%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET882+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 : n003.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 12:44:54 PM UTC 2026
% Result : Theorem 0.05s 0.43s
% Output : Refutation 0.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 6 unt; 0 def)
% Number of atoms : 44 ( 28 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 41 ( 18 ~; 16 |; 2 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 37 ( 35 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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,X2] :
( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
<=> ( ~ in(X0,X2)
& ( in(X1,X2)
| X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l39_zfmisc_1) ).
fof(f7,conjecture,
! [X0,X1] :
( X0 != X1
=> set_difference(unordered_pair(X0,X1),singleton(X1)) = singleton(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_zfmisc_1) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
( X0 != X1
=> set_difference(unordered_pair(X0,X1),singleton(X1)) = singleton(X0) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f10,plain,
? [X0,X1] :
( singleton(X0) != set_difference(unordered_pair(X0,X1),singleton(X1))
& X0 != X1 ),
inference(ennf_transformation,[],[f8]) ).
fof(f13,plain,
! [X2,X0,X1] :
( X0 != X2
| in(X2,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f3]) ).
fof(f14,plain,
! [X2,X0,X1] :
( X0 = X2
| ~ in(X2,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f3]) ).
fof(f18,plain,
! [X2,X0,X1] :
( ~ in(X1,X2)
| in(X0,X2)
| singleton(X0) = set_difference(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f4]) ).
fof(f23,plain,
sK3 != sK4,
inference(cnf_transformation,[],[f10]) ).
fof(f24,plain,
singleton(sK3) != set_difference(unordered_pair(sK3,sK4),singleton(sK4)),
inference(cnf_transformation,[],[f10]) ).
fof(f25,plain,
! [X2,X0] :
( X0 = X2
| ~ in(X2,singleton(X0)) ),
inference(equality_resolution,[],[f14]) ).
fof(f26,plain,
! [X2,X1] :
( in(X2,X1)
| singleton(X2) != X1 ),
inference(equality_resolution,[],[f13]) ).
fof(f27,plain,
! [X2] : in(X2,singleton(X2)),
inference(equality_resolution,[],[f26]) ).
fof(f32,plain,
! [X2,X0] :
( in(X2,singleton(X0))
| X0 = X2 ),
inference(consistent_polarity_flipping,[],[f25]) ).
fof(f33,plain,
! [X2] : ~ in(X2,singleton(X2)),
inference(consistent_polarity_flipping,[],[f27]) ).
fof(f36,plain,
! [X2,X0,X1] :
( ~ in(X0,X2)
| in(X1,X2)
| singleton(X0) = set_difference(unordered_pair(X0,X1),X2) ),
inference(consistent_polarity_flipping,[],[f18]) ).
fof(f55,plain,
! [X2,X0,X1] :
( in(X0,singleton(X1))
| singleton(X2) = set_difference(unordered_pair(X2,X0),singleton(X1))
| X1 = X2 ),
inference(resolution,[],[f36,f32]) ).
fof(f95,plain,
! [X0,X1] :
( singleton(X0) = set_difference(unordered_pair(X0,X1),singleton(X1))
| X0 = X1 ),
inference(resolution,[],[f55,f33]) ).
fof(f113,plain,
( singleton(sK3) != singleton(sK3)
| sK3 = sK4 ),
inference(superposition,[],[f24,f95]) ).
fof(f122,plain,
sK3 = sK4,
inference(trivial_inequality_removal,[],[f113]) ).
fof(f125,plain,
$false,
inference(forward_subsumption_resolution,[],[f122,f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET882+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 03:07:56 UTC 2026
% 0.05/0.36 % CPUTime :
% 0.05/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.05/0.39 Running first-order model finding
% 0.05/0.39 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
% 0.05/0.43 % (1144399)Will run a generic schedule for satisfiability detection.
% 0.05/0.43 % (1144405)% WARNING: option uhcvi not known.
% 0.05/0.43 % (1144405)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=80395143:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.05/0.43 % (1144405) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1144399-1144405"...
% 0.05/0.43 % (1144405)...printing done.
% 0.05/0.43 % (1144405)Refutation found. Thanks to Tanya!
% 0.05/0.43 % SZS status Theorem for theBenchmark
% 0.05/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.05/0.43 % (1144405)------------------------------
% 0.05/0.43 % (1144405)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.05/0.43 % (1144405)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.05/0.43 % (1144405)CaDiCaL version: 2.1.3
% 0.05/0.43 % (1144405)Termination reason: Refutation
% 0.05/0.43 % (1144405)Time elapsed: 0.003 s
% 0.05/0.43 % (1144405)Peak memory usage: 12 MB
% 0.05/0.43 % (1144405)Instructions burned: 6 (million)
% 0.05/0.43 % (1144399)Success in time 0.037 s
% 0.05/0.43 % Vampire exiting
%------------------------------------------------------------------------------