%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP029-1 : 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 : n005.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 10:16:26 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.45s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 25 ( 12 unt; 0 def)
% Number of atoms : 45 ( 8 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 41 ( 21 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 54 ( 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP002-0.ax',total_function1) ).
fof(f2,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X3)
| ~ product(X0,X1,X2)
| X2 = X3 ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP002-0.ax',total_function2) ).
fof(f3,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2)
| product(X0,X4,X5) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP002-0.ax',associativity1) ).
fof(f4,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X1,X3,X4)
| ~ product(X0,X1,X2)
| ~ product(X0,X4,X5)
| product(X2,X3,X5) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP002-0.ax',associativity2) ).
fof(f5,axiom,
! [X0] : product(identity,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f6,axiom,
! [X0] : product(inverse(X0),X0,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f7,negated_conjecture,
! [X0] : ~ product(not_right_identity(X0),X0,not_right_identity(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_there_is_a_right_identity) ).
fof(f8,plain,
! [X0,X1] :
( ~ product(identity,X0,X1)
| X0 = X1 ),
inference(resolution,[],[f2,f5]) ).
fof(f9,plain,
! [X0,X1] :
( ~ product(inverse(X0),X0,X1)
| identity = X1 ),
inference(resolution,[],[f2,f6]) ).
fof(f11,plain,
! [X2,X3,X0,X1] :
( ~ product(X3,X0,identity)
| ~ product(X0,X1,X2)
| product(X3,X2,X1) ),
inference(resolution,[],[f3,f5]) ).
fof(f17,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,inverse(X1),X2)
| ~ product(X0,identity,X3)
| product(X2,X1,X3) ),
inference(resolution,[],[f4,f6]) ).
fof(f27,plain,
! [X2,X0,X1] :
( product(inverse(X0),X2,X1)
| ~ product(X0,X1,X2) ),
inference(resolution,[],[f11,f6]) ).
fof(f35,plain,
! [X0,X1] :
( ~ product(X0,X1,X0)
| identity = X1 ),
inference(resolution,[],[f27,f9]) ).
fof(f44,plain,
! [X0,X1] :
( ~ product(inverse(inverse(X0)),identity,X1)
| product(identity,X0,X1) ),
inference(resolution,[],[f17,f6]) ).
fof(f45,plain,
! [X2,X0,X1] :
( product(multiply(X0,inverse(X2)),X2,X1)
| ~ product(X0,identity,X1) ),
inference(resolution,[],[f17,f1]) ).
fof(f48,plain,
! [X0,X1] :
( ~ product(X1,inverse(X1),X0)
| identity = X0 ),
inference(resolution,[],[f35,f27]) ).
fof(f55,plain,
! [X0] : identity = multiply(X0,inverse(X0)),
inference(resolution,[],[f48,f1]) ).
fof(f132,plain,
! [X0] : product(identity,X0,multiply(inverse(inverse(X0)),identity)),
inference(resolution,[],[f44,f1]) ).
fof(f136,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(resolution,[],[f132,f8]) ).
fof(f174,plain,
! [X0] : product(inverse(inverse(X0)),identity,X0),
inference(superposition,[],[f1,f136]) ).
fof(f219,plain,
! [X0,X1] :
( ~ product(X0,identity,X1)
| product(identity,X0,X1) ),
inference(superposition,[],[f45,f55]) ).
fof(f290,plain,
! [X0] : product(identity,inverse(inverse(X0)),X0),
inference(resolution,[],[f219,f174]) ).
fof(f312,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(resolution,[],[f290,f8]) ).
fof(f336,plain,
! [X0] : product(X0,identity,X0),
inference(superposition,[],[f174,f312]) ).
fof(f392,plain,
$false,
inference(resolution,[],[f336,f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP029-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n005.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 09:15:17 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.15/0.41 Running first-order model finding
% 0.15/0.41 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
% 0.15/0.45 % (3714978)Will run a generic schedule for satisfiability detection.
% 0.15/0.45 % (3714986)dis+10_1_sil=32000:sp=arity:random_seed=309082663:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.45 % (3714986) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3714978-3714986"...
% 0.15/0.45 % (3714986)...printing done.
% 0.15/0.45 % (3714986)Refutation found. Thanks to Tanya!
% 0.15/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.45 % (3714986)------------------------------
% 0.15/0.45 % (3714986)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.45 % (3714986)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.45 % (3714986)CaDiCaL version: 2.1.3
% 0.15/0.45 % (3714986)Termination reason: Refutation
% 0.15/0.45 % (3714986)Time elapsed: 0.005 s
% 0.15/0.45 % (3714986)Peak memory usage: 11 MB
% 0.15/0.45 % (3714986)Instructions burned: 14 (million)
% 0.15/0.45 % (3714978)Success in time 0.03 s
% 0.15/0.45 % Vampire exiting
%------------------------------------------------------------------------------