%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : LCL454+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 : 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 08:49:21 AM UTC 2026
% Result : Theorem 0.96s 1.20s
% Output : Proof 0.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 78 ( 40 unt; 0 def)
% Number of atoms : 182 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 177 ( 73 ~; 69 |; 29 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 7 ( 6 usr; 6 prp; 0-1 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 87 ( 1 sgn 52 !; 26 ?)
% 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(implies_1,axiom,
( implies_1
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,X))) ),
file('LCL006+0.ax',implies_1) ).
fof(implies_2,axiom,
( implies_2
<=> ! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
file('LCL006+0.ax',implies_2) ).
fof(or_3,axiom,
( or_3
<=> ! [X,Y,Z] : is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z)))) ),
file('LCL006+0.ax',or_3) ).
fof(r1,axiom,
( r1
<=> ! [P] : is_a_theorem(implies(or(P,P),P)) ),
file('LCL006+0.ax',r1) ).
fof(hilbert_modus_ponens,axiom,
modus_ponens,
file('LCL006+2.ax',hilbert_modus_ponens) ).
fof(hilbert_implies_1,axiom,
implies_1,
file('LCL006+2.ax',hilbert_implies_1) ).
fof(hilbert_implies_2,axiom,
implies_2,
file('LCL006+2.ax',hilbert_implies_2) ).
fof(hilbert_or_3,axiom,
or_3,
file('LCL006+2.ax',hilbert_or_3) ).
fof(principia_r1,conjecture,
r1,
file('theBenchmark.p',principia_r1) ).
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_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_5,plain,
( is_a_theorem(implies(U_13,implies(U_12,U_13)))
| ~ implies_1 ),
inference(clausify,[status(thm)],[f_4_4]) ).
fof(f_5_1,plain,
( ( implies_2
| ? [X,Y] : ~ is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) )
& ( ! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))
| ~ implies_2 ) ),
inference(fof_nnf,[status(thm)],[implies_2]) ).
fof(f_5_2,plain,
( ( implies_2
| ? [U_19,U_18] : ~ is_a_theorem(implies(implies(U_19,implies(U_19,U_18)),implies(U_19,U_18))) )
& ( ! [U_17,U_16] : is_a_theorem(implies(implies(U_17,implies(U_17,U_16)),implies(U_17,U_16)))
| ~ implies_2 ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ( implies_2
| ? [U_18] : ~ is_a_theorem(implies(implies(sK9,implies(sK9,U_18)),implies(sK9,U_18))) )
& ( ! [U_17,U_16] : is_a_theorem(implies(implies(U_17,implies(U_17,U_16)),implies(U_17,U_16)))
| ~ implies_2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_19,sK9)],[f_5_2]) ).
fof(f_5_4,plain,
( ( implies_2
| ~ is_a_theorem(implies(implies(sK9,implies(sK9,sK10)),implies(sK9,sK10))) )
& ( ! [U_17,U_16] : is_a_theorem(implies(implies(U_17,implies(U_17,U_16)),implies(U_17,U_16)))
| ~ implies_2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_18,sK10)],[f_5_3]) ).
cnf(f_5_5,plain,
( is_a_theorem(implies(implies(U_17,implies(U_17,U_16)),implies(U_17,U_16)))
| ~ implies_2 ),
inference(clausify,[status(thm)],[f_5_4]) ).
fof(f_12_1,plain,
( ( or_3
| ? [X,Y,Z] : ~ is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z)))) )
& ( ! [X,Y,Z] : is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))
| ~ or_3 ) ),
inference(fof_nnf,[status(thm)],[or_3]) ).
fof(f_12_2,plain,
( ( or_3
| ? [U_51,U_50,U_49] : ~ is_a_theorem(implies(implies(U_51,U_49),implies(implies(U_50,U_49),implies(or(U_51,U_50),U_49)))) )
& ( ! [U_48,U_47,U_46] : is_a_theorem(implies(implies(U_48,U_46),implies(implies(U_47,U_46),implies(or(U_48,U_47),U_46))))
| ~ or_3 ) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
( ( or_3
| ? [U_50,U_49] : ~ is_a_theorem(implies(implies(sK24,U_49),implies(implies(U_50,U_49),implies(or(sK24,U_50),U_49)))) )
& ( ! [U_48,U_47,U_46] : is_a_theorem(implies(implies(U_48,U_46),implies(implies(U_47,U_46),implies(or(U_48,U_47),U_46))))
| ~ or_3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_51,sK24)],[f_12_2]) ).
fof(f_12_4,plain,
( ( or_3
| ? [U_49] : ~ is_a_theorem(implies(implies(sK24,U_49),implies(implies(sK25,U_49),implies(or(sK24,sK25),U_49)))) )
& ( ! [U_48,U_47,U_46] : is_a_theorem(implies(implies(U_48,U_46),implies(implies(U_47,U_46),implies(or(U_48,U_47),U_46))))
| ~ or_3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_50,sK25)],[f_12_3]) ).
fof(f_12_5,plain,
( ( or_3
| ~ is_a_theorem(implies(implies(sK24,sK26),implies(implies(sK25,sK26),implies(or(sK24,sK25),sK26)))) )
& ( ! [U_48,U_47,U_46] : is_a_theorem(implies(implies(U_48,U_46),implies(implies(U_47,U_46),implies(or(U_48,U_47),U_46))))
| ~ or_3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_49,sK26)],[f_12_4]) ).
cnf(f_12_6,plain,
( is_a_theorem(implies(implies(U_48,U_46),implies(implies(U_47,U_46),implies(or(U_48,U_47),U_46))))
| ~ or_3 ),
inference(clausify,[status(thm)],[f_12_5]) ).
fof(f_22_1,plain,
( ( r1
| ? [P] : ~ is_a_theorem(implies(or(P,P),P)) )
& ( ! [P] : is_a_theorem(implies(or(P,P),P))
| ~ r1 ) ),
inference(fof_nnf,[status(thm)],[r1]) ).
fof(f_22_2,plain,
( ( r1
| ? [U_89] : ~ is_a_theorem(implies(or(U_89,U_89),U_89)) )
& ( ! [U_88] : is_a_theorem(implies(or(U_88,U_88),U_88))
| ~ r1 ) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
( ( r1
| ~ is_a_theorem(implies(or(sK45,sK45),sK45)) )
& ( ! [U_88] : is_a_theorem(implies(or(U_88,U_88),U_88))
| ~ r1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_89,sK45)],[f_22_2]) ).
cnf(f_22_5,plain,
( r1
| ~ is_a_theorem(implies(or(sK45,sK45),sK45)) ),
inference(clausify,[status(thm)],[f_22_3]) ).
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_37_1,plain,
implies_1,
inference(fof_nnf,[status(thm)],[hilbert_implies_1]) ).
cnf(f_37_2,plain,
implies_1,
inference(clausify,[status(thm)],[f_37_1]) ).
fof(f_38_1,plain,
implies_2,
inference(fof_nnf,[status(thm)],[hilbert_implies_2]) ).
cnf(f_38_2,plain,
implies_2,
inference(clausify,[status(thm)],[f_38_1]) ).
fof(f_45_1,plain,
or_3,
inference(fof_nnf,[status(thm)],[hilbert_or_3]) ).
cnf(f_45_2,plain,
or_3,
inference(clausify,[status(thm)],[f_45_1]) ).
fof(f_53_1,negated_conjecture,
~ r1,
inference(negate,[status(cth)],[principia_r1]) ).
fof(f_53_2,negated_conjecture,
~ r1,
inference(definitional_conversion,[status(esa)],[f_53_1]) ).
cnf(f_53_3,negated_conjecture,
~ r1,
inference(clausify,[status(thm)],[f_53_2]) ).
cnf(t1,plain,
~ r1,
inference(start,[status(thm),parent(0:0)],[f_53_3]) ).
cnf(t2,plain,
( ~ is_a_theorem(implies(or(sK45,sK45),sK45))
| r1 ),
inference(extension,[status(thm),parent(t1:1)],[f_22_5]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ is_a_theorem(implies(sK45,sK45))
| ~ is_a_theorem(implies(implies(sK45,sK45),implies(or(sK45,sK45),sK45)))
| ~ modus_ponens
| is_a_theorem(implies(or(sK45,sK45),sK45)) ),
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,
( ~ is_a_theorem(implies(implies(sK45,sK45),implies(implies(sK45,sK45),implies(or(sK45,sK45),sK45))))
| ~ is_a_theorem(implies(implies(implies(sK45,sK45),implies(implies(sK45,sK45),implies(or(sK45,sK45),sK45))),implies(implies(sK45,sK45),implies(or(sK45,sK45),sK45))))
| ~ modus_ponens
| is_a_theorem(implies(implies(sK45,sK45),implies(or(sK45,sK45),sK45))) ),
inference(extension,[status(thm),parent(t4:3)],[f_1_5]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
modus_ponens,
inference(lemma_extension,[status(thm),parent(t8:2)],[l3:1]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( ~ implies_2
| is_a_theorem(implies(implies(implies(sK45,sK45),implies(implies(sK45,sK45),implies(or(sK45,sK45),sK45))),implies(implies(sK45,sK45),implies(or(sK45,sK45),sK45)))) ),
inference(extension,[status(thm),parent(t8:3)],[f_5_5]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
cnf(t14,plain,
implies_2,
inference(extension,[status(thm),parent(t12:2)],[f_38_2]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
( ~ or_3
| is_a_theorem(implies(implies(sK45,sK45),implies(implies(sK45,sK45),implies(or(sK45,sK45),sK45)))) ),
inference(extension,[status(thm),parent(t8:4)],[f_12_6]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t8:4]) ).
cnf(t18,plain,
or_3,
inference(extension,[status(thm),parent(t16:2)],[f_45_2]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
( ~ is_a_theorem(implies(sK45,implies(sK45,sK45)))
| ~ is_a_theorem(implies(implies(sK45,implies(sK45,sK45)),implies(sK45,sK45)))
| ~ modus_ponens
| is_a_theorem(implies(sK45,sK45)) ),
inference(extension,[status(thm),parent(t4:4)],[f_1_5]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t4:4]) ).
cnf(t22,plain,
modus_ponens,
inference(lemma_extension,[status(thm),parent(t20:2)],[l3:1]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
( ~ implies_2
| is_a_theorem(implies(implies(sK45,implies(sK45,sK45)),implies(sK45,sK45))) ),
inference(extension,[status(thm),parent(t20:3)],[f_5_5]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t20:3]) ).
cnf(t26,plain,
implies_2,
inference(extension,[status(thm),parent(t24:2)],[f_38_2]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
( ~ implies_1
| is_a_theorem(implies(sK45,implies(sK45,sK45))) ),
inference(extension,[status(thm),parent(t20:4)],[f_4_5]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t20:4]) ).
cnf(t30,plain,
implies_1,
inference(extension,[status(thm),parent(t28:2)],[f_37_2]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL454+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
% 0.11/0.37 % Computer : n014.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 19 15:05:20 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.96/1.20 % SZS status Theorem for theBenchmark
% 0.96/1.20 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------