%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : LCL483+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 08:49:24 AM UTC 2026
% Result : Theorem 17.95s 18.28s
% Output : Proof 17.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 15
% Syntax : Number of formulae : 82 ( 42 unt; 0 def)
% Number of atoms : 146 ( 42 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 119 ( 55 ~; 51 |; 8 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 69 ( 0 sgn 38 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(modus_tollens,axiom,
( modus_tollens
<=> ! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),
file('LCL006+0.ax',modus_tollens) ).
fof(r3,axiom,
( r3
<=> ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) ),
file('LCL006+0.ax',r3) ).
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(op_implies_or,axiom,
( op_implies_or
=> ! [X,Y] : implies(X,Y) = or(not(X),Y) ),
file('LCL006+1.ax',op_implies_or) ).
fof(principia_op_implies_or,axiom,
op_implies_or,
file('LCL006+4.ax',principia_op_implies_or) ).
fof(principia_r3,axiom,
r3,
file('LCL006+4.ax',principia_r3) ).
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_modus_tollens,conjecture,
modus_tollens,
file('theBenchmark.p',hilbert_modus_tollens) ).
fof(f_3_1,plain,
( ( modus_tollens
| ? [X,Y] : ~ is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) )
& ( ! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))
| ~ modus_tollens ) ),
inference(fof_nnf,[status(thm)],[modus_tollens]) ).
fof(f_3_2,plain,
( ( modus_tollens
| ? [U_11,U_10] : ~ is_a_theorem(implies(implies(not(U_10),not(U_11)),implies(U_11,U_10))) )
& ( ! [U_9,U_8] : is_a_theorem(implies(implies(not(U_8),not(U_9)),implies(U_9,U_8)))
| ~ modus_tollens ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ( modus_tollens
| ? [U_10] : ~ is_a_theorem(implies(implies(not(U_10),not(sK5)),implies(sK5,U_10))) )
& ( ! [U_9,U_8] : is_a_theorem(implies(implies(not(U_8),not(U_9)),implies(U_9,U_8)))
| ~ modus_tollens ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_11,sK5)],[f_3_2]) ).
fof(f_3_4,plain,
( ( modus_tollens
| ~ is_a_theorem(implies(implies(not(sK6),not(sK5)),implies(sK5,sK6))) )
& ( ! [U_9,U_8] : is_a_theorem(implies(implies(not(U_8),not(U_9)),implies(U_9,U_8)))
| ~ modus_tollens ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_10,sK6)],[f_3_3]) ).
cnf(f_3_6,plain,
( modus_tollens
| ~ is_a_theorem(implies(implies(not(sK6),not(sK5)),implies(sK5,sK6))) ),
inference(clausify,[status(thm)],[f_3_4]) ).
fof(f_24_1,plain,
( ( r3
| ? [P,Q] : ~ is_a_theorem(implies(or(P,Q),or(Q,P))) )
& ( ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P)))
| ~ r3 ) ),
inference(fof_nnf,[status(thm)],[r3]) ).
fof(f_24_2,plain,
( ( r3
| ? [U_97,U_96] : ~ is_a_theorem(implies(or(U_97,U_96),or(U_96,U_97))) )
& ( ! [U_95,U_94] : is_a_theorem(implies(or(U_95,U_94),or(U_94,U_95)))
| ~ r3 ) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
( ( r3
| ? [U_96] : ~ is_a_theorem(implies(or(sK48,U_96),or(U_96,sK48))) )
& ( ! [U_95,U_94] : is_a_theorem(implies(or(U_95,U_94),or(U_94,U_95)))
| ~ r3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_97,sK48)],[f_24_2]) ).
fof(f_24_4,plain,
( ( r3
| ~ is_a_theorem(implies(or(sK48,sK49),or(sK49,sK48))) )
& ( ! [U_95,U_94] : is_a_theorem(implies(or(U_95,U_94),or(U_94,U_95)))
| ~ r3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_96,sK49)],[f_24_3]) ).
cnf(f_24_5,plain,
( is_a_theorem(implies(or(U_95,U_94),or(U_94,U_95)))
| ~ r3 ),
inference(clausify,[status(thm)],[f_24_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_30_1,plain,
( ! [X,Y] : implies(X,Y) = or(not(X),Y)
| ~ op_implies_or ),
inference(fof_nnf,[status(thm)],[op_implies_or]) ).
fof(f_30_2,plain,
( ! [U_117,U_116] : implies(U_117,U_116) = or(not(U_117),U_116)
| ~ op_implies_or ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
( implies(U_117,U_116) = or(not(U_117),U_116)
| ~ op_implies_or ),
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_32_1,plain,
op_implies_or,
inference(fof_nnf,[status(thm)],[principia_op_implies_or]) ).
cnf(f_32_2,plain,
op_implies_or,
inference(clausify,[status(thm)],[f_32_1]) ).
fof(f_38_1,plain,
r3,
inference(fof_nnf,[status(thm)],[principia_r3]) ).
cnf(f_38_2,plain,
r3,
inference(clausify,[status(thm)],[f_38_1]) ).
fof(f_42_1,plain,
op_or,
inference(fof_nnf,[status(thm)],[hilbert_op_or]) ).
cnf(f_42_2,plain,
op_or,
inference(clausify,[status(thm)],[f_42_1]) ).
fof(f_43_1,plain,
op_implies_and,
inference(fof_nnf,[status(thm)],[hilbert_op_implies_and]) ).
cnf(f_43_2,plain,
op_implies_and,
inference(clausify,[status(thm)],[f_43_1]) ).
fof(f_45_1,negated_conjecture,
~ modus_tollens,
inference(negate,[status(cth)],[hilbert_modus_tollens]) ).
fof(f_45_2,negated_conjecture,
~ modus_tollens,
inference(definitional_conversion,[status(esa)],[f_45_1]) ).
cnf(f_45_3,negated_conjecture,
~ modus_tollens,
inference(clausify,[status(thm)],[f_45_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_8,axiom,
( or(Eq_x_0,Eq_x_1) = or(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,
~ modus_tollens,
inference(start,[status(thm),parent(0:0)],[f_45_3]) ).
cnf(t2,plain,
( ~ is_a_theorem(implies(implies(not(sK6),not(sK5)),implies(sK5,sK6)))
| modus_tollens ),
inference(extension,[status(thm),parent(t1:1)],[f_3_6]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ is_a_theorem(implies(not(and(not(sK6),not(not(sK5)))),or(not(sK5),sK6)))
| implies(not(and(not(sK6),not(not(sK5)))),or(not(sK5),sK6)) != implies(implies(not(sK6),not(sK5)),implies(sK5,sK6))
| is_a_theorem(implies(implies(not(sK6),not(sK5)),implies(sK5,sK6))) ),
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,
( or(not(sK5),sK6) != implies(sK5,sK6)
| not(and(not(sK6),not(not(sK5)))) != implies(not(sK6),not(sK5))
| implies(not(and(not(sK6),not(not(sK5)))),or(not(sK5),sK6)) = implies(implies(not(sK6),not(sK5)),implies(sK5,sK6)) ),
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,
( implies(not(sK6),not(sK5)) != not(and(not(sK6),not(not(sK5))))
| not(and(not(sK6),not(not(sK5)))) = implies(not(sK6),not(sK5)) ),
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_implies_and
| implies(not(sK6),not(sK5)) = not(and(not(sK6),not(not(sK5)))) ),
inference(extension,[status(thm),parent(t8:2)],[f_29_3]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
op_implies_and,
inference(extension,[status(thm),parent(t10:2)],[f_43_2]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( implies(sK5,sK6) != or(not(sK5),sK6)
| or(not(sK5),sK6) = implies(sK5,sK6) ),
inference(extension,[status(thm),parent(t6:3)],[equality_2]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t6:3]) ).
cnf(t16,plain,
( ~ op_implies_or
| implies(sK5,sK6) = or(not(sK5),sK6) ),
inference(extension,[status(thm),parent(t14:2)],[f_30_3]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
op_implies_or,
inference(extension,[status(thm),parent(t16:2)],[f_32_2]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
( ~ is_a_theorem(implies(or(sK6,not(sK5)),or(not(sK5),sK6)))
| implies(or(sK6,not(sK5)),or(not(sK5),sK6)) != implies(not(and(not(sK6),not(not(sK5)))),or(not(sK5),sK6))
| is_a_theorem(implies(not(and(not(sK6),not(not(sK5)))),or(not(sK5),sK6))) ),
inference(extension,[status(thm),parent(t4:3)],[equality_9]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t4:3]) ).
cnf(t22,plain,
( or(not(sK5),sK6) != or(not(sK5),sK6)
| or(sK6,not(sK5)) != not(and(not(sK6),not(not(sK5))))
| implies(or(sK6,not(sK5)),or(not(sK5),sK6)) = implies(not(and(not(sK6),not(not(sK5)))),or(not(sK5),sK6)) ),
inference(extension,[status(thm),parent(t20:2)],[equality_4]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
( ~ op_or
| or(sK6,not(sK5)) = not(and(not(sK6),not(not(sK5)))) ),
inference(extension,[status(thm),parent(t22:2)],[f_27_3]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
op_or,
inference(extension,[status(thm),parent(t24:2)],[f_42_2]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
( sK6 != sK6
| not(sK5) != not(sK5)
| or(not(sK5),sK6) = or(not(sK5),sK6) ),
inference(extension,[status(thm),parent(t22:3)],[equality_8]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t22:3]) ).
cnf(t30,plain,
not(sK5) = not(sK5),
inference(extension,[status(thm),parent(t28:2)],[equality_1]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
sK6 = sK6,
inference(extension,[status(thm),parent(t28:3)],[equality_1]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t28:3]) ).
cnf(t34,plain,
( ~ r3
| is_a_theorem(implies(or(sK6,not(sK5)),or(not(sK5),sK6))) ),
inference(extension,[status(thm),parent(t20:3)],[f_24_5]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t20:3]) ).
cnf(t36,plain,
r3,
inference(extension,[status(thm),parent(t34:2)],[f_38_2]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t34:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL483+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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 19 15:04:49 UTC 2026
% 0.09/0.36 % CPUTime :
% 17.95/18.28 % SZS status Theorem for theBenchmark
% 17.95/18.28 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------