%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : LCL540+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 : n005.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 3.55s 3.89s
% Output : Proof 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 52 ( 26 unt; 0 def)
% Number of atoms : 144 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 149 ( 57 ~; 57 |; 30 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 4 prp; 0-1 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn 30 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(modus_ponens,axiom,
( modus_ponens
<=> ! [X,Y] :
( ( is_a_theorem(implies(X,Y))
& is_a_theorem(X) )
=> is_a_theorem(Y) ) ),
file('LCL006+0.ax',modus_ponens) ).
fof(and_3,axiom,
( and_3
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
file('LCL006+0.ax',and_3) ).
fof(hilbert_modus_ponens,axiom,
modus_ponens,
file('LCL006+2.ax',hilbert_modus_ponens) ).
fof(hilbert_and_3,axiom,
and_3,
file('LCL006+2.ax',hilbert_and_3) ).
fof(adjunction,axiom,
( adjunction
<=> ! [X,Y] :
( ( is_a_theorem(Y)
& is_a_theorem(X) )
=> is_a_theorem(and(X,Y)) ) ),
file('LCL007+0.ax',adjunction) ).
fof(s1_0_adjunction,conjecture,
adjunction,
file('theBenchmark.p',s1_0_adjunction) ).
fof(f_1_1,plain,
( ( modus_ponens
| ? [X,Y] :
( ~ is_a_theorem(Y)
& is_a_theorem(implies(X,Y))
& is_a_theorem(X) ) )
& ( ! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X) )
| ~ modus_ponens ) ),
inference(fof_nnf,[status(thm)],[modus_ponens]) ).
fof(f_1_2,plain,
( ( modus_ponens
| ? [U_3,U_2] :
( ~ is_a_theorem(U_2)
& is_a_theorem(implies(U_3,U_2))
& is_a_theorem(U_3) ) )
& ( ! [U_1,U_0] :
( is_a_theorem(U_0)
| ~ is_a_theorem(implies(U_1,U_0))
| ~ is_a_theorem(U_1) )
| ~ modus_ponens ) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
( ( modus_ponens
| ? [U_2] :
( ~ is_a_theorem(U_2)
& is_a_theorem(implies(sK1,U_2))
& is_a_theorem(sK1) ) )
& ( ! [U_1,U_0] :
( is_a_theorem(U_0)
| ~ is_a_theorem(implies(U_1,U_0))
| ~ is_a_theorem(U_1) )
| ~ modus_ponens ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_3,sK1)],[f_1_2]) ).
fof(f_1_4,plain,
( ( modus_ponens
| ( ~ is_a_theorem(sK2)
& is_a_theorem(implies(sK1,sK2))
& is_a_theorem(sK1) ) )
& ( ! [U_1,U_0] :
( is_a_theorem(U_0)
| ~ is_a_theorem(implies(U_1,U_0))
| ~ is_a_theorem(U_1) )
| ~ modus_ponens ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_2,sK2)],[f_1_3]) ).
cnf(f_1_5,plain,
( is_a_theorem(U_0)
| ~ is_a_theorem(implies(U_1,U_0))
| ~ is_a_theorem(U_1)
| ~ modus_ponens ),
inference(clausify,[status(thm)],[f_1_4]) ).
fof(f_9_1,plain,
( ( and_3
| ? [X,Y] : ~ is_a_theorem(implies(X,implies(Y,and(X,Y)))) )
& ( ! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y))))
| ~ and_3 ) ),
inference(fof_nnf,[status(thm)],[and_3]) ).
fof(f_9_2,plain,
( ( and_3
| ? [U_37,U_36] : ~ is_a_theorem(implies(U_37,implies(U_36,and(U_37,U_36)))) )
& ( ! [U_35,U_34] : is_a_theorem(implies(U_35,implies(U_34,and(U_35,U_34))))
| ~ and_3 ) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
( ( and_3
| ? [U_36] : ~ is_a_theorem(implies(sK18,implies(U_36,and(sK18,U_36)))) )
& ( ! [U_35,U_34] : is_a_theorem(implies(U_35,implies(U_34,and(U_35,U_34))))
| ~ and_3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_37,sK18)],[f_9_2]) ).
fof(f_9_4,plain,
( ( and_3
| ~ is_a_theorem(implies(sK18,implies(sK19,and(sK18,sK19)))) )
& ( ! [U_35,U_34] : is_a_theorem(implies(U_35,implies(U_34,and(U_35,U_34))))
| ~ and_3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_36,sK19)],[f_9_3]) ).
cnf(f_9_5,plain,
( is_a_theorem(implies(U_35,implies(U_34,and(U_35,U_34))))
| ~ and_3 ),
inference(clausify,[status(thm)],[f_9_4]) ).
fof(f_35_1,plain,
modus_ponens,
inference(fof_nnf,[status(thm)],[hilbert_modus_ponens]) ).
cnf(f_35_2,plain,
modus_ponens,
inference(clausify,[status(thm)],[f_35_1]) ).
fof(f_42_1,plain,
and_3,
inference(fof_nnf,[status(thm)],[hilbert_and_3]) ).
cnf(f_42_2,plain,
and_3,
inference(clausify,[status(thm)],[f_42_1]) ).
fof(f_52_1,plain,
( ( adjunction
| ? [X,Y] :
( ~ is_a_theorem(and(X,Y))
& is_a_theorem(Y)
& is_a_theorem(X) ) )
& ( ! [X,Y] :
( is_a_theorem(and(X,Y))
| ~ is_a_theorem(Y)
| ~ is_a_theorem(X) )
| ~ adjunction ) ),
inference(fof_nnf,[status(thm)],[adjunction]) ).
fof(f_52_2,plain,
( ( adjunction
| ? [U_129,U_128] :
( ~ is_a_theorem(and(U_129,U_128))
& is_a_theorem(U_128)
& is_a_theorem(U_129) ) )
& ( ! [U_127,U_126] :
( is_a_theorem(and(U_127,U_126))
| ~ is_a_theorem(U_126)
| ~ is_a_theorem(U_127) )
| ~ adjunction ) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
fof(f_52_3,plain,
( ( adjunction
| ? [U_128] :
( ~ is_a_theorem(and(sK59,U_128))
& is_a_theorem(U_128)
& is_a_theorem(sK59) ) )
& ( ! [U_127,U_126] :
( is_a_theorem(and(U_127,U_126))
| ~ is_a_theorem(U_126)
| ~ is_a_theorem(U_127) )
| ~ adjunction ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_129,sK59)],[f_52_2]) ).
fof(f_52_4,plain,
( ( adjunction
| ( ~ is_a_theorem(and(sK59,sK60))
& is_a_theorem(sK60)
& is_a_theorem(sK59) ) )
& ( ! [U_127,U_126] :
( is_a_theorem(and(U_127,U_126))
| ~ is_a_theorem(U_126)
| ~ is_a_theorem(U_127) )
| ~ adjunction ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_128,sK60)],[f_52_3]) ).
cnf(f_52_6,plain,
( is_a_theorem(sK59)
| adjunction ),
inference(clausify,[status(thm)],[f_52_4]) ).
cnf(f_52_7,plain,
( is_a_theorem(sK60)
| adjunction ),
inference(clausify,[status(thm)],[f_52_4]) ).
cnf(f_52_8,plain,
( ~ is_a_theorem(and(sK59,sK60))
| adjunction ),
inference(clausify,[status(thm)],[f_52_4]) ).
fof(f_89_1,negated_conjecture,
~ adjunction,
inference(negate,[status(cth)],[s1_0_adjunction]) ).
fof(f_89_2,negated_conjecture,
~ adjunction,
inference(definitional_conversion,[status(esa)],[f_89_1]) ).
cnf(f_89_3,negated_conjecture,
~ adjunction,
inference(clausify,[status(thm)],[f_89_2]) ).
cnf(t1,plain,
~ adjunction,
inference(start,[status(thm),parent(0:0)],[f_89_3]) ).
cnf(t2,plain,
( is_a_theorem(sK59)
| adjunction ),
inference(extension,[status(thm),parent(t1:1)],[f_52_6]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( is_a_theorem(implies(sK60,and(sK59,sK60)))
| ~ is_a_theorem(implies(sK59,implies(sK60,and(sK59,sK60))))
| ~ modus_ponens
| ~ is_a_theorem(sK59) ),
inference(extension,[status(thm),parent(t2:2)],[f_1_5]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
modus_ponens,
inference(extension,[status(thm),parent(t4:2)],[f_35_2]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(l3,lemma,
modus_ponens,
inference(lemma,[status(cth),parent(t4:2),below(t2:2)],[t4:2]) ).
cnf(t8,plain,
( ~ and_3
| is_a_theorem(implies(sK59,implies(sK60,and(sK59,sK60)))) ),
inference(extension,[status(thm),parent(t4:3)],[f_9_5]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
and_3,
inference(extension,[status(thm),parent(t8:2)],[f_42_2]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( ~ is_a_theorem(sK60)
| is_a_theorem(and(sK59,sK60))
| ~ modus_ponens
| ~ is_a_theorem(implies(sK60,and(sK59,sK60))) ),
inference(extension,[status(thm),parent(t4:4)],[f_1_5]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t4:4]) ).
cnf(t14,plain,
modus_ponens,
inference(lemma_extension,[status(thm),parent(t12:2)],[l3:1]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
( adjunction
| ~ is_a_theorem(and(sK59,sK60)) ),
inference(extension,[status(thm),parent(t12:3)],[f_52_8]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t12:3]) ).
cnf(t18,plain,
$false,
inference(reduction,[status(thm),parent(t16:2)],[t16:2,t1:1]) ).
cnf(t19,plain,
( adjunction
| is_a_theorem(sK60) ),
inference(extension,[status(thm),parent(t12:4)],[f_52_7]) ).
cnf(t20,plain,
$false,
inference(connection,[status(thm),parent(t19:1)],[t19:1,t12:4]) ).
cnf(t21,plain,
$false,
inference(reduction,[status(thm),parent(t19:2)],[t19:2,t1:1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL540+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
% 0.07/0.35 % Computer : n005.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 19 15:12:48 UTC 2026
% 0.07/0.36 % CPUTime :
% 3.55/3.89 % SZS status Theorem for theBenchmark
% 3.55/3.89 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------