%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : COL003-7 : TPTP v9.3.1. Released v1.2.0.
% 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 : n002.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 08:14:18 AM UTC 2026
% Result : Unsatisfiable 235.90s 236.24s
% Output : Proof 236.23s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(b_definition,axiom,
apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)),
file('theBenchmark.p',b_definition) ).
cnf(w_definition,axiom,
apply(apply(w,X),Y) = apply(apply(X,Y),Y),
file('theBenchmark.p',w_definition) ).
cnf(strong_fixed_point,axiom,
( fixed_point(Strong_fixed_point)
| apply(Strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(Strong_fixed_point,fixed_pt)) ),
file('theBenchmark.p',strong_fixed_point) ).
cnf(prove_strong_fixed_point,negated_conjecture,
~ fixed_point(apply(apply(b,apply(apply(b,apply(apply(b,apply(w,w)),apply(b,w))),b)),b)),
file('theBenchmark.p',prove_strong_fixed_point) ).
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,
( apply(Eq_x_0,Eq_x_1) = apply(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,
( fixed_point(Eq_y_0)
| ~ fixed_point(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
% 0.00/0.05 % Problem : COL003-7 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 This is a CNF_UNS_RFO_SEQ_HRN problem
% 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.45 % Computer : n002.cluster.edu
% 0.17/0.45 % Model : x86_64 x86_64
% 0.17/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.45 % Memory : 8046.5625MB
% 0.17/0.45 % OS : Linux 6.8.0-71-generic
% 0.17/0.45 % CPULimit : 300
% 0.17/0.45 % WCLimit : 300
% 0.17/0.45 % DateTime : Sun Sep 20 14:30:16 UTC 2026
% 0.17/0.45 % CPUTime :
% 235.90/236.24 % SZS status Unsatisfiable for theBenchmark
% 235.90/236.24 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------