%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : LCL506+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 : n010.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 08:49:26 AM UTC 2026
% Result : Theorem 0.14s 0.42s
% Output : Proof 0.14s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% 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(substitution_of_equivalents,axiom,
( substitution_of_equivalents
<=> ! [X,Y] :
( is_a_theorem(equiv(X,Y))
=> X = Y ) ),
file('LCL006+0.ax',substitution_of_equivalents) ).
fof(modus_tollens,axiom,
( modus_tollens
<=> ! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),
file('LCL006+0.ax',modus_tollens) ).
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(implies_3,axiom,
( implies_3
<=> ! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) ),
file('LCL006+0.ax',implies_3) ).
fof(and_1,axiom,
( and_1
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),X)) ),
file('LCL006+0.ax',and_1) ).
fof(and_2,axiom,
( and_2
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),Y)) ),
file('LCL006+0.ax',and_2) ).
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(or_1,axiom,
( or_1
<=> ! [X,Y] : is_a_theorem(implies(X,or(X,Y))) ),
file('LCL006+0.ax',or_1) ).
fof(or_2,axiom,
( or_2
<=> ! [X,Y] : is_a_theorem(implies(Y,or(X,Y))) ),
file('LCL006+0.ax',or_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(equivalence_1,axiom,
( equivalence_1
<=> ! [X,Y] : is_a_theorem(implies(equiv(X,Y),implies(X,Y))) ),
file('LCL006+0.ax',equivalence_1) ).
fof(equivalence_2,axiom,
( equivalence_2
<=> ! [X,Y] : is_a_theorem(implies(equiv(X,Y),implies(Y,X))) ),
file('LCL006+0.ax',equivalence_2) ).
fof(equivalence_3,axiom,
( equivalence_3
<=> ! [X,Y] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y)))) ),
file('LCL006+0.ax',equivalence_3) ).
fof(kn1,axiom,
( kn1
<=> ! [P] : is_a_theorem(implies(P,and(P,P))) ),
file('LCL006+0.ax',kn1) ).
fof(kn2,axiom,
( kn2
<=> ! [P,Q] : is_a_theorem(implies(and(P,Q),P)) ),
file('LCL006+0.ax',kn2) ).
fof(kn3,axiom,
( kn3
<=> ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) ),
file('LCL006+0.ax',kn3) ).
fof(cn1,axiom,
( cn1
<=> ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R)))) ),
file('LCL006+0.ax',cn1) ).
fof(cn2,axiom,
( cn2
<=> ! [P,Q] : is_a_theorem(implies(P,implies(not(P),Q))) ),
file('LCL006+0.ax',cn2) ).
fof(cn3,axiom,
( cn3
<=> ! [P] : is_a_theorem(implies(implies(not(P),P),P)) ),
file('LCL006+0.ax',cn3) ).
fof(r1,axiom,
( r1
<=> ! [P] : is_a_theorem(implies(or(P,P),P)) ),
file('LCL006+0.ax',r1) ).
fof(r2,axiom,
( r2
<=> ! [P,Q] : is_a_theorem(implies(Q,or(P,Q))) ),
file('LCL006+0.ax',r2) ).
fof(r3,axiom,
( r3
<=> ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) ),
file('LCL006+0.ax',r3) ).
fof(r4,axiom,
( r4
<=> ! [P,Q,R] : is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) ),
file('LCL006+0.ax',r4) ).
fof(r5,axiom,
( r5
<=> ! [P,Q,R] : is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ),
file('LCL006+0.ax',r5) ).
fof(op_or,axiom,
( op_or
=> ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
file('LCL006+1.ax',op_or) ).
fof(op_and,axiom,
( op_and
=> ! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) ),
file('LCL006+1.ax',op_and) ).
fof(op_implies_and,axiom,
( op_implies_and
=> ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ),
file('LCL006+1.ax',op_implies_and) ).
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(op_equiv,axiom,
( op_equiv
=> ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
file('LCL006+1.ax',op_equiv) ).
fof(rosser_op_or,axiom,
op_or,
file('LCL006+5.ax',rosser_op_or) ).
fof(rosser_op_implies_and,axiom,
op_implies_and,
file('LCL006+5.ax',rosser_op_implies_and) ).
fof(rosser_op_equiv,axiom,
op_equiv,
file('LCL006+5.ax',rosser_op_equiv) ).
fof(rosser_modus_ponens,axiom,
modus_ponens,
file('LCL006+5.ax',rosser_modus_ponens) ).
fof(rosser_kn1,axiom,
kn1,
file('LCL006+5.ax',rosser_kn1) ).
fof(rosser_kn2,axiom,
kn2,
file('LCL006+5.ax',rosser_kn2) ).
fof(rosser_kn3,axiom,
kn3,
file('LCL006+5.ax',rosser_kn3) ).
fof(use_substitution_of_equivalents,axiom,
substitution_of_equivalents,
file('LCL006+5.ax',use_substitution_of_equivalents) ).
fof(hilbert_op_or,axiom,
op_or,
file('theBenchmark.p',hilbert_op_or) ).
fof(hilbert_op_implies_and,axiom,
op_implies_and,
file('theBenchmark.p',hilbert_op_implies_and) ).
fof(hilbert_op_equiv,axiom,
op_equiv,
file('theBenchmark.p',hilbert_op_equiv) ).
fof(hilbert_and_1,conjecture,
and_1,
file('theBenchmark.p',hilbert_and_1) ).
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]) ).
cnf(f_1_6,plain,
( is_a_theorem(sK1)
| modus_ponens ),
inference(clausify,[status(thm)],[f_1_4]) ).
cnf(f_1_7,plain,
( is_a_theorem(implies(sK1,sK2))
| modus_ponens ),
inference(clausify,[status(thm)],[f_1_4]) ).
cnf(f_1_8,plain,
( ~ is_a_theorem(sK2)
| modus_ponens ),
inference(clausify,[status(thm)],[f_1_4]) ).
fof(f_2_1,plain,
( ( substitution_of_equivalents
| ? [X,Y] :
( X != Y
& is_a_theorem(equiv(X,Y)) ) )
& ( ! [X,Y] :
( X = Y
| ~ is_a_theorem(equiv(X,Y)) )
| ~ substitution_of_equivalents ) ),
inference(fof_nnf,[status(thm)],[substitution_of_equivalents]) ).
fof(f_2_2,plain,
( ( substitution_of_equivalents
| ? [U_7,U_6] :
( U_7 != U_6
& is_a_theorem(equiv(U_7,U_6)) ) )
& ( ! [U_5,U_4] :
( U_5 = U_4
| ~ is_a_theorem(equiv(U_5,U_4)) )
| ~ substitution_of_equivalents ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ( substitution_of_equivalents
| ? [U_6] :
( sK3 != U_6
& is_a_theorem(equiv(sK3,U_6)) ) )
& ( ! [U_5,U_4] :
( U_5 = U_4
| ~ is_a_theorem(equiv(U_5,U_4)) )
| ~ substitution_of_equivalents ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_7,sK3)],[f_2_2]) ).
fof(f_2_4,plain,
( ( substitution_of_equivalents
| ( sK3 != sK4
& is_a_theorem(equiv(sK3,sK4)) ) )
& ( ! [U_5,U_4] :
( U_5 = U_4
| ~ is_a_theorem(equiv(U_5,U_4)) )
| ~ substitution_of_equivalents ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_6,sK4)],[f_2_3]) ).
cnf(f_2_5,plain,
( U_5 = U_4
| ~ is_a_theorem(equiv(U_5,U_4))
| ~ substitution_of_equivalents ),
inference(clausify,[status(thm)],[f_2_4]) ).
cnf(f_2_6,plain,
( is_a_theorem(equiv(sK3,sK4))
| substitution_of_equivalents ),
inference(clausify,[status(thm)],[f_2_4]) ).
cnf(f_2_7,plain,
( sK3 != sK4
| substitution_of_equivalents ),
inference(clausify,[status(thm)],[f_2_4]) ).
fof(f_3_1,plain,
( ( modus_tollens
| ? [X,Y] : ~ is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) )
& ( ! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))
| ~ modus_tollens ) ),
inference(fof_nnf,[status(thm)],[modus_tollens]) ).
fof(f_3_2,plain,
( ( modus_tollens
| ? [U_11,U_10] : ~ is_a_theorem(implies(implies(not(U_10),not(U_11)),implies(U_11,U_10))) )
& ( ! [U_9,U_8] : is_a_theorem(implies(implies(not(U_8),not(U_9)),implies(U_9,U_8)))
| ~ modus_tollens ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ( modus_tollens
| ? [U_10] : ~ is_a_theorem(implies(implies(not(U_10),not(sK5)),implies(sK5,U_10))) )
& ( ! [U_9,U_8] : is_a_theorem(implies(implies(not(U_8),not(U_9)),implies(U_9,U_8)))
| ~ modus_tollens ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_11,sK5)],[f_3_2]) ).
fof(f_3_4,plain,
( ( modus_tollens
| ~ is_a_theorem(implies(implies(not(sK6),not(sK5)),implies(sK5,sK6))) )
& ( ! [U_9,U_8] : is_a_theorem(implies(implies(not(U_8),not(U_9)),implies(U_9,U_8)))
| ~ modus_tollens ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_10,sK6)],[f_3_3]) ).
cnf(f_3_5,plain,
( is_a_theorem(implies(implies(not(U_8),not(U_9)),implies(U_9,U_8)))
| ~ modus_tollens ),
inference(clausify,[status(thm)],[f_3_4]) ).
cnf(f_3_6,plain,
( modus_tollens
| ~ is_a_theorem(implies(implies(not(sK6),not(sK5)),implies(sK5,sK6))) ),
inference(clausify,[status(thm)],[f_3_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]) ).
cnf(f_4_6,plain,
( implies_1
| ~ is_a_theorem(implies(sK7,implies(sK8,sK7))) ),
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]) ).
cnf(f_5_6,plain,
( implies_2
| ~ is_a_theorem(implies(implies(sK9,implies(sK9,sK10)),implies(sK9,sK10))) ),
inference(clausify,[status(thm)],[f_5_4]) ).
fof(f_6_1,plain,
( ( implies_3
| ? [X,Y,Z] : ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )
& ( ! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| ~ implies_3 ) ),
inference(fof_nnf,[status(thm)],[implies_3]) ).
fof(f_6_2,plain,
( ( implies_3
| ? [U_25,U_24,U_23] : ~ is_a_theorem(implies(implies(U_25,U_24),implies(implies(U_24,U_23),implies(U_25,U_23)))) )
& ( ! [U_22,U_21,U_20] : is_a_theorem(implies(implies(U_22,U_21),implies(implies(U_21,U_20),implies(U_22,U_20))))
| ~ implies_3 ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ( implies_3
| ? [U_24,U_23] : ~ is_a_theorem(implies(implies(sK11,U_24),implies(implies(U_24,U_23),implies(sK11,U_23)))) )
& ( ! [U_22,U_21,U_20] : is_a_theorem(implies(implies(U_22,U_21),implies(implies(U_21,U_20),implies(U_22,U_20))))
| ~ implies_3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_25,sK11)],[f_6_2]) ).
fof(f_6_4,plain,
( ( implies_3
| ? [U_23] : ~ is_a_theorem(implies(implies(sK11,sK12),implies(implies(sK12,U_23),implies(sK11,U_23)))) )
& ( ! [U_22,U_21,U_20] : is_a_theorem(implies(implies(U_22,U_21),implies(implies(U_21,U_20),implies(U_22,U_20))))
| ~ implies_3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_24,sK12)],[f_6_3]) ).
fof(f_6_5,plain,
( ( implies_3
| ~ is_a_theorem(implies(implies(sK11,sK12),implies(implies(sK12,sK13),implies(sK11,sK13)))) )
& ( ! [U_22,U_21,U_20] : is_a_theorem(implies(implies(U_22,U_21),implies(implies(U_21,U_20),implies(U_22,U_20))))
| ~ implies_3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_23,sK13)],[f_6_4]) ).
cnf(f_6_6,plain,
( is_a_theorem(implies(implies(U_22,U_21),implies(implies(U_21,U_20),implies(U_22,U_20))))
| ~ implies_3 ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_7,plain,
( implies_3
| ~ is_a_theorem(implies(implies(sK11,sK12),implies(implies(sK12,sK13),implies(sK11,sK13)))) ),
inference(clausify,[status(thm)],[f_6_5]) ).
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]) ).
cnf(f_7_6,plain,
( and_1
| ~ is_a_theorem(implies(and(sK14,sK15),sK14)) ),
inference(clausify,[status(thm)],[f_7_4]) ).
fof(f_8_1,plain,
( ( and_2
| ? [X,Y] : ~ is_a_theorem(implies(and(X,Y),Y)) )
& ( ! [X,Y] : is_a_theorem(implies(and(X,Y),Y))
| ~ and_2 ) ),
inference(fof_nnf,[status(thm)],[and_2]) ).
fof(f_8_2,plain,
( ( and_2
| ? [U_33,U_32] : ~ is_a_theorem(implies(and(U_33,U_32),U_32)) )
& ( ! [U_31,U_30] : is_a_theorem(implies(and(U_31,U_30),U_30))
| ~ and_2 ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ( and_2
| ? [U_32] : ~ is_a_theorem(implies(and(sK16,U_32),U_32)) )
& ( ! [U_31,U_30] : is_a_theorem(implies(and(U_31,U_30),U_30))
| ~ and_2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_33,sK16)],[f_8_2]) ).
fof(f_8_4,plain,
( ( and_2
| ~ is_a_theorem(implies(and(sK16,sK17),sK17)) )
& ( ! [U_31,U_30] : is_a_theorem(implies(and(U_31,U_30),U_30))
| ~ and_2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_32,sK17)],[f_8_3]) ).
cnf(f_8_5,plain,
( is_a_theorem(implies(and(U_31,U_30),U_30))
| ~ and_2 ),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(f_8_6,plain,
( and_2
| ~ is_a_theorem(implies(and(sK16,sK17),sK17)) ),
inference(clausify,[status(thm)],[f_8_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]) ).
cnf(f_9_6,plain,
( and_3
| ~ is_a_theorem(implies(sK18,implies(sK19,and(sK18,sK19)))) ),
inference(clausify,[status(thm)],[f_9_4]) ).
fof(f_10_1,plain,
( ( or_1
| ? [X,Y] : ~ is_a_theorem(implies(X,or(X,Y))) )
& ( ! [X,Y] : is_a_theorem(implies(X,or(X,Y)))
| ~ or_1 ) ),
inference(fof_nnf,[status(thm)],[or_1]) ).
fof(f_10_2,plain,
( ( or_1
| ? [U_41,U_40] : ~ is_a_theorem(implies(U_41,or(U_41,U_40))) )
& ( ! [U_39,U_38] : is_a_theorem(implies(U_39,or(U_39,U_38)))
| ~ or_1 ) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
( ( or_1
| ? [U_40] : ~ is_a_theorem(implies(sK20,or(sK20,U_40))) )
& ( ! [U_39,U_38] : is_a_theorem(implies(U_39,or(U_39,U_38)))
| ~ or_1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_41,sK20)],[f_10_2]) ).
fof(f_10_4,plain,
( ( or_1
| ~ is_a_theorem(implies(sK20,or(sK20,sK21))) )
& ( ! [U_39,U_38] : is_a_theorem(implies(U_39,or(U_39,U_38)))
| ~ or_1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_40,sK21)],[f_10_3]) ).
cnf(f_10_5,plain,
( is_a_theorem(implies(U_39,or(U_39,U_38)))
| ~ or_1 ),
inference(clausify,[status(thm)],[f_10_4]) ).
cnf(f_10_6,plain,
( or_1
| ~ is_a_theorem(implies(sK20,or(sK20,sK21))) ),
inference(clausify,[status(thm)],[f_10_4]) ).
fof(f_11_1,plain,
( ( or_2
| ? [X,Y] : ~ is_a_theorem(implies(Y,or(X,Y))) )
& ( ! [X,Y] : is_a_theorem(implies(Y,or(X,Y)))
| ~ or_2 ) ),
inference(fof_nnf,[status(thm)],[or_2]) ).
fof(f_11_2,plain,
( ( or_2
| ? [U_45,U_44] : ~ is_a_theorem(implies(U_44,or(U_45,U_44))) )
& ( ! [U_43,U_42] : is_a_theorem(implies(U_42,or(U_43,U_42)))
| ~ or_2 ) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
( ( or_2
| ? [U_44] : ~ is_a_theorem(implies(U_44,or(sK22,U_44))) )
& ( ! [U_43,U_42] : is_a_theorem(implies(U_42,or(U_43,U_42)))
| ~ or_2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_45,sK22)],[f_11_2]) ).
fof(f_11_4,plain,
( ( or_2
| ~ is_a_theorem(implies(sK23,or(sK22,sK23))) )
& ( ! [U_43,U_42] : is_a_theorem(implies(U_42,or(U_43,U_42)))
| ~ or_2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_44,sK23)],[f_11_3]) ).
cnf(f_11_5,plain,
( is_a_theorem(implies(U_42,or(U_43,U_42)))
| ~ or_2 ),
inference(clausify,[status(thm)],[f_11_4]) ).
cnf(f_11_6,plain,
( or_2
| ~ is_a_theorem(implies(sK23,or(sK22,sK23))) ),
inference(clausify,[status(thm)],[f_11_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]) ).
cnf(f_12_7,plain,
( or_3
| ~ is_a_theorem(implies(implies(sK24,sK26),implies(implies(sK25,sK26),implies(or(sK24,sK25),sK26)))) ),
inference(clausify,[status(thm)],[f_12_5]) ).
fof(f_13_1,plain,
( ( equivalence_1
| ? [X,Y] : ~ is_a_theorem(implies(equiv(X,Y),implies(X,Y))) )
& ( ! [X,Y] : is_a_theorem(implies(equiv(X,Y),implies(X,Y)))
| ~ equivalence_1 ) ),
inference(fof_nnf,[status(thm)],[equivalence_1]) ).
fof(f_13_2,plain,
( ( equivalence_1
| ? [U_55,U_54] : ~ is_a_theorem(implies(equiv(U_55,U_54),implies(U_55,U_54))) )
& ( ! [U_53,U_52] : is_a_theorem(implies(equiv(U_53,U_52),implies(U_53,U_52)))
| ~ equivalence_1 ) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
( ( equivalence_1
| ? [U_54] : ~ is_a_theorem(implies(equiv(sK27,U_54),implies(sK27,U_54))) )
& ( ! [U_53,U_52] : is_a_theorem(implies(equiv(U_53,U_52),implies(U_53,U_52)))
| ~ equivalence_1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_55,sK27)],[f_13_2]) ).
fof(f_13_4,plain,
( ( equivalence_1
| ~ is_a_theorem(implies(equiv(sK27,sK28),implies(sK27,sK28))) )
& ( ! [U_53,U_52] : is_a_theorem(implies(equiv(U_53,U_52),implies(U_53,U_52)))
| ~ equivalence_1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_54,sK28)],[f_13_3]) ).
cnf(f_13_5,plain,
( is_a_theorem(implies(equiv(U_53,U_52),implies(U_53,U_52)))
| ~ equivalence_1 ),
inference(clausify,[status(thm)],[f_13_4]) ).
cnf(f_13_6,plain,
( equivalence_1
| ~ is_a_theorem(implies(equiv(sK27,sK28),implies(sK27,sK28))) ),
inference(clausify,[status(thm)],[f_13_4]) ).
fof(f_14_1,plain,
( ( equivalence_2
| ? [X,Y] : ~ is_a_theorem(implies(equiv(X,Y),implies(Y,X))) )
& ( ! [X,Y] : is_a_theorem(implies(equiv(X,Y),implies(Y,X)))
| ~ equivalence_2 ) ),
inference(fof_nnf,[status(thm)],[equivalence_2]) ).
fof(f_14_2,plain,
( ( equivalence_2
| ? [U_59,U_58] : ~ is_a_theorem(implies(equiv(U_59,U_58),implies(U_58,U_59))) )
& ( ! [U_57,U_56] : is_a_theorem(implies(equiv(U_57,U_56),implies(U_56,U_57)))
| ~ equivalence_2 ) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
( ( equivalence_2
| ? [U_58] : ~ is_a_theorem(implies(equiv(sK29,U_58),implies(U_58,sK29))) )
& ( ! [U_57,U_56] : is_a_theorem(implies(equiv(U_57,U_56),implies(U_56,U_57)))
| ~ equivalence_2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_59,sK29)],[f_14_2]) ).
fof(f_14_4,plain,
( ( equivalence_2
| ~ is_a_theorem(implies(equiv(sK29,sK30),implies(sK30,sK29))) )
& ( ! [U_57,U_56] : is_a_theorem(implies(equiv(U_57,U_56),implies(U_56,U_57)))
| ~ equivalence_2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_58,sK30)],[f_14_3]) ).
cnf(f_14_5,plain,
( is_a_theorem(implies(equiv(U_57,U_56),implies(U_56,U_57)))
| ~ equivalence_2 ),
inference(clausify,[status(thm)],[f_14_4]) ).
cnf(f_14_6,plain,
( equivalence_2
| ~ is_a_theorem(implies(equiv(sK29,sK30),implies(sK30,sK29))) ),
inference(clausify,[status(thm)],[f_14_4]) ).
fof(f_15_1,plain,
( ( equivalence_3
| ? [X,Y] : ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y)))) )
& ( ! [X,Y] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))
| ~ equivalence_3 ) ),
inference(fof_nnf,[status(thm)],[equivalence_3]) ).
fof(f_15_2,plain,
( ( equivalence_3
| ? [U_63,U_62] : ~ is_a_theorem(implies(implies(U_63,U_62),implies(implies(U_62,U_63),equiv(U_63,U_62)))) )
& ( ! [U_61,U_60] : is_a_theorem(implies(implies(U_61,U_60),implies(implies(U_60,U_61),equiv(U_61,U_60))))
| ~ equivalence_3 ) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
( ( equivalence_3
| ? [U_62] : ~ is_a_theorem(implies(implies(sK31,U_62),implies(implies(U_62,sK31),equiv(sK31,U_62)))) )
& ( ! [U_61,U_60] : is_a_theorem(implies(implies(U_61,U_60),implies(implies(U_60,U_61),equiv(U_61,U_60))))
| ~ equivalence_3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_63,sK31)],[f_15_2]) ).
fof(f_15_4,plain,
( ( equivalence_3
| ~ is_a_theorem(implies(implies(sK31,sK32),implies(implies(sK32,sK31),equiv(sK31,sK32)))) )
& ( ! [U_61,U_60] : is_a_theorem(implies(implies(U_61,U_60),implies(implies(U_60,U_61),equiv(U_61,U_60))))
| ~ equivalence_3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_62,sK32)],[f_15_3]) ).
cnf(f_15_5,plain,
( is_a_theorem(implies(implies(U_61,U_60),implies(implies(U_60,U_61),equiv(U_61,U_60))))
| ~ equivalence_3 ),
inference(clausify,[status(thm)],[f_15_4]) ).
cnf(f_15_6,plain,
( equivalence_3
| ~ is_a_theorem(implies(implies(sK31,sK32),implies(implies(sK32,sK31),equiv(sK31,sK32)))) ),
inference(clausify,[status(thm)],[f_15_4]) ).
fof(f_16_1,plain,
( ( kn1
| ? [P] : ~ is_a_theorem(implies(P,and(P,P))) )
& ( ! [P] : is_a_theorem(implies(P,and(P,P)))
| ~ kn1 ) ),
inference(fof_nnf,[status(thm)],[kn1]) ).
fof(f_16_2,plain,
( ( kn1
| ? [U_65] : ~ is_a_theorem(implies(U_65,and(U_65,U_65))) )
& ( ! [U_64] : is_a_theorem(implies(U_64,and(U_64,U_64)))
| ~ kn1 ) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
( ( kn1
| ~ is_a_theorem(implies(sK33,and(sK33,sK33))) )
& ( ! [U_64] : is_a_theorem(implies(U_64,and(U_64,U_64)))
| ~ kn1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_65,sK33)],[f_16_2]) ).
cnf(f_16_4,plain,
( is_a_theorem(implies(U_64,and(U_64,U_64)))
| ~ kn1 ),
inference(clausify,[status(thm)],[f_16_3]) ).
cnf(f_16_5,plain,
( kn1
| ~ is_a_theorem(implies(sK33,and(sK33,sK33))) ),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
( ( kn2
| ? [P,Q] : ~ is_a_theorem(implies(and(P,Q),P)) )
& ( ! [P,Q] : is_a_theorem(implies(and(P,Q),P))
| ~ kn2 ) ),
inference(fof_nnf,[status(thm)],[kn2]) ).
fof(f_17_2,plain,
( ( kn2
| ? [U_69,U_68] : ~ is_a_theorem(implies(and(U_69,U_68),U_69)) )
& ( ! [U_67,U_66] : is_a_theorem(implies(and(U_67,U_66),U_67))
| ~ kn2 ) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
( ( kn2
| ? [U_68] : ~ is_a_theorem(implies(and(sK34,U_68),sK34)) )
& ( ! [U_67,U_66] : is_a_theorem(implies(and(U_67,U_66),U_67))
| ~ kn2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_69,sK34)],[f_17_2]) ).
fof(f_17_4,plain,
( ( kn2
| ~ is_a_theorem(implies(and(sK34,sK35),sK34)) )
& ( ! [U_67,U_66] : is_a_theorem(implies(and(U_67,U_66),U_67))
| ~ kn2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_68,sK35)],[f_17_3]) ).
cnf(f_17_5,plain,
( is_a_theorem(implies(and(U_67,U_66),U_67))
| ~ kn2 ),
inference(clausify,[status(thm)],[f_17_4]) ).
cnf(f_17_6,plain,
( kn2
| ~ is_a_theorem(implies(and(sK34,sK35),sK34)) ),
inference(clausify,[status(thm)],[f_17_4]) ).
fof(f_18_1,plain,
( ( kn3
| ? [P,Q,R] : ~ is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) )
& ( ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))
| ~ kn3 ) ),
inference(fof_nnf,[status(thm)],[kn3]) ).
fof(f_18_2,plain,
( ( kn3
| ? [U_75,U_74,U_73] : ~ is_a_theorem(implies(implies(U_75,U_74),implies(not(and(U_74,U_73)),not(and(U_73,U_75))))) )
& ( ! [U_72,U_71,U_70] : is_a_theorem(implies(implies(U_72,U_71),implies(not(and(U_71,U_70)),not(and(U_70,U_72)))))
| ~ kn3 ) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
( ( kn3
| ? [U_74,U_73] : ~ is_a_theorem(implies(implies(sK36,U_74),implies(not(and(U_74,U_73)),not(and(U_73,sK36))))) )
& ( ! [U_72,U_71,U_70] : is_a_theorem(implies(implies(U_72,U_71),implies(not(and(U_71,U_70)),not(and(U_70,U_72)))))
| ~ kn3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_75,sK36)],[f_18_2]) ).
fof(f_18_4,plain,
( ( kn3
| ? [U_73] : ~ is_a_theorem(implies(implies(sK36,sK37),implies(not(and(sK37,U_73)),not(and(U_73,sK36))))) )
& ( ! [U_72,U_71,U_70] : is_a_theorem(implies(implies(U_72,U_71),implies(not(and(U_71,U_70)),not(and(U_70,U_72)))))
| ~ kn3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_74,sK37)],[f_18_3]) ).
fof(f_18_5,plain,
( ( kn3
| ~ is_a_theorem(implies(implies(sK36,sK37),implies(not(and(sK37,sK38)),not(and(sK38,sK36))))) )
& ( ! [U_72,U_71,U_70] : is_a_theorem(implies(implies(U_72,U_71),implies(not(and(U_71,U_70)),not(and(U_70,U_72)))))
| ~ kn3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_73,sK38)],[f_18_4]) ).
cnf(f_18_6,plain,
( is_a_theorem(implies(implies(U_72,U_71),implies(not(and(U_71,U_70)),not(and(U_70,U_72)))))
| ~ kn3 ),
inference(clausify,[status(thm)],[f_18_5]) ).
cnf(f_18_7,plain,
( kn3
| ~ is_a_theorem(implies(implies(sK36,sK37),implies(not(and(sK37,sK38)),not(and(sK38,sK36))))) ),
inference(clausify,[status(thm)],[f_18_5]) ).
fof(f_19_1,plain,
( ( cn1
| ? [P,Q,R] : ~ is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R)))) )
& ( ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))
| ~ cn1 ) ),
inference(fof_nnf,[status(thm)],[cn1]) ).
fof(f_19_2,plain,
( ( cn1
| ? [U_81,U_80,U_79] : ~ is_a_theorem(implies(implies(U_81,U_80),implies(implies(U_80,U_79),implies(U_81,U_79)))) )
& ( ! [U_78,U_77,U_76] : is_a_theorem(implies(implies(U_78,U_77),implies(implies(U_77,U_76),implies(U_78,U_76))))
| ~ cn1 ) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
( ( cn1
| ? [U_80,U_79] : ~ is_a_theorem(implies(implies(sK39,U_80),implies(implies(U_80,U_79),implies(sK39,U_79)))) )
& ( ! [U_78,U_77,U_76] : is_a_theorem(implies(implies(U_78,U_77),implies(implies(U_77,U_76),implies(U_78,U_76))))
| ~ cn1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_81,sK39)],[f_19_2]) ).
fof(f_19_4,plain,
( ( cn1
| ? [U_79] : ~ is_a_theorem(implies(implies(sK39,sK40),implies(implies(sK40,U_79),implies(sK39,U_79)))) )
& ( ! [U_78,U_77,U_76] : is_a_theorem(implies(implies(U_78,U_77),implies(implies(U_77,U_76),implies(U_78,U_76))))
| ~ cn1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_80,sK40)],[f_19_3]) ).
fof(f_19_5,plain,
( ( cn1
| ~ is_a_theorem(implies(implies(sK39,sK40),implies(implies(sK40,sK41),implies(sK39,sK41)))) )
& ( ! [U_78,U_77,U_76] : is_a_theorem(implies(implies(U_78,U_77),implies(implies(U_77,U_76),implies(U_78,U_76))))
| ~ cn1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_79,sK41)],[f_19_4]) ).
cnf(f_19_6,plain,
( is_a_theorem(implies(implies(U_78,U_77),implies(implies(U_77,U_76),implies(U_78,U_76))))
| ~ cn1 ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_7,plain,
( cn1
| ~ is_a_theorem(implies(implies(sK39,sK40),implies(implies(sK40,sK41),implies(sK39,sK41)))) ),
inference(clausify,[status(thm)],[f_19_5]) ).
fof(f_20_1,plain,
( ( cn2
| ? [P,Q] : ~ is_a_theorem(implies(P,implies(not(P),Q))) )
& ( ! [P,Q] : is_a_theorem(implies(P,implies(not(P),Q)))
| ~ cn2 ) ),
inference(fof_nnf,[status(thm)],[cn2]) ).
fof(f_20_2,plain,
( ( cn2
| ? [U_85,U_84] : ~ is_a_theorem(implies(U_85,implies(not(U_85),U_84))) )
& ( ! [U_83,U_82] : is_a_theorem(implies(U_83,implies(not(U_83),U_82)))
| ~ cn2 ) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
( ( cn2
| ? [U_84] : ~ is_a_theorem(implies(sK42,implies(not(sK42),U_84))) )
& ( ! [U_83,U_82] : is_a_theorem(implies(U_83,implies(not(U_83),U_82)))
| ~ cn2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_85,sK42)],[f_20_2]) ).
fof(f_20_4,plain,
( ( cn2
| ~ is_a_theorem(implies(sK42,implies(not(sK42),sK43))) )
& ( ! [U_83,U_82] : is_a_theorem(implies(U_83,implies(not(U_83),U_82)))
| ~ cn2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_84,sK43)],[f_20_3]) ).
cnf(f_20_5,plain,
( is_a_theorem(implies(U_83,implies(not(U_83),U_82)))
| ~ cn2 ),
inference(clausify,[status(thm)],[f_20_4]) ).
cnf(f_20_6,plain,
( cn2
| ~ is_a_theorem(implies(sK42,implies(not(sK42),sK43))) ),
inference(clausify,[status(thm)],[f_20_4]) ).
fof(f_21_1,plain,
( ( cn3
| ? [P] : ~ is_a_theorem(implies(implies(not(P),P),P)) )
& ( ! [P] : is_a_theorem(implies(implies(not(P),P),P))
| ~ cn3 ) ),
inference(fof_nnf,[status(thm)],[cn3]) ).
fof(f_21_2,plain,
( ( cn3
| ? [U_87] : ~ is_a_theorem(implies(implies(not(U_87),U_87),U_87)) )
& ( ! [U_86] : is_a_theorem(implies(implies(not(U_86),U_86),U_86))
| ~ cn3 ) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
( ( cn3
| ~ is_a_theorem(implies(implies(not(sK44),sK44),sK44)) )
& ( ! [U_86] : is_a_theorem(implies(implies(not(U_86),U_86),U_86))
| ~ cn3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_87,sK44)],[f_21_2]) ).
cnf(f_21_4,plain,
( is_a_theorem(implies(implies(not(U_86),U_86),U_86))
| ~ cn3 ),
inference(clausify,[status(thm)],[f_21_3]) ).
cnf(f_21_5,plain,
( cn3
| ~ is_a_theorem(implies(implies(not(sK44),sK44),sK44)) ),
inference(clausify,[status(thm)],[f_21_3]) ).
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_4,plain,
( is_a_theorem(implies(or(U_88,U_88),U_88))
| ~ r1 ),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_5,plain,
( r1
| ~ is_a_theorem(implies(or(sK45,sK45),sK45)) ),
inference(clausify,[status(thm)],[f_22_3]) ).
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]) ).
cnf(f_23_6,plain,
( r2
| ~ is_a_theorem(implies(sK47,or(sK46,sK47))) ),
inference(clausify,[status(thm)],[f_23_4]) ).
fof(f_24_1,plain,
( ( r3
| ? [P,Q] : ~ is_a_theorem(implies(or(P,Q),or(Q,P))) )
& ( ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P)))
| ~ r3 ) ),
inference(fof_nnf,[status(thm)],[r3]) ).
fof(f_24_2,plain,
( ( r3
| ? [U_97,U_96] : ~ is_a_theorem(implies(or(U_97,U_96),or(U_96,U_97))) )
& ( ! [U_95,U_94] : is_a_theorem(implies(or(U_95,U_94),or(U_94,U_95)))
| ~ r3 ) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
( ( r3
| ? [U_96] : ~ is_a_theorem(implies(or(sK48,U_96),or(U_96,sK48))) )
& ( ! [U_95,U_94] : is_a_theorem(implies(or(U_95,U_94),or(U_94,U_95)))
| ~ r3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_97,sK48)],[f_24_2]) ).
fof(f_24_4,plain,
( ( r3
| ~ is_a_theorem(implies(or(sK48,sK49),or(sK49,sK48))) )
& ( ! [U_95,U_94] : is_a_theorem(implies(or(U_95,U_94),or(U_94,U_95)))
| ~ r3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_96,sK49)],[f_24_3]) ).
cnf(f_24_5,plain,
( is_a_theorem(implies(or(U_95,U_94),or(U_94,U_95)))
| ~ r3 ),
inference(clausify,[status(thm)],[f_24_4]) ).
cnf(f_24_6,plain,
( r3
| ~ is_a_theorem(implies(or(sK48,sK49),or(sK49,sK48))) ),
inference(clausify,[status(thm)],[f_24_4]) ).
fof(f_25_1,plain,
( ( r4
| ? [P,Q,R] : ~ is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) )
& ( ! [P,Q,R] : is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))
| ~ r4 ) ),
inference(fof_nnf,[status(thm)],[r4]) ).
fof(f_25_2,plain,
( ( r4
| ? [U_103,U_102,U_101] : ~ is_a_theorem(implies(or(U_103,or(U_102,U_101)),or(U_102,or(U_103,U_101)))) )
& ( ! [U_100,U_99,U_98] : is_a_theorem(implies(or(U_100,or(U_99,U_98)),or(U_99,or(U_100,U_98))))
| ~ r4 ) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
( ( r4
| ? [U_102,U_101] : ~ is_a_theorem(implies(or(sK50,or(U_102,U_101)),or(U_102,or(sK50,U_101)))) )
& ( ! [U_100,U_99,U_98] : is_a_theorem(implies(or(U_100,or(U_99,U_98)),or(U_99,or(U_100,U_98))))
| ~ r4 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_103,sK50)],[f_25_2]) ).
fof(f_25_4,plain,
( ( r4
| ? [U_101] : ~ is_a_theorem(implies(or(sK50,or(sK51,U_101)),or(sK51,or(sK50,U_101)))) )
& ( ! [U_100,U_99,U_98] : is_a_theorem(implies(or(U_100,or(U_99,U_98)),or(U_99,or(U_100,U_98))))
| ~ r4 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_102,sK51)],[f_25_3]) ).
fof(f_25_5,plain,
( ( r4
| ~ is_a_theorem(implies(or(sK50,or(sK51,sK52)),or(sK51,or(sK50,sK52)))) )
& ( ! [U_100,U_99,U_98] : is_a_theorem(implies(or(U_100,or(U_99,U_98)),or(U_99,or(U_100,U_98))))
| ~ r4 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_101,sK52)],[f_25_4]) ).
cnf(f_25_6,plain,
( is_a_theorem(implies(or(U_100,or(U_99,U_98)),or(U_99,or(U_100,U_98))))
| ~ r4 ),
inference(clausify,[status(thm)],[f_25_5]) ).
cnf(f_25_7,plain,
( r4
| ~ is_a_theorem(implies(or(sK50,or(sK51,sK52)),or(sK51,or(sK50,sK52)))) ),
inference(clausify,[status(thm)],[f_25_5]) ).
fof(f_26_1,plain,
( ( r5
| ? [P,Q,R] : ~ is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) )
& ( ! [P,Q,R] : is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))
| ~ r5 ) ),
inference(fof_nnf,[status(thm)],[r5]) ).
fof(f_26_2,plain,
( ( r5
| ? [U_109,U_108,U_107] : ~ is_a_theorem(implies(implies(U_108,U_107),implies(or(U_109,U_108),or(U_109,U_107)))) )
& ( ! [U_106,U_105,U_104] : is_a_theorem(implies(implies(U_105,U_104),implies(or(U_106,U_105),or(U_106,U_104))))
| ~ r5 ) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
( ( r5
| ? [U_108,U_107] : ~ is_a_theorem(implies(implies(U_108,U_107),implies(or(sK53,U_108),or(sK53,U_107)))) )
& ( ! [U_106,U_105,U_104] : is_a_theorem(implies(implies(U_105,U_104),implies(or(U_106,U_105),or(U_106,U_104))))
| ~ r5 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_109,sK53)],[f_26_2]) ).
fof(f_26_4,plain,
( ( r5
| ? [U_107] : ~ is_a_theorem(implies(implies(sK54,U_107),implies(or(sK53,sK54),or(sK53,U_107)))) )
& ( ! [U_106,U_105,U_104] : is_a_theorem(implies(implies(U_105,U_104),implies(or(U_106,U_105),or(U_106,U_104))))
| ~ r5 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_108,sK54)],[f_26_3]) ).
fof(f_26_5,plain,
( ( r5
| ~ is_a_theorem(implies(implies(sK54,sK55),implies(or(sK53,sK54),or(sK53,sK55)))) )
& ( ! [U_106,U_105,U_104] : is_a_theorem(implies(implies(U_105,U_104),implies(or(U_106,U_105),or(U_106,U_104))))
| ~ r5 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_107,sK55)],[f_26_4]) ).
cnf(f_26_6,plain,
( is_a_theorem(implies(implies(U_105,U_104),implies(or(U_106,U_105),or(U_106,U_104))))
| ~ r5 ),
inference(clausify,[status(thm)],[f_26_5]) ).
cnf(f_26_7,plain,
( r5
| ~ is_a_theorem(implies(implies(sK54,sK55),implies(or(sK53,sK54),or(sK53,sK55)))) ),
inference(clausify,[status(thm)],[f_26_5]) ).
fof(f_27_1,plain,
( ! [X,Y] : or(X,Y) = not(and(not(X),not(Y)))
| ~ op_or ),
inference(fof_nnf,[status(thm)],[op_or]) ).
fof(f_27_2,plain,
( ! [U_111,U_110] : or(U_111,U_110) = not(and(not(U_111),not(U_110)))
| ~ op_or ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
( or(U_111,U_110) = not(and(not(U_111),not(U_110)))
| ~ op_or ),
inference(clausify,[status(thm)],[f_27_2]) ).
fof(f_28_1,plain,
( ! [X,Y] : and(X,Y) = not(or(not(X),not(Y)))
| ~ op_and ),
inference(fof_nnf,[status(thm)],[op_and]) ).
fof(f_28_2,plain,
( ! [U_113,U_112] : and(U_113,U_112) = not(or(not(U_113),not(U_112)))
| ~ op_and ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
( and(U_113,U_112) = not(or(not(U_113),not(U_112)))
| ~ op_and ),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_1,plain,
( ! [X,Y] : implies(X,Y) = not(and(X,not(Y)))
| ~ op_implies_and ),
inference(fof_nnf,[status(thm)],[op_implies_and]) ).
fof(f_29_2,plain,
( ! [U_115,U_114] : implies(U_115,U_114) = not(and(U_115,not(U_114)))
| ~ op_implies_and ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
( implies(U_115,U_114) = not(and(U_115,not(U_114)))
| ~ op_implies_and ),
inference(clausify,[status(thm)],[f_29_2]) ).
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_31_1,plain,
( ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X))
| ~ op_equiv ),
inference(fof_nnf,[status(thm)],[op_equiv]) ).
fof(f_31_2,plain,
( ! [U_119,U_118] : equiv(U_119,U_118) = and(implies(U_119,U_118),implies(U_118,U_119))
| ~ op_equiv ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
cnf(f_31_3,plain,
( equiv(U_119,U_118) = and(implies(U_119,U_118),implies(U_118,U_119))
| ~ op_equiv ),
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_32_1,plain,
op_or,
inference(fof_nnf,[status(thm)],[rosser_op_or]) ).
cnf(f_32_2,plain,
op_or,
inference(clausify,[status(thm)],[f_32_1]) ).
fof(f_33_1,plain,
op_implies_and,
inference(fof_nnf,[status(thm)],[rosser_op_implies_and]) ).
cnf(f_33_2,plain,
op_implies_and,
inference(clausify,[status(thm)],[f_33_1]) ).
fof(f_34_1,plain,
op_equiv,
inference(fof_nnf,[status(thm)],[rosser_op_equiv]) ).
cnf(f_34_2,plain,
op_equiv,
inference(clausify,[status(thm)],[f_34_1]) ).
fof(f_35_1,plain,
modus_ponens,
inference(fof_nnf,[status(thm)],[rosser_modus_ponens]) ).
cnf(f_35_2,plain,
modus_ponens,
inference(clausify,[status(thm)],[f_35_1]) ).
fof(f_36_1,plain,
kn1,
inference(fof_nnf,[status(thm)],[rosser_kn1]) ).
cnf(f_36_2,plain,
kn1,
inference(clausify,[status(thm)],[f_36_1]) ).
fof(f_37_1,plain,
kn2,
inference(fof_nnf,[status(thm)],[rosser_kn2]) ).
cnf(f_37_2,plain,
kn2,
inference(clausify,[status(thm)],[f_37_1]) ).
fof(f_38_1,plain,
kn3,
inference(fof_nnf,[status(thm)],[rosser_kn3]) ).
cnf(f_38_2,plain,
kn3,
inference(clausify,[status(thm)],[f_38_1]) ).
fof(f_39_1,plain,
substitution_of_equivalents,
inference(fof_nnf,[status(thm)],[use_substitution_of_equivalents]) ).
cnf(f_39_2,plain,
substitution_of_equivalents,
inference(clausify,[status(thm)],[f_39_1]) ).
fof(f_40_1,plain,
op_or,
inference(fof_nnf,[status(thm)],[hilbert_op_or]) ).
cnf(f_40_2,plain,
op_or,
inference(clausify,[status(thm)],[f_40_1]) ).
fof(f_41_1,plain,
op_implies_and,
inference(fof_nnf,[status(thm)],[hilbert_op_implies_and]) ).
cnf(f_41_2,plain,
op_implies_and,
inference(clausify,[status(thm)],[f_41_1]) ).
fof(f_42_1,plain,
op_equiv,
inference(fof_nnf,[status(thm)],[hilbert_op_equiv]) ).
cnf(f_42_2,plain,
op_equiv,
inference(clausify,[status(thm)],[f_42_1]) ).
fof(f_43_1,negated_conjecture,
~ and_1,
inference(negate,[status(cth)],[hilbert_and_1]) ).
fof(f_43_2,negated_conjecture,
~ and_1,
inference(definitional_conversion,[status(esa)],[f_43_1]) ).
cnf(f_43_3,negated_conjecture,
~ and_1,
inference(clausify,[status(thm)],[f_43_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_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
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_5,axiom,
( equiv(Eq_x_0,Eq_x_1) = equiv(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( not(Eq_x_0) = not(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( and(Eq_x_0,Eq_x_1) = and(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( or(Eq_x_0,Eq_x_1) = or(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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL506+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
% 0.08/0.36 % Computer : n010.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 19 15:10:53 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.42 % SZS status Theorem for theBenchmark
% 0.14/0.42 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------