%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP035-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : 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 7.71s 1.56s
% Output : Proof 7.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 50 ( 42 unt; 0 def)
% Number of atoms : 74 ( 16 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 54 ( 30 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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; 5 con; 0-4 aty)
% Number of variables : 60 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f7,axiom,
( product(U,Z,W)
| ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity2) ).
fof(f7_nnf,plain,
! [X,Y,U,Z,V,W] :
( product(U,Z,W)
| ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,Y,U,Z,V,W] :
( product(U,Z,W)
| ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi7,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X1,X3,X4),true,ifeq(product(X0,X4,X5),true,product(X2,X3,X5),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(f11,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_c) ).
fof(f11_nnf,plain,
product(a,b,c),
inference(nnf_transformation,[status(thm)],[f11]) ).
cnf(c11,plain,
product(a,b,c),
inference(cnf_transformation,[status(esa)],[f11_nnf]) ).
cnf(hi11,axiom,
product(a,b,c) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
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(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(h9,plain,
product(c,inverse(b),a) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi11,hi3,hi1]) ).
cnf(h34,plain,
product(a,inverse(inverse(b)),c) = true,
inference(hyper_resolution,[status(thm)],[hi7,h9,hi3,hi1]) ).
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(f10,hypothesis,
subgroup_member(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_in_subgroup) ).
fof(f10_nnf,plain,
subgroup_member(b),
inference(nnf_transformation,[status(thm)],[f10]) ).
cnf(c10,plain,
subgroup_member(b),
inference(cnf_transformation,[status(esa)],[f10_nnf]) ).
cnf(hi10,axiom,
subgroup_member(b) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(h7,plain,
subgroup_member(identity) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi10,hi10,hi3]) ).
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(h17,plain,
subgroup_member(inverse(b)) = true,
inference(hyper_resolution,[status(thm)],[hi8,h7,hi10,hi0]) ).
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(t3,plain,
subgroup_member(c) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi9,h17,h34]) ).
cnf(t417,plain,
subgroup_member(c) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(f12,negated_conjecture,
~ subgroup_member(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_is_in_subgroup) ).
fof(f12_nnf,plain,
~ subgroup_member(c),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
~ subgroup_member(c),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
~ subgroup_member(c),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(goal_0,negated_conjecture,
subgroup_member(c) != true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t417]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP035-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 13:25:50 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 7.71/1.56 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.71/1.56 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------