%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : LCL484+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 : n014.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 1.79s 2.06s
% Output : Proof 1.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 51 ( 25 unt; 0 def)
% Number of atoms : 97 ( 21 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 85 ( 39 ~; 35 |; 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(implies_1,axiom,
( implies_1
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,X))) ),
file('LCL006+0.ax',implies_1) ).
fof(r2,axiom,
( r2
<=> ! [P,Q] : is_a_theorem(implies(Q,or(P,Q))) ),
file('LCL006+0.ax',r2) ).
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_r2,axiom,
r2,
file('LCL006+4.ax',principia_r2) ).
fof(hilbert_implies_1,conjecture,
implies_1,
file('theBenchmark.p',hilbert_implies_1) ).
fof(f_4_1,plain,
( ( implies_1
| ? [X,Y] : ~ is_a_theorem(implies(X,implies(Y,X))) )
& ( ! [X,Y] : is_a_theorem(implies(X,implies(Y,X)))
| ~ implies_1 ) ),
inference(fof_nnf,[status(thm)],[implies_1]) ).
fof(f_4_2,plain,
( ( implies_1
| ? [U_15,U_14] : ~ is_a_theorem(implies(U_15,implies(U_14,U_15))) )
& ( ! [U_13,U_12] : is_a_theorem(implies(U_13,implies(U_12,U_13)))
| ~ implies_1 ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ( implies_1
| ? [U_14] : ~ is_a_theorem(implies(sK7,implies(U_14,sK7))) )
& ( ! [U_13,U_12] : is_a_theorem(implies(U_13,implies(U_12,U_13)))
| ~ implies_1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_15,sK7)],[f_4_2]) ).
fof(f_4_4,plain,
( ( implies_1
| ~ is_a_theorem(implies(sK7,implies(sK8,sK7))) )
& ( ! [U_13,U_12] : is_a_theorem(implies(U_13,implies(U_12,U_13)))
| ~ implies_1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_14,sK8)],[f_4_3]) ).
cnf(f_4_6,plain,
( implies_1
| ~ is_a_theorem(implies(sK7,implies(sK8,sK7))) ),
inference(clausify,[status(thm)],[f_4_4]) ).
fof(f_23_1,plain,
( ( r2
| ? [P,Q] : ~ is_a_theorem(implies(Q,or(P,Q))) )
& ( ! [P,Q] : is_a_theorem(implies(Q,or(P,Q)))
| ~ r2 ) ),
inference(fof_nnf,[status(thm)],[r2]) ).
fof(f_23_2,plain,
( ( r2
| ? [U_93,U_92] : ~ is_a_theorem(implies(U_92,or(U_93,U_92))) )
& ( ! [U_91,U_90] : is_a_theorem(implies(U_90,or(U_91,U_90)))
| ~ r2 ) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
( ( r2
| ? [U_92] : ~ is_a_theorem(implies(U_92,or(sK46,U_92))) )
& ( ! [U_91,U_90] : is_a_theorem(implies(U_90,or(U_91,U_90)))
| ~ r2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_93,sK46)],[f_23_2]) ).
fof(f_23_4,plain,
( ( r2
| ~ is_a_theorem(implies(sK47,or(sK46,sK47))) )
& ( ! [U_91,U_90] : is_a_theorem(implies(U_90,or(U_91,U_90)))
| ~ r2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_92,sK47)],[f_23_3]) ).
cnf(f_23_5,plain,
( is_a_theorem(implies(U_90,or(U_91,U_90)))
| ~ r2 ),
inference(clausify,[status(thm)],[f_23_4]) ).
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_37_1,plain,
r2,
inference(fof_nnf,[status(thm)],[principia_r2]) ).
cnf(f_37_2,plain,
r2,
inference(clausify,[status(thm)],[f_37_1]) ).
fof(f_45_1,negated_conjecture,
~ implies_1,
inference(negate,[status(cth)],[hilbert_implies_1]) ).
fof(f_45_2,negated_conjecture,
~ implies_1,
inference(definitional_conversion,[status(esa)],[f_45_1]) ).
cnf(f_45_3,negated_conjecture,
~ implies_1,
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_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,
~ implies_1,
inference(start,[status(thm),parent(0:0)],[f_45_3]) ).
cnf(t2,plain,
( ~ is_a_theorem(implies(sK7,implies(sK8,sK7)))
| implies_1 ),
inference(extension,[status(thm),parent(t1:1)],[f_4_6]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ is_a_theorem(implies(sK7,or(not(sK8),sK7)))
| implies(sK7,or(not(sK8),sK7)) != implies(sK7,implies(sK8,sK7))
| is_a_theorem(implies(sK7,implies(sK8,sK7))) ),
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(sK8),sK7) != implies(sK8,sK7)
| sK7 != sK7
| implies(sK7,or(not(sK8),sK7)) = implies(sK7,implies(sK8,sK7)) ),
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,
( sK7 != sK7
| sK7 = sK7 ),
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,
sK7 = sK7,
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,
( implies(sK8,sK7) != or(not(sK8),sK7)
| or(not(sK8),sK7) = implies(sK8,sK7) ),
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_implies_or
| implies(sK8,sK7) = or(not(sK8),sK7) ),
inference(extension,[status(thm),parent(t12:2)],[f_30_3]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
op_implies_or,
inference(extension,[status(thm),parent(t14:2)],[f_32_2]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
( ~ r2
| is_a_theorem(implies(sK7,or(not(sK8),sK7))) ),
inference(extension,[status(thm),parent(t4:3)],[f_23_5]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t4:3]) ).
cnf(t20,plain,
r2,
inference(extension,[status(thm),parent(t18:2)],[f_37_2]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL484+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ 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
% 0.08/0.34 % Computer : n014.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 19 15:06:50 UTC 2026
% 0.08/0.35 % CPUTime :
% 1.79/2.06 % SZS status Theorem for theBenchmark
% 1.79/2.06 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------