%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP037-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n003.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 7.63s 1.41s
% Output : Proof 7.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 70 ( 50 unt; 0 def)
% Number of atoms : 110 ( 31 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 87 ( 47 ~; 40 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 4 ( 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 : 114 ( 0 sgn 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f10,hypothesis,
( product(A,another_identity,A)
| ~ subgroup_member(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',another_right_identity) ).
fof(f10_nnf,plain,
! [A] :
( product(A,another_identity,A)
| ~ subgroup_member(A) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [A] :
( product(A,another_identity,A)
| ~ subgroup_member(A) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( product(X0,another_identity,X0)
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi10,axiom,
ifeq(subgroup_member(X0),true,product(X0,another_identity,X0),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(f17,hypothesis,
subgroup_member(another_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',another_identity_in_subgroup) ).
fof(f17_nnf,plain,
subgroup_member(another_identity),
inference(nnf_transformation,[status(thm)],[f17]) ).
cnf(c17,plain,
subgroup_member(another_identity),
inference(cnf_transformation,[status(esa)],[f17_nnf]) ).
cnf(hi17,axiom,
subgroup_member(another_identity) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(h8,plain,
product(another_identity,another_identity,another_identity) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi17]) ).
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(f2,axiom,
product(inverse(X),X,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f2_nnf,plain,
! [X] : product(inverse(X),X,identity),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X] : product(inverse(X),X,identity),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
product(inverse(X0),X0,identity),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
product(inverse(X0),X0,identity) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h27,plain,
product(identity,another_identity,identity) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi2,h8,hi2]) ).
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(h41,plain,
product(V0,another_identity,V0) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi1,h27,hi1]) ).
cnf(f6,axiom,
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity1) ).
fof(f6_nnf,plain,
! [X,Y,U,Z,V,W] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y,U,Z,V,W] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi6,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X1,X3,X4),true,ifeq(product(X2,X3,X5),true,product(X0,X4,X5),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
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(h52,plain,
product(inverse(V0),V0,another_identity) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi2,h41,hi0]) ).
cnf(f11,hypothesis,
( product(A,another_inverse(A),another_identity)
| ~ subgroup_member(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',another_right_inverse) ).
fof(f11_nnf,plain,
! [A] :
( product(A,another_inverse(A),another_identity)
| ~ subgroup_member(A) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A] :
( product(A,another_inverse(A),another_identity)
| ~ subgroup_member(A) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( product(X0,another_inverse(X0),another_identity)
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi11,axiom,
ifeq(subgroup_member(X0),true,product(X0,another_inverse(X0),another_identity),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(f16,hypothesis,
subgroup_member(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_in_subgroup) ).
fof(f16_nnf,plain,
subgroup_member(a),
inference(nnf_transformation,[status(thm)],[f16]) ).
cnf(c16,plain,
subgroup_member(a),
inference(cnf_transformation,[status(esa)],[f16_nnf]) ).
cnf(hi16,axiom,
subgroup_member(a) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(h2,plain,
product(a,another_inverse(a),another_identity) = true,
inference(hyper_resolution,[status(thm)],[hi11,hi16]) ).
cnf(f15,hypothesis,
( D = A
| ~ product(D,B,C)
| ~ product(A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f15_nnf,plain,
! [A,B,C,D] :
( D = A
| ~ product(D,B,C)
| ~ product(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [A,B,C,D] :
( D = A
| ~ product(D,B,C)
| ~ product(A,B,C) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( X3 = X0
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(hi15,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X3,X1,X2),true,X3,X0),X0) = X0,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t12,plain,
inverse(another_inverse(a)) = a,
inference(hyper_resolution,[status(thm)],[hi15,h2,h52]) ).
cnf(t250,plain,
inverse(another_inverse(a)) = a,
inference(orient,[status(thm)],[t12]) ).
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(t16,plain,
inverse(inverse(X1)) = X1,
inference(hyper_resolution,[status(thm)],[hi15,hi2,hi3]) ).
cnf(t239,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t16]) ).
cnf(f18,negated_conjecture,
inverse(a) != another_inverse(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_two_inverses_are_equal) ).
fof(f18_nnf,plain,
inverse(a) != another_inverse(a),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
inverse(a) != another_inverse(a),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
inverse(a) != another_inverse(a),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(goal_0,negated_conjecture,
inverse(a) != another_inverse(a),
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(g0_0,plain,
inverse(a) != inverse(inverse(another_inverse(a))),
inference(rw,[status(thm)],[goal_0,t250]) ).
cnf(g0_1,plain,
inverse(a) != another_inverse(a),
inference(rw,[status(thm)],[g0_0,t239]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP037-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n003.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Wed Sep 23 13:21:35 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 7.63/1.41 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.63/1.41 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------