%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP005-1 : TPTP v9.3.1. Released v1.0.0.
% 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 10:16:20 AM UTC 2026
% Result : Unsatisfiable 0.21s 0.50s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 1
% Number of leaves : 9
% Syntax : Number of formulae : 10 ( 7 unt; 0 def)
% Number of atoms : 19 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 19 ( 10 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 19 ( 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : product(identity,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : product(X0,identity,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
fof(f3,axiom,
! [X0] : product(X0,inverse(X0),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
fof(f4,axiom,
! [X0] : product(inverse(X0),X0,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f5,axiom,
an_element(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_of_set) ).
fof(f6,axiom,
! [X2,X0,X1] :
( ~ an_element(X0)
| ~ an_element(X1)
| ~ product(X0,inverse(X1),X2)
| an_element(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condition) ).
fof(f7,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X0,X1,X2)
| ~ product(X1,X3,X4)
| ~ product(X2,X3,X5)
| product(X0,X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity1) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X0,X1,X2)
| ~ product(X1,X3,X4)
| ~ product(X0,X4,X5)
| product(X2,X3,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity2) ).
fof(f9,negated_conjecture,
~ an_element(identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_identity_is_an_element) ).
fof(f23,plain,
$false,
inference(finite_model_not_found_(exhaustively_excluded_all_possible_domain_size_assignments),[],[f1,f2,f3,f4,f5,f6,f7,f8,f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP005-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.14/0.40 % Computer : n011.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sun Sep 27 09:13:15 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.14/0.45 Running first-order model finding
% 0.14/0.46 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
% 0.21/0.50 % (2133993)Will run a generic schedule for satisfiability detection.
% 0.21/0.50 % (2133998)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2426378122_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.50 % TRYING [1]
% 0.21/0.50 % TRYING [2]
% 0.21/0.50 % TRYING [3]
% 0.21/0.50 % TRYING [4]
% 0.21/0.50 % (2134002)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4285183352:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.50 % (2133998) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2133993-2133998"...
% 0.21/0.50 % (2133999)% WARNING: option uhcvi not known.
% 0.21/0.50 % (2133998)...printing done.
% 0.21/0.50 % (2133998)Refutation found. Thanks to Tanya!
% 0.21/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.21/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.50 % (2133998)------------------------------
% 0.21/0.50 % (2133998)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.50 % (2133998)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.50 % (2133998)CaDiCaL version: 2.1.3
% 0.21/0.50 % (2133998)Termination reason: Refutation
% 0.21/0.50 % (2133998)Time elapsed: 0.007 s
% 0.21/0.50 % (2133998)Peak memory usage: 11 MB
% 0.21/0.50 % (2133998)Instructions burned: 16 (million)
% 0.21/0.50 % (2133993)Success in time 0.029 s
% 0.21/0.50 % Vampire exiting
%------------------------------------------------------------------------------