%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP006-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 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 : Fri Sep 25 01:24:54 PM UTC 2026
% Result : Unsatisfiable 3.27s 0.82s
% Output : Proof 3.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 25 unt; 0 def)
% Number of atoms : 41 ( 9 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 30 ( 18 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-4 aty)
% Number of variables : 25 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f4,axiom,
( an_element(Z)
| ~ product(X,inverse(Y),Z)
| ~ an_element(Y)
| ~ an_element(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condition) ).
fof(f4_nnf,plain,
! [X,Y,Z] :
( an_element(Z)
| ~ product(X,inverse(Y),Z)
| ~ an_element(Y)
| ~ an_element(X) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y,Z] :
( an_element(Z)
| ~ product(X,inverse(Y),Z)
| ~ an_element(Y)
| ~ an_element(X) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( an_element(X2)
| ~ product(X0,inverse(X1),X2)
| ~ an_element(X1)
| ~ an_element(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi4,axiom,
ifeq(an_element(X0),true,ifeq(an_element(X1),true,ifeq(product(X0,inverse(X1),X2),true,an_element(X2),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(f7,hypothesis,
an_element(the_element),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_of_set) ).
fof(f7_nnf,plain,
an_element(the_element),
inference(nnf_transformation,[status(thm)],[f7]) ).
cnf(c7,plain,
an_element(the_element),
inference(cnf_transformation,[status(esa)],[f7_nnf]) ).
cnf(hi7,axiom,
an_element(the_element) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(f2,axiom,
product(X,inverse(X),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
fof(f2_nnf,plain,
! [X] : product(X,inverse(X),identity),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X] : product(X,inverse(X),identity),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
product(X0,inverse(X0),identity),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
product(X0,inverse(X0),identity) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h8,plain,
an_element(identity) = true,
inference(hyper_resolution,[status(thm)],[hi4,hi7,hi7,hi2]) ).
cnf(f0,axiom,
product(identity,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f0_nnf,plain,
! [X] : product(identity,X,X),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] : product(identity,X,X),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
product(identity,X0,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
product(identity,X0,X0) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t3,plain,
an_element(inverse(the_element)) = true,
inference(hyper_resolution,[status(thm)],[hi4,h8,hi7,hi0]) ).
cnf(t109,plain,
an_element(inverse(the_element)) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(f8,negated_conjecture,
~ an_element(inverse(the_element)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_inverse_is_in_set) ).
fof(f8_nnf,plain,
~ an_element(inverse(the_element)),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
~ an_element(inverse(the_element)),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
~ an_element(inverse(the_element)),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(goal_0,negated_conjecture,
an_element(inverse(the_element)) != true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t109]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP006-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n003.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 13:14:04 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.27/0.82 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.27/0.82 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------