TSTP Solution File: LCL538+1 by ConnectPP---0.3.0
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%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : LCL538+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Mar 25 14:20:35 EDT 2024
% Result : Theorem 2.25s 2.41s
% Output : Proof 2.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : LCL538+1 : TPTP v8.1.2. Released v3.3.0.
% 0.04/0.13 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Mar 20 18:39:57 EDT 2024
% 0.13/0.35 % CPUTime :
% 2.25/2.41 % SZS status Theorem for theBenchmark
% 2.25/2.41 % SZS output start Proof for theBenchmark
% 2.25/2.41
% 2.25/2.41 % Formula: modus_ponens ( axiom ) converted to clauses:
% 2.25/2.41 cnf(modus_ponens-1, axiom, ( ~modus_ponens | ~is_a_theorem(_u1) | ~is_a_theorem(implies(_u1, _u0)) | is_a_theorem(_u0) )).
% 2.25/2.41 cnf(modus_ponens-2, axiom, ( modus_ponens | is_a_theorem(skolem1) )).
% 2.25/2.41 cnf(modus_ponens-3, axiom, ( modus_ponens | is_a_theorem(implies(skolem1, skolem2)) )).
% 2.25/2.41 cnf(modus_ponens-4, axiom, ( modus_ponens | ~is_a_theorem(skolem2) )).
% 2.25/2.41
% 2.25/2.41 % Formula: substitution_of_equivalents ( axiom ) converted to clauses:
% 2.25/2.41 cnf(substitution_of_equivalents-1, axiom, ( ~substitution_of_equivalents | ~is_a_theorem(equiv(_u5, _u4)) | ( _u5 = _u4) )).
% 2.25/2.41 cnf(substitution_of_equivalents-2, axiom, ( substitution_of_equivalents | is_a_theorem(equiv(skolem3, skolem4)) )).
% 2.25/2.41 cnf(substitution_of_equivalents-3, axiom, ( substitution_of_equivalents | ( skolem3 != skolem4) )).
% 2.25/2.41
% 2.25/2.41 % Formula: modus_tollens ( axiom ) converted to clauses:
% 2.25/2.41 cnf(modus_tollens-1, axiom, ( ~modus_tollens | is_a_theorem(implies(implies(not(_u8), not(_u9)), implies(_u9, _u8))) )).
% 2.25/2.41 cnf(modus_tollens-2, axiom, ( ~is_a_theorem(implies(implies(not(skolem6), not(skolem5)), implies(skolem5, skolem6))) | modus_tollens )).
% 2.25/2.41
% 2.25/2.41 % Formula: implies_1 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(implies_1-1, axiom, ( ~implies_1 | is_a_theorem(implies(_u13, implies(_u12, _u13))) )).
% 2.25/2.41 cnf(implies_1-2, axiom, ( ~is_a_theorem(implies(skolem7, implies(skolem8, skolem7))) | implies_1 )).
% 2.25/2.41
% 2.25/2.41 % Formula: implies_2 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(implies_2-1, axiom, ( ~implies_2 | is_a_theorem(implies(implies(_u17, implies(_u17, _u16)), implies(_u17, _u16))) )).
% 2.25/2.41 cnf(implies_2-2, axiom, ( ~is_a_theorem(implies(implies(skolem9, implies(skolem9, skolem10)), implies(skolem9, skolem10))) | implies_2 )).
% 2.25/2.41
% 2.25/2.41 % Formula: implies_3 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(implies_3-1, axiom, ( ~implies_3 | is_a_theorem(implies(implies(_u22, _u21), implies(implies(_u21, _u20), implies(_u22, _u20)))) )).
% 2.25/2.41 cnf(implies_3-2, axiom, ( ~is_a_theorem(implies(implies(skolem11, skolem12), implies(implies(skolem12, skolem13), implies(skolem11, skolem13)))) | implies_3 )).
% 2.25/2.41
% 2.25/2.41 % Formula: and_1 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(and_1-1, axiom, ( ~and_1 | is_a_theorem(implies(and(_u27, _u26), _u27)) )).
% 2.25/2.41 cnf(and_1-2, axiom, ( ~is_a_theorem(implies(and(skolem14, skolem15), skolem14)) | and_1 )).
% 2.25/2.41
% 2.25/2.41 % Formula: and_2 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(and_2-1, axiom, ( ~and_2 | is_a_theorem(implies(and(_u31, _u30), _u30)) )).
% 2.25/2.41 cnf(and_2-2, axiom, ( ~is_a_theorem(implies(and(skolem16, skolem17), skolem17)) | and_2 )).
% 2.25/2.41
% 2.25/2.41 % Formula: and_3 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(and_3-1, axiom, ( ~and_3 | is_a_theorem(implies(_u35, implies(_u34, and(_u35, _u34)))) )).
% 2.25/2.41 cnf(and_3-2, axiom, ( ~is_a_theorem(implies(skolem18, implies(skolem19, and(skolem18, skolem19)))) | and_3 )).
% 2.25/2.41
% 2.25/2.41 % Formula: or_1 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(or_1-1, axiom, ( ~or_1 | is_a_theorem(implies(_u39, or(_u39, _u38))) )).
% 2.25/2.41 cnf(or_1-2, axiom, ( ~is_a_theorem(implies(skolem20, or(skolem20, skolem21))) | or_1 )).
% 2.25/2.41
% 2.25/2.41 % Formula: or_2 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(or_2-1, axiom, ( ~or_2 | is_a_theorem(implies(_u42, or(_u43, _u42))) )).
% 2.25/2.41 cnf(or_2-2, axiom, ( ~is_a_theorem(implies(skolem23, or(skolem22, skolem23))) | or_2 )).
% 2.25/2.41
% 2.25/2.41 % Formula: or_3 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(or_3-1, axiom, ( ~or_3 | is_a_theorem(implies(implies(_u48, _u46), implies(implies(_u47, _u46), implies(or(_u48, _u47), _u46)))) )).
% 2.25/2.41 cnf(or_3-2, axiom, ( ~is_a_theorem(implies(implies(skolem24, skolem26), implies(implies(skolem25, skolem26), implies(or(skolem24, skolem25), skolem26)))) | or_3 )).
% 2.25/2.41
% 2.25/2.41 % Formula: equivalence_1 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(equivalence_1-1, axiom, ( ~equivalence_1 | is_a_theorem(implies(equiv(_u53, _u52), implies(_u53, _u52))) )).
% 2.25/2.41 cnf(equivalence_1-2, axiom, ( ~is_a_theorem(implies(equiv(skolem27, skolem28), implies(skolem27, skolem28))) | equivalence_1 )).
% 2.25/2.41
% 2.25/2.41 % Formula: equivalence_2 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(equivalence_2-1, axiom, ( ~equivalence_2 | is_a_theorem(implies(equiv(_u57, _u56), implies(_u56, _u57))) )).
% 2.25/2.41 cnf(equivalence_2-2, axiom, ( ~is_a_theorem(implies(equiv(skolem29, skolem30), implies(skolem30, skolem29))) | equivalence_2 )).
% 2.25/2.41
% 2.25/2.41 % Formula: equivalence_3 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(equivalence_3-1, axiom, ( ~equivalence_3 | is_a_theorem(implies(implies(_u61, _u60), implies(implies(_u60, _u61), equiv(_u61, _u60)))) )).
% 2.25/2.41 cnf(equivalence_3-2, axiom, ( ~is_a_theorem(implies(implies(skolem31, skolem32), implies(implies(skolem32, skolem31), equiv(skolem31, skolem32)))) | equivalence_3 )).
% 2.25/2.41
% 2.25/2.41 % Formula: kn1 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(kn1-1, axiom, ( ~kn1 | is_a_theorem(implies(_u64, and(_u64, _u64))) )).
% 2.25/2.41 cnf(kn1-2, axiom, ( ~is_a_theorem(implies(skolem33, and(skolem33, skolem33))) | kn1 )).
% 2.25/2.41
% 2.25/2.41 % Formula: kn2 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(kn2-1, axiom, ( ~kn2 | is_a_theorem(implies(and(_u67, _u66), _u67)) )).
% 2.25/2.41 cnf(kn2-2, axiom, ( ~is_a_theorem(implies(and(skolem34, skolem35), skolem34)) | kn2 )).
% 2.25/2.41
% 2.25/2.41 % Formula: kn3 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(kn3-1, axiom, ( ~kn3 | is_a_theorem(implies(implies(_u72, _u71), implies(not(and(_u71, _u70)), not(and(_u70, _u72))))) )).
% 2.25/2.41 cnf(kn3-2, axiom, ( ~is_a_theorem(implies(implies(skolem36, skolem37), implies(not(and(skolem37, skolem38)), not(and(skolem38, skolem36))))) | kn3 )).
% 2.25/2.41
% 2.25/2.41 % Formula: cn1 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(cn1-1, axiom, ( ~cn1 | is_a_theorem(implies(implies(_u78, _u77), implies(implies(_u77, _u76), implies(_u78, _u76)))) )).
% 2.25/2.41 cnf(cn1-2, axiom, ( ~is_a_theorem(implies(implies(skolem39, skolem40), implies(implies(skolem40, skolem41), implies(skolem39, skolem41)))) | cn1 )).
% 2.25/2.41
% 2.25/2.41 % Formula: cn2 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(cn2-1, axiom, ( ~cn2 | is_a_theorem(implies(_u83, implies(not(_u83), _u82))) )).
% 2.25/2.41 cnf(cn2-2, axiom, ( ~is_a_theorem(implies(skolem42, implies(not(skolem42), skolem43))) | cn2 )).
% 2.25/2.41
% 2.25/2.41 % Formula: cn3 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(cn3-1, axiom, ( ~cn3 | is_a_theorem(implies(implies(not(_u86), _u86), _u86)) )).
% 2.25/2.41 cnf(cn3-2, axiom, ( ~is_a_theorem(implies(implies(not(skolem44), skolem44), skolem44)) | cn3 )).
% 2.25/2.41
% 2.25/2.41 % Formula: r1 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(r1-1, axiom, ( ~r1 | is_a_theorem(implies(or(_u88, _u88), _u88)) )).
% 2.25/2.41 cnf(r1-2, axiom, ( ~is_a_theorem(implies(or(skolem45, skolem45), skolem45)) | r1 )).
% 2.25/2.41
% 2.25/2.41 % Formula: r2 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(r2-1, axiom, ( ~r2 | is_a_theorem(implies(_u90, or(_u91, _u90))) )).
% 2.25/2.41 cnf(r2-2, axiom, ( ~is_a_theorem(implies(skolem47, or(skolem46, skolem47))) | r2 )).
% 2.25/2.41
% 2.25/2.41 % Formula: r3 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(r3-1, axiom, ( ~r3 | is_a_theorem(implies(or(_u95, _u94), or(_u94, _u95))) )).
% 2.25/2.41 cnf(r3-2, axiom, ( ~is_a_theorem(implies(or(skolem48, skolem49), or(skolem49, skolem48))) | r3 )).
% 2.25/2.41
% 2.25/2.41 % Formula: r4 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(r4-1, axiom, ( ~r4 | is_a_theorem(implies(or(_u100, or(_u99, _u98)), or(_u99, or(_u100, _u98)))) )).
% 2.25/2.41 cnf(r4-2, axiom, ( ~is_a_theorem(implies(or(skolem50, or(skolem51, skolem52)), or(skolem51, or(skolem50, skolem52)))) | r4 )).
% 2.25/2.41
% 2.25/2.41 % Formula: r5 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(r5-1, axiom, ( ~r5 | is_a_theorem(implies(implies(_u105, _u104), implies(or(_u106, _u105), or(_u106, _u104)))) )).
% 2.25/2.41 cnf(r5-2, axiom, ( ~is_a_theorem(implies(implies(skolem54, skolem55), implies(or(skolem53, skolem54), or(skolem53, skolem55)))) | r5 )).
% 2.25/2.41
% 2.25/2.41 % Formula: op_or ( axiom ) converted to clauses:
% 2.25/2.41 cnf(op_or-1, axiom, ( ~op_or | ( or(_u111, _u110) = not(and(not(_u111), not(_u110)))) )).
% 2.25/2.41
% 2.25/2.41 % Formula: op_and ( axiom ) converted to clauses:
% 2.25/2.41 cnf(op_and-1, axiom, ( ~op_and | ( and(_u113, _u112) = not(or(not(_u113), not(_u112)))) )).
% 2.25/2.41
% 2.25/2.41 % Formula: op_implies_and ( axiom ) converted to clauses:
% 2.25/2.41 cnf(op_implies_and-1, axiom, ( ~op_implies_and | ( implies(_u115, _u114) = not(and(_u115, not(_u114)))) )).
% 2.25/2.41
% 2.25/2.41 % Formula: op_implies_or ( axiom ) converted to clauses:
% 2.25/2.41 cnf(op_implies_or-1, axiom, ( ~op_implies_or | ( implies(_u117, _u116) = or(not(_u117), _u116)) )).
% 2.25/2.41
% 2.25/2.41 % Formula: op_equiv ( axiom ) converted to clauses:
% 2.25/2.41 cnf(op_equiv-1, axiom, ( ~op_equiv | ( equiv(_u119, _u118) = and(implies(_u119, _u118), implies(_u118, _u119))) )).
% 2.25/2.41
% 2.25/2.41 % Formula: hilbert_op_or ( axiom ) converted to clauses:
% 2.25/2.41 cnf(hilbert_op_or-1, axiom, ( op_or )).
% 2.25/2.41
% 2.25/2.41 % Formula: hilbert_op_implies_and ( axiom ) converted to clauses:
% 2.25/2.41 cnf(hilbert_op_implies_and-1, axiom, ( op_implies_and )).
% 2.25/2.41
% 2.25/2.41 % Formula: hilbert_op_equiv ( axiom ) converted to clauses:
% 2.25/2.41 cnf(hilbert_op_equiv-1, axiom, ( op_equiv )).
% 2.25/2.41
% 2.25/2.41 % Formula: hilbert_modus_ponens ( axiom ) converted to clauses:
% 2.25/2.41 cnf(hilbert_modus_ponens-1, axiom, ( modus_ponens )).
% 2.25/2.41
% 2.25/2.41 % Formula: hilbert_modus_tollens ( axiom ) converted to clauses:
% 2.25/2.41 cnf(hilbert_modus_tollens-1, axiom, ( modus_tollens )).
% 2.25/2.41
% 2.25/2.41 % Formula: hilbert_implies_1 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(hilbert_implies_1-1, axiom, ( implies_1 )).
% 2.25/2.41
% 2.25/2.41 % Formula: hilbert_implies_2 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(hilbert_implies_2-1, axiom, ( implies_2 )).
% 2.25/2.41
% 2.25/2.41 % Formula: hilbert_implies_3 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(hilbert_implies_3-1, axiom, ( implies_3 )).
% 2.25/2.41
% 2.25/2.41 % Formula: hilbert_and_1 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(hilbert_and_1-1, axiom, ( and_1 )).
% 2.25/2.41
% 2.25/2.41 % Formula: hilbert_and_2 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(hilbert_and_2-1, axiom, ( and_2 )).
% 2.25/2.41
% 2.25/2.41 % Formula: hilbert_and_3 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(hilbert_and_3-1, axiom, ( and_3 )).
% 2.25/2.41
% 2.25/2.41 % Formula: hilbert_or_1 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(hilbert_or_1-1, axiom, ( or_1 )).
% 2.25/2.41
% 2.25/2.41 % Formula: hilbert_or_2 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(hilbert_or_2-1, axiom, ( or_2 )).
% 2.25/2.41
% 2.25/2.41 % Formula: hilbert_or_3 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(hilbert_or_3-1, axiom, ( or_3 )).
% 2.25/2.41
% 2.25/2.41 % Formula: hilbert_equivalence_1 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(hilbert_equivalence_1-1, axiom, ( equivalence_1 )).
% 2.25/2.41
% 2.25/2.41 % Formula: hilbert_equivalence_2 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(hilbert_equivalence_2-1, axiom, ( equivalence_2 )).
% 2.25/2.41
% 2.25/2.41 % Formula: hilbert_equivalence_3 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(hilbert_equivalence_3-1, axiom, ( equivalence_3 )).
% 2.25/2.41
% 2.25/2.41 % Formula: substitution_of_equivalents ( axiom ) converted to clauses:
% 2.25/2.41 cnf(substitution_of_equivalents-1, axiom, ( substitution_of_equivalents )).
% 2.25/2.41
% 2.25/2.41 % Formula: necessitation ( axiom ) converted to clauses:
% 2.25/2.41 cnf(necessitation-1, axiom, ( ~necessitation | ~is_a_theorem(_u120) | is_a_theorem(necessarily(_u120)) )).
% 2.25/2.41 cnf(necessitation-2, axiom, ( necessitation | is_a_theorem(skolem56) )).
% 2.25/2.41 cnf(necessitation-3, axiom, ( necessitation | ~is_a_theorem(necessarily(skolem56)) )).
% 2.25/2.41
% 2.25/2.41 % Formula: modus_ponens_strict_implies ( axiom ) converted to clauses:
% 2.25/2.41 cnf(modus_ponens_strict_implies-1, axiom, ( ~modus_ponens_strict_implies | ~is_a_theorem(_u123) | ~is_a_theorem(strict_implies(_u123, _u122)) | is_a_theorem(_u122) )).
% 2.25/2.41 cnf(modus_ponens_strict_implies-2, axiom, ( modus_ponens_strict_implies | is_a_theorem(skolem57) )).
% 2.25/2.41 cnf(modus_ponens_strict_implies-3, axiom, ( modus_ponens_strict_implies | is_a_theorem(strict_implies(skolem57, skolem58)) )).
% 2.25/2.41 cnf(modus_ponens_strict_implies-4, axiom, ( modus_ponens_strict_implies | ~is_a_theorem(skolem58) )).
% 2.25/2.41
% 2.25/2.41 % Formula: adjunction ( axiom ) converted to clauses:
% 2.25/2.41 cnf(adjunction-1, axiom, ( ~adjunction | ~is_a_theorem(_u127) | ~is_a_theorem(_u126) | is_a_theorem(and(_u127, _u126)) )).
% 2.25/2.41 cnf(adjunction-2, axiom, ( adjunction | is_a_theorem(skolem59) )).
% 2.25/2.41 cnf(adjunction-3, axiom, ( adjunction | is_a_theorem(skolem60) )).
% 2.25/2.41 cnf(adjunction-4, axiom, ( adjunction | ~is_a_theorem(and(skolem59, skolem60)) )).
% 2.25/2.41
% 2.25/2.41 % Formula: substitution_strict_equiv ( axiom ) converted to clauses:
% 2.25/2.41 cnf(substitution_strict_equiv-1, axiom, ( ~substitution_strict_equiv | ~is_a_theorem(strict_equiv(_u131, _u130)) | ( _u131 = _u130) )).
% 2.25/2.41 cnf(substitution_strict_equiv-2, axiom, ( substitution_strict_equiv | is_a_theorem(strict_equiv(skolem61, skolem62)) )).
% 2.25/2.41 cnf(substitution_strict_equiv-3, axiom, ( substitution_strict_equiv | ( skolem61 != skolem62) )).
% 2.25/2.41
% 2.25/2.41 % Formula: axiom_K ( axiom ) converted to clauses:
% 2.25/2.41 cnf(axiom_K-1, axiom, ( ~axiom_K | is_a_theorem(implies(necessarily(implies(_u135, _u134)), implies(necessarily(_u135), necessarily(_u134)))) )).
% 2.25/2.41 cnf(axiom_K-2, axiom, ( ~is_a_theorem(implies(necessarily(implies(skolem63, skolem64)), implies(necessarily(skolem63), necessarily(skolem64)))) | axiom_K )).
% 2.25/2.41
% 2.25/2.41 % Formula: axiom_M ( axiom ) converted to clauses:
% 2.25/2.41 cnf(axiom_M-1, axiom, ( ~axiom_M | is_a_theorem(implies(necessarily(_u138), _u138)) )).
% 2.25/2.41 cnf(axiom_M-2, axiom, ( ~is_a_theorem(implies(necessarily(skolem65), skolem65)) | axiom_M )).
% 2.25/2.41
% 2.25/2.41 % Formula: axiom_4 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(axiom_4-1, axiom, ( ~axiom_4 | is_a_theorem(implies(necessarily(_u140), necessarily(necessarily(_u140)))) )).
% 2.25/2.41 cnf(axiom_4-2, axiom, ( ~is_a_theorem(implies(necessarily(skolem66), necessarily(necessarily(skolem66)))) | axiom_4 )).
% 2.25/2.41
% 2.25/2.41 % Formula: axiom_B ( axiom ) converted to clauses:
% 2.25/2.41 cnf(axiom_B-1, axiom, ( ~axiom_B | is_a_theorem(implies(_u142, necessarily(possibly(_u142)))) )).
% 2.25/2.41 cnf(axiom_B-2, axiom, ( ~is_a_theorem(implies(skolem67, necessarily(possibly(skolem67)))) | axiom_B )).
% 2.25/2.41
% 2.25/2.41 % Formula: axiom_5 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(axiom_5-1, axiom, ( ~axiom_5 | is_a_theorem(implies(possibly(_u144), necessarily(possibly(_u144)))) )).
% 2.25/2.41 cnf(axiom_5-2, axiom, ( ~is_a_theorem(implies(possibly(skolem68), necessarily(possibly(skolem68)))) | axiom_5 )).
% 2.25/2.41
% 2.25/2.41 % Formula: axiom_s1 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(axiom_s1-1, axiom, ( ~axiom_s1 | is_a_theorem(implies(and(necessarily(implies(_u148, _u147)), necessarily(implies(_u147, _u146))), necessarily(implies(_u148, _u146)))) )).
% 2.25/2.41 cnf(axiom_s1-2, axiom, ( ~is_a_theorem(implies(and(necessarily(implies(skolem69, skolem70)), necessarily(implies(skolem70, skolem71))), necessarily(implies(skolem69, skolem71)))) | axiom_s1 )).
% 2.25/2.41
% 2.25/2.41 % Formula: axiom_s2 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(axiom_s2-1, axiom, ( ~axiom_s2 | is_a_theorem(strict_implies(possibly(and(_u153, _u152)), and(possibly(_u153), possibly(_u152)))) )).
% 2.25/2.41 cnf(axiom_s2-2, axiom, ( ~is_a_theorem(strict_implies(possibly(and(skolem72, skolem73)), and(possibly(skolem72), possibly(skolem73)))) | axiom_s2 )).
% 2.25/2.41
% 2.25/2.41 % Formula: axiom_s3 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(axiom_s3-1, axiom, ( ~axiom_s3 | is_a_theorem(strict_implies(strict_implies(_u157, _u156), strict_implies(not(possibly(_u156)), not(possibly(_u157))))) )).
% 2.25/2.41 cnf(axiom_s3-2, axiom, ( ~is_a_theorem(strict_implies(strict_implies(skolem74, skolem75), strict_implies(not(possibly(skolem75)), not(possibly(skolem74))))) | axiom_s3 )).
% 2.25/2.41
% 2.25/2.41 % Formula: axiom_s4 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(axiom_s4-1, axiom, ( ~axiom_s4 | is_a_theorem(strict_implies(necessarily(_u160), necessarily(necessarily(_u160)))) )).
% 2.25/2.41 cnf(axiom_s4-2, axiom, ( ~is_a_theorem(strict_implies(necessarily(skolem76), necessarily(necessarily(skolem76)))) | axiom_s4 )).
% 2.25/2.41
% 2.25/2.41 % Formula: axiom_m1 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(axiom_m1-1, axiom, ( ~axiom_m1 | is_a_theorem(strict_implies(and(_u163, _u162), and(_u162, _u163))) )).
% 2.25/2.41 cnf(axiom_m1-2, axiom, ( ~is_a_theorem(strict_implies(and(skolem77, skolem78), and(skolem78, skolem77))) | axiom_m1 )).
% 2.25/2.41
% 2.25/2.41 % Formula: axiom_m2 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(axiom_m2-1, axiom, ( ~axiom_m2 | is_a_theorem(strict_implies(and(_u167, _u166), _u167)) )).
% 2.25/2.41 cnf(axiom_m2-2, axiom, ( ~is_a_theorem(strict_implies(and(skolem79, skolem80), skolem79)) | axiom_m2 )).
% 2.25/2.41
% 2.25/2.41 % Formula: axiom_m3 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(axiom_m3-1, axiom, ( ~axiom_m3 | is_a_theorem(strict_implies(and(and(_u172, _u171), _u170), and(_u172, and(_u171, _u170)))) )).
% 2.25/2.41 cnf(axiom_m3-2, axiom, ( ~is_a_theorem(strict_implies(and(and(skolem81, skolem82), skolem83), and(skolem81, and(skolem82, skolem83)))) | axiom_m3 )).
% 2.25/2.41
% 2.25/2.41 % Formula: axiom_m4 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(axiom_m4-1, axiom, ( ~axiom_m4 | is_a_theorem(strict_implies(_u176, and(_u176, _u176))) )).
% 2.25/2.41 cnf(axiom_m4-2, axiom, ( ~is_a_theorem(strict_implies(skolem84, and(skolem84, skolem84))) | axiom_m4 )).
% 2.25/2.41
% 2.25/2.41 % Formula: axiom_m5 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(axiom_m5-1, axiom, ( ~axiom_m5 | is_a_theorem(strict_implies(and(strict_implies(_u180, _u179), strict_implies(_u179, _u178)), strict_implies(_u180, _u178))) )).
% 2.25/2.41 cnf(axiom_m5-2, axiom, ( ~is_a_theorem(strict_implies(and(strict_implies(skolem85, skolem86), strict_implies(skolem86, skolem87)), strict_implies(skolem85, skolem87))) | axiom_m5 )).
% 2.25/2.41
% 2.25/2.41 % Formula: axiom_m6 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(axiom_m6-1, axiom, ( ~axiom_m6 | is_a_theorem(strict_implies(_u184, possibly(_u184))) )).
% 2.25/2.41 cnf(axiom_m6-2, axiom, ( ~is_a_theorem(strict_implies(skolem88, possibly(skolem88))) | axiom_m6 )).
% 2.25/2.41
% 2.25/2.41 % Formula: axiom_m7 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(axiom_m7-1, axiom, ( ~axiom_m7 | is_a_theorem(strict_implies(possibly(and(_u187, _u186)), _u187)) )).
% 2.25/2.41 cnf(axiom_m7-2, axiom, ( ~is_a_theorem(strict_implies(possibly(and(skolem89, skolem90)), skolem89)) | axiom_m7 )).
% 2.25/2.41
% 2.25/2.41 % Formula: axiom_m8 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(axiom_m8-1, axiom, ( ~axiom_m8 | is_a_theorem(strict_implies(strict_implies(_u191, _u190), strict_implies(possibly(_u191), possibly(_u190)))) )).
% 2.25/2.41 cnf(axiom_m8-2, axiom, ( ~is_a_theorem(strict_implies(strict_implies(skolem91, skolem92), strict_implies(possibly(skolem91), possibly(skolem92)))) | axiom_m8 )).
% 2.25/2.41
% 2.25/2.41 % Formula: axiom_m9 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(axiom_m9-1, axiom, ( ~axiom_m9 | is_a_theorem(strict_implies(possibly(possibly(_u194)), possibly(_u194))) )).
% 2.25/2.41 cnf(axiom_m9-2, axiom, ( ~is_a_theorem(strict_implies(possibly(possibly(skolem93)), possibly(skolem93))) | axiom_m9 )).
% 2.25/2.41
% 2.25/2.41 % Formula: axiom_m10 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(axiom_m10-1, axiom, ( ~axiom_m10 | is_a_theorem(strict_implies(possibly(_u196), necessarily(possibly(_u196)))) )).
% 2.25/2.41 cnf(axiom_m10-2, axiom, ( ~is_a_theorem(strict_implies(possibly(skolem94), necessarily(possibly(skolem94)))) | axiom_m10 )).
% 2.25/2.41
% 2.25/2.41 % Formula: op_possibly ( axiom ) converted to clauses:
% 2.25/2.41 cnf(op_possibly-1, axiom, ( ~op_possibly | ( possibly(_u198) = not(necessarily(not(_u198)))) )).
% 2.25/2.41
% 2.25/2.41 % Formula: op_necessarily ( axiom ) converted to clauses:
% 2.25/2.41 cnf(op_necessarily-1, axiom, ( ~op_necessarily | ( necessarily(_u199) = not(possibly(not(_u199)))) )).
% 2.25/2.41
% 2.25/2.41 % Formula: op_strict_implies ( axiom ) converted to clauses:
% 2.25/2.41 cnf(op_strict_implies-1, axiom, ( ~op_strict_implies | ( strict_implies(_u201, _u200) = necessarily(implies(_u201, _u200))) )).
% 2.25/2.41
% 2.25/2.41 % Formula: op_strict_equiv ( axiom ) converted to clauses:
% 2.25/2.41 cnf(op_strict_equiv-1, axiom, ( ~op_strict_equiv | ( strict_equiv(_u203, _u202) = and(strict_implies(_u203, _u202), strict_implies(_u202, _u203))) )).
% 2.25/2.41
% 2.25/2.41 % Formula: km4b_op_possibly ( axiom ) converted to clauses:
% 2.25/2.41 cnf(km4b_op_possibly-1, axiom, ( op_possibly )).
% 2.25/2.41
% 2.25/2.41 % Formula: km4b_necessitation ( axiom ) converted to clauses:
% 2.25/2.41 cnf(km4b_necessitation-1, axiom, ( necessitation )).
% 2.25/2.41
% 2.25/2.41 % Formula: km4b_axiom_K ( axiom ) converted to clauses:
% 2.25/2.41 cnf(km4b_axiom_K-1, axiom, ( axiom_K )).
% 2.25/2.41
% 2.25/2.41 % Formula: km4b_axiom_M ( axiom ) converted to clauses:
% 2.25/2.41 cnf(km4b_axiom_M-1, axiom, ( axiom_M )).
% 2.25/2.41
% 2.25/2.41 % Formula: km4b_axiom_4 ( axiom ) converted to clauses:
% 2.25/2.41 cnf(km4b_axiom_4-1, axiom, ( axiom_4 )).
% 2.25/2.41
% 2.25/2.41 % Formula: km4b_axiom_B ( axiom ) converted to clauses:
% 2.25/2.41 cnf(km4b_axiom_B-1, axiom, ( axiom_B )).
% 2.25/2.41
% 2.25/2.41 % Formula: s1_0_op_possibly ( axiom ) converted to clauses:
% 2.25/2.41 cnf(s1_0_op_possibly-1, axiom, ( op_possibly )).
% 2.25/2.41
% 2.25/2.41 % Formula: s1_0_op_or ( axiom ) converted to clauses:
% 2.25/2.41 cnf(s1_0_op_or-1, axiom, ( op_or )).
% 2.25/2.41
% 2.25/2.41 % Formula: s1_0_op_implies ( axiom ) converted to clauses:
% 2.25/2.41 cnf(s1_0_op_implies-1, axiom, ( op_implies )).
% 2.25/2.41
% 2.25/2.41 % Formula: s1_0_op_strict_implies ( axiom ) converted to clauses:
% 2.25/2.41 cnf(s1_0_op_strict_implies-1, axiom, ( op_strict_implies )).
% 2.25/2.41
% 2.25/2.41 % Formula: s1_0_op_equiv ( axiom ) converted to clauses:
% 2.25/2.41 cnf(s1_0_op_equiv-1, axiom, ( op_equiv )).
% 2.25/2.41
% 2.25/2.41 % Formula: s1_0_op_strict_equiv ( axiom ) converted to clauses:
% 2.25/2.41 cnf(s1_0_op_strict_equiv-1, axiom, ( op_strict_equiv )).
% 2.25/2.41
% 2.25/2.41 % Formula: s1_0_modus_ponens_strict_implies ( conjecture ) (definitionally) converted to clauses:
% 2.25/2.41 cnf(s1_0_modus_ponens_strict_implies-1, negated_conjecture, ( ~modus_ponens_strict_implies )).
% 2.25/2.41
% 2.25/2.41 % Problem matrix:
% 2.25/2.41 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 2.25/2.41 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 2.25/2.41 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 2.25/2.41 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( implies(__eqx_0, __eqx_1) = implies(__eqy_0, __eqy_1)) )).
% 2.25/2.41 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( equiv(__eqx_0, __eqx_1) = equiv(__eqy_0, __eqy_1)) )).
% 2.25/2.41 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( not(__eqx_0) = not(__eqy_0)) )).
% 2.25/2.41 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( and(__eqx_0, __eqx_1) = and(__eqy_0, __eqy_1)) )).
% 2.25/2.41 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( or(__eqx_0, __eqx_1) = or(__eqy_0, __eqy_1)) )).
% 2.25/2.41 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( necessarily(__eqx_0) = necessarily(__eqy_0)) )).
% 2.25/2.41 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( strict_implies(__eqx_0, __eqx_1) = strict_implies(__eqy_0, __eqy_1)) )).
% 2.25/2.41 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( strict_equiv(__eqx_0, __eqx_1) = strict_equiv(__eqy_0, __eqy_1)) )).
% 2.25/2.41 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( possibly(__eqx_0) = possibly(__eqy_0)) )).
% 2.25/2.41 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ~is_a_theorem(__eqx_0) | is_a_theorem(__eqy_0) )).
% 2.25/2.41 cnf(matrix-13, plain, ( ~modus_ponens | ~is_a_theorem(_u1) | ~is_a_theorem(implies(_u1, _u0)) | is_a_theorem(_u0) )).
% 2.25/2.41 cnf(matrix-14, plain, ( modus_ponens | is_a_theorem(skolem1) )).
% 2.25/2.41 cnf(matrix-15, plain, ( modus_ponens | is_a_theorem(implies(skolem1, skolem2)) )).
% 2.25/2.41 cnf(matrix-16, plain, ( modus_ponens | ~is_a_theorem(skolem2) )).
% 2.25/2.41 cnf(matrix-17, plain, ( ~substitution_of_equivalents | ~is_a_theorem(equiv(_u5, _u4)) | ( _u5 = _u4) )).
% 2.25/2.41 cnf(matrix-18, plain, ( substitution_of_equivalents | is_a_theorem(equiv(skolem3, skolem4)) )).
% 2.25/2.41 cnf(matrix-19, plain, ( substitution_of_equivalents | ( skolem3 != skolem4) )).
% 2.25/2.41 cnf(matrix-20, plain, ( ~modus_tollens | is_a_theorem(implies(implies(not(_u8), not(_u9)), implies(_u9, _u8))) )).
% 2.25/2.41 cnf(matrix-21, plain, ( ~is_a_theorem(implies(implies(not(skolem6), not(skolem5)), implies(skolem5, skolem6))) | modus_tollens )).
% 2.25/2.41 cnf(matrix-22, plain, ( ~implies_1 | is_a_theorem(implies(_u13, implies(_u12, _u13))) )).
% 2.25/2.41 cnf(matrix-23, plain, ( ~is_a_theorem(implies(skolem7, implies(skolem8, skolem7))) | implies_1 )).
% 2.25/2.41 cnf(matrix-24, plain, ( ~implies_2 | is_a_theorem(implies(implies(_u17, implies(_u17, _u16)), implies(_u17, _u16))) )).
% 2.25/2.41 cnf(matrix-25, plain, ( ~is_a_theorem(implies(implies(skolem9, implies(skolem9, skolem10)), implies(skolem9, skolem10))) | implies_2 )).
% 2.25/2.41 cnf(matrix-26, plain, ( ~implies_3 | is_a_theorem(implies(implies(_u22, _u21), implies(implies(_u21, _u20), implies(_u22, _u20)))) )).
% 2.25/2.41 cnf(matrix-27, plain, ( ~is_a_theorem(implies(implies(skolem11, skolem12), implies(implies(skolem12, skolem13), implies(skolem11, skolem13)))) | implies_3 )).
% 2.25/2.41 cnf(matrix-28, plain, ( ~and_1 | is_a_theorem(implies(and(_u27, _u26), _u27)) )).
% 2.25/2.41 cnf(matrix-29, plain, ( ~is_a_theorem(implies(and(skolem14, skolem15), skolem14)) | and_1 )).
% 2.25/2.41 cnf(matrix-30, plain, ( ~and_2 | is_a_theorem(implies(and(_u31, _u30), _u30)) )).
% 2.25/2.41 cnf(matrix-31, plain, ( ~is_a_theorem(implies(and(skolem16, skolem17), skolem17)) | and_2 )).
% 2.25/2.41 cnf(matrix-32, plain, ( ~and_3 | is_a_theorem(implies(_u35, implies(_u34, and(_u35, _u34)))) )).
% 2.25/2.41 cnf(matrix-33, plain, ( ~is_a_theorem(implies(skolem18, implies(skolem19, and(skolem18, skolem19)))) | and_3 )).
% 2.25/2.41 cnf(matrix-34, plain, ( ~or_1 | is_a_theorem(implies(_u39, or(_u39, _u38))) )).
% 2.25/2.41 cnf(matrix-35, plain, ( ~is_a_theorem(implies(skolem20, or(skolem20, skolem21))) | or_1 )).
% 2.25/2.41 cnf(matrix-36, plain, ( ~or_2 | is_a_theorem(implies(_u42, or(_u43, _u42))) )).
% 2.25/2.41 cnf(matrix-37, plain, ( ~is_a_theorem(implies(skolem23, or(skolem22, skolem23))) | or_2 )).
% 2.25/2.41 cnf(matrix-38, plain, ( ~or_3 | is_a_theorem(implies(implies(_u48, _u46), implies(implies(_u47, _u46), implies(or(_u48, _u47), _u46)))) )).
% 2.25/2.41 cnf(matrix-39, plain, ( ~is_a_theorem(implies(implies(skolem24, skolem26), implies(implies(skolem25, skolem26), implies(or(skolem24, skolem25), skolem26)))) | or_3 )).
% 2.25/2.41 cnf(matrix-40, plain, ( ~equivalence_1 | is_a_theorem(implies(equiv(_u53, _u52), implies(_u53, _u52))) )).
% 2.25/2.41 cnf(matrix-41, plain, ( ~is_a_theorem(implies(equiv(skolem27, skolem28), implies(skolem27, skolem28))) | equivalence_1 )).
% 2.25/2.41 cnf(matrix-42, plain, ( ~equivalence_2 | is_a_theorem(implies(equiv(_u57, _u56), implies(_u56, _u57))) )).
% 2.25/2.41 cnf(matrix-43, plain, ( ~is_a_theorem(implies(equiv(skolem29, skolem30), implies(skolem30, skolem29))) | equivalence_2 )).
% 2.25/2.41 cnf(matrix-44, plain, ( ~equivalence_3 | is_a_theorem(implies(implies(_u61, _u60), implies(implies(_u60, _u61), equiv(_u61, _u60)))) )).
% 2.25/2.41 cnf(matrix-45, plain, ( ~is_a_theorem(implies(implies(skolem31, skolem32), implies(implies(skolem32, skolem31), equiv(skolem31, skolem32)))) | equivalence_3 )).
% 2.25/2.41 cnf(matrix-46, plain, ( ~kn1 | is_a_theorem(implies(_u64, and(_u64, _u64))) )).
% 2.25/2.41 cnf(matrix-47, plain, ( ~is_a_theorem(implies(skolem33, and(skolem33, skolem33))) | kn1 )).
% 2.25/2.41 cnf(matrix-48, plain, ( ~kn2 | is_a_theorem(implies(and(_u67, _u66), _u67)) )).
% 2.25/2.41 cnf(matrix-49, plain, ( ~is_a_theorem(implies(and(skolem34, skolem35), skolem34)) | kn2 )).
% 2.25/2.41 cnf(matrix-50, plain, ( ~kn3 | is_a_theorem(implies(implies(_u72, _u71), implies(not(and(_u71, _u70)), not(and(_u70, _u72))))) )).
% 2.25/2.41 cnf(matrix-51, plain, ( ~is_a_theorem(implies(implies(skolem36, skolem37), implies(not(and(skolem37, skolem38)), not(and(skolem38, skolem36))))) | kn3 )).
% 2.25/2.41 cnf(matrix-52, plain, ( ~cn1 | is_a_theorem(implies(implies(_u78, _u77), implies(implies(_u77, _u76), implies(_u78, _u76)))) )).
% 2.25/2.41 cnf(matrix-53, plain, ( ~is_a_theorem(implies(implies(skolem39, skolem40), implies(implies(skolem40, skolem41), implies(skolem39, skolem41)))) | cn1 )).
% 2.25/2.41 cnf(matrix-54, plain, ( ~cn2 | is_a_theorem(implies(_u83, implies(not(_u83), _u82))) )).
% 2.25/2.41 cnf(matrix-55, plain, ( ~is_a_theorem(implies(skolem42, implies(not(skolem42), skolem43))) | cn2 )).
% 2.25/2.41 cnf(matrix-56, plain, ( ~cn3 | is_a_theorem(implies(implies(not(_u86), _u86), _u86)) )).
% 2.25/2.41 cnf(matrix-57, plain, ( ~is_a_theorem(implies(implies(not(skolem44), skolem44), skolem44)) | cn3 )).
% 2.25/2.41 cnf(matrix-58, plain, ( ~r1 | is_a_theorem(implies(or(_u88, _u88), _u88)) )).
% 2.25/2.41 cnf(matrix-59, plain, ( ~is_a_theorem(implies(or(skolem45, skolem45), skolem45)) | r1 )).
% 2.25/2.41 cnf(matrix-60, plain, ( ~r2 | is_a_theorem(implies(_u90, or(_u91, _u90))) )).
% 2.25/2.41 cnf(matrix-61, plain, ( ~is_a_theorem(implies(skolem47, or(skolem46, skolem47))) | r2 )).
% 2.25/2.41 cnf(matrix-62, plain, ( ~r3 | is_a_theorem(implies(or(_u95, _u94), or(_u94, _u95))) )).
% 2.25/2.41 cnf(matrix-63, plain, ( ~is_a_theorem(implies(or(skolem48, skolem49), or(skolem49, skolem48))) | r3 )).
% 2.25/2.41 cnf(matrix-64, plain, ( ~r4 | is_a_theorem(implies(or(_u100, or(_u99, _u98)), or(_u99, or(_u100, _u98)))) )).
% 2.25/2.41 cnf(matrix-65, plain, ( ~is_a_theorem(implies(or(skolem50, or(skolem51, skolem52)), or(skolem51, or(skolem50, skolem52)))) | r4 )).
% 2.25/2.41 cnf(matrix-66, plain, ( ~r5 | is_a_theorem(implies(implies(_u105, _u104), implies(or(_u106, _u105), or(_u106, _u104)))) )).
% 2.25/2.41 cnf(matrix-67, plain, ( ~is_a_theorem(implies(implies(skolem54, skolem55), implies(or(skolem53, skolem54), or(skolem53, skolem55)))) | r5 )).
% 2.25/2.41 cnf(matrix-68, plain, ( ~op_or | ( or(_u111, _u110) = not(and(not(_u111), not(_u110)))) )).
% 2.25/2.41 cnf(matrix-69, plain, ( ~op_and | ( and(_u113, _u112) = not(or(not(_u113), not(_u112)))) )).
% 2.25/2.41 cnf(matrix-70, plain, ( ~op_implies_and | ( implies(_u115, _u114) = not(and(_u115, not(_u114)))) )).
% 2.25/2.41 cnf(matrix-71, plain, ( ~op_implies_or | ( implies(_u117, _u116) = or(not(_u117), _u116)) )).
% 2.25/2.41 cnf(matrix-72, plain, ( ~op_equiv | ( equiv(_u119, _u118) = and(implies(_u119, _u118), implies(_u118, _u119))) )).
% 2.25/2.41 cnf(matrix-73, plain, ( op_or )).
% 2.25/2.41 cnf(matrix-74, plain, ( op_implies_and )).
% 2.25/2.41 cnf(matrix-75, plain, ( op_equiv )).
% 2.25/2.41 cnf(matrix-76, plain, ( modus_ponens )).
% 2.25/2.41 cnf(matrix-77, plain, ( modus_tollens )).
% 2.25/2.41 cnf(matrix-78, plain, ( implies_1 )).
% 2.25/2.41 cnf(matrix-79, plain, ( implies_2 )).
% 2.25/2.41 cnf(matrix-80, plain, ( implies_3 )).
% 2.25/2.41 cnf(matrix-81, plain, ( and_1 )).
% 2.25/2.41 cnf(matrix-82, plain, ( and_2 )).
% 2.25/2.41 cnf(matrix-83, plain, ( and_3 )).
% 2.25/2.41 cnf(matrix-84, plain, ( or_1 )).
% 2.25/2.41 cnf(matrix-85, plain, ( or_2 )).
% 2.25/2.41 cnf(matrix-86, plain, ( or_3 )).
% 2.25/2.41 cnf(matrix-87, plain, ( equivalence_1 )).
% 2.25/2.41 cnf(matrix-88, plain, ( equivalence_2 )).
% 2.25/2.41 cnf(matrix-89, plain, ( equivalence_3 )).
% 2.25/2.41 cnf(matrix-90, plain, ( substitution_of_equivalents )).
% 2.25/2.41 cnf(matrix-91, plain, ( ~necessitation | ~is_a_theorem(_u120) | is_a_theorem(necessarily(_u120)) )).
% 2.25/2.41 cnf(matrix-92, plain, ( necessitation | is_a_theorem(skolem56) )).
% 2.25/2.41 cnf(matrix-93, plain, ( necessitation | ~is_a_theorem(necessarily(skolem56)) )).
% 2.25/2.41 cnf(matrix-94, plain, ( ~modus_ponens_strict_implies | ~is_a_theorem(_u123) | ~is_a_theorem(strict_implies(_u123, _u122)) | is_a_theorem(_u122) )).
% 2.25/2.41 cnf(matrix-95, plain, ( modus_ponens_strict_implies | is_a_theorem(skolem57) )).
% 2.25/2.41 cnf(matrix-96, plain, ( modus_ponens_strict_implies | is_a_theorem(strict_implies(skolem57, skolem58)) )).
% 2.25/2.41 cnf(matrix-97, plain, ( modus_ponens_strict_implies | ~is_a_theorem(skolem58) )).
% 2.25/2.41 cnf(matrix-98, plain, ( ~adjunction | ~is_a_theorem(_u127) | ~is_a_theorem(_u126) | is_a_theorem(and(_u127, _u126)) )).
% 2.25/2.41 cnf(matrix-99, plain, ( adjunction | is_a_theorem(skolem59) )).
% 2.25/2.41 cnf(matrix-100, plain, ( adjunction | is_a_theorem(skolem60) )).
% 2.25/2.41 cnf(matrix-101, plain, ( adjunction | ~is_a_theorem(and(skolem59, skolem60)) )).
% 2.25/2.41 cnf(matrix-102, plain, ( ~substitution_strict_equiv | ~is_a_theorem(strict_equiv(_u131, _u130)) | ( _u131 = _u130) )).
% 2.25/2.41 cnf(matrix-103, plain, ( substitution_strict_equiv | is_a_theorem(strict_equiv(skolem61, skolem62)) )).
% 2.25/2.41 cnf(matrix-104, plain, ( substitution_strict_equiv | ( skolem61 != skolem62) )).
% 2.25/2.41 cnf(matrix-105, plain, ( ~axiom_K | is_a_theorem(implies(necessarily(implies(_u135, _u134)), implies(necessarily(_u135), necessarily(_u134)))) )).
% 2.25/2.41 cnf(matrix-106, plain, ( ~is_a_theorem(implies(necessarily(implies(skolem63, skolem64)), implies(necessarily(skolem63), necessarily(skolem64)))) | axiom_K )).
% 2.25/2.41 cnf(matrix-107, plain, ( ~axiom_M | is_a_theorem(implies(necessarily(_u138), _u138)) )).
% 2.25/2.41 cnf(matrix-108, plain, ( ~is_a_theorem(implies(necessarily(skolem65), skolem65)) | axiom_M )).
% 2.25/2.41 cnf(matrix-109, plain, ( ~axiom_4 | is_a_theorem(implies(necessarily(_u140), necessarily(necessarily(_u140)))) )).
% 2.25/2.41 cnf(matrix-110, plain, ( ~is_a_theorem(implies(necessarily(skolem66), necessarily(necessarily(skolem66)))) | axiom_4 )).
% 2.25/2.41 cnf(matrix-111, plain, ( ~axiom_B | is_a_theorem(implies(_u142, necessarily(possibly(_u142)))) )).
% 2.25/2.41 cnf(matrix-112, plain, ( ~is_a_theorem(implies(skolem67, necessarily(possibly(skolem67)))) | axiom_B )).
% 2.25/2.41 cnf(matrix-113, plain, ( ~axiom_5 | is_a_theorem(implies(possibly(_u144), necessarily(possibly(_u144)))) )).
% 2.25/2.41 cnf(matrix-114, plain, ( ~is_a_theorem(implies(possibly(skolem68), necessarily(possibly(skolem68)))) | axiom_5 )).
% 2.25/2.41 cnf(matrix-115, plain, ( ~axiom_s1 | is_a_theorem(implies(and(necessarily(implies(_u148, _u147)), necessarily(implies(_u147, _u146))), necessarily(implies(_u148, _u146)))) )).
% 2.25/2.41 cnf(matrix-116, plain, ( ~is_a_theorem(implies(and(necessarily(implies(skolem69, skolem70)), necessarily(implies(skolem70, skolem71))), necessarily(implies(skolem69, skolem71)))) | axiom_s1 )).
% 2.25/2.41 cnf(matrix-117, plain, ( ~axiom_s2 | is_a_theorem(strict_implies(possibly(and(_u153, _u152)), and(possibly(_u153), possibly(_u152)))) )).
% 2.25/2.41 cnf(matrix-118, plain, ( ~is_a_theorem(strict_implies(possibly(and(skolem72, skolem73)), and(possibly(skolem72), possibly(skolem73)))) | axiom_s2 )).
% 2.25/2.41 cnf(matrix-119, plain, ( ~axiom_s3 | is_a_theorem(strict_implies(strict_implies(_u157, _u156), strict_implies(not(possibly(_u156)), not(possibly(_u157))))) )).
% 2.25/2.41 cnf(matrix-120, plain, ( ~is_a_theorem(strict_implies(strict_implies(skolem74, skolem75), strict_implies(not(possibly(skolem75)), not(possibly(skolem74))))) | axiom_s3 )).
% 2.25/2.41 cnf(matrix-121, plain, ( ~axiom_s4 | is_a_theorem(strict_implies(necessarily(_u160), necessarily(necessarily(_u160)))) )).
% 2.25/2.41 cnf(matrix-122, plain, ( ~is_a_theorem(strict_implies(necessarily(skolem76), necessarily(necessarily(skolem76)))) | axiom_s4 )).
% 2.25/2.41 cnf(matrix-123, plain, ( ~axiom_m1 | is_a_theorem(strict_implies(and(_u163, _u162), and(_u162, _u163))) )).
% 2.25/2.41 cnf(matrix-124, plain, ( ~is_a_theorem(strict_implies(and(skolem77, skolem78), and(skolem78, skolem77))) | axiom_m1 )).
% 2.25/2.41 cnf(matrix-125, plain, ( ~axiom_m2 | is_a_theorem(strict_implies(and(_u167, _u166), _u167)) )).
% 2.25/2.41 cnf(matrix-126, plain, ( ~is_a_theorem(strict_implies(and(skolem79, skolem80), skolem79)) | axiom_m2 )).
% 2.25/2.41 cnf(matrix-127, plain, ( ~axiom_m3 | is_a_theorem(strict_implies(and(and(_u172, _u171), _u170), and(_u172, and(_u171, _u170)))) )).
% 2.25/2.41 cnf(matrix-128, plain, ( ~is_a_theorem(strict_implies(and(and(skolem81, skolem82), skolem83), and(skolem81, and(skolem82, skolem83)))) | axiom_m3 )).
% 2.25/2.41 cnf(matrix-129, plain, ( ~axiom_m4 | is_a_theorem(strict_implies(_u176, and(_u176, _u176))) )).
% 2.25/2.41 cnf(matrix-130, plain, ( ~is_a_theorem(strict_implies(skolem84, and(skolem84, skolem84))) | axiom_m4 )).
% 2.25/2.41 cnf(matrix-131, plain, ( ~axiom_m5 | is_a_theorem(strict_implies(and(strict_implies(_u180, _u179), strict_implies(_u179, _u178)), strict_implies(_u180, _u178))) )).
% 2.25/2.41 cnf(matrix-132, plain, ( ~is_a_theorem(strict_implies(and(strict_implies(skolem85, skolem86), strict_implies(skolem86, skolem87)), strict_implies(skolem85, skolem87))) | axiom_m5 )).
% 2.25/2.41 cnf(matrix-133, plain, ( ~axiom_m6 | is_a_theorem(strict_implies(_u184, possibly(_u184))) )).
% 2.25/2.41 cnf(matrix-134, plain, ( ~is_a_theorem(strict_implies(skolem88, possibly(skolem88))) | axiom_m6 )).
% 2.25/2.41 cnf(matrix-135, plain, ( ~axiom_m7 | is_a_theorem(strict_implies(possibly(and(_u187, _u186)), _u187)) )).
% 2.25/2.41 cnf(matrix-136, plain, ( ~is_a_theorem(strict_implies(possibly(and(skolem89, skolem90)), skolem89)) | axiom_m7 )).
% 2.25/2.41 cnf(matrix-137, plain, ( ~axiom_m8 | is_a_theorem(strict_implies(strict_implies(_u191, _u190), strict_implies(possibly(_u191), possibly(_u190)))) )).
% 2.25/2.41 cnf(matrix-138, plain, ( ~is_a_theorem(strict_implies(strict_implies(skolem91, skolem92), strict_implies(possibly(skolem91), possibly(skolem92)))) | axiom_m8 )).
% 2.25/2.41 cnf(matrix-139, plain, ( ~axiom_m9 | is_a_theorem(strict_implies(possibly(possibly(_u194)), possibly(_u194))) )).
% 2.25/2.41 cnf(matrix-140, plain, ( ~is_a_theorem(strict_implies(possibly(possibly(skolem93)), possibly(skolem93))) | axiom_m9 )).
% 2.25/2.41 cnf(matrix-141, plain, ( ~axiom_m10 | is_a_theorem(strict_implies(possibly(_u196), necessarily(possibly(_u196)))) )).
% 2.25/2.41 cnf(matrix-142, plain, ( ~is_a_theorem(strict_implies(possibly(skolem94), necessarily(possibly(skolem94)))) | axiom_m10 )).
% 2.25/2.41 cnf(matrix-143, plain, ( ~op_possibly | ( possibly(_u198) = not(necessarily(not(_u198)))) )).
% 2.25/2.41 cnf(matrix-144, plain, ( ~op_necessarily | ( necessarily(_u199) = not(possibly(not(_u199)))) )).
% 2.25/2.41 cnf(matrix-145, plain, ( ~op_strict_implies | ( strict_implies(_u201, _u200) = necessarily(implies(_u201, _u200))) )).
% 2.25/2.41 cnf(matrix-146, plain, ( ~op_strict_equiv | ( strict_equiv(_u203, _u202) = and(strict_implies(_u203, _u202), strict_implies(_u202, _u203))) )).
% 2.25/2.41 cnf(matrix-147, plain, ( op_possibly )).
% 2.25/2.41 cnf(matrix-148, plain, ( necessitation )).
% 2.25/2.41 cnf(matrix-149, plain, ( axiom_K )).
% 2.25/2.41 cnf(matrix-150, plain, ( axiom_M )).
% 2.25/2.41 cnf(matrix-151, plain, ( axiom_4 )).
% 2.25/2.41 cnf(matrix-152, plain, ( axiom_B )).
% 2.25/2.41 cnf(matrix-153, plain, ( op_possibly )).
% 2.25/2.41 cnf(matrix-154, plain, ( op_or )).
% 2.25/2.41 cnf(matrix-155, plain, ( op_implies )).
% 2.25/2.41 cnf(matrix-156, plain, ( op_strict_implies )).
% 2.25/2.41 cnf(matrix-157, plain, ( op_equiv )).
% 2.25/2.41 cnf(matrix-158, plain, ( op_strict_equiv )).
% 2.25/2.41 cnf(matrix-159, plain, ( ~modus_ponens_strict_implies )).
% 2.25/2.41
% 2.25/2.41 % Proof stack:
% 2.25/2.41 cnf(proof-stack, plain,
% 2.25/2.41 proof_stack(
% 2.25/2.41 start(159),
% 2.25/2.41 left_branch(0, 97, 0, 2),
% 2.25/2.41 left_branch(0, 13, 3, 3),
% 2.25/2.41 left_branch(0, 76, 0, 4),
% 2.25/2.41 right_branch(4),
% 2.25/2.41 left_branch(0, 13, 3, 5),
% 2.25/2.41 lemmata(0, 0),
% 2.25/2.41 left_branch(0, 107, 1, 7),
% 2.25/2.41 left_branch(0, 150, 0, 8),
% 2.25/2.41 right_branch(8),
% 2.25/2.41 right_branch(7),
% 2.25/2.41 left_branch(0, 12, 2, 8),
% 2.25/2.41 left_branch(0, 145, 1, 9),
% 2.25/2.41 left_branch(0, 156, 0, 10),
% 2.25/2.41 right_branch(10),
% 2.25/2.41 right_branch(9),
% 2.25/2.41 left_branch(0, 96, 1, 10),
% 2.25/2.41 reduction(0, 0),
% 2.25/2.41 right_branch(10),
% 2.25/2.41 right_branch(8),
% 2.25/2.41 right_branch(5),
% 2.25/2.41 left_branch(0, 95, 1, 6),
% 2.25/2.41 reduction(0, 0),
% 2.25/2.41 right_branch(6),
% 2.25/2.41 right_branch(3),
% 2.25/2.41 right_branch(2)
% 2.25/2.41 )).
% 2.25/2.41 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------