%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP131-1.002 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n013.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 3.73s 6.10s
% Output : Proof 3.73s
% 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 : 84 ( 3 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/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(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/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(p44,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/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(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(p39,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(p76,plain,
( product(e_1,e_1,e_1)
| equalish(e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[p44,p39]) ).
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,Y2,X2)
| ~ product(Z2,Y1,X1)
| ~ product(X2,Y2,Z1)
| ~ product(X1,Y1,Z1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg1_1) ).
fof(f8_nnf,plain,
! [X1,Y1,Z1,X2,Y2,Z2] :
( equalish(X1,X2)
| ~ product(Z2,Y2,X2)
| ~ product(Z2,Y1,X1)
| ~ 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,Y2,X2)
| ~ product(Z2,Y1,X1)
| ~ product(X2,Y2,Z1)
| ~ product(X1,Y1,Z1) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( equalish(X0,X3)
| ~ product(X5,X4,X3)
| ~ product(X5,X1,X0)
| ~ product(X3,X4,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p11,plain,
( equalish(X0,X2)
| ~ product(X2,X1,X0)
| ~ product(X2,X3,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,X0,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p21,p11]) ).
cnf(p52,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(p102,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)],[p76,p52]) ).
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)],[p102]) ).
cnf(p129,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/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(p133,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)],[p129,c6]) ).
cnf(p145,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)],[p133,p76]) ).
cnf(p148,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)],[p145]) ).
cnf(p149,plain,
( equalish(e_2,e_1)
| product(e_1,e_1,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p148]) ).
cnf(p10,plain,
( equalish(X0,X2)
| ~ product(X0,X3,X2)
| ~ product(X2,X3,X0)
| ~ product(X0,X1,X0) ),
inference(factoring,[status(thm)],[c8]) ).
cnf(p159,plain,
( equalish(e_1,X0)
| ~ product(e_1,X1,X0)
| ~ product(X0,X1,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[p149,p10]) ).
cnf(p168,plain,
( ~ product(e_1,X0,e_2)
| ~ product(e_2,X0,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p159]) ).
cnf(p53,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(p80,plain,
( product(e_2,e_1,e_1)
| equalish(e_2,e_1)
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[p53,p44]) ).
cnf(p172,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)],[p168,p80]) ).
cnf(p176,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)],[p172]) ).
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(p41,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p19,c1]) ).
cnf(p179,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)],[p176,p41]) ).
cnf(p164,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)],[p149,c7]) ).
cnf(p167,plain,
( ~ product(e_2,e_1,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p164]) ).
cnf(p186,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)],[p179,p167]) ).
cnf(p187,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)],[p186]) ).
cnf(p189,plain,
( product(e_1,e_2,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p187]) ).
cnf(p163,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)],[p149,c6]) ).
cnf(p166,plain,
( ~ product(e_1,e_2,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p163]) ).
cnf(p204,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)],[p189,p166]) ).
cnf(p205,plain,
( equalish(e_2,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p204]) ).
cnf(p207,plain,
( equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p205]) ).
cnf(f3,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/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(p208,plain,
equalish(e_1,e_2),
inference(resolution,[status(thm)],[p207,c3]) ).
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(p217,plain,
$false,
inference(resolution,[status(thm)],[p208,c2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP131-1.002 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/5.37 % Computer : n013.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Wed Sep 23 13:46:58 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.73/6.10 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.73/6.10 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------