%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : LCL536+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 08:49:28 AM UTC 2026
% Result : Theorem 2.43s 7.75s
% Output : Proof 2.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 53 ( 26 unt; 0 def)
% Number of atoms : 109 ( 11 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 99 ( 43 ~; 39 |; 12 &)
% ( 3 <=>; 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 18 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(necessitation,axiom,
( necessitation
<=> ! [X] :
( is_a_theorem(X)
=> is_a_theorem(necessarily(X)) ) ),
file('LCL007+0.ax',necessitation) ).
fof(axiom_5,axiom,
( axiom_5
<=> ! [X] : is_a_theorem(implies(possibly(X),necessarily(possibly(X)))) ),
file('LCL007+0.ax',axiom_5) ).
fof(axiom_m10,axiom,
( axiom_m10
<=> ! [X] : is_a_theorem(strict_implies(possibly(X),necessarily(possibly(X)))) ),
file('LCL007+0.ax',axiom_m10) ).
fof(op_strict_implies,axiom,
( op_strict_implies
=> ! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) ),
file('LCL007+1.ax',op_strict_implies) ).
fof(km5_necessitation,axiom,
necessitation,
file('LCL007+2.ax',km5_necessitation) ).
fof(km5_axiom_5,axiom,
axiom_5,
file('LCL007+2.ax',km5_axiom_5) ).
fof(s1_0_op_strict_implies,axiom,
op_strict_implies,
file('theBenchmark.p',s1_0_op_strict_implies) ).
fof(s1_0_m10_axiom_m10,conjecture,
axiom_m10,
file('theBenchmark.p',s1_0_m10_axiom_m10) ).
fof(f_50_1,plain,
( ( necessitation
| ? [X] :
( ~ is_a_theorem(necessarily(X))
& is_a_theorem(X) ) )
& ( ! [X] :
( is_a_theorem(necessarily(X))
| ~ is_a_theorem(X) )
| ~ necessitation ) ),
inference(fof_nnf,[status(thm)],[necessitation]) ).
fof(f_50_2,plain,
( ( necessitation
| ? [U_121] :
( ~ is_a_theorem(necessarily(U_121))
& is_a_theorem(U_121) ) )
& ( ! [U_120] :
( is_a_theorem(necessarily(U_120))
| ~ is_a_theorem(U_120) )
| ~ necessitation ) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
fof(f_50_3,plain,
( ( necessitation
| ( ~ is_a_theorem(necessarily(sK56))
& is_a_theorem(sK56) ) )
& ( ! [U_120] :
( is_a_theorem(necessarily(U_120))
| ~ is_a_theorem(U_120) )
| ~ necessitation ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_121,sK56)],[f_50_2]) ).
cnf(f_50_4,plain,
( is_a_theorem(necessarily(U_120))
| ~ is_a_theorem(U_120)
| ~ necessitation ),
inference(clausify,[status(thm)],[f_50_3]) ).
fof(f_58_1,plain,
( ( axiom_5
| ? [X] : ~ is_a_theorem(implies(possibly(X),necessarily(possibly(X)))) )
& ( ! [X] : is_a_theorem(implies(possibly(X),necessarily(possibly(X))))
| ~ axiom_5 ) ),
inference(fof_nnf,[status(thm)],[axiom_5]) ).
fof(f_58_2,plain,
( ( axiom_5
| ? [U_145] : ~ is_a_theorem(implies(possibly(U_145),necessarily(possibly(U_145)))) )
& ( ! [U_144] : is_a_theorem(implies(possibly(U_144),necessarily(possibly(U_144))))
| ~ axiom_5 ) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
fof(f_58_3,plain,
( ( axiom_5
| ~ is_a_theorem(implies(possibly(sK68),necessarily(possibly(sK68)))) )
& ( ! [U_144] : is_a_theorem(implies(possibly(U_144),necessarily(possibly(U_144))))
| ~ axiom_5 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK68]),skolemize(U_145,sK68)],[f_58_2]) ).
cnf(f_58_4,plain,
( is_a_theorem(implies(possibly(U_144),necessarily(possibly(U_144))))
| ~ axiom_5 ),
inference(clausify,[status(thm)],[f_58_3]) ).
fof(f_72_1,plain,
( ( axiom_m10
| ? [X] : ~ is_a_theorem(strict_implies(possibly(X),necessarily(possibly(X)))) )
& ( ! [X] : is_a_theorem(strict_implies(possibly(X),necessarily(possibly(X))))
| ~ axiom_m10 ) ),
inference(fof_nnf,[status(thm)],[axiom_m10]) ).
fof(f_72_2,plain,
( ( axiom_m10
| ? [U_197] : ~ is_a_theorem(strict_implies(possibly(U_197),necessarily(possibly(U_197)))) )
& ( ! [U_196] : is_a_theorem(strict_implies(possibly(U_196),necessarily(possibly(U_196))))
| ~ axiom_m10 ) ),
inference(variable_rename,[status(thm)],[f_72_1]) ).
fof(f_72_3,plain,
( ( axiom_m10
| ~ is_a_theorem(strict_implies(possibly(sK94),necessarily(possibly(sK94)))) )
& ( ! [U_196] : is_a_theorem(strict_implies(possibly(U_196),necessarily(possibly(U_196))))
| ~ axiom_m10 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK94]),skolemize(U_197,sK94)],[f_72_2]) ).
cnf(f_72_5,plain,
( axiom_m10
| ~ is_a_theorem(strict_implies(possibly(sK94),necessarily(possibly(sK94)))) ),
inference(clausify,[status(thm)],[f_72_3]) ).
fof(f_75_1,plain,
( ! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y))
| ~ op_strict_implies ),
inference(fof_nnf,[status(thm)],[op_strict_implies]) ).
fof(f_75_2,plain,
( ! [U_201,U_200] : strict_implies(U_201,U_200) = necessarily(implies(U_201,U_200))
| ~ op_strict_implies ),
inference(variable_rename,[status(thm)],[f_75_1]) ).
cnf(f_75_3,plain,
( strict_implies(U_201,U_200) = necessarily(implies(U_201,U_200))
| ~ op_strict_implies ),
inference(clausify,[status(thm)],[f_75_2]) ).
fof(f_78_1,plain,
necessitation,
inference(fof_nnf,[status(thm)],[km5_necessitation]) ).
cnf(f_78_2,plain,
necessitation,
inference(clausify,[status(thm)],[f_78_1]) ).
fof(f_81_1,plain,
axiom_5,
inference(fof_nnf,[status(thm)],[km5_axiom_5]) ).
cnf(f_81_2,plain,
axiom_5,
inference(clausify,[status(thm)],[f_81_1]) ).
fof(f_85_1,plain,
op_strict_implies,
inference(fof_nnf,[status(thm)],[s1_0_op_strict_implies]) ).
cnf(f_85_2,plain,
op_strict_implies,
inference(clausify,[status(thm)],[f_85_1]) ).
fof(f_88_1,negated_conjecture,
~ axiom_m10,
inference(negate,[status(cth)],[s1_0_m10_axiom_m10]) ).
fof(f_88_2,negated_conjecture,
~ axiom_m10,
inference(definitional_conversion,[status(esa)],[f_88_1]) ).
cnf(f_88_3,negated_conjecture,
~ axiom_m10,
inference(clausify,[status(thm)],[f_88_2]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_13,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,
~ axiom_m10,
inference(start,[status(thm),parent(0:0)],[f_88_3]) ).
cnf(t2,plain,
( ~ is_a_theorem(strict_implies(possibly(sK94),necessarily(possibly(sK94))))
| axiom_m10 ),
inference(extension,[status(thm),parent(t1:1)],[f_72_5]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ is_a_theorem(necessarily(implies(possibly(sK94),necessarily(possibly(sK94)))))
| necessarily(implies(possibly(sK94),necessarily(possibly(sK94)))) != strict_implies(possibly(sK94),necessarily(possibly(sK94)))
| is_a_theorem(strict_implies(possibly(sK94),necessarily(possibly(sK94)))) ),
inference(extension,[status(thm),parent(t2:2)],[equality_13]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( strict_implies(possibly(sK94),necessarily(possibly(sK94))) != necessarily(implies(possibly(sK94),necessarily(possibly(sK94))))
| necessarily(implies(possibly(sK94),necessarily(possibly(sK94)))) = strict_implies(possibly(sK94),necessarily(possibly(sK94))) ),
inference(extension,[status(thm),parent(t4:2)],[equality_2]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ op_strict_implies
| strict_implies(possibly(sK94),necessarily(possibly(sK94))) = necessarily(implies(possibly(sK94),necessarily(possibly(sK94)))) ),
inference(extension,[status(thm),parent(t6:2)],[f_75_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
op_strict_implies,
inference(extension,[status(thm),parent(t8:2)],[f_85_2]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( ~ is_a_theorem(implies(possibly(sK94),necessarily(possibly(sK94))))
| ~ necessitation
| is_a_theorem(necessarily(implies(possibly(sK94),necessarily(possibly(sK94))))) ),
inference(extension,[status(thm),parent(t4:3)],[f_50_4]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t4:3]) ).
cnf(t14,plain,
necessitation,
inference(extension,[status(thm),parent(t12:2)],[f_78_2]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
( ~ axiom_5
| is_a_theorem(implies(possibly(sK94),necessarily(possibly(sK94)))) ),
inference(extension,[status(thm),parent(t12:3)],[f_58_4]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t12:3]) ).
cnf(t18,plain,
axiom_5,
inference(extension,[status(thm),parent(t16:2)],[f_81_2]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL536+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
% 0.11/5.39 % Computer : n014.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Sat Sep 19 15:12:27 UTC 2026
% 0.11/5.39 % CPUTime :
% 2.43/7.75 % SZS status Theorem for theBenchmark
% 2.43/7.75 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------