%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : LCL529+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 : n012.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 08:49:27 AM UTC 2026
% Result : Theorem 1.04s 1.36s
% Output : Proof 1.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 55 ( 26 unt; 0 def)
% Number of atoms : 117 ( 11 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 109 ( 47 ~; 43 |; 14 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 51 ( 1 sgn 30 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(and_1,axiom,
( and_1
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),X)) ),
file('LCL006+0.ax',and_1) ).
fof(hilbert_and_1,axiom,
and_1,
file('LCL006+2.ax',hilbert_and_1) ).
fof(necessitation,axiom,
( necessitation
<=> ! [X] :
( is_a_theorem(X)
=> is_a_theorem(necessarily(X)) ) ),
file('LCL007+0.ax',necessitation) ).
fof(axiom_m2,axiom,
( axiom_m2
<=> ! [X,Y] : is_a_theorem(strict_implies(and(X,Y),X)) ),
file('LCL007+0.ax',axiom_m2) ).
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(s1_0_op_strict_implies,axiom,
op_strict_implies,
file('theBenchmark.p',s1_0_op_strict_implies) ).
fof(s1_0_axiom_m2,conjecture,
axiom_m2,
file('theBenchmark.p',s1_0_axiom_m2) ).
fof(f_7_1,plain,
( ( and_1
| ? [X,Y] : ~ is_a_theorem(implies(and(X,Y),X)) )
& ( ! [X,Y] : is_a_theorem(implies(and(X,Y),X))
| ~ and_1 ) ),
inference(fof_nnf,[status(thm)],[and_1]) ).
fof(f_7_2,plain,
( ( and_1
| ? [U_29,U_28] : ~ is_a_theorem(implies(and(U_29,U_28),U_29)) )
& ( ! [U_27,U_26] : is_a_theorem(implies(and(U_27,U_26),U_27))
| ~ and_1 ) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ( and_1
| ? [U_28] : ~ is_a_theorem(implies(and(sK14,U_28),sK14)) )
& ( ! [U_27,U_26] : is_a_theorem(implies(and(U_27,U_26),U_27))
| ~ and_1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_29,sK14)],[f_7_2]) ).
fof(f_7_4,plain,
( ( and_1
| ~ is_a_theorem(implies(and(sK14,sK15),sK14)) )
& ( ! [U_27,U_26] : is_a_theorem(implies(and(U_27,U_26),U_27))
| ~ and_1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_28,sK15)],[f_7_3]) ).
cnf(f_7_5,plain,
( is_a_theorem(implies(and(U_27,U_26),U_27))
| ~ and_1 ),
inference(clausify,[status(thm)],[f_7_4]) ).
fof(f_40_1,plain,
and_1,
inference(fof_nnf,[status(thm)],[hilbert_and_1]) ).
cnf(f_40_2,plain,
and_1,
inference(clausify,[status(thm)],[f_40_1]) ).
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_64_1,plain,
( ( axiom_m2
| ? [X,Y] : ~ is_a_theorem(strict_implies(and(X,Y),X)) )
& ( ! [X,Y] : is_a_theorem(strict_implies(and(X,Y),X))
| ~ axiom_m2 ) ),
inference(fof_nnf,[status(thm)],[axiom_m2]) ).
fof(f_64_2,plain,
( ( axiom_m2
| ? [U_169,U_168] : ~ is_a_theorem(strict_implies(and(U_169,U_168),U_169)) )
& ( ! [U_167,U_166] : is_a_theorem(strict_implies(and(U_167,U_166),U_167))
| ~ axiom_m2 ) ),
inference(variable_rename,[status(thm)],[f_64_1]) ).
fof(f_64_3,plain,
( ( axiom_m2
| ? [U_168] : ~ is_a_theorem(strict_implies(and(sK79,U_168),sK79)) )
& ( ! [U_167,U_166] : is_a_theorem(strict_implies(and(U_167,U_166),U_167))
| ~ axiom_m2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK79]),skolemize(U_169,sK79)],[f_64_2]) ).
fof(f_64_4,plain,
( ( axiom_m2
| ~ is_a_theorem(strict_implies(and(sK79,sK80),sK79)) )
& ( ! [U_167,U_166] : is_a_theorem(strict_implies(and(U_167,U_166),U_167))
| ~ axiom_m2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK80]),skolemize(U_168,sK80)],[f_64_3]) ).
cnf(f_64_6,plain,
( axiom_m2
| ~ is_a_theorem(strict_implies(and(sK79,sK80),sK79)) ),
inference(clausify,[status(thm)],[f_64_4]) ).
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_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_m2,
inference(negate,[status(cth)],[s1_0_axiom_m2]) ).
fof(f_88_2,negated_conjecture,
~ axiom_m2,
inference(definitional_conversion,[status(esa)],[f_88_1]) ).
cnf(f_88_3,negated_conjecture,
~ axiom_m2,
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_m2,
inference(start,[status(thm),parent(0:0)],[f_88_3]) ).
cnf(t2,plain,
( ~ is_a_theorem(strict_implies(and(sK79,sK80),sK79))
| axiom_m2 ),
inference(extension,[status(thm),parent(t1:1)],[f_64_6]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ is_a_theorem(necessarily(implies(and(sK79,sK80),sK79)))
| necessarily(implies(and(sK79,sK80),sK79)) != strict_implies(and(sK79,sK80),sK79)
| is_a_theorem(strict_implies(and(sK79,sK80),sK79)) ),
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(and(sK79,sK80),sK79) != necessarily(implies(and(sK79,sK80),sK79))
| necessarily(implies(and(sK79,sK80),sK79)) = strict_implies(and(sK79,sK80),sK79) ),
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(and(sK79,sK80),sK79) = necessarily(implies(and(sK79,sK80),sK79)) ),
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(and(sK79,sK80),sK79))
| ~ necessitation
| is_a_theorem(necessarily(implies(and(sK79,sK80),sK79))) ),
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,
( ~ and_1
| is_a_theorem(implies(and(sK79,sK80),sK79)) ),
inference(extension,[status(thm),parent(t12:3)],[f_7_5]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t12:3]) ).
cnf(t18,plain,
and_1,
inference(extension,[status(thm),parent(t16:2)],[f_40_2]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL529+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.01 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.02 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Sat Sep 19 15:11:52 UTC 2026
% 0.04/0.31 % CPUTime :
% 1.04/1.36 % SZS status Theorem for theBenchmark
% 1.04/1.36 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------