1,sK7)],[f60]) ).
fof(f114,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X2))
| ~ member(X0,universal_class)
| X0 != X1 ),
inference(cnf_transformation,[],[f67]) ).
fof(f115,plain,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[],[f5]) ).
fof(f116,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f117,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
inference(cnf_transformation,[],[f7]) ).
fof(f191,plain,
~ member(singleton(sK6),ordered_pair(sK6,sK7)),
inference(cnf_transformation,[],[f103]) ).
fof(f192,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f117,f116,f116]) ).
fof(f229,plain,
~ member(unordered_pair(sK6,sK6),unordered_pair(unordered_pair(sK6,sK6),unordered_pair(sK6,unordered_pair(sK7,sK7)))),
inference(definition_unfolding,[],[f191,f116,f192]) ).
fof(f232,plain,
! [X2,X1] :
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
inference(equality_resolution,[],[f114]) ).
fof(f275,plain,
~ member(unordered_pair(sK6,sK6),universal_class),
inference(resolution,[],[f232,f229]) ).
fof(f277,plain,
$false,
inference(forward_subsumption_resolution,[],[f275,f115]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET101+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.36 % Computer : n011.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 28 00:41:46 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 Running first-order model finding
% 0.11/0.39 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
% 0.11/0.43 % (2914169)Will run a generic schedule for satisfiability detection.
% 0.11/0.43 % (2914177)dis+10_1_sil=32000:sp=arity:random_seed=1918242676:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.43 % (2914177) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2914169-2914177"...
% 0.11/0.43 % (2914177)...printing done.
% 0.11/0.43 % (2914175)% WARNING: option uhcvi not known.
% 0.11/0.43 % (2914177)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 % (2914177)------------------------------
% 0.11/0.43 % (2914177)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.43 % (2914177)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.43 % (2914177)CaDiCaL version: 2.1.3
% 0.11/0.43 % (2914177)Termination reason: Refutation
% 0.11/0.43 % (2914177)Time elapsed: 0.003 s
% 0.11/0.43 % (2914177)Peak memory usage: 11 MB
% 0.11/0.43 % (2914177)Instructions burned: 6 (million)
% 0.11/0.43 % (2914169)Success in time 0.027 s
% 0.11/0.43 % Vampire exiting
%------------------------------------------------------------------------------