%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GRP126-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 : Thu Sep 24 08:41:21 AM UTC 2026
% Result : Unsatisfiable 0.20s 0.49s
% Output : Proof 0.20s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(row_surjectivity,axiom,
( product(e_4,X,Y)
| product(e_3,X,Y)
| product(e_2,X,Y)
| product(e_1,X,Y)
| ~ group_element(Y)
| ~ group_element(X) ),
file('theBenchmark.p',row_surjectivity) ).
cnf(column_surjectivity,axiom,
( product(X,e_4,Y)
| product(X,e_3,Y)
| product(X,e_2,Y)
| product(X,e_1,Y)
| ~ group_element(Y)
| ~ group_element(X) ),
file('theBenchmark.p',column_surjectivity) ).
cnf(qg4_1,negated_conjecture,
( ~ product(Y,X,Z2)
| ~ product(Z1,Z2,Y)
| product(X,Y,Z1) ),
file('theBenchmark.p',qg4_1) ).
cnf(qg4_2,negated_conjecture,
( ~ product(X,Y,Z1)
| ~ product(Z1,Z2,Y)
| product(Y,X,Z2) ),
file('theBenchmark.p',qg4_2) ).
cnf(element_1,axiom,
group_element(e_1),
file('theBenchmark.p',element_1) ).
cnf(element_2,axiom,
group_element(e_2),
file('theBenchmark.p',element_2) ).
cnf(element_3,axiom,
group_element(e_3),
file('theBenchmark.p',element_3) ).
cnf(element_4,axiom,
group_element(e_4),
file('theBenchmark.p',element_4) ).
cnf(e_1_is_not_e_2,axiom,
~ equalish(e_1,e_2),
file('theBenchmark.p',e_1_is_not_e_2) ).
cnf(e_1_is_not_e_3,axiom,
~ equalish(e_1,e_3),
file('theBenchmark.p',e_1_is_not_e_3) ).
cnf(e_1_is_not_e_4,axiom,
~ equalish(e_1,e_4),
file('theBenchmark.p',e_1_is_not_e_4) ).
cnf(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1),
file('theBenchmark.p',e_2_is_not_e_1) ).
cnf(e_2_is_not_e_3,axiom,
~ equalish(e_2,e_3),
file('theBenchmark.p',e_2_is_not_e_3) ).
cnf(e_2_is_not_e_4,axiom,
~ equalish(e_2,e_4),
file('theBenchmark.p',e_2_is_not_e_4) ).
cnf(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1),
file('theBenchmark.p',e_3_is_not_e_1) ).
cnf(e_3_is_not_e_2,axiom,
~ equalish(e_3,e_2),
file('theBenchmark.p',e_3_is_not_e_2) ).
cnf(e_3_is_not_e_4,axiom,
~ equalish(e_3,e_4),
file('theBenchmark.p',e_3_is_not_e_4) ).
cnf(e_4_is_not_e_1,axiom,
~ equalish(e_4,e_1),
file('theBenchmark.p',e_4_is_not_e_1) ).
cnf(e_4_is_not_e_2,axiom,
~ equalish(e_4,e_2),
file('theBenchmark.p',e_4_is_not_e_2) ).
cnf(e_4_is_not_e_3,axiom,
~ equalish(e_4,e_3),
file('theBenchmark.p',e_4_is_not_e_3) ).
cnf(product_total_function1,axiom,
( product(X,Y,e_4)
| product(X,Y,e_3)
| product(X,Y,e_2)
| product(X,Y,e_1)
| ~ group_element(Y)
| ~ group_element(X) ),
file('theBenchmark.p',product_total_function1) ).
cnf(product_total_function2,axiom,
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
file('theBenchmark.p',product_total_function2) ).
cnf(product_right_cancellation,axiom,
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
file('theBenchmark.p',product_right_cancellation) ).
cnf(product_left_cancellation,axiom,
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
file('theBenchmark.p',product_left_cancellation) ).
cnf(product_idempotence,axiom,
product(X,X,X),
file('theBenchmark.p',product_idempotence) ).
cnf(qg4,negated_conjecture,
( product(Z1,Z2,Y)
| ~ product(Y,X,Z2)
| ~ product(X,Y,Z1) ),
file('theBenchmark.p',qg4) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP126-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 This is a CNF_UNS_EPR_NEQ_NHN problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n009.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 19 08:47:42 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.20/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.20/0.49 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------