%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP036-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n018.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 8.33s 6.67s
% Output : Proof 8.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 59 ( 43 unt; 0 def)
% Number of atoms : 95 ( 27 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 78 ( 42 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 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 : 93 ( 0 sgn 36 !; 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(f14,hypothesis,
subgroup_member(another_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',another_identity_in_subgroup) ).
fof(f14_nnf,plain,
subgroup_member(another_identity),
inference(nnf_transformation,[status(thm)],[f14]) ).
cnf(c14,plain,
subgroup_member(another_identity),
inference(cnf_transformation,[status(esa)],[f14_nnf]) ).
cnf(hi14,axiom,
subgroup_member(another_identity) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
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(h13,plain,
subgroup_member(identity) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi14,hi14,hi3]) ).
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(h107,plain,
product(identity,another_identity,identity) = true,
inference(hyper_resolution,[status(thm)],[hi10,h13]) ).
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(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(h6,plain,
product(identity,V0,inverse(inverse(V0))) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi2,hi2,hi1]) ).
cnf(f5,axiom,
( Z = W
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function2) ).
fof(f5_nnf,plain,
! [X,Y,Z,W] :
( Z = W
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,Y,Z,W] :
( Z = W
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi5,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X0,X1,X3),true,X2,X3),X3) = X3,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t5,plain,
inverse(inverse(another_identity)) = identity,
inference(hyper_resolution,[status(thm)],[hi5,h6,h107]) ).
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(t4,plain,
inverse(inverse(X1)) = X1,
inference(hyper_resolution,[status(thm)],[hi5,hi0,h6]) ).
cnf(t256,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t4]) ).
cnf(t269,plain,
another_identity = identity,
inference(step,[status(thm)],[t5,t256]) ).
cnf(t267,plain,
another_identity = identity,
inference(orient,[status(thm)],[t269]) ).
cnf(f15,negated_conjecture,
identity != another_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_identity_equals_another_identity) ).
fof(f15_nnf,plain,
identity != another_identity,
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
identity != another_identity,
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
identity != another_identity,
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(goal_0,negated_conjecture,
identity != another_identity,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(g0_0,plain,
identity != identity,
inference(rw,[status(thm)],[goal_0,t267]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP036-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/5.37 % Computer : n018.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Wed Sep 23 13:22:22 UTC 2026
% 0.11/5.37 % CPUTime :
% 0.11/5.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 8.33/6.67 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.33/6.67 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------