%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP008-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n002.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 01:24:54 PM UTC 2026
% Result : Unsatisfiable 75.46s 10.13s
% Output : Proof 75.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 22 unt; 0 def)
% Number of atoms : 86 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 74 ( 32 ~; 42 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 60 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f6,axiom,
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox/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(f0,axiom,
product(identity,X,X),
file('/export/starexec/sandbox/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(p22,plain,
( product(identity,X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c6,c0]) ).
cnf(f1,axiom,
product(X,identity,X),
file('/export/starexec/sandbox/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(p60,plain,
( product(identity,X0,X1)
| ~ product(X0,identity,X1) ),
inference(resolution,[status(thm)],[p22,c1]) ).
cnf(f9,axiom,
( q(A)
| product(A,j(A),h(A))
| product(j(A),A,h(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown_meaning3) ).
fof(f9_nnf,plain,
! [A] :
( q(A)
| product(A,j(A),h(A))
| product(j(A),A,h(A)) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A] :
( q(A)
| product(A,j(A),h(A))
| product(j(A),A,h(A)) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( q(X0)
| product(X0,j(X0),h(X0))
| product(j(X0),X0,h(X0)) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p66,plain,
( q(identity)
| product(identity,j(identity),h(identity))
| product(identity,j(identity),h(identity)) ),
inference(resolution,[status(thm)],[p60,c9]) ).
cnf(p548,plain,
( q(identity)
| product(identity,j(identity),h(identity)) ),
inference(factoring,[status(thm)],[p66]) ).
cnf(f3,axiom,
product(X,inverse(X),identity),
file('/export/starexec/sandbox/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(p25,plain,
( product(X0,X2,X3)
| ~ product(identity,X1,X3)
| ~ product(inverse(X0),X1,X2) ),
inference(resolution,[status(thm)],[c6,c3]) ).
cnf(f2,axiom,
product(inverse(X),X,identity),
file('/export/starexec/sandbox/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(p82,plain,
( product(X0,identity,X1)
| ~ product(identity,X0,X1) ),
inference(resolution,[status(thm)],[p25,c2]) ).
cnf(p555,plain,
( product(j(identity),identity,h(identity))
| q(identity) ),
inference(resolution,[status(thm)],[p548,p82]) ).
cnf(f10,axiom,
( q(A)
| ~ product(A,j(A),h(A))
| ~ product(j(A),A,h(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown_meaning4) ).
fof(f10_nnf,plain,
! [A] :
( q(A)
| ~ product(A,j(A),h(A))
| ~ product(j(A),A,h(A)) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [A] :
( q(A)
| ~ product(A,j(A),h(A))
| ~ product(j(A),A,h(A)) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( q(X0)
| ~ product(X0,j(X0),h(X0))
| ~ product(j(X0),X0,h(X0)) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p566,plain,
( q(identity)
| ~ product(identity,j(identity),h(identity))
| q(identity) ),
inference(resolution,[status(thm)],[p555,c10]) ).
cnf(p1640,plain,
( ~ product(identity,j(identity),h(identity))
| q(identity) ),
inference(factoring,[status(thm)],[p566]) ).
cnf(p1641,plain,
( q(identity)
| q(identity) ),
inference(resolution,[status(thm)],[p1640,p548]) ).
cnf(p1642,plain,
q(identity),
inference(factoring,[status(thm)],[p1641]) ).
cnf(f11,negated_conjecture,
~ q(identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_identity_is_q) ).
fof(f11_nnf,plain,
~ q(identity),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
~ q(identity),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
~ q(identity),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p1643,plain,
$false,
inference(resolution,[status(thm)],[p1642,c11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP008-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n002.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Wed Sep 23 13:15:03 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 75.46/10.13 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 75.46/10.13 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------