%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP135-1.002 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n010.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 01:25:24 PM UTC 2026
% Result : Unsatisfiable 4.32s 1.10s
% Output : Proof 4.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 48 ( 13 unt; 0 def)
% Number of atoms : 110 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 105 ( 43 ~; 62 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 62 ( 0 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f4,axiom,
( product(X,Y,e_2)
| product(X,Y,e_1)
| ~ group_element(Y)
| ~ group_element(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).
fof(f4_nnf,plain,
! [X,Y] :
( product(X,Y,e_2)
| product(X,Y,e_1)
| ~ group_element(Y)
| ~ group_element(X) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y] :
( product(X,Y,e_2)
| product(X,Y,e_1)
| ~ group_element(Y)
| ~ group_element(X) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(f1,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
fof(f1_nnf,plain,
group_element(e_2),
inference(nnf_transformation,[status(thm)],[f1]) ).
cnf(c1,plain,
group_element(e_2),
inference(cnf_transformation,[status(esa)],[f1_nnf]) ).
cnf(p13,plain,
( product(e_2,X0,e_2)
| product(e_2,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[c4,c1]) ).
cnf(f0,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
fof(f0_nnf,plain,
group_element(e_1),
inference(nnf_transformation,[status(thm)],[f0]) ).
cnf(c0,plain,
group_element(e_1),
inference(cnf_transformation,[status(esa)],[f0_nnf]) ).
cnf(p37,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[p13,c0]) ).
cnf(f8,negated_conjecture,
( product(Z2,Y,X)
| ~ product(Z1,Y,Z2)
| ~ product(Y,X,Z1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3) ).
fof(f8_nnf,plain,
! [Y,X,Z1,Z2] :
( product(Z2,Y,X)
| ~ product(Z1,Y,Z2)
| ~ product(Y,X,Z1) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [Y,X,Z1,Z2] :
( product(Z2,Y,X)
| ~ product(Z1,Y,Z2)
| ~ product(Y,X,Z1) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( product(X3,X0,X1)
| ~ product(X2,X0,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p44,plain,
( product(X0,e_2,e_1)
| ~ product(e_2,e_2,X0)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[p37,c8]) ).
cnf(p11,plain,
( product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0) ),
inference(factoring,[status(thm)],[c4]) ).
cnf(p15,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[p11,c1]) ).
cnf(p49,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_1)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[p44,p15]) ).
cnf(p64,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_1,e_1) ),
inference(factoring,[status(thm)],[p49]) ).
cnf(p69,plain,
( product(e_1,e_2,e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[p64,p44]) ).
cnf(p72,plain,
( product(e_1,e_2,e_1)
| product(e_2,e_1,e_1) ),
inference(factoring,[status(thm)],[p69]) ).
cnf(p14,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p11,c0]) ).
cnf(p16,plain,
( product(X0,e_1,e_1)
| ~ product(e_2,e_1,X0)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p14,c8]) ).
cnf(p47,plain,
( product(e_2,e_1,e_1)
| product(e_1,e_1,e_1)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[p37,p16]) ).
cnf(p51,plain,
( product(e_1,e_1,e_1)
| product(e_2,e_1,e_1) ),
inference(factoring,[status(thm)],[p47]) ).
cnf(p21,plain,
( ~ product(e_2,e_1,e_1)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p16]) ).
cnf(p56,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p51,p21]) ).
cnf(p58,plain,
product(e_1,e_1,e_1),
inference(factoring,[status(thm)],[p56]) ).
cnf(f7,axiom,
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f7_nnf,plain,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p62,plain,
( equalish(e_1,X0)
| ~ product(X0,e_1,e_1) ),
inference(resolution,[status(thm)],[p58,c7]) ).
cnf(p78,plain,
( equalish(e_1,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p72,p62]) ).
cnf(f6,axiom,
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f6_nnf,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p61,plain,
( equalish(e_1,X0)
| ~ product(e_1,X0,e_1) ),
inference(resolution,[status(thm)],[p58,c6]) ).
cnf(p83,plain,
( equalish(e_1,e_2)
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[p78,p61]) ).
cnf(p86,plain,
equalish(e_1,e_2),
inference(factoring,[status(thm)],[p83]) ).
cnf(f2,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f2_nnf,plain,
~ equalish(e_1,e_2),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
~ equalish(e_1,e_2),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p87,plain,
$false,
inference(resolution,[status(thm)],[p86,c2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP135-1.002 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n010.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 13:50:01 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.32/1.10 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.32/1.10 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------