%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP005-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.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 5.45s 1.23s
% Output : Proof 5.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 20 unt; 0 def)
% Number of atoms : 36 ( 8 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 : 20 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f4,axiom,
an_element(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_of_set) ).
fof(f4_nnf,plain,
an_element(a),
inference(nnf_transformation,[status(thm)],[f4]) ).
cnf(c4,plain,
an_element(a),
inference(cnf_transformation,[status(esa)],[f4_nnf]) ).
cnf(hi4,axiom,
an_element(a) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h0,plain,
an_element(a) = true,
inference(hyper_resolution,[status(thm)],[hi4]) ).
cnf(f5,axiom,
( an_element(Z)
| ~ product(X,inverse(Y),Z)
| ~ an_element(Y)
| ~ an_element(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condition) ).
fof(f5_nnf,plain,
! [X,Y,Z] :
( an_element(Z)
| ~ product(X,inverse(Y),Z)
| ~ an_element(Y)
| ~ an_element(X) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,Y,Z] :
( an_element(Z)
| ~ product(X,inverse(Y),Z)
| ~ an_element(Y)
| ~ an_element(X) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( an_element(X2)
| ~ product(X0,inverse(X1),X2)
| ~ an_element(X1)
| ~ an_element(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi5,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)],[c5]) ).
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(t1,plain,
an_element(identity) = true,
inference(hyper_resolution,[status(thm)],[hi5,hi4,h0,hi2]) ).
cnf(t53,plain,
an_element(identity) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(f8,negated_conjecture,
~ an_element(identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_identity_is_an_element) ).
fof(f8_nnf,plain,
~ an_element(identity),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
~ an_element(identity),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
~ an_element(identity),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(goal_0,negated_conjecture,
an_element(identity) != true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t53]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP005-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.38 % Computer : n001.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 : Wed Sep 23 13:17:34 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.45/1.23 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.45/1.23 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------