%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GRP124-7.004 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 08:41:20 AM UTC 2026
% Result : Unsatisfiable 0.14s 5.42s
% Output : Proof 0.14s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(e_1_then_e_2,axiom,
next(e_1,e_2),
file('theBenchmark.p',e_1_then_e_2) ).
cnf(e_2_then_e_3,axiom,
next(e_2,e_3),
file('theBenchmark.p',e_2_then_e_3) ).
cnf(e_3_then_e_4,axiom,
next(e_3,e_4),
file('theBenchmark.p',e_3_then_e_4) ).
cnf(e_2_greater_e_1,axiom,
greater(e_2,e_1),
file('theBenchmark.p',e_2_greater_e_1) ).
cnf(e_3_greater_e_1,axiom,
greater(e_3,e_1),
file('theBenchmark.p',e_3_greater_e_1) ).
cnf(e_4_greater_e_1,axiom,
greater(e_4,e_1),
file('theBenchmark.p',e_4_greater_e_1) ).
cnf(e_3_greater_e_2,axiom,
greater(e_3,e_2),
file('theBenchmark.p',e_3_greater_e_2) ).
cnf(e_4_greater_e_2,axiom,
greater(e_4,e_2),
file('theBenchmark.p',e_4_greater_e_2) ).
cnf(e_4_greater_e_3,axiom,
greater(e_4,e_3),
file('theBenchmark.p',e_4_greater_e_3) ).
cnf(no_redundancy,axiom,
( ~ greater(Y,X1)
| ~ next(X,X1)
| ~ product(X,e_1,Y) ),
file('theBenchmark.p',no_redundancy) ).
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(product1_total_function1,axiom,
( product1(X,Y,e_4)
| product1(X,Y,e_3)
| product1(X,Y,e_2)
| product1(X,Y,e_1)
| ~ group_element(Y)
| ~ group_element(X) ),
file('theBenchmark.p',product1_total_function1) ).
cnf(product1_total_function2,axiom,
( equalish(W,Z)
| ~ product1(X,Y,Z)
| ~ product1(X,Y,W) ),
file('theBenchmark.p',product1_total_function2) ).
cnf(product1_right_cancellation,axiom,
( equalish(W,Z)
| ~ product1(X,Z,Y)
| ~ product1(X,W,Y) ),
file('theBenchmark.p',product1_right_cancellation) ).
cnf(product1_left_cancellation,axiom,
( equalish(W,Z)
| ~ product1(Z,Y,X)
| ~ product1(W,Y,X) ),
file('theBenchmark.p',product1_left_cancellation) ).
cnf(product1_idempotence,axiom,
product1(X,X,X),
file('theBenchmark.p',product1_idempotence) ).
cnf(product2_total_function1,axiom,
( product2(X,Y,e_4)
| product2(X,Y,e_3)
| product2(X,Y,e_2)
| product2(X,Y,e_1)
| ~ group_element(Y)
| ~ group_element(X) ),
file('theBenchmark.p',product2_total_function1) ).
cnf(product2_total_function2,axiom,
( equalish(W,Z)
| ~ product2(X,Y,Z)
| ~ product2(X,Y,W) ),
file('theBenchmark.p',product2_total_function2) ).
cnf(product2_right_cancellation,axiom,
( equalish(W,Z)
| ~ product2(X,Z,Y)
| ~ product2(X,W,Y) ),
file('theBenchmark.p',product2_right_cancellation) ).
cnf(product2_left_cancellation,axiom,
( equalish(W,Z)
| ~ product2(Z,Y,X)
| ~ product2(W,Y,X) ),
file('theBenchmark.p',product2_left_cancellation) ).
cnf(product2_idempotence,axiom,
product2(X,X,X),
file('theBenchmark.p',product2_idempotence) ).
cnf(qg2a,negated_conjecture,
( product2(Z2,Y,X)
| ~ product1(Z1,X,Z2)
| ~ product1(X,Y,Z1) ),
file('theBenchmark.p',qg2a) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP124-7.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.03 This is a CNF_UNS_EPR_NEQ_NHN problem
% 0.00/0.03 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n011.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Sat Sep 19 08:46:30 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.14/5.42 % SZS status Unsatisfiable for theBenchmark
% 0.14/5.42 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------