%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : LCL469+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 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 : n009.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 08:49:23 AM UTC 2026
% Result : Theorem 17.15s 17.44s
% Output : Proof 17.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 70 ( 36 unt; 0 def)
% Number of atoms : 126 ( 33 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 104 ( 48 ~; 44 |; 8 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 57 ( 1 sgn 32 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(or_1,axiom,
( or_1
<=> ! [X,Y] : is_a_theorem(implies(X,or(X,Y))) ),
file('LCL006+0.ax',or_1) ).
fof(cn2,axiom,
( cn2
<=> ! [P,Q] : is_a_theorem(implies(P,implies(not(P),Q))) ),
file('LCL006+0.ax',cn2) ).
fof(op_or,axiom,
( op_or
=> ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
file('LCL006+1.ax',op_or) ).
fof(op_implies_and,axiom,
( op_implies_and
=> ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ),
file('LCL006+1.ax',op_implies_and) ).
fof(luka_cn2,axiom,
cn2,
file('LCL006+3.ax',luka_cn2) ).
fof(hilbert_op_or,axiom,
op_or,
file('theBenchmark.p',hilbert_op_or) ).
fof(hilbert_op_implies_and,axiom,
op_implies_and,
file('theBenchmark.p',hilbert_op_implies_and) ).
fof(hilbert_or_1,conjecture,
or_1,
file('theBenchmark.p',hilbert_or_1) ).
fof(f_10_1,plain,
( ( or_1
| ? [X,Y] : ~ is_a_theorem(implies(X,or(X,Y))) )
& ( ! [X,Y] : is_a_theorem(implies(X,or(X,Y)))
| ~ or_1 ) ),
inference(fof_nnf,[status(thm)],[or_1]) ).
fof(f_10_2,plain,
( ( or_1
| ? [U_41,U_40] : ~ is_a_theorem(implies(U_41,or(U_41,U_40))) )
& ( ! [U_39,U_38] : is_a_theorem(implies(U_39,or(U_39,U_38)))
| ~ or_1 ) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
( ( or_1
| ? [U_40] : ~ is_a_theorem(implies(sK20,or(sK20,U_40))) )
& ( ! [U_39,U_38] : is_a_theorem(implies(U_39,or(U_39,U_38)))
| ~ or_1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_41,sK20)],[f_10_2]) ).
fof(f_10_4,plain,
( ( or_1
| ~ is_a_theorem(implies(sK20,or(sK20,sK21))) )
& ( ! [U_39,U_38] : is_a_theorem(implies(U_39,or(U_39,U_38)))
| ~ or_1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_40,sK21)],[f_10_3]) ).
cnf(f_10_6,plain,
( or_1
| ~ is_a_theorem(implies(sK20,or(sK20,sK21))) ),
inference(clausify,[status(thm)],[f_10_4]) ).
fof(f_20_1,plain,
( ( cn2
| ? [P,Q] : ~ is_a_theorem(implies(P,implies(not(P),Q))) )
& ( ! [P,Q] : is_a_theorem(implies(P,implies(not(P),Q)))
| ~ cn2 ) ),
inference(fof_nnf,[status(thm)],[cn2]) ).
fof(f_20_2,plain,
( ( cn2
| ? [U_85,U_84] : ~ is_a_theorem(implies(U_85,implies(not(U_85),U_84))) )
& ( ! [U_83,U_82] : is_a_theorem(implies(U_83,implies(not(U_83),U_82)))
| ~ cn2 ) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
( ( cn2
| ? [U_84] : ~ is_a_theorem(implies(sK42,implies(not(sK42),U_84))) )
& ( ! [U_83,U_82] : is_a_theorem(implies(U_83,implies(not(U_83),U_82)))
| ~ cn2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_85,sK42)],[f_20_2]) ).
fof(f_20_4,plain,
( ( cn2
| ~ is_a_theorem(implies(sK42,implies(not(sK42),sK43))) )
& ( ! [U_83,U_82] : is_a_theorem(implies(U_83,implies(not(U_83),U_82)))
| ~ cn2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_84,sK43)],[f_20_3]) ).
cnf(f_20_5,plain,
( is_a_theorem(implies(U_83,implies(not(U_83),U_82)))
| ~ cn2 ),
inference(clausify,[status(thm)],[f_20_4]) ).
fof(f_27_1,plain,
( ! [X,Y] : or(X,Y) = not(and(not(X),not(Y)))
| ~ op_or ),
inference(fof_nnf,[status(thm)],[op_or]) ).
fof(f_27_2,plain,
( ! [U_111,U_110] : or(U_111,U_110) = not(and(not(U_111),not(U_110)))
| ~ op_or ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
( or(U_111,U_110) = not(and(not(U_111),not(U_110)))
| ~ op_or ),
inference(clausify,[status(thm)],[f_27_2]) ).
fof(f_29_1,plain,
( ! [X,Y] : implies(X,Y) = not(and(X,not(Y)))
| ~ op_implies_and ),
inference(fof_nnf,[status(thm)],[op_implies_and]) ).
fof(f_29_2,plain,
( ! [U_115,U_114] : implies(U_115,U_114) = not(and(U_115,not(U_114)))
| ~ op_implies_and ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
( implies(U_115,U_114) = not(and(U_115,not(U_114)))
| ~ op_implies_and ),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_37_1,plain,
cn2,
inference(fof_nnf,[status(thm)],[luka_cn2]) ).
cnf(f_37_2,plain,
cn2,
inference(clausify,[status(thm)],[f_37_1]) ).
fof(f_40_1,plain,
op_or,
inference(fof_nnf,[status(thm)],[hilbert_op_or]) ).
cnf(f_40_2,plain,
op_or,
inference(clausify,[status(thm)],[f_40_1]) ).
fof(f_41_1,plain,
op_implies_and,
inference(fof_nnf,[status(thm)],[hilbert_op_implies_and]) ).
cnf(f_41_2,plain,
op_implies_and,
inference(clausify,[status(thm)],[f_41_1]) ).
fof(f_43_1,negated_conjecture,
~ or_1,
inference(negate,[status(cth)],[hilbert_or_1]) ).
fof(f_43_2,negated_conjecture,
~ or_1,
inference(definitional_conversion,[status(esa)],[f_43_1]) ).
cnf(f_43_3,negated_conjecture,
~ or_1,
inference(clausify,[status(thm)],[f_43_2]) ).
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_4,axiom,
( implies(Eq_x_0,Eq_x_1) = implies(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( is_a_theorem(Eq_y_0)
| ~ is_a_theorem(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(t1,plain,
~ or_1,
inference(start,[status(thm),parent(0:0)],[f_43_3]) ).
cnf(t2,plain,
( ~ is_a_theorem(implies(sK20,or(sK20,sK21)))
| or_1 ),
inference(extension,[status(thm),parent(t1:1)],[f_10_6]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ is_a_theorem(implies(sK20,not(and(not(sK20),not(sK21)))))
| implies(sK20,not(and(not(sK20),not(sK21)))) != implies(sK20,or(sK20,sK21))
| is_a_theorem(implies(sK20,or(sK20,sK21))) ),
inference(extension,[status(thm),parent(t2:2)],[equality_9]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( not(and(not(sK20),not(sK21))) != or(sK20,sK21)
| sK20 != sK20
| implies(sK20,not(and(not(sK20),not(sK21)))) = implies(sK20,or(sK20,sK21)) ),
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,
( sK20 != sK20
| sK20 = sK20 ),
inference(extension,[status(thm),parent(t6:2)],[equality_2]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
sK20 = sK20,
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,
( or(sK20,sK21) != not(and(not(sK20),not(sK21)))
| not(and(not(sK20),not(sK21))) = or(sK20,sK21) ),
inference(extension,[status(thm),parent(t6:3)],[equality_2]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t6:3]) ).
cnf(t14,plain,
( ~ op_or
| or(sK20,sK21) = not(and(not(sK20),not(sK21))) ),
inference(extension,[status(thm),parent(t12:2)],[f_27_3]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
op_or,
inference(extension,[status(thm),parent(t14:2)],[f_40_2]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
( ~ is_a_theorem(implies(sK20,implies(not(sK20),sK21)))
| implies(sK20,implies(not(sK20),sK21)) != implies(sK20,not(and(not(sK20),not(sK21))))
| is_a_theorem(implies(sK20,not(and(not(sK20),not(sK21))))) ),
inference(extension,[status(thm),parent(t4:3)],[equality_9]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t4:3]) ).
cnf(t20,plain,
( implies(not(sK20),sK21) != not(and(not(sK20),not(sK21)))
| sK20 != sK20
| implies(sK20,implies(not(sK20),sK21)) = implies(sK20,not(and(not(sK20),not(sK21)))) ),
inference(extension,[status(thm),parent(t18:2)],[equality_4]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
( sK20 != sK20
| sK20 = sK20 ),
inference(extension,[status(thm),parent(t20:2)],[equality_2]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
sK20 = sK20,
inference(extension,[status(thm),parent(t22:2)],[equality_1]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
( ~ op_implies_and
| implies(not(sK20),sK21) = not(and(not(sK20),not(sK21))) ),
inference(extension,[status(thm),parent(t20:3)],[f_29_3]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t20:3]) ).
cnf(t28,plain,
op_implies_and,
inference(extension,[status(thm),parent(t26:2)],[f_41_2]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
( ~ cn2
| is_a_theorem(implies(sK20,implies(not(sK20),sK21))) ),
inference(extension,[status(thm),parent(t18:3)],[f_20_5]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t18:3]) ).
cnf(t32,plain,
cn2,
inference(extension,[status(thm),parent(t30:2)],[f_37_2]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t30:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL469+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ 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
% 0.08/0.36 % Computer : n009.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 19 15:06:12 UTC 2026
% 0.08/0.37 % CPUTime :
% 17.15/17.44 % SZS status Theorem for theBenchmark
% 17.15/17.44 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------