%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : ALG012-1 : TPTP v9.3.1. Released v2.7.0.
% 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 : n026.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 08:11:34 AM UTC 2026
% Result : Unsatisfiable 276.13s 276.42s
% Output : Proof 277.04s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(f_is_associative,axiom,
f(X,f(Y,Z)) = f(f(X,Y),Z),
file('theBenchmark.p',f_is_associative) ).
cnf(partitions_union,axiom,
( d2(X)
| d1(X)
| c(X) ),
file('theBenchmark.p',partitions_union) ).
cnf(partitions_exclusive_c_d1,hypothesis,
( ~ d1(X)
| ~ c(X) ),
file('theBenchmark.p',partitions_exclusive_c_d1) ).
cnf(partitions_exclusive_c_d2,hypothesis,
( ~ d2(X)
| ~ c(X) ),
file('theBenchmark.p',partitions_exclusive_c_d2) ).
cnf(partitions_exclusive_d1_d2,hypothesis,
( ~ d2(X)
| ~ d1(X) ),
file('theBenchmark.p',partitions_exclusive_d1_d2) ).
cnf(partition_c_not_empty,hypothesis,
c(a1),
file('theBenchmark.p',partition_c_not_empty) ).
cnf(partition_d1_not_empty,hypothesis,
d1(a2),
file('theBenchmark.p',partition_d1_not_empty) ).
cnf(partition_d2_not_empty,hypothesis,
d2(a3),
file('theBenchmark.p',partition_d2_not_empty) ).
cnf(conjecture_1,negated_conjecture,
( ~ c(Y)
| ~ c(X)
| d1(f(X,Y))
| d2(f(X,Y)) ),
file('theBenchmark.p',conjecture_1) ).
cnf(conjecture_2,negated_conjecture,
( ~ d1(Y)
| ~ d1(X)
| c(f(X,Y)) ),
file('theBenchmark.p',conjecture_2) ).
cnf(conjecture_3,negated_conjecture,
( ~ d2(Y)
| ~ d2(X)
| c(f(X,Y)) ),
file('theBenchmark.p',conjecture_3) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( f(Eq_x_0,Eq_x_1) = f(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( c(Eq_y_0)
| ~ c(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_6,axiom,
( d1(Eq_y_0)
| ~ d1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_7,axiom,
( d2(Eq_y_0)
| ~ d2(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG012-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n026.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 : Sun Sep 20 08:42:08 UTC 2026
% 0.10/0.38 % CPUTime :
% 276.13/276.42 % SZS status Unsatisfiable for theBenchmark
% 276.13/276.42 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------