%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP031-1 : 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 : 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 0.12s 0.46s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 14 ( 7 unt; 0 def)
% Number of atoms : 25 ( 5 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 23 ( 12 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 30 ( 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/GRP002-0.ax',associativity1) ).
fof(f5,axiom,
! [X0] : product(identity,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f6,axiom,
! [X0] : product(inverse(X0),X0,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f7,negated_conjecture,
! [X0] : ~ product(a,X0,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_has_an_inverse) ).
fof(f15,plain,
! [X0,X1] :
( ~ product(inverse(X0),X0,X1)
| identity = X1 ),
inference(resolution,[],[f2,f6]) ).
fof(f131,plain,
! [X2,X3,X0,X1] :
( ~ product(X3,X0,identity)
| ~ product(X0,X1,X2)
| product(X3,X2,X1) ),
inference(resolution,[],[f3,f5]) ).
fof(f146,plain,
! [X2,X0,X1] :
( product(inverse(X0),X2,X1)
| ~ product(X0,X1,X2) ),
inference(resolution,[],[f131,f6]) ).
fof(f168,plain,
! [X0,X1] :
( ~ product(X0,X1,X0)
| identity = X1 ),
inference(resolution,[],[f146,f15]) ).
fof(f184,plain,
! [X0,X1] :
( ~ product(X1,inverse(X1),X0)
| identity = X0 ),
inference(resolution,[],[f168,f146]) ).
fof(f192,plain,
! [X0] : identity = multiply(X0,inverse(X0)),
inference(resolution,[],[f184,f1]) ).
fof(f206,plain,
! [X0] : product(X0,inverse(X0),identity),
inference(superposition,[],[f1,f192]) ).
fof(f216,plain,
$false,
inference(resolution,[],[f206,f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP031-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n005.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 09:15:02 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.42 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
% 0.12/0.46 % (3714167)Will run a generic schedule for satisfiability detection.
% 0.12/0.46 % (3714174)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1321171566:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.12/0.46 % (3714173)% WARNING: option uhcvi not known.
% 0.12/0.46 % (3714174) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3714167-3714174"...
% 0.12/0.46 % (3714174)...printing done.
% 0.12/0.46 % (3714174)Refutation found. Thanks to Tanya!
% 0.12/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.46 % (3714174)------------------------------
% 0.12/0.46 % (3714174)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.46 % (3714174)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.46 % (3714174)CaDiCaL version: 2.1.3
% 0.12/0.46 % (3714174)Termination reason: Refutation
% 0.12/0.46 % (3714174)Time elapsed: 0.003 s
% 0.12/0.46 % (3714174)Peak memory usage: 11 MB
% 0.12/0.46 % (3714174)Instructions burned: 5 (million)
% 0.12/0.46 % (3714167)Success in time 0.033 s
% 0.12/0.46 % Vampire exiting
%------------------------------------------------------------------------------