%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP034-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n019.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 01:25:00 PM UTC 2026
% Result : Unsatisfiable 4.62s 6.45s
% Output : Proof 4.62s
% 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(f6,axiom,
( subgroup_member(C)
| ~ product(B,inverse(A),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_subgroup) ).
fof(f6_nnf,plain,
! [A,B,C] :
( subgroup_member(C)
| ~ product(B,inverse(A),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B,C] :
( subgroup_member(C)
| ~ product(B,inverse(A),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( subgroup_member(X2)
| ~ product(X1,inverse(X0),X2)
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi6,axiom,
ifeq(subgroup_member(X0),true,ifeq(subgroup_member(X1),true,ifeq(product(X1,inverse(X0),X2),true,subgroup_member(X2),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(f7,hypothesis,
subgroup_member(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_in_subgroup) ).
fof(f7_nnf,plain,
subgroup_member(a),
inference(nnf_transformation,[status(thm)],[f7]) ).
cnf(c7,plain,
subgroup_member(a),
inference(cnf_transformation,[status(esa)],[f7_nnf]) ).
cnf(hi7,axiom,
subgroup_member(a) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(f3,axiom,
product(X,inverse(X),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
fof(f3_nnf,plain,
! [X] : product(X,inverse(X),identity),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X] : product(X,inverse(X),identity),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
product(X0,inverse(X0),identity),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
product(X0,inverse(X0),identity) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h31,plain,
subgroup_member(identity) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi7,hi7,hi3]) ).
cnf(f1,axiom,
product(identity,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f1_nnf,plain,
! [X] : product(identity,X,X),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X] : product(identity,X,X),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
product(identity,X0,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
product(identity,X0,X0) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t2,plain,
subgroup_member(inverse(a)) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi7,h31,hi1]) ).
cnf(t258,plain,
subgroup_member(inverse(a)) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(f8,negated_conjecture,
~ subgroup_member(inverse(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_inverse_is_in_subgroup) ).
fof(f8_nnf,plain,
~ subgroup_member(inverse(a)),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
~ subgroup_member(inverse(a)),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
~ subgroup_member(inverse(a)),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(goal_0,negated_conjecture,
subgroup_member(inverse(a)) != true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t258]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP034-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/5.59 % Computer : n019.cluster.edu
% 0.10/5.59 % Model : x86_64 x86_64
% 0.10/5.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.59 % Memory : 8046.5625MB
% 0.10/5.59 % OS : Linux 6.8.0-71-generic
% 0.10/5.59 % CPULimit : 300
% 0.10/5.59 % WCLimit : 300
% 0.10/5.59 % DateTime : Wed Sep 23 13:20:40 UTC 2026
% 0.10/5.59 % CPUTime :
% 0.10/5.59 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.62/6.45 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.62/6.45 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------