%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : COL004-3 : TPTP v9.3.1. Released v1.0.0.
% 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 : n018.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 30.34s 30.66s
% Output : Proof 30.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of clauses : 62 ( 45 unt; 0 nHn; 56 RR)
% Number of literals : 93 ( 66 equ; 33 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 25 ( 5 sgn)
% 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(k_definition,axiom,
apply(apply(k,X),Y) = X,
file('theBenchmark.p',k_definition) ).
cnf(prove_u_combinator,negated_conjecture,
apply(apply(apply(apply(s,apply(k,apply(s,apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),x),y) != apply(y,apply(apply(x,x),y)),
file('theBenchmark.p',prove_u_combinator) ).
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(s,apply(k,apply(s,apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),x),y) != apply(y,apply(apply(x,x),y)),
inference(start,[status(thm),parent(0:0)],[prove_u_combinator]) ).
cnf(t2,plain,
( apply(apply(apply(apply(k,apply(s,apply(apply(s,k),k))),x),apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x)),apply(apply(k,y),U_187)) != apply(y,apply(apply(x,x),y))
| apply(apply(apply(apply(s,apply(k,apply(s,apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),x),y) != apply(apply(apply(apply(k,apply(s,apply(apply(s,k),k))),x),apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x)),apply(apply(k,y),U_187))
| apply(apply(apply(apply(s,apply(k,apply(s,apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),x),y) = apply(y,apply(apply(x,x),y)) ),
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,
( y != apply(apply(k,y),U_187)
| apply(apply(apply(s,apply(k,apply(s,apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),x) != apply(apply(apply(k,apply(s,apply(apply(s,k),k))),x),apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x))
| apply(apply(apply(apply(s,apply(k,apply(s,apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),x),y) = apply(apply(apply(apply(k,apply(s,apply(apply(s,k),k))),x),apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x)),apply(apply(k,y),U_187)) ),
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,
apply(apply(apply(s,apply(k,apply(s,apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),x) = apply(apply(apply(k,apply(s,apply(apply(s,k),k))),x),apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x)),
inference(extension,[status(thm),parent(t4:2)],[s_definition]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( apply(apply(k,y),U_187) != y
| y = apply(apply(k,y),U_187) ),
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,
apply(apply(k,y),U_187) = y,
inference(extension,[status(thm),parent(t8:2)],[k_definition]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(apply(apply(s,k),k),x),apply(apply(apply(s,k),k),x))),y) != apply(y,apply(apply(x,x),y))
| apply(apply(apply(apply(k,apply(s,apply(apply(s,k),k))),x),apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x)),apply(apply(k,y),U_187)) != apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(apply(apply(s,k),k),x),apply(apply(apply(s,k),k),x))),y)
| apply(apply(apply(apply(k,apply(s,apply(apply(s,k),k))),x),apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x)),apply(apply(k,y),U_187)) = apply(y,apply(apply(x,x),y)) ),
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(k,y),U_187) != y
| apply(apply(apply(k,apply(s,apply(apply(s,k),k))),x),apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x)) != apply(apply(s,apply(apply(s,k),k)),apply(apply(apply(apply(s,k),k),x),apply(apply(apply(s,k),k),x)))
| apply(apply(apply(apply(k,apply(s,apply(apply(s,k),k))),x),apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x)),apply(apply(k,y),U_187)) = apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(apply(apply(s,k),k),x),apply(apply(apply(s,k),k),x))),y) ),
inference(extension,[status(thm),parent(t12:2)],[equality_4]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
( apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x) != apply(apply(apply(apply(s,k),k),x),apply(apply(apply(s,k),k),x))
| apply(apply(k,apply(s,apply(apply(s,k),k))),x) != apply(s,apply(apply(s,k),k))
| apply(apply(apply(k,apply(s,apply(apply(s,k),k))),x),apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x)) = apply(apply(s,apply(apply(s,k),k)),apply(apply(apply(apply(s,k),k),x),apply(apply(apply(s,k),k),x))) ),
inference(extension,[status(thm),parent(t14:2)],[equality_4]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
apply(apply(k,apply(s,apply(apply(s,k),k))),x) = apply(s,apply(apply(s,k),k)),
inference(extension,[status(thm),parent(t16:2)],[k_definition]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x) = apply(apply(apply(apply(s,k),k),x),apply(apply(apply(s,k),k),x)),
inference(extension,[status(thm),parent(t16:3)],[s_definition]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t16:3]) ).
cnf(t22,plain,
apply(apply(k,y),U_187) = y,
inference(extension,[status(thm),parent(t14:3)],[k_definition]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t14:3]) ).
cnf(t24,plain,
( apply(apply(apply(apply(s,k),k),y),apply(apply(apply(apply(apply(s,k),k),x),apply(apply(apply(s,k),k),x)),y)) != apply(y,apply(apply(x,x),y))
| apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(apply(apply(s,k),k),x),apply(apply(apply(s,k),k),x))),y) != apply(apply(apply(apply(s,k),k),y),apply(apply(apply(apply(apply(s,k),k),x),apply(apply(apply(s,k),k),x)),y))
| apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(apply(apply(s,k),k),x),apply(apply(apply(s,k),k),x))),y) = apply(y,apply(apply(x,x),y)) ),
inference(extension,[status(thm),parent(t12:3)],[equality_3]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t12:3]) ).
cnf(t26,plain,
apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(apply(apply(s,k),k),x),apply(apply(apply(s,k),k),x))),y) = apply(apply(apply(apply(s,k),k),y),apply(apply(apply(apply(apply(s,k),k),x),apply(apply(apply(s,k),k),x)),y)),
inference(extension,[status(thm),parent(t24:2)],[s_definition]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
( apply(apply(apply(apply(apply(s,k),k),x),apply(apply(apply(s,k),k),x)),y) != apply(apply(x,x),y)
| apply(apply(apply(s,k),k),y) != y
| apply(apply(apply(apply(s,k),k),y),apply(apply(apply(apply(apply(s,k),k),x),apply(apply(apply(s,k),k),x)),y)) = apply(y,apply(apply(x,x),y)) ),
inference(extension,[status(thm),parent(t24:3)],[equality_4]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t24:3]) ).
cnf(t30,plain,
( apply(apply(k,y),apply(k,y)) != y
| apply(apply(apply(s,k),k),y) != apply(apply(k,y),apply(k,y))
| apply(apply(apply(s,k),k),y) = y ),
inference(extension,[status(thm),parent(t28:2)],[equality_3]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
apply(apply(apply(s,k),k),y) = apply(apply(k,y),apply(k,y)),
inference(extension,[status(thm),parent(t30:2)],[s_definition]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t30:2]) ).
cnf(t34,plain,
apply(apply(k,y),apply(k,y)) = y,
inference(extension,[status(thm),parent(t30:3)],[k_definition]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t30:3]) ).
cnf(t36,plain,
( y != y
| apply(apply(apply(apply(s,k),k),x),apply(apply(apply(s,k),k),x)) != apply(x,x)
| apply(apply(apply(apply(apply(s,k),k),x),apply(apply(apply(s,k),k),x)),y) = apply(apply(x,x),y) ),
inference(extension,[status(thm),parent(t28:3)],[equality_4]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t28:3]) ).
cnf(t38,plain,
( apply(apply(apply(s,k),k),x) != x
| apply(apply(apply(s,k),k),x) != x
| apply(apply(apply(apply(s,k),k),x),apply(apply(apply(s,k),k),x)) = apply(x,x) ),
inference(extension,[status(thm),parent(t36:2)],[equality_4]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t36:2]) ).
cnf(t40,plain,
( apply(apply(k,x),apply(k,x)) != x
| apply(apply(apply(s,k),k),x) != apply(apply(k,x),apply(k,x))
| apply(apply(apply(s,k),k),x) = x ),
inference(extension,[status(thm),parent(t38:2)],[equality_3]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t38:2]) ).
cnf(t42,plain,
apply(apply(apply(s,k),k),x) = apply(apply(k,x),apply(k,x)),
inference(extension,[status(thm),parent(t40:2)],[s_definition]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t40:2]) ).
cnf(t44,plain,
apply(apply(k,x),apply(k,x)) = x,
inference(extension,[status(thm),parent(t40:3)],[k_definition]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t40:3]) ).
cnf(l20,lemma,
apply(apply(apply(s,k),k),x) = x,
inference(lemma,[status(cth),parent(t38:2),below(t36:2)],[t38:2]) ).
cnf(t46,plain,
apply(apply(apply(s,k),k),x) = x,
inference(lemma_extension,[status(thm),parent(t38:3)],[l20:1]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t38:3]) ).
cnf(t48,plain,
( apply(apply(k,y),U_230) != y
| y != apply(apply(k,y),U_230)
| y = y ),
inference(extension,[status(thm),parent(t36:3)],[equality_3]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t36:3]) ).
cnf(t50,plain,
( apply(apply(k,y),U_230) != y
| y = apply(apply(k,y),U_230) ),
inference(extension,[status(thm),parent(t48:2)],[equality_2]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t48:2]) ).
cnf(t52,plain,
apply(apply(k,y),U_230) = y,
inference(extension,[status(thm),parent(t50:2)],[k_definition]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t50:2]) ).
cnf(t54,plain,
apply(apply(k,y),U_230) = y,
inference(extension,[status(thm),parent(t48:3)],[k_definition]) ).
cnf(t55,plain,
$false,
inference(connection,[status(thm),parent(t54:1)],[t54:1,t48:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL004-3 : TPTP v9.3.1. Released v1.0.0.
% 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
% 0.08/0.37 % Computer : n018.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sun Sep 20 14:33:57 UTC 2026
% 0.08/0.37 % CPUTime :
% 30.34/30.66 % SZS status Unsatisfiable for theBenchmark
% 30.34/30.66 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------