%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : COL066-2 : TPTP v9.3.1. Bugfixed 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 : n010.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 08:14:30 AM UTC 2026
% Result : Unsatisfiable 30.54s 36.21s
% Output : Proof 30.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 7
% Syntax : Number of clauses : 114 ( 79 unt; 0 nHn; 111 RR)
% Number of literals : 171 ( 118 equ; 59 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(q_definition,axiom,
apply(apply(apply(q,X),Y),Z) = apply(Y,apply(X,Z)),
file('theBenchmark.p',q_definition) ).
cnf(w_definition,axiom,
apply(apply(w,X),Y) = apply(apply(X,Y),Y),
file('theBenchmark.p',w_definition) ).
cnf(prove_p_combinator,negated_conjecture,
apply(apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
file('theBenchmark.p',prove_p_combinator) ).
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(apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(start,[status(thm),parent(0:0)],[prove_p_combinator]) ).
cnf(t2,plain,
( apply(apply(apply(apply(apply(w,apply(q,apply(q,q))),apply(q,x)),y),y),z) != apply(apply(x,y),apply(apply(x,y),z))
| apply(apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y),z) != apply(apply(apply(apply(apply(w,apply(q,apply(q,q))),apply(q,x)),y),y),z)
| apply(apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y),z) = apply(apply(x,y),apply(apply(x,y),z)) ),
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,
( z != z
| apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y) != apply(apply(apply(apply(w,apply(q,apply(q,q))),apply(q,x)),y),y)
| apply(apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y),z) = apply(apply(apply(apply(apply(w,apply(q,apply(q,q))),apply(q,x)),y),y),z) ),
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,
( y != y
| apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y) != apply(apply(apply(w,apply(q,apply(q,q))),apply(q,x)),y)
| apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y) = apply(apply(apply(apply(w,apply(q,apply(q,q))),apply(q,x)),y),y) ),
inference(extension,[status(thm),parent(t4:2)],[equality_4]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( y != y
| apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x) != apply(apply(w,apply(q,apply(q,q))),apply(q,x))
| apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y) = apply(apply(apply(w,apply(q,apply(q,q))),apply(q,x)),y) ),
inference(extension,[status(thm),parent(t6:2)],[equality_4]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x) = apply(apply(w,apply(q,apply(q,q))),apply(q,x)),
inference(extension,[status(thm),parent(t8:2)],[q_definition]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( y != y
| y = y ),
inference(extension,[status(thm),parent(t8:3)],[equality_2]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
cnf(t14,plain,
y = y,
inference(extension,[status(thm),parent(t12:2)],[equality_1]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
( y != y
| y = y ),
inference(extension,[status(thm),parent(t6:3)],[equality_2]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t6:3]) ).
cnf(t18,plain,
y = y,
inference(extension,[status(thm),parent(t16:2)],[equality_1]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
( z != z
| z = z ),
inference(extension,[status(thm),parent(t4:3)],[equality_2]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t4:3]) ).
cnf(t22,plain,
z = z,
inference(extension,[status(thm),parent(t20:2)],[equality_1]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
( apply(apply(apply(apply(apply(apply(q,apply(q,q)),apply(q,x)),apply(q,x)),y),y),z) != apply(apply(x,y),apply(apply(x,y),z))
| apply(apply(apply(apply(apply(w,apply(q,apply(q,q))),apply(q,x)),y),y),z) != apply(apply(apply(apply(apply(apply(q,apply(q,q)),apply(q,x)),apply(q,x)),y),y),z)
| apply(apply(apply(apply(apply(w,apply(q,apply(q,q))),apply(q,x)),y),y),z) = apply(apply(x,y),apply(apply(x,y),z)) ),
inference(extension,[status(thm),parent(t2:3)],[equality_3]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t2:3]) ).
cnf(t26,plain,
( z != z
| apply(apply(apply(apply(w,apply(q,apply(q,q))),apply(q,x)),y),y) != apply(apply(apply(apply(apply(q,apply(q,q)),apply(q,x)),apply(q,x)),y),y)
| apply(apply(apply(apply(apply(w,apply(q,apply(q,q))),apply(q,x)),y),y),z) = apply(apply(apply(apply(apply(apply(q,apply(q,q)),apply(q,x)),apply(q,x)),y),y),z) ),
inference(extension,[status(thm),parent(t24:2)],[equality_4]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
( y != y
| apply(apply(apply(w,apply(q,apply(q,q))),apply(q,x)),y) != apply(apply(apply(apply(q,apply(q,q)),apply(q,x)),apply(q,x)),y)
| apply(apply(apply(apply(w,apply(q,apply(q,q))),apply(q,x)),y),y) = apply(apply(apply(apply(apply(q,apply(q,q)),apply(q,x)),apply(q,x)),y),y) ),
inference(extension,[status(thm),parent(t26:2)],[equality_4]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
( y != y
| apply(apply(w,apply(q,apply(q,q))),apply(q,x)) != apply(apply(apply(q,apply(q,q)),apply(q,x)),apply(q,x))
| apply(apply(apply(w,apply(q,apply(q,q))),apply(q,x)),y) = apply(apply(apply(apply(q,apply(q,q)),apply(q,x)),apply(q,x)),y) ),
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(w,apply(q,apply(q,q))),apply(q,x)) = apply(apply(apply(q,apply(q,q)),apply(q,x)),apply(q,x)),
inference(extension,[status(thm),parent(t30:2)],[w_definition]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t30:2]) ).
cnf(t34,plain,
( y != y
| y = y ),
inference(extension,[status(thm),parent(t30:3)],[equality_2]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t30:3]) ).
cnf(t36,plain,
y = y,
inference(extension,[status(thm),parent(t34:2)],[equality_1]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t34:2]) ).
cnf(t38,plain,
( y != y
| y = y ),
inference(extension,[status(thm),parent(t28:3)],[equality_2]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t28:3]) ).
cnf(t40,plain,
y = y,
inference(extension,[status(thm),parent(t38:2)],[equality_1]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t38:2]) ).
cnf(t42,plain,
( z != z
| z = z ),
inference(extension,[status(thm),parent(t26:3)],[equality_2]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t26:3]) ).
cnf(t44,plain,
z = z,
inference(extension,[status(thm),parent(t42:2)],[equality_1]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t42:2]) ).
cnf(t46,plain,
( apply(apply(apply(apply(apply(q,x),apply(apply(q,q),apply(q,x))),y),y),z) != apply(apply(x,y),apply(apply(x,y),z))
| apply(apply(apply(apply(apply(apply(q,apply(q,q)),apply(q,x)),apply(q,x)),y),y),z) != apply(apply(apply(apply(apply(q,x),apply(apply(q,q),apply(q,x))),y),y),z)
| apply(apply(apply(apply(apply(apply(q,apply(q,q)),apply(q,x)),apply(q,x)),y),y),z) = apply(apply(x,y),apply(apply(x,y),z)) ),
inference(extension,[status(thm),parent(t24:3)],[equality_3]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t24:3]) ).
cnf(t48,plain,
( z != z
| apply(apply(apply(apply(apply(q,apply(q,q)),apply(q,x)),apply(q,x)),y),y) != apply(apply(apply(apply(q,x),apply(apply(q,q),apply(q,x))),y),y)
| apply(apply(apply(apply(apply(apply(q,apply(q,q)),apply(q,x)),apply(q,x)),y),y),z) = apply(apply(apply(apply(apply(q,x),apply(apply(q,q),apply(q,x))),y),y),z) ),
inference(extension,[status(thm),parent(t46:2)],[equality_4]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t46:2]) ).
cnf(t50,plain,
( y != y
| apply(apply(apply(apply(q,apply(q,q)),apply(q,x)),apply(q,x)),y) != apply(apply(apply(q,x),apply(apply(q,q),apply(q,x))),y)
| apply(apply(apply(apply(apply(q,apply(q,q)),apply(q,x)),apply(q,x)),y),y) = apply(apply(apply(apply(q,x),apply(apply(q,q),apply(q,x))),y),y) ),
inference(extension,[status(thm),parent(t48:2)],[equality_4]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t48:2]) ).
cnf(t52,plain,
( y != y
| apply(apply(apply(q,apply(q,q)),apply(q,x)),apply(q,x)) != apply(apply(q,x),apply(apply(q,q),apply(q,x)))
| apply(apply(apply(apply(q,apply(q,q)),apply(q,x)),apply(q,x)),y) = apply(apply(apply(q,x),apply(apply(q,q),apply(q,x))),y) ),
inference(extension,[status(thm),parent(t50:2)],[equality_4]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t50:2]) ).
cnf(t54,plain,
apply(apply(apply(q,apply(q,q)),apply(q,x)),apply(q,x)) = apply(apply(q,x),apply(apply(q,q),apply(q,x))),
inference(extension,[status(thm),parent(t52:2)],[q_definition]) ).
cnf(t55,plain,
$false,
inference(connection,[status(thm),parent(t54:1)],[t54:1,t52:2]) ).
cnf(t56,plain,
( y != y
| y = y ),
inference(extension,[status(thm),parent(t52:3)],[equality_2]) ).
cnf(t57,plain,
$false,
inference(connection,[status(thm),parent(t56:1)],[t56:1,t52:3]) ).
cnf(t58,plain,
y = y,
inference(extension,[status(thm),parent(t56:2)],[equality_1]) ).
cnf(t59,plain,
$false,
inference(connection,[status(thm),parent(t58:1)],[t58:1,t56:2]) ).
cnf(t60,plain,
( y != y
| y = y ),
inference(extension,[status(thm),parent(t50:3)],[equality_2]) ).
cnf(t61,plain,
$false,
inference(connection,[status(thm),parent(t60:1)],[t60:1,t50:3]) ).
cnf(t62,plain,
y = y,
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,
( z != z
| z = z ),
inference(extension,[status(thm),parent(t48:3)],[equality_2]) ).
cnf(t65,plain,
$false,
inference(connection,[status(thm),parent(t64:1)],[t64:1,t48:3]) ).
cnf(t66,plain,
z = z,
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(apply(apply(q,q),apply(q,x)),apply(x,y)),y),z) != apply(apply(x,y),apply(apply(x,y),z))
| apply(apply(apply(apply(apply(q,x),apply(apply(q,q),apply(q,x))),y),y),z) != apply(apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y),z)
| apply(apply(apply(apply(apply(q,x),apply(apply(q,q),apply(q,x))),y),y),z) = apply(apply(x,y),apply(apply(x,y),z)) ),
inference(extension,[status(thm),parent(t46:3)],[equality_3]) ).
cnf(t69,plain,
$false,
inference(connection,[status(thm),parent(t68:1)],[t68:1,t46:3]) ).
cnf(t70,plain,
( z != z
| apply(apply(apply(apply(q,x),apply(apply(q,q),apply(q,x))),y),y) != apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y)
| apply(apply(apply(apply(apply(q,x),apply(apply(q,q),apply(q,x))),y),y),z) = apply(apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y),z) ),
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,
( y != y
| apply(apply(apply(q,x),apply(apply(q,q),apply(q,x))),y) != apply(apply(apply(q,q),apply(q,x)),apply(x,y))
| apply(apply(apply(apply(q,x),apply(apply(q,q),apply(q,x))),y),y) = apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y) ),
inference(extension,[status(thm),parent(t70:2)],[equality_4]) ).
cnf(t73,plain,
$false,
inference(connection,[status(thm),parent(t72:1)],[t72:1,t70:2]) ).
cnf(t74,plain,
apply(apply(apply(q,x),apply(apply(q,q),apply(q,x))),y) = apply(apply(apply(q,q),apply(q,x)),apply(x,y)),
inference(extension,[status(thm),parent(t72:2)],[q_definition]) ).
cnf(t75,plain,
$false,
inference(connection,[status(thm),parent(t74:1)],[t74:1,t72:2]) ).
cnf(t76,plain,
( y != y
| y = y ),
inference(extension,[status(thm),parent(t72:3)],[equality_2]) ).
cnf(t77,plain,
$false,
inference(connection,[status(thm),parent(t76:1)],[t76:1,t72:3]) ).
cnf(t78,plain,
y = y,
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,
( z != z
| z = z ),
inference(extension,[status(thm),parent(t70:3)],[equality_2]) ).
cnf(t81,plain,
$false,
inference(connection,[status(thm),parent(t80:1)],[t80:1,t70:3]) ).
cnf(t82,plain,
z = z,
inference(extension,[status(thm),parent(t80:2)],[equality_1]) ).
cnf(t83,plain,
$false,
inference(connection,[status(thm),parent(t82:1)],[t82:1,t80:2]) ).
cnf(t84,plain,
( apply(apply(apply(apply(q,x),apply(q,apply(x,y))),y),z) != apply(apply(x,y),apply(apply(x,y),z))
| apply(apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y),z) != apply(apply(apply(apply(q,x),apply(q,apply(x,y))),y),z)
| apply(apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y),z) = apply(apply(x,y),apply(apply(x,y),z)) ),
inference(extension,[status(thm),parent(t68:3)],[equality_3]) ).
cnf(t85,plain,
$false,
inference(connection,[status(thm),parent(t84:1)],[t84:1,t68:3]) ).
cnf(t86,plain,
( z != z
| apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y) != apply(apply(apply(q,x),apply(q,apply(x,y))),y)
| apply(apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y),z) = apply(apply(apply(apply(q,x),apply(q,apply(x,y))),y),z) ),
inference(extension,[status(thm),parent(t84:2)],[equality_4]) ).
cnf(t87,plain,
$false,
inference(connection,[status(thm),parent(t86:1)],[t86:1,t84:2]) ).
cnf(t88,plain,
( y != y
| apply(apply(apply(q,q),apply(q,x)),apply(x,y)) != apply(apply(q,x),apply(q,apply(x,y)))
| apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y) = apply(apply(apply(q,x),apply(q,apply(x,y))),y) ),
inference(extension,[status(thm),parent(t86:2)],[equality_4]) ).
cnf(t89,plain,
$false,
inference(connection,[status(thm),parent(t88:1)],[t88:1,t86:2]) ).
cnf(t90,plain,
apply(apply(apply(q,q),apply(q,x)),apply(x,y)) = apply(apply(q,x),apply(q,apply(x,y))),
inference(extension,[status(thm),parent(t88:2)],[q_definition]) ).
cnf(t91,plain,
$false,
inference(connection,[status(thm),parent(t90:1)],[t90:1,t88:2]) ).
cnf(t92,plain,
y = y,
inference(extension,[status(thm),parent(t88:3)],[equality_1]) ).
cnf(t93,plain,
$false,
inference(connection,[status(thm),parent(t92:1)],[t92:1,t88:3]) ).
cnf(t94,plain,
( z != z
| z = z ),
inference(extension,[status(thm),parent(t86:3)],[equality_2]) ).
cnf(t95,plain,
$false,
inference(connection,[status(thm),parent(t94:1)],[t94:1,t86:3]) ).
cnf(t96,plain,
z = z,
inference(extension,[status(thm),parent(t94:2)],[equality_1]) ).
cnf(t97,plain,
$false,
inference(connection,[status(thm),parent(t96:1)],[t96:1,t94:2]) ).
cnf(t98,plain,
( apply(apply(apply(q,apply(x,y)),apply(x,y)),z) != apply(apply(x,y),apply(apply(x,y),z))
| apply(apply(apply(apply(q,x),apply(q,apply(x,y))),y),z) != apply(apply(apply(q,apply(x,y)),apply(x,y)),z)
| apply(apply(apply(apply(q,x),apply(q,apply(x,y))),y),z) = apply(apply(x,y),apply(apply(x,y),z)) ),
inference(extension,[status(thm),parent(t84:3)],[equality_3]) ).
cnf(t99,plain,
$false,
inference(connection,[status(thm),parent(t98:1)],[t98:1,t84:3]) ).
cnf(t100,plain,
( z != z
| apply(apply(apply(q,x),apply(q,apply(x,y))),y) != apply(apply(q,apply(x,y)),apply(x,y))
| apply(apply(apply(apply(q,x),apply(q,apply(x,y))),y),z) = apply(apply(apply(q,apply(x,y)),apply(x,y)),z) ),
inference(extension,[status(thm),parent(t98:2)],[equality_4]) ).
cnf(t101,plain,
$false,
inference(connection,[status(thm),parent(t100:1)],[t100:1,t98:2]) ).
cnf(t102,plain,
apply(apply(apply(q,x),apply(q,apply(x,y))),y) = apply(apply(q,apply(x,y)),apply(x,y)),
inference(extension,[status(thm),parent(t100:2)],[q_definition]) ).
cnf(t103,plain,
$false,
inference(connection,[status(thm),parent(t102:1)],[t102:1,t100:2]) ).
cnf(t104,plain,
z = z,
inference(extension,[status(thm),parent(t100:3)],[equality_1]) ).
cnf(t105,plain,
$false,
inference(connection,[status(thm),parent(t104:1)],[t104:1,t100:3]) ).
cnf(t106,plain,
apply(apply(apply(q,apply(x,y)),apply(x,y)),z) = apply(apply(x,y),apply(apply(x,y),z)),
inference(extension,[status(thm),parent(t98:3)],[q_definition]) ).
cnf(t107,plain,
$false,
inference(connection,[status(thm),parent(t106:1)],[t106:1,t98:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL066-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% 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
% 0.08/5.78 % Computer : n010.cluster.edu
% 0.08/5.78 % Model : x86_64 x86_64
% 0.08/5.78 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.78 % Memory : 8046.5625MB
% 0.08/5.78 % OS : Linux 6.8.0-71-generic
% 0.08/5.78 % CPULimit : 300
% 0.08/5.78 % WCLimit : 300
% 0.08/5.78 % DateTime : Sun Sep 20 14:56:04 UTC 2026
% 0.08/5.78 % CPUTime :
% 30.54/36.21 % SZS status Unsatisfiable for theBenchmark
% 30.54/36.21 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------