%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP132-1.002 : TPTP v9.3.1. Released v1.2.0.
% 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 01:25:22 PM UTC 2026
% Result : Unsatisfiable 4.30s 1.10s
% Output : Proof 4.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 8
% Syntax : Number of formulae : 69 ( 16 unt; 0 def)
% Number of atoms : 206 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 210 ( 73 ~; 137 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 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 : 81 ( 0 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f4,axiom,
( product(X,Y,e_2)
| product(X,Y,e_1)
| ~ group_element(Y)
| ~ group_element(X) ),
file('/export/starexec/sandbox2/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/sandbox2/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(p20,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/sandbox2/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(p57,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[p20,c0]) ).
cnf(f7,axiom,
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
file('/export/starexec/sandbox2/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(p18,plain,
( product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0) ),
inference(factoring,[status(thm)],[c4]) ).
cnf(p21,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p18,c0]) ).
cnf(p40,plain,
( product(e_1,e_1,e_1)
| equalish(e_1,X0)
| ~ product(X0,e_1,e_2) ),
inference(resolution,[status(thm)],[c7,p21]) ).
cnf(p79,plain,
( product(e_1,e_1,e_1)
| equalish(e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[p57,p40]) ).
cnf(p22,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[p18,c1]) ).
cnf(f8,negated_conjecture,
( equalish(X1,X2)
| ~ product(Z2,X2,Y2)
| ~ product(Z2,X1,Y1)
| ~ product(X2,Y2,Z1)
| ~ product(X1,Y1,Z1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg2_1) ).
fof(f8_nnf,plain,
! [X1,Y1,Z1,X2,Y2,Z2] :
( equalish(X1,X2)
| ~ product(Z2,X2,Y2)
| ~ product(Z2,X1,Y1)
| ~ product(X2,Y2,Z1)
| ~ product(X1,Y1,Z1) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X1,Y1,Z1,X2,Y2,Z2] :
( equalish(X1,X2)
| ~ product(Z2,X2,Y2)
| ~ product(Z2,X1,Y1)
| ~ product(X2,Y2,Z1)
| ~ product(X1,Y1,Z1) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( equalish(X0,X3)
| ~ product(X5,X3,X4)
| ~ product(X5,X0,X1)
| ~ product(X3,X4,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p13,plain,
( equalish(X0,X2)
| ~ product(X2,X0,X1)
| ~ product(X2,X2,X2)
| ~ product(X0,X1,X2) ),
inference(factoring,[status(thm)],[c8]) ).
cnf(p24,plain,
( equalish(e_1,e_2)
| ~ product(e_2,e_1,e_1)
| ~ product(e_2,e_2,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p21,p13]) ).
cnf(p50,plain,
( equalish(e_1,e_2)
| ~ product(e_2,e_1,e_1)
| product(e_1,e_1,e_1)
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[p22,p24]) ).
cnf(p104,plain,
( equalish(e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_2,e_2,e_1)
| product(e_1,e_1,e_1)
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[p79,p50]) ).
cnf(p119,plain,
( equalish(e_1,e_2)
| product(e_2,e_2,e_1)
| product(e_1,e_1,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p104]) ).
cnf(p120,plain,
( product(e_2,e_2,e_1)
| product(e_1,e_1,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p119]) ).
cnf(f6,axiom,
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
file('/export/starexec/sandbox2/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(p124,plain,
( equalish(e_2,X0)
| ~ product(e_2,X0,e_1)
| product(e_1,e_1,e_1)
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[p120,c6]) ).
cnf(p136,plain,
( product(e_1,e_1,e_1)
| equalish(e_1,e_2)
| equalish(e_2,e_1)
| product(e_1,e_1,e_1)
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[p124,p79]) ).
cnf(p146,plain,
( equalish(e_1,e_2)
| equalish(e_2,e_1)
| product(e_1,e_1,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p136]) ).
cnf(p147,plain,
( equalish(e_2,e_1)
| product(e_1,e_1,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p146]) ).
cnf(p10,plain,
( equalish(X0,X1)
| ~ product(X0,X1,X2)
| ~ product(X1,X2,X0)
| ~ product(X0,X0,X0) ),
inference(factoring,[status(thm)],[c8]) ).
cnf(p149,plain,
( equalish(e_1,X0)
| ~ product(e_1,X0,X1)
| ~ product(X0,X1,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[p147,p10]) ).
cnf(p165,plain,
( ~ product(e_1,e_2,X0)
| ~ product(e_2,X0,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p149]) ).
cnf(p54,plain,
( equalish(e_2,X0)
| ~ product(e_2,X0,e_2)
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[p22,c6]) ).
cnf(p82,plain,
( product(e_2,e_1,e_1)
| equalish(e_2,e_1)
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[p54,p57]) ).
cnf(p169,plain,
( product(e_2,e_1,e_1)
| equalish(e_2,e_1)
| ~ product(e_1,e_2,e_2)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[p165,p82]) ).
cnf(p173,plain,
( product(e_2,e_1,e_1)
| ~ product(e_1,e_2,e_2)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p169]) ).
cnf(p19,plain,
( product(e_1,X0,e_2)
| product(e_1,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[c4,c0]) ).
cnf(p45,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p19,c1]) ).
cnf(p174,plain,
( product(e_1,e_2,e_1)
| product(e_2,e_1,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[p173,p45]) ).
cnf(p154,plain,
( equalish(e_1,X0)
| ~ product(X0,e_1,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[p147,c7]) ).
cnf(p164,plain,
( ~ product(e_2,e_1,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p154]) ).
cnf(p183,plain,
( equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[p174,p164]) ).
cnf(p186,plain,
( equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p183]) ).
cnf(p188,plain,
( product(e_1,e_2,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p186]) ).
cnf(p153,plain,
( equalish(e_1,X0)
| ~ product(e_1,X0,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[p147,c6]) ).
cnf(p163,plain,
( ~ product(e_1,e_2,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p153]) ).
cnf(p195,plain,
( equalish(e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[p188,p163]) ).
cnf(p196,plain,
( equalish(e_2,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p195]) ).
cnf(p204,plain,
( equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p196]) ).
cnf(f3,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
fof(f3_nnf,plain,
~ equalish(e_2,e_1),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
~ equalish(e_2,e_1),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
~ equalish(e_2,e_1),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p205,plain,
equalish(e_1,e_2),
inference(resolution,[status(thm)],[p204,c3]) ).
cnf(f2,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/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(p206,plain,
$false,
inference(resolution,[status(thm)],[p205,c2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP132-1.002 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n018.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 13:49:48 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.30/1.10 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.30/1.10 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------