%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP038-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n016.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 01:25:01 PM UTC 2026
% Result : Unsatisfiable 5.94s 1.26s
% Output : Proof 5.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 22 unt; 0 def)
% Number of atoms : 38 ( 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 : 6 ( 6 usr; 4 con; 0-4 aty)
% Number of variables : 15 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f11,hypothesis,
subgroup_member(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_in_subgroup) ).
fof(f11_nnf,plain,
subgroup_member(a),
inference(nnf_transformation,[status(thm)],[f11]) ).
cnf(c11,plain,
subgroup_member(a),
inference(cnf_transformation,[status(esa)],[f11_nnf]) ).
cnf(hi11,axiom,
subgroup_member(a) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(f12,hypothesis,
subgroup_member(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_in_subgroup) ).
fof(f12_nnf,plain,
subgroup_member(b),
inference(nnf_transformation,[status(thm)],[f12]) ).
cnf(c12,plain,
subgroup_member(b),
inference(cnf_transformation,[status(esa)],[f12_nnf]) ).
cnf(hi12,axiom,
subgroup_member(b) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(f13,hypothesis,
product(a,inverse(b),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_inverse_b_is_c) ).
fof(f13_nnf,plain,
product(a,inverse(b),c),
inference(nnf_transformation,[status(thm)],[f13]) ).
cnf(c13,plain,
product(a,inverse(b),c),
inference(cnf_transformation,[status(esa)],[f13_nnf]) ).
cnf(hi13,axiom,
product(a,inverse(b),c) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t3,plain,
subgroup_member(c) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi11,hi12,hi13]) ).
cnf(t223,plain,
subgroup_member(c) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(f14,negated_conjecture,
~ subgroup_member(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_is_in_subgroup) ).
fof(f14_nnf,plain,
~ subgroup_member(c),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
~ subgroup_member(c),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
~ subgroup_member(c),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(goal_0,negated_conjecture,
subgroup_member(c) != true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t223]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP038-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n016.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 13:25:26 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.94/1.26 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.94/1.26 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------