%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : COL002-2 : 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 : 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 08:14:16 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.40s
% Output : Proof 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 8
% Syntax : Number of clauses : 29 ( 21 unt; 0 nHn; 25 RR)
% Number of literals : 43 ( 29 equ; 16 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 17 ( 0 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(b_definition,axiom,
apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)),
file('theBenchmark.p',b_definition) ).
cnf(i_definition,axiom,
apply(i,X) = X,
file('theBenchmark.p',i_definition) ).
cnf(weak_fixed_point,axiom,
( fixed_point(Weak_sage)
| Weak_sage != apply(fixed_pt,Weak_sage) ),
file('theBenchmark.p',weak_fixed_point) ).
cnf(prove_weak_fixed_point,negated_conjecture,
~ fixed_point(apply(apply(apply(s,apply(b,X)),i),apply(apply(s,apply(b,X)),i))),
file('theBenchmark.p',prove_weak_fixed_point) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
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,
~ fixed_point(apply(apply(apply(s,apply(b,apply(i,fixed_pt))),i),apply(apply(s,apply(b,apply(i,fixed_pt))),i))),
inference(start,[status(thm),parent(0:0)],[prove_weak_fixed_point]) ).
cnf(t2,plain,
( apply(apply(apply(s,apply(b,apply(i,fixed_pt))),i),apply(apply(s,apply(b,apply(i,fixed_pt))),i)) != apply(fixed_pt,apply(apply(apply(s,apply(b,apply(i,fixed_pt))),i),apply(apply(s,apply(b,apply(i,fixed_pt))),i)))
| fixed_point(apply(apply(apply(s,apply(b,apply(i,fixed_pt))),i),apply(apply(s,apply(b,apply(i,fixed_pt))),i))) ),
inference(extension,[status(thm),parent(t1:1)],[weak_fixed_point]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( apply(apply(apply(b,apply(i,fixed_pt)),apply(apply(s,apply(b,apply(i,fixed_pt))),i)),apply(i,apply(apply(s,apply(b,apply(i,fixed_pt))),i))) != apply(fixed_pt,apply(apply(apply(s,apply(b,apply(i,fixed_pt))),i),apply(apply(s,apply(b,apply(i,fixed_pt))),i)))
| apply(apply(apply(s,apply(b,apply(i,fixed_pt))),i),apply(apply(s,apply(b,apply(i,fixed_pt))),i)) != apply(apply(apply(b,apply(i,fixed_pt)),apply(apply(s,apply(b,apply(i,fixed_pt))),i)),apply(i,apply(apply(s,apply(b,apply(i,fixed_pt))),i)))
| apply(apply(apply(s,apply(b,apply(i,fixed_pt))),i),apply(apply(s,apply(b,apply(i,fixed_pt))),i)) = apply(fixed_pt,apply(apply(apply(s,apply(b,apply(i,fixed_pt))),i),apply(apply(s,apply(b,apply(i,fixed_pt))),i))) ),
inference(extension,[status(thm),parent(t2:2)],[equality_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
apply(apply(apply(s,apply(b,apply(i,fixed_pt))),i),apply(apply(s,apply(b,apply(i,fixed_pt))),i)) = apply(apply(apply(b,apply(i,fixed_pt)),apply(apply(s,apply(b,apply(i,fixed_pt))),i)),apply(i,apply(apply(s,apply(b,apply(i,fixed_pt))),i))),
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(i,fixed_pt),apply(apply(apply(s,apply(b,apply(i,fixed_pt))),i),apply(i,apply(apply(s,apply(b,apply(i,fixed_pt))),i)))) != apply(fixed_pt,apply(apply(apply(s,apply(b,apply(i,fixed_pt))),i),apply(apply(s,apply(b,apply(i,fixed_pt))),i)))
| apply(apply(apply(b,apply(i,fixed_pt)),apply(apply(s,apply(b,apply(i,fixed_pt))),i)),apply(i,apply(apply(s,apply(b,apply(i,fixed_pt))),i))) != apply(apply(i,fixed_pt),apply(apply(apply(s,apply(b,apply(i,fixed_pt))),i),apply(i,apply(apply(s,apply(b,apply(i,fixed_pt))),i))))
| apply(apply(apply(b,apply(i,fixed_pt)),apply(apply(s,apply(b,apply(i,fixed_pt))),i)),apply(i,apply(apply(s,apply(b,apply(i,fixed_pt))),i))) = apply(fixed_pt,apply(apply(apply(s,apply(b,apply(i,fixed_pt))),i),apply(apply(s,apply(b,apply(i,fixed_pt))),i))) ),
inference(extension,[status(thm),parent(t4:3)],[equality_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
apply(apply(apply(b,apply(i,fixed_pt)),apply(apply(s,apply(b,apply(i,fixed_pt))),i)),apply(i,apply(apply(s,apply(b,apply(i,fixed_pt))),i))) = apply(apply(i,fixed_pt),apply(apply(apply(s,apply(b,apply(i,fixed_pt))),i),apply(i,apply(apply(s,apply(b,apply(i,fixed_pt))),i)))),
inference(extension,[status(thm),parent(t8:2)],[b_definition]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( apply(apply(apply(s,apply(b,apply(i,fixed_pt))),i),apply(i,apply(apply(s,apply(b,apply(i,fixed_pt))),i))) != apply(apply(apply(s,apply(b,apply(i,fixed_pt))),i),apply(apply(s,apply(b,apply(i,fixed_pt))),i))
| apply(i,fixed_pt) != fixed_pt
| apply(apply(i,fixed_pt),apply(apply(apply(s,apply(b,apply(i,fixed_pt))),i),apply(i,apply(apply(s,apply(b,apply(i,fixed_pt))),i)))) = apply(fixed_pt,apply(apply(apply(s,apply(b,apply(i,fixed_pt))),i),apply(apply(s,apply(b,apply(i,fixed_pt))),i))) ),
inference(extension,[status(thm),parent(t8:3)],[equality_4]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
cnf(t14,plain,
apply(i,fixed_pt) = fixed_pt,
inference(extension,[status(thm),parent(t12:2)],[i_definition]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
( apply(i,apply(apply(s,apply(b,apply(i,fixed_pt))),i)) != apply(apply(s,apply(b,apply(i,fixed_pt))),i)
| apply(apply(s,apply(b,apply(i,fixed_pt))),i) != apply(apply(s,apply(b,apply(i,fixed_pt))),i)
| apply(apply(apply(s,apply(b,apply(i,fixed_pt))),i),apply(i,apply(apply(s,apply(b,apply(i,fixed_pt))),i))) = apply(apply(apply(s,apply(b,apply(i,fixed_pt))),i),apply(apply(s,apply(b,apply(i,fixed_pt))),i)) ),
inference(extension,[status(thm),parent(t12:3)],[equality_4]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t12:3]) ).
cnf(t18,plain,
apply(apply(s,apply(b,apply(i,fixed_pt))),i) = apply(apply(s,apply(b,apply(i,fixed_pt))),i),
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,
apply(i,apply(apply(s,apply(b,apply(i,fixed_pt))),i)) = apply(apply(s,apply(b,apply(i,fixed_pt))),i),
inference(extension,[status(thm),parent(t16:3)],[i_definition]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t16:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL002-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_HRN problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n002.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sun Sep 20 14:24:33 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.40 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------