%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : LCL512+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 : n001.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 08:49:26 AM UTC 2026
% Result : Theorem 7.45s 7.70s
% Output : Proof 7.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 57 ( 29 unt; 0 def)
% Number of atoms : 106 ( 27 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 91 ( 42 ~; 38 |; 8 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 49 ( 1 sgn 26 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(equivalence_1,axiom,
( equivalence_1
<=> ! [X,Y] : is_a_theorem(implies(equiv(X,Y),implies(X,Y))) ),
file('LCL006+0.ax',equivalence_1) ).
fof(kn2,axiom,
( kn2
<=> ! [P,Q] : is_a_theorem(implies(and(P,Q),P)) ),
file('LCL006+0.ax',kn2) ).
fof(op_equiv,axiom,
( op_equiv
=> ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
file('LCL006+1.ax',op_equiv) ).
fof(rosser_kn2,axiom,
kn2,
file('LCL006+5.ax',rosser_kn2) ).
fof(hilbert_op_equiv,axiom,
op_equiv,
file('theBenchmark.p',hilbert_op_equiv) ).
fof(hilbert_equivalence_1,conjecture,
equivalence_1,
file('theBenchmark.p',hilbert_equivalence_1) ).
fof(f_13_1,plain,
( ( equivalence_1
| ? [X,Y] : ~ is_a_theorem(implies(equiv(X,Y),implies(X,Y))) )
& ( ! [X,Y] : is_a_theorem(implies(equiv(X,Y),implies(X,Y)))
| ~ equivalence_1 ) ),
inference(fof_nnf,[status(thm)],[equivalence_1]) ).
fof(f_13_2,plain,
( ( equivalence_1
| ? [U_55,U_54] : ~ is_a_theorem(implies(equiv(U_55,U_54),implies(U_55,U_54))) )
& ( ! [U_53,U_52] : is_a_theorem(implies(equiv(U_53,U_52),implies(U_53,U_52)))
| ~ equivalence_1 ) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
( ( equivalence_1
| ? [U_54] : ~ is_a_theorem(implies(equiv(sK27,U_54),implies(sK27,U_54))) )
& ( ! [U_53,U_52] : is_a_theorem(implies(equiv(U_53,U_52),implies(U_53,U_52)))
| ~ equivalence_1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_55,sK27)],[f_13_2]) ).
fof(f_13_4,plain,
( ( equivalence_1
| ~ is_a_theorem(implies(equiv(sK27,sK28),implies(sK27,sK28))) )
& ( ! [U_53,U_52] : is_a_theorem(implies(equiv(U_53,U_52),implies(U_53,U_52)))
| ~ equivalence_1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_54,sK28)],[f_13_3]) ).
cnf(f_13_6,plain,
( equivalence_1
| ~ is_a_theorem(implies(equiv(sK27,sK28),implies(sK27,sK28))) ),
inference(clausify,[status(thm)],[f_13_4]) ).
fof(f_17_1,plain,
( ( kn2
| ? [P,Q] : ~ is_a_theorem(implies(and(P,Q),P)) )
& ( ! [P,Q] : is_a_theorem(implies(and(P,Q),P))
| ~ kn2 ) ),
inference(fof_nnf,[status(thm)],[kn2]) ).
fof(f_17_2,plain,
( ( kn2
| ? [U_69,U_68] : ~ is_a_theorem(implies(and(U_69,U_68),U_69)) )
& ( ! [U_67,U_66] : is_a_theorem(implies(and(U_67,U_66),U_67))
| ~ kn2 ) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
( ( kn2
| ? [U_68] : ~ is_a_theorem(implies(and(sK34,U_68),sK34)) )
& ( ! [U_67,U_66] : is_a_theorem(implies(and(U_67,U_66),U_67))
| ~ kn2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_69,sK34)],[f_17_2]) ).
fof(f_17_4,plain,
( ( kn2
| ~ is_a_theorem(implies(and(sK34,sK35),sK34)) )
& ( ! [U_67,U_66] : is_a_theorem(implies(and(U_67,U_66),U_67))
| ~ kn2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_68,sK35)],[f_17_3]) ).
cnf(f_17_5,plain,
( is_a_theorem(implies(and(U_67,U_66),U_67))
| ~ kn2 ),
inference(clausify,[status(thm)],[f_17_4]) ).
fof(f_31_1,plain,
( ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X))
| ~ op_equiv ),
inference(fof_nnf,[status(thm)],[op_equiv]) ).
fof(f_31_2,plain,
( ! [U_119,U_118] : equiv(U_119,U_118) = and(implies(U_119,U_118),implies(U_118,U_119))
| ~ op_equiv ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
cnf(f_31_3,plain,
( equiv(U_119,U_118) = and(implies(U_119,U_118),implies(U_118,U_119))
| ~ op_equiv ),
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_37_1,plain,
kn2,
inference(fof_nnf,[status(thm)],[rosser_kn2]) ).
cnf(f_37_2,plain,
kn2,
inference(clausify,[status(thm)],[f_37_1]) ).
fof(f_42_1,plain,
op_equiv,
inference(fof_nnf,[status(thm)],[hilbert_op_equiv]) ).
cnf(f_42_2,plain,
op_equiv,
inference(clausify,[status(thm)],[f_42_1]) ).
fof(f_43_1,negated_conjecture,
~ equivalence_1,
inference(negate,[status(cth)],[hilbert_equivalence_1]) ).
fof(f_43_2,negated_conjecture,
~ equivalence_1,
inference(definitional_conversion,[status(esa)],[f_43_1]) ).
cnf(f_43_3,negated_conjecture,
~ equivalence_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,
~ equivalence_1,
inference(start,[status(thm),parent(0:0)],[f_43_3]) ).
cnf(t2,plain,
( ~ is_a_theorem(implies(equiv(sK27,sK28),implies(sK27,sK28)))
| equivalence_1 ),
inference(extension,[status(thm),parent(t1:1)],[f_13_6]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ is_a_theorem(implies(and(implies(sK27,sK28),implies(sK28,sK27)),implies(sK27,sK28)))
| implies(and(implies(sK27,sK28),implies(sK28,sK27)),implies(sK27,sK28)) != implies(equiv(sK27,sK28),implies(sK27,sK28))
| is_a_theorem(implies(equiv(sK27,sK28),implies(sK27,sK28))) ),
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,
( implies(sK27,sK28) != implies(sK27,sK28)
| and(implies(sK27,sK28),implies(sK28,sK27)) != equiv(sK27,sK28)
| implies(and(implies(sK27,sK28),implies(sK28,sK27)),implies(sK27,sK28)) = implies(equiv(sK27,sK28),implies(sK27,sK28)) ),
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,
( equiv(sK27,sK28) != and(implies(sK27,sK28),implies(sK28,sK27))
| and(implies(sK27,sK28),implies(sK28,sK27)) = equiv(sK27,sK28) ),
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,
( ~ op_equiv
| equiv(sK27,sK28) = and(implies(sK27,sK28),implies(sK28,sK27)) ),
inference(extension,[status(thm),parent(t8:2)],[f_31_3]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
op_equiv,
inference(extension,[status(thm),parent(t10:2)],[f_42_2]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( sK28 != sK28
| sK27 != sK27
| implies(sK27,sK28) = implies(sK27,sK28) ),
inference(extension,[status(thm),parent(t6:3)],[equality_4]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t6:3]) ).
cnf(t16,plain,
( sK27 != sK27
| sK27 = sK27 ),
inference(extension,[status(thm),parent(t14:2)],[equality_2]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
sK27 = sK27,
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,
( sK28 != sK28
| sK28 = sK28 ),
inference(extension,[status(thm),parent(t14:3)],[equality_2]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t14:3]) ).
cnf(t22,plain,
sK28 = sK28,
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,
( ~ kn2
| is_a_theorem(implies(and(implies(sK27,sK28),implies(sK28,sK27)),implies(sK27,sK28))) ),
inference(extension,[status(thm),parent(t4:3)],[f_17_5]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t4:3]) ).
cnf(t26,plain,
kn2,
inference(extension,[status(thm),parent(t24:2)],[f_37_2]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL512+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
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sat Sep 19 15:16:41 UTC 2026
% 0.10/0.38 % CPUTime :
% 7.45/7.70 % SZS status Theorem for theBenchmark
% 7.45/7.70 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------