%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : COL030-1 : 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 : n005.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 08:14:22 AM UTC 2026
% Result : Unsatisfiable 4.50s 4.82s
% Output : Proof 4.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 8
% Syntax : Number of clauses : 27 ( 18 unt; 0 nHn; 24 RR)
% Number of literals : 41 ( 32 equ; 16 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 18 ( 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(l_definition,axiom,
apply(apply(l,X),Y) = apply(X,apply(Y,Y)),
file('theBenchmark.p',l_definition) ).
cnf(prove_fixed_point,negated_conjecture,
apply(Y,f(Y)) != apply(f(Y),apply(Y,f(Y))),
file('theBenchmark.p',prove_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,
( f(Eq_x_0) = f(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(t1,plain,
apply(apply(apply(s,l),l),f(apply(apply(s,l),l))) != apply(f(apply(apply(s,l),l)),apply(apply(apply(s,l),l),f(apply(apply(s,l),l)))),
inference(start,[status(thm),parent(0:0)],[prove_fixed_point]) ).
cnf(t2,plain,
( apply(f(apply(apply(s,l),l)),apply(apply(l,f(apply(apply(s,l),l))),apply(l,f(apply(apply(s,l),l))))) != apply(f(apply(apply(s,l),l)),apply(apply(apply(s,l),l),f(apply(apply(s,l),l))))
| apply(apply(apply(s,l),l),f(apply(apply(s,l),l))) != apply(f(apply(apply(s,l),l)),apply(apply(l,f(apply(apply(s,l),l))),apply(l,f(apply(apply(s,l),l)))))
| apply(apply(apply(s,l),l),f(apply(apply(s,l),l))) = apply(f(apply(apply(s,l),l)),apply(apply(apply(s,l),l),f(apply(apply(s,l),l)))) ),
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,
( apply(apply(l,f(apply(apply(s,l),l))),apply(l,f(apply(apply(s,l),l)))) != apply(f(apply(apply(s,l),l)),apply(apply(l,f(apply(apply(s,l),l))),apply(l,f(apply(apply(s,l),l)))))
| apply(apply(apply(s,l),l),f(apply(apply(s,l),l))) != apply(apply(l,f(apply(apply(s,l),l))),apply(l,f(apply(apply(s,l),l))))
| apply(apply(apply(s,l),l),f(apply(apply(s,l),l))) = apply(f(apply(apply(s,l),l)),apply(apply(l,f(apply(apply(s,l),l))),apply(l,f(apply(apply(s,l),l))))) ),
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,l),l),f(apply(apply(s,l),l))) = apply(apply(l,f(apply(apply(s,l),l))),apply(l,f(apply(apply(s,l),l)))),
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(l,f(apply(apply(s,l),l))),apply(l,f(apply(apply(s,l),l)))) = apply(f(apply(apply(s,l),l)),apply(apply(l,f(apply(apply(s,l),l))),apply(l,f(apply(apply(s,l),l))))),
inference(extension,[status(thm),parent(t4:3)],[l_definition]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
( apply(apply(l,f(apply(apply(s,l),l))),apply(l,f(apply(apply(s,l),l)))) != apply(apply(apply(s,l),l),f(apply(apply(s,l),l)))
| f(apply(apply(s,l),l)) != f(apply(apply(s,l),l))
| apply(f(apply(apply(s,l),l)),apply(apply(l,f(apply(apply(s,l),l))),apply(l,f(apply(apply(s,l),l))))) = apply(f(apply(apply(s,l),l)),apply(apply(apply(s,l),l),f(apply(apply(s,l),l)))) ),
inference(extension,[status(thm),parent(t2:3)],[equality_4]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t2:3]) ).
cnf(t12,plain,
( apply(apply(s,l),l) != apply(apply(s,l),l)
| f(apply(apply(s,l),l)) = f(apply(apply(s,l),l)) ),
inference(extension,[status(thm),parent(t10:2)],[equality_5]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
apply(apply(s,l),l) = apply(apply(s,l),l),
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,
( apply(apply(apply(s,l),l),f(apply(apply(s,l),l))) != apply(apply(l,f(apply(apply(s,l),l))),apply(l,f(apply(apply(s,l),l))))
| apply(apply(l,f(apply(apply(s,l),l))),apply(l,f(apply(apply(s,l),l)))) = apply(apply(apply(s,l),l),f(apply(apply(s,l),l))) ),
inference(extension,[status(thm),parent(t10:3)],[equality_2]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t10:3]) ).
cnf(t18,plain,
apply(apply(apply(s,l),l),f(apply(apply(s,l),l))) = apply(apply(l,f(apply(apply(s,l),l))),apply(l,f(apply(apply(s,l),l)))),
inference(extension,[status(thm),parent(t16:2)],[s_definition]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL030-1 : 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
% 0.08/0.39 % Computer : n005.cluster.edu
% 0.08/0.39 % Model : x86_64 x86_64
% 0.08/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.39 % Memory : 8046.5625MB
% 0.08/0.39 % OS : Linux 6.8.0-71-generic
% 0.08/0.39 % CPULimit : 300
% 0.08/0.39 % WCLimit : 300
% 0.08/0.39 % DateTime : Sun Sep 20 14:34:04 UTC 2026
% 0.08/0.39 % CPUTime :
% 4.50/4.82 % SZS status Unsatisfiable for theBenchmark
% 4.50/4.82 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------