%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : COL002-4 : TPTP v9.3.1. Bugfixed v3.1.0.
% 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 : 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 08:14:17 AM UTC 2026
% Result : Unsatisfiable 0.33s 0.67s
% Output : Proof 0.33s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(s_definition,axiom,
apply(apply(apply(s,X),Y),Z) = apply(apply(X,Z),apply(Y,Z)),
file('theBenchmark.p',s_definition) ).
cnf(b_definition,axiom,
apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)),
file('theBenchmark.p',b_definition) ).
cnf(c_definition,axiom,
apply(apply(apply(c,X),Y),Z) = apply(apply(X,Z),Y),
file('theBenchmark.p',c_definition) ).
cnf(i_definition,axiom,
apply(i,X) = X,
file('theBenchmark.p',i_definition) ).
cnf(weak_fixed_point,axiom,
weak_fixed_point(X) = apply(apply(apply(s,apply(b,X)),i),apply(apply(s,apply(b,X)),i)),
file('theBenchmark.p',weak_fixed_point) ).
cnf(prove_weak_fixed_point,negated_conjecture,
weak_fixed_point(fixed_pt) != apply(fixed_pt,weak_fixed_point(fixed_pt)),
file('theBenchmark.p',prove_weak_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,
( weak_fixed_point(Eq_x_0) = weak_fixed_point(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL002-4 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.03 This is a CNF_UNS_RFO_PEQ_UEQ 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
% 0.09/0.41 % Computer : n026.cluster.edu
% 0.09/0.41 % Model : x86_64 x86_64
% 0.09/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.41 % Memory : 8046.5625MB
% 0.09/0.41 % OS : Linux 6.8.0-71-generic
% 0.09/0.41 % CPULimit : 300
% 0.09/0.41 % WCLimit : 300
% 0.09/0.41 % DateTime : Sun Sep 20 14:26:23 UTC 2026
% 0.09/0.41 % CPUTime :
% 0.33/0.67 % SZS status Unsatisfiable for theBenchmark
% 0.33/0.67 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------