%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP006-1 : 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 : n006.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 10:16:20 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.46s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 12 unt; 3 def)
% Number of atoms : 50 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 48 ( 26 ~; 19 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 4 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 12 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : product(identity,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f3,axiom,
! [X0] : product(X0,inverse(X0),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
fof(f5,axiom,
! [X2,X0,X1] :
( ~ product(X0,inverse(X1),X2)
| ~ an_element(X1)
| ~ an_element(X0)
| an_element(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condition) ).
fof(f8,axiom,
an_element(the_element),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_of_set) ).
fof(f9,negated_conjecture,
~ an_element(inverse(the_element)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_b_inverse_is_in_set) ).
fof(f15,definition,
( spl0_1
<=> an_element(identity) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f23,definition,
( spl0_3
<=> ! [X0] : ~ an_element(X0) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f24,plain,
( ! [X0] : ~ an_element(X0)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f23]) ).
fof(f27,definition,
( spl0_4
<=> ! [X0] :
( ~ an_element(X0)
| an_element(inverse(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f28,plain,
( ! [X0] :
( an_element(inverse(X0))
| ~ an_element(X0) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f27]) ).
fof(f38,plain,
( $false
| ~ spl0_3 ),
inference(backward_subsumption_resolution,[],[f8,f24]) ).
fof(f40,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f38]) ).
fof(f41,plain,
! [X0] :
( ~ an_element(X0)
| ~ an_element(identity)
| an_element(inverse(X0)) ),
inference(resolution,[],[f5,f1]) ).
fof(f42,plain,
! [X0] :
( ~ an_element(X0)
| ~ an_element(X0)
| an_element(identity) ),
inference(resolution,[],[f5,f3]) ).
fof(f44,plain,
! [X0] :
( ~ an_element(X0)
| an_element(identity) ),
inference(duplicate_literal_removal,[],[f42]) ).
fof(f46,plain,
( spl0_1
| spl0_3 ),
inference(avatar_split_clause,[],[f44,f23,f15]) ).
fof(f47,plain,
( ~ spl0_1
| spl0_4 ),
inference(avatar_split_clause,[],[f41,f27,f15]) ).
fof(f48,plain,
( ~ an_element(the_element)
| ~ spl0_4 ),
inference(resolution,[],[f28,f9]) ).
fof(f49,plain,
( $false
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f48,f8]) ).
fof(f50,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[],[f49]) ).
cnf(s4,plain,
~ spl0_3,
inference(sat_conversion,[],[f40]) ).
cnf(s6,plain,
( spl0_1
| spl0_3 ),
inference(sat_conversion,[],[f46]) ).
cnf(s7,plain,
( ~ spl0_1
| spl0_4 ),
inference(sat_conversion,[],[f47]) ).
cnf(s8,plain,
~ spl0_4,
inference(sat_conversion,[],[f50]) ).
cnf(s9,plain,
~ spl0_1,
inference(rat,[],[s7,s8]) ).
cnf(s10,plain,
spl0_3,
inference(rat,[],[s6,s9]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s4,s10]) ).
fof(f51,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP006-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n006.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 09:13:11 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 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
% 0.11/0.46 % (2719263)Will run a generic schedule for satisfiability detection.
% 0.11/0.46 % (2719275)% WARNING: option uhcvi not known.
% 0.11/0.46 % (2719275)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2659139321:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.46 % (2719275) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2719263-2719275"...
% 0.11/0.46 % (2719275)...printing done.
% 0.11/0.46 % (2719275)Refutation found. Thanks to Tanya!
% 0.11/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.46 % (2719275)------------------------------
% 0.11/0.46 % (2719275)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.46 % (2719275)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.46 % (2719275)CaDiCaL version: 2.1.3
% 0.11/0.46 % (2719275)Termination reason: Refutation
% 0.11/0.46 % (2719275)Time elapsed: 0.002 s
% 0.11/0.46 % (2719275)Peak memory usage: 12 MB
% 0.11/0.46 % (2719275)Instructions burned: 1 (million)
% 0.11/0.46 % (2719263)Success in time 0.027 s
% 0.11/0.46 % Vampire exiting
%------------------------------------------------------------------------------