%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : COL003-14 : TPTP v9.3.1. Released v2.1.0.
% 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 : n012.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 71.75s 72.02s
% Output : Proof 71.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of clauses : 142 ( 101 unt; 0 nHn; 139 RR)
% Number of literals : 212 ( 146 equ; 72 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn)
% 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,
strong_fixed_point = apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,w),b))),b),
file('theBenchmark.p',strong_fixed_point) ).
cnf(prove_strong_fixed_point,negated_conjecture,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
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(t1,plain,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
inference(start,[status(thm),parent(0:0)],[prove_strong_fixed_point]) ).
cnf(t2,plain,
( apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,w),b))),b),fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt))
| apply(strong_fixed_point,fixed_pt) != apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,w),b))),b),fixed_pt)
| apply(strong_fixed_point,fixed_pt) = apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) ),
inference(extension,[status(thm),parent(t1:1)],[equality_3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( fixed_pt != fixed_pt
| strong_fixed_point != apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,w),b))),b)
| apply(strong_fixed_point,fixed_pt) = apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,w),b))),b),fixed_pt) ),
inference(extension,[status(thm),parent(t2:2)],[equality_4]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
strong_fixed_point = apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,w),b))),b),
inference(extension,[status(thm),parent(t4:2)],[strong_fixed_point]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( fixed_pt != fixed_pt
| fixed_pt = fixed_pt ),
inference(extension,[status(thm),parent(t4:3)],[equality_2]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
fixed_pt = fixed_pt,
inference(extension,[status(thm),parent(t8:2)],[equality_1]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( apply(apply(apply(b,apply(w,w)),apply(apply(b,w),b)),apply(b,fixed_pt)) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt))
| apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,w),b))),b),fixed_pt) != apply(apply(apply(b,apply(w,w)),apply(apply(b,w),b)),apply(b,fixed_pt))
| apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,w),b))),b),fixed_pt) = apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) ),
inference(extension,[status(thm),parent(t2:3)],[equality_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t2:3]) ).
cnf(t14,plain,
apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,w),b))),b),fixed_pt) = apply(apply(apply(b,apply(w,w)),apply(apply(b,w),b)),apply(b,fixed_pt)),
inference(extension,[status(thm),parent(t12:2)],[b_definition]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
( apply(apply(w,w),apply(apply(apply(b,w),b),apply(b,fixed_pt))) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt))
| apply(apply(apply(b,apply(w,w)),apply(apply(b,w),b)),apply(b,fixed_pt)) != apply(apply(w,w),apply(apply(apply(b,w),b),apply(b,fixed_pt)))
| apply(apply(apply(b,apply(w,w)),apply(apply(b,w),b)),apply(b,fixed_pt)) = apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) ),
inference(extension,[status(thm),parent(t12:3)],[equality_3]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t12:3]) ).
cnf(t18,plain,
apply(apply(apply(b,apply(w,w)),apply(apply(b,w),b)),apply(b,fixed_pt)) = apply(apply(w,w),apply(apply(apply(b,w),b),apply(b,fixed_pt))),
inference(extension,[status(thm),parent(t16:2)],[b_definition]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
( apply(apply(w,apply(apply(apply(b,w),b),apply(b,fixed_pt))),apply(apply(apply(b,w),b),apply(b,fixed_pt))) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt))
| apply(apply(w,w),apply(apply(apply(b,w),b),apply(b,fixed_pt))) != apply(apply(w,apply(apply(apply(b,w),b),apply(b,fixed_pt))),apply(apply(apply(b,w),b),apply(b,fixed_pt)))
| apply(apply(w,w),apply(apply(apply(b,w),b),apply(b,fixed_pt))) = apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) ),
inference(extension,[status(thm),parent(t16:3)],[equality_3]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t16:3]) ).
cnf(t22,plain,
apply(apply(w,w),apply(apply(apply(b,w),b),apply(b,fixed_pt))) = apply(apply(w,apply(apply(apply(b,w),b),apply(b,fixed_pt))),apply(apply(apply(b,w),b),apply(b,fixed_pt))),
inference(extension,[status(thm),parent(t20:2)],[w_definition]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
( apply(apply(apply(apply(apply(b,w),b),apply(b,fixed_pt)),apply(apply(apply(b,w),b),apply(b,fixed_pt))),apply(apply(apply(b,w),b),apply(b,fixed_pt))) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt))
| apply(apply(w,apply(apply(apply(b,w),b),apply(b,fixed_pt))),apply(apply(apply(b,w),b),apply(b,fixed_pt))) != apply(apply(apply(apply(apply(b,w),b),apply(b,fixed_pt)),apply(apply(apply(b,w),b),apply(b,fixed_pt))),apply(apply(apply(b,w),b),apply(b,fixed_pt)))
| apply(apply(w,apply(apply(apply(b,w),b),apply(b,fixed_pt))),apply(apply(apply(b,w),b),apply(b,fixed_pt))) = apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) ),
inference(extension,[status(thm),parent(t20:3)],[equality_3]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t20:3]) ).
cnf(t26,plain,
apply(apply(w,apply(apply(apply(b,w),b),apply(b,fixed_pt))),apply(apply(apply(b,w),b),apply(b,fixed_pt))) = apply(apply(apply(apply(apply(b,w),b),apply(b,fixed_pt)),apply(apply(apply(b,w),b),apply(b,fixed_pt))),apply(apply(apply(b,w),b),apply(b,fixed_pt))),
inference(extension,[status(thm),parent(t24:2)],[w_definition]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
( apply(apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt))
| apply(apply(apply(apply(apply(b,w),b),apply(b,fixed_pt)),apply(apply(apply(b,w),b),apply(b,fixed_pt))),apply(apply(apply(b,w),b),apply(b,fixed_pt))) != apply(apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt))))
| apply(apply(apply(apply(apply(b,w),b),apply(b,fixed_pt)),apply(apply(apply(b,w),b),apply(b,fixed_pt))),apply(apply(apply(b,w),b),apply(b,fixed_pt))) = apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) ),
inference(extension,[status(thm),parent(t24:3)],[equality_3]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t24:3]) ).
cnf(t30,plain,
( apply(apply(apply(b,w),b),apply(b,fixed_pt)) != apply(w,apply(b,apply(b,fixed_pt)))
| apply(apply(apply(apply(b,w),b),apply(b,fixed_pt)),apply(apply(apply(b,w),b),apply(b,fixed_pt))) != apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt))))
| apply(apply(apply(apply(apply(b,w),b),apply(b,fixed_pt)),apply(apply(apply(b,w),b),apply(b,fixed_pt))),apply(apply(apply(b,w),b),apply(b,fixed_pt))) = apply(apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt)))) ),
inference(extension,[status(thm),parent(t28:2)],[equality_4]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
( apply(apply(apply(b,w),b),apply(b,fixed_pt)) != apply(w,apply(b,apply(b,fixed_pt)))
| apply(apply(apply(b,w),b),apply(b,fixed_pt)) != apply(w,apply(b,apply(b,fixed_pt)))
| apply(apply(apply(apply(b,w),b),apply(b,fixed_pt)),apply(apply(apply(b,w),b),apply(b,fixed_pt))) = apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt)))) ),
inference(extension,[status(thm),parent(t30:2)],[equality_4]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t30:2]) ).
cnf(t34,plain,
apply(apply(apply(b,w),b),apply(b,fixed_pt)) = apply(w,apply(b,apply(b,fixed_pt))),
inference(extension,[status(thm),parent(t32:2)],[b_definition]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t32:2]) ).
cnf(t36,plain,
apply(apply(apply(b,w),b),apply(b,fixed_pt)) = apply(w,apply(b,apply(b,fixed_pt))),
inference(extension,[status(thm),parent(t32:3)],[b_definition]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t32:3]) ).
cnf(t38,plain,
apply(apply(apply(b,w),b),apply(b,fixed_pt)) = apply(w,apply(b,apply(b,fixed_pt))),
inference(extension,[status(thm),parent(t30:3)],[b_definition]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t30:3]) ).
cnf(l15,lemma,
apply(apply(apply(apply(apply(b,w),b),apply(b,fixed_pt)),apply(apply(apply(b,w),b),apply(b,fixed_pt))),apply(apply(apply(b,w),b),apply(b,fixed_pt))) = apply(apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt)))),
inference(lemma,[status(cth),parent(t28:2),below(t24:3)],[t28:2]) ).
cnf(t40,plain,
( apply(apply(apply(apply(b,apply(b,fixed_pt)),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt))
| apply(apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt)))) != apply(apply(apply(apply(b,apply(b,fixed_pt)),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt))))
| apply(apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt)))) = apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) ),
inference(extension,[status(thm),parent(t28:3)],[equality_3]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t28:3]) ).
cnf(t42,plain,
( apply(w,apply(b,apply(b,fixed_pt))) != apply(w,apply(b,apply(b,fixed_pt)))
| apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt)))) != apply(apply(apply(b,apply(b,fixed_pt)),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt))))
| apply(apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt)))) = apply(apply(apply(apply(b,apply(b,fixed_pt)),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt)))) ),
inference(extension,[status(thm),parent(t40:2)],[equality_4]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t40:2]) ).
cnf(t44,plain,
apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt)))) = apply(apply(apply(b,apply(b,fixed_pt)),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt)))),
inference(extension,[status(thm),parent(t42:2)],[w_definition]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t42:2]) ).
cnf(t46,plain,
( apply(b,apply(b,fixed_pt)) != apply(b,apply(b,fixed_pt))
| w != w
| apply(w,apply(b,apply(b,fixed_pt))) = apply(w,apply(b,apply(b,fixed_pt))) ),
inference(extension,[status(thm),parent(t42:3)],[equality_4]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t42:3]) ).
cnf(t48,plain,
( w != w
| w = w ),
inference(extension,[status(thm),parent(t46:2)],[equality_2]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t46:2]) ).
cnf(t50,plain,
w = w,
inference(extension,[status(thm),parent(t48:2)],[equality_1]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t48:2]) ).
cnf(t52,plain,
( apply(b,fixed_pt) != apply(b,fixed_pt)
| b != b
| apply(b,apply(b,fixed_pt)) = apply(b,apply(b,fixed_pt)) ),
inference(extension,[status(thm),parent(t46:3)],[equality_4]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t46:3]) ).
cnf(t54,plain,
( b != b
| b = b ),
inference(extension,[status(thm),parent(t52:2)],[equality_2]) ).
cnf(t55,plain,
$false,
inference(connection,[status(thm),parent(t54:1)],[t54:1,t52:2]) ).
cnf(t56,plain,
b = b,
inference(extension,[status(thm),parent(t54:2)],[equality_1]) ).
cnf(t57,plain,
$false,
inference(connection,[status(thm),parent(t56:1)],[t56:1,t54:2]) ).
cnf(t58,plain,
( fixed_pt != fixed_pt
| b != b
| apply(b,fixed_pt) = apply(b,fixed_pt) ),
inference(extension,[status(thm),parent(t52:3)],[equality_4]) ).
cnf(t59,plain,
$false,
inference(connection,[status(thm),parent(t58:1)],[t58:1,t52:3]) ).
cnf(t60,plain,
( b != b
| b = b ),
inference(extension,[status(thm),parent(t58:2)],[equality_2]) ).
cnf(t61,plain,
$false,
inference(connection,[status(thm),parent(t60:1)],[t60:1,t58:2]) ).
cnf(t62,plain,
b = b,
inference(extension,[status(thm),parent(t60:2)],[equality_1]) ).
cnf(t63,plain,
$false,
inference(connection,[status(thm),parent(t62:1)],[t62:1,t60:2]) ).
cnf(t64,plain,
( fixed_pt != fixed_pt
| fixed_pt = fixed_pt ),
inference(extension,[status(thm),parent(t58:3)],[equality_2]) ).
cnf(t65,plain,
$false,
inference(connection,[status(thm),parent(t64:1)],[t64:1,t58:3]) ).
cnf(t66,plain,
fixed_pt = fixed_pt,
inference(extension,[status(thm),parent(t64:2)],[equality_1]) ).
cnf(t67,plain,
$false,
inference(connection,[status(thm),parent(t66:1)],[t66:1,t64:2]) ).
cnf(t68,plain,
( apply(apply(apply(b,fixed_pt),apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt))))),apply(w,apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt))
| apply(apply(apply(apply(b,apply(b,fixed_pt)),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt)))) != apply(apply(apply(b,fixed_pt),apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt))))),apply(w,apply(b,apply(b,fixed_pt))))
| apply(apply(apply(apply(b,apply(b,fixed_pt)),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt)))) = apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) ),
inference(extension,[status(thm),parent(t40:3)],[equality_3]) ).
cnf(t69,plain,
$false,
inference(connection,[status(thm),parent(t68:1)],[t68:1,t40:3]) ).
cnf(t70,plain,
( apply(w,apply(b,apply(b,fixed_pt))) != apply(w,apply(b,apply(b,fixed_pt)))
| apply(apply(apply(b,apply(b,fixed_pt)),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt)))) != apply(apply(b,fixed_pt),apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt)))))
| apply(apply(apply(apply(b,apply(b,fixed_pt)),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt)))) = apply(apply(apply(b,fixed_pt),apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt))))),apply(w,apply(b,apply(b,fixed_pt)))) ),
inference(extension,[status(thm),parent(t68:2)],[equality_4]) ).
cnf(t71,plain,
$false,
inference(connection,[status(thm),parent(t70:1)],[t70:1,t68:2]) ).
cnf(t72,plain,
apply(apply(apply(b,apply(b,fixed_pt)),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt)))) = apply(apply(b,fixed_pt),apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt))))),
inference(extension,[status(thm),parent(t70:2)],[b_definition]) ).
cnf(t73,plain,
$false,
inference(connection,[status(thm),parent(t72:1)],[t72:1,t70:2]) ).
cnf(t74,plain,
( apply(b,apply(b,fixed_pt)) != apply(b,apply(b,fixed_pt))
| w != w
| apply(w,apply(b,apply(b,fixed_pt))) = apply(w,apply(b,apply(b,fixed_pt))) ),
inference(extension,[status(thm),parent(t70:3)],[equality_4]) ).
cnf(t75,plain,
$false,
inference(connection,[status(thm),parent(t74:1)],[t74:1,t70:3]) ).
cnf(t76,plain,
( w != w
| w = w ),
inference(extension,[status(thm),parent(t74:2)],[equality_2]) ).
cnf(t77,plain,
$false,
inference(connection,[status(thm),parent(t76:1)],[t76:1,t74:2]) ).
cnf(t78,plain,
w = w,
inference(extension,[status(thm),parent(t76:2)],[equality_1]) ).
cnf(t79,plain,
$false,
inference(connection,[status(thm),parent(t78:1)],[t78:1,t76:2]) ).
cnf(t80,plain,
( apply(b,fixed_pt) != apply(b,fixed_pt)
| b != b
| apply(b,apply(b,fixed_pt)) = apply(b,apply(b,fixed_pt)) ),
inference(extension,[status(thm),parent(t74:3)],[equality_4]) ).
cnf(t81,plain,
$false,
inference(connection,[status(thm),parent(t80:1)],[t80:1,t74:3]) ).
cnf(t82,plain,
( b != b
| b = b ),
inference(extension,[status(thm),parent(t80:2)],[equality_2]) ).
cnf(t83,plain,
$false,
inference(connection,[status(thm),parent(t82:1)],[t82:1,t80:2]) ).
cnf(t84,plain,
b = b,
inference(extension,[status(thm),parent(t82:2)],[equality_1]) ).
cnf(t85,plain,
$false,
inference(connection,[status(thm),parent(t84:1)],[t84:1,t82:2]) ).
cnf(t86,plain,
( fixed_pt != fixed_pt
| b != b
| apply(b,fixed_pt) = apply(b,fixed_pt) ),
inference(extension,[status(thm),parent(t80:3)],[equality_4]) ).
cnf(t87,plain,
$false,
inference(connection,[status(thm),parent(t86:1)],[t86:1,t80:3]) ).
cnf(t88,plain,
( b != b
| b = b ),
inference(extension,[status(thm),parent(t86:2)],[equality_2]) ).
cnf(t89,plain,
$false,
inference(connection,[status(thm),parent(t88:1)],[t88:1,t86:2]) ).
cnf(t90,plain,
b = b,
inference(extension,[status(thm),parent(t88:2)],[equality_1]) ).
cnf(t91,plain,
$false,
inference(connection,[status(thm),parent(t90:1)],[t90:1,t88:2]) ).
cnf(t92,plain,
( fixed_pt != fixed_pt
| fixed_pt = fixed_pt ),
inference(extension,[status(thm),parent(t86:3)],[equality_2]) ).
cnf(t93,plain,
$false,
inference(connection,[status(thm),parent(t92:1)],[t92:1,t86:3]) ).
cnf(t94,plain,
fixed_pt = fixed_pt,
inference(extension,[status(thm),parent(t92:2)],[equality_1]) ).
cnf(t95,plain,
$false,
inference(connection,[status(thm),parent(t94:1)],[t94:1,t92:2]) ).
cnf(t96,plain,
( apply(fixed_pt,apply(apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt))))) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt))
| apply(apply(apply(b,fixed_pt),apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt))))),apply(w,apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt)))))
| apply(apply(apply(b,fixed_pt),apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt))))),apply(w,apply(b,apply(b,fixed_pt)))) = apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) ),
inference(extension,[status(thm),parent(t68:3)],[equality_3]) ).
cnf(t97,plain,
$false,
inference(connection,[status(thm),parent(t96:1)],[t96:1,t68:3]) ).
cnf(t98,plain,
apply(apply(apply(b,fixed_pt),apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt))))),apply(w,apply(b,apply(b,fixed_pt)))) = apply(fixed_pt,apply(apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt))))),
inference(extension,[status(thm),parent(t96:2)],[b_definition]) ).
cnf(t99,plain,
$false,
inference(connection,[status(thm),parent(t98:1)],[t98:1,t96:2]) ).
cnf(t100,plain,
( apply(apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt)))) != apply(strong_fixed_point,fixed_pt)
| fixed_pt != fixed_pt
| apply(fixed_pt,apply(apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt))))) = apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) ),
inference(extension,[status(thm),parent(t96:3)],[equality_4]) ).
cnf(t101,plain,
$false,
inference(connection,[status(thm),parent(t100:1)],[t100:1,t96:3]) ).
cnf(t102,plain,
fixed_pt = fixed_pt,
inference(extension,[status(thm),parent(t100:2)],[equality_1]) ).
cnf(t103,plain,
$false,
inference(connection,[status(thm),parent(t102:1)],[t102:1,t100:2]) ).
cnf(t104,plain,
( apply(strong_fixed_point,fixed_pt) != apply(apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt))))
| apply(apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt)))) = apply(strong_fixed_point,fixed_pt) ),
inference(extension,[status(thm),parent(t100:3)],[equality_2]) ).
cnf(t105,plain,
$false,
inference(connection,[status(thm),parent(t104:1)],[t104:1,t100:3]) ).
cnf(t106,plain,
( apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,w),b))),b),fixed_pt) != apply(apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt))))
| apply(strong_fixed_point,fixed_pt) != apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,w),b))),b),fixed_pt)
| apply(strong_fixed_point,fixed_pt) = apply(apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt)))) ),
inference(extension,[status(thm),parent(t104:2)],[equality_3]) ).
cnf(t107,plain,
$false,
inference(connection,[status(thm),parent(t106:1)],[t106:1,t104:2]) ).
cnf(t108,plain,
( fixed_pt != fixed_pt
| strong_fixed_point != apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,w),b))),b)
| apply(strong_fixed_point,fixed_pt) = apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,w),b))),b),fixed_pt) ),
inference(extension,[status(thm),parent(t106:2)],[equality_4]) ).
cnf(t109,plain,
$false,
inference(connection,[status(thm),parent(t108:1)],[t108:1,t106:2]) ).
cnf(t110,plain,
strong_fixed_point = apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,w),b))),b),
inference(extension,[status(thm),parent(t108:2)],[strong_fixed_point]) ).
cnf(t111,plain,
$false,
inference(connection,[status(thm),parent(t110:1)],[t110:1,t108:2]) ).
cnf(t112,plain,
( fixed_pt != fixed_pt
| fixed_pt = fixed_pt ),
inference(extension,[status(thm),parent(t108:3)],[equality_2]) ).
cnf(t113,plain,
$false,
inference(connection,[status(thm),parent(t112:1)],[t112:1,t108:3]) ).
cnf(t114,plain,
fixed_pt = fixed_pt,
inference(extension,[status(thm),parent(t112:2)],[equality_1]) ).
cnf(t115,plain,
$false,
inference(connection,[status(thm),parent(t114:1)],[t114:1,t112:2]) ).
cnf(t116,plain,
( apply(apply(apply(b,apply(w,w)),apply(apply(b,w),b)),apply(b,fixed_pt)) != apply(apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt))))
| apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,w),b))),b),fixed_pt) != apply(apply(apply(b,apply(w,w)),apply(apply(b,w),b)),apply(b,fixed_pt))
| apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,w),b))),b),fixed_pt) = apply(apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt)))) ),
inference(extension,[status(thm),parent(t106:3)],[equality_3]) ).
cnf(t117,plain,
$false,
inference(connection,[status(thm),parent(t116:1)],[t116:1,t106:3]) ).
cnf(t118,plain,
apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,w),b))),b),fixed_pt) = apply(apply(apply(b,apply(w,w)),apply(apply(b,w),b)),apply(b,fixed_pt)),
inference(extension,[status(thm),parent(t116:2)],[b_definition]) ).
cnf(t119,plain,
$false,
inference(connection,[status(thm),parent(t118:1)],[t118:1,t116:2]) ).
cnf(t120,plain,
( apply(apply(w,w),apply(apply(apply(b,w),b),apply(b,fixed_pt))) != apply(apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt))))
| apply(apply(apply(b,apply(w,w)),apply(apply(b,w),b)),apply(b,fixed_pt)) != apply(apply(w,w),apply(apply(apply(b,w),b),apply(b,fixed_pt)))
| apply(apply(apply(b,apply(w,w)),apply(apply(b,w),b)),apply(b,fixed_pt)) = apply(apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt)))) ),
inference(extension,[status(thm),parent(t116:3)],[equality_3]) ).
cnf(t121,plain,
$false,
inference(connection,[status(thm),parent(t120:1)],[t120:1,t116:3]) ).
cnf(t122,plain,
apply(apply(apply(b,apply(w,w)),apply(apply(b,w),b)),apply(b,fixed_pt)) = apply(apply(w,w),apply(apply(apply(b,w),b),apply(b,fixed_pt))),
inference(extension,[status(thm),parent(t120:2)],[b_definition]) ).
cnf(t123,plain,
$false,
inference(connection,[status(thm),parent(t122:1)],[t122:1,t120:2]) ).
cnf(t124,plain,
( apply(apply(w,apply(apply(apply(b,w),b),apply(b,fixed_pt))),apply(apply(apply(b,w),b),apply(b,fixed_pt))) != apply(apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt))))
| apply(apply(w,w),apply(apply(apply(b,w),b),apply(b,fixed_pt))) != apply(apply(w,apply(apply(apply(b,w),b),apply(b,fixed_pt))),apply(apply(apply(b,w),b),apply(b,fixed_pt)))
| apply(apply(w,w),apply(apply(apply(b,w),b),apply(b,fixed_pt))) = apply(apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt)))) ),
inference(extension,[status(thm),parent(t120:3)],[equality_3]) ).
cnf(t125,plain,
$false,
inference(connection,[status(thm),parent(t124:1)],[t124:1,t120:3]) ).
cnf(t126,plain,
apply(apply(w,w),apply(apply(apply(b,w),b),apply(b,fixed_pt))) = apply(apply(w,apply(apply(apply(b,w),b),apply(b,fixed_pt))),apply(apply(apply(b,w),b),apply(b,fixed_pt))),
inference(extension,[status(thm),parent(t124:2)],[w_definition]) ).
cnf(t127,plain,
$false,
inference(connection,[status(thm),parent(t126:1)],[t126:1,t124:2]) ).
cnf(t128,plain,
( apply(apply(apply(apply(apply(b,w),b),apply(b,fixed_pt)),apply(apply(apply(b,w),b),apply(b,fixed_pt))),apply(apply(apply(b,w),b),apply(b,fixed_pt))) != apply(apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt))))
| apply(apply(w,apply(apply(apply(b,w),b),apply(b,fixed_pt))),apply(apply(apply(b,w),b),apply(b,fixed_pt))) != apply(apply(apply(apply(apply(b,w),b),apply(b,fixed_pt)),apply(apply(apply(b,w),b),apply(b,fixed_pt))),apply(apply(apply(b,w),b),apply(b,fixed_pt)))
| apply(apply(w,apply(apply(apply(b,w),b),apply(b,fixed_pt))),apply(apply(apply(b,w),b),apply(b,fixed_pt))) = apply(apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt)))) ),
inference(extension,[status(thm),parent(t124:3)],[equality_3]) ).
cnf(t129,plain,
$false,
inference(connection,[status(thm),parent(t128:1)],[t128:1,t124:3]) ).
cnf(t130,plain,
apply(apply(w,apply(apply(apply(b,w),b),apply(b,fixed_pt))),apply(apply(apply(b,w),b),apply(b,fixed_pt))) = apply(apply(apply(apply(apply(b,w),b),apply(b,fixed_pt)),apply(apply(apply(b,w),b),apply(b,fixed_pt))),apply(apply(apply(b,w),b),apply(b,fixed_pt))),
inference(extension,[status(thm),parent(t128:2)],[w_definition]) ).
cnf(t131,plain,
$false,
inference(connection,[status(thm),parent(t130:1)],[t130:1,t128:2]) ).
cnf(t132,plain,
apply(apply(apply(apply(apply(b,w),b),apply(b,fixed_pt)),apply(apply(apply(b,w),b),apply(b,fixed_pt))),apply(apply(apply(b,w),b),apply(b,fixed_pt))) = apply(apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt)))),
inference(lemma_extension,[status(thm),parent(t128:3)],[l15:1]) ).
cnf(t133,plain,
$false,
inference(connection,[status(thm),parent(t132:1)],[t132:1,t128:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : COL003-14 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.01 This is a CNF_UNS_RFO_PEQ_UEQ problem
% 0.00/0.02 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.31 % Computer : n012.cluster.edu
% 0.03/0.31 % Model : x86_64 x86_64
% 0.03/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.31 % Memory : 8046.5625MB
% 0.03/0.31 % OS : Linux 6.8.0-71-generic
% 0.03/0.31 % CPULimit : 300
% 0.03/0.31 % WCLimit : 300
% 0.03/0.31 % DateTime : Sun Sep 20 14:32:09 UTC 2026
% 0.03/0.31 % CPUTime :
% 71.75/72.02 % SZS status Unsatisfiable for theBenchmark
% 71.75/72.02 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------