%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP033-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : 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 01:25:00 PM UTC 2026
% Result : Unsatisfiable 3.88s 0.93s
% Output : Proof 3.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 30 unt; 0 def)
% Number of atoms : 66 ( 14 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 54 ( 30 ~; 24 |; 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 : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 40 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f10,hypothesis,
( subgroup_member(j(A))
| ~ subgroup_member(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subgr2_clause1) ).
fof(f10_nnf,plain,
! [A] :
( subgroup_member(j(A))
| ~ subgroup_member(A) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [A] :
( subgroup_member(j(A))
| ~ subgroup_member(A) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( subgroup_member(j(X0))
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi10,axiom,
ifeq(subgroup_member(X0),true,subgroup_member(j(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(f9,hypothesis,
subgroup_member(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_in_subgroup) ).
fof(f9_nnf,plain,
subgroup_member(a),
inference(nnf_transformation,[status(thm)],[f9]) ).
cnf(c9,plain,
subgroup_member(a),
inference(cnf_transformation,[status(esa)],[f9_nnf]) ).
cnf(hi9,axiom,
subgroup_member(a) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(h0,plain,
subgroup_member(j(a)) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi9]) ).
cnf(h1,plain,
subgroup_member(j(j(a))) = true,
inference(hyper_resolution,[status(thm)],[hi10,h0]) ).
cnf(f8,axiom,
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_product_and_inverse) ).
fof(f8_nnf,plain,
! [A,B,C] :
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B,C] :
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( subgroup_member(X2)
| ~ product(X0,inverse(X1),X2)
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi8,axiom,
ifeq(subgroup_member(X0),true,ifeq(subgroup_member(X1),true,ifeq(product(X0,inverse(X1),X2),true,subgroup_member(X2),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
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(h9,plain,
subgroup_member(identity) = true,
inference(hyper_resolution,[status(thm)],[hi8,h1,h1,hi3]) ).
cnf(f11,negated_conjecture,
( ~ subgroup_member(A)
| ~ product(A,j(A),j(A))
| ~ product(j(A),A,j(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_subgr2) ).
fof(f11_nnf,plain,
! [A] :
( ~ subgroup_member(A)
| ~ product(A,j(A),j(A))
| ~ product(j(A),A,j(A)) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A] :
( ~ subgroup_member(A)
| ~ product(A,j(A),j(A))
| ~ product(j(A),A,j(A)) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( ~ subgroup_member(X0)
| ~ product(X0,j(X0),j(X0))
| ~ product(j(X0),X0,j(X0)) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi11,negated_conjecture,
ifeq(product(j(X0),X0,j(X0)),true,ifeq(product(X0,j(X0),j(X0)),true,ifeq(subgroup_member(X0),true,false,true),true),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(f1,axiom,
product(X,identity,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
fof(f1_nnf,plain,
! [X] : product(X,identity,X),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X] : product(X,identity,X),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
product(X0,identity,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
product(X0,identity,X0) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(f0,axiom,
product(identity,X,X),
file('/export/starexec/sandbox2/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(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi11,hi1,hi0,h9]) ).
cnf(t250,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t250]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP033-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n001.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 : Wed Sep 23 13:25:06 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.88/0.93 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.88/0.93 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------