TSTP Solution File: LCL528+1 by Etableau---0.67
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Etableau---0.67
% Problem : LCL528+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : etableau --auto --tsmdo --quicksat=10000 --tableau=1 --tableau-saturation=1 -s -p --tableau-cores=8 --cpu-limit=%d %s
% Computer : n017.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 : 600s
% DateTime : Sun Jul 17 10:22:50 EDT 2022
% Result : Theorem 3.75s 0.87s
% Output : CNFRefutation 3.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL528+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : etableau --auto --tsmdo --quicksat=10000 --tableau=1 --tableau-saturation=1 -s -p --tableau-cores=8 --cpu-limit=%d %s
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 3 02:58:26 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.38 # No SInE strategy applied
% 0.19/0.38 # Auto-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 0.19/0.38 # and selection function SelectComplexExceptUniqMaxHorn.
% 0.19/0.38 #
% 0.19/0.38 # Presaturation interreduction done
% 0.19/0.38 # Number of axioms: 146 Number of unprocessed: 115
% 0.19/0.38 # Tableaux proof search.
% 0.19/0.38 # APR header successfully linked.
% 0.19/0.38 # Hello from C++
% 0.19/0.39 # The folding up rule is enabled...
% 0.19/0.39 # Local unification is enabled...
% 0.19/0.39 # Any saturation attempts will use folding labels...
% 0.19/0.39 # 115 beginning clauses after preprocessing and clausification
% 0.19/0.39 # Creating start rules for all 1 conjectures.
% 0.19/0.39 # There are 1 start rule candidates:
% 0.19/0.39 # Found 54 unit axioms.
% 0.19/0.39 # 1 start rule tableaux created.
% 0.19/0.39 # 61 extension rule candidate clauses
% 0.19/0.39 # 54 unit axiom clauses
% 0.19/0.39
% 0.19/0.39 # Requested 8, 32 cores available to the main process.
% 0.19/0.39 # There are not enough tableaux to fork, creating more from the initial 1
% 0.19/0.39 # Creating equality axioms
% 0.19/0.39 # Ran out of tableaux, making start rules for all clauses
% 0.19/0.39 # Returning from population with 115 new_tableaux and 0 remaining starting tableaux.
% 0.19/0.39 # We now have 115 tableaux to operate on
% 3.75/0.87 # There were 2 total branch saturation attempts.
% 3.75/0.87 # There were 0 of these attempts blocked.
% 3.75/0.87 # There were 0 deferred branch saturation attempts.
% 3.75/0.87 # There were 0 free duplicated saturations.
% 3.75/0.87 # There were 2 total successful branch saturations.
% 3.75/0.87 # There were 0 successful branch saturations in interreduction.
% 3.75/0.87 # There were 0 successful branch saturations on the branch.
% 3.75/0.87 # There were 2 successful branch saturations after the branch.
% 3.75/0.87 # SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.75/0.87 # SZS output start for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.75/0.87 # Begin clausification derivation
% 3.75/0.87
% 3.75/0.87 # End clausification derivation
% 3.75/0.87 # Begin listing active clauses obtained from FOF to CNF conversion
% 3.75/0.87 cnf(i_0_64, plain, (modus_ponens)).
% 3.75/0.87 cnf(i_0_78, plain, (substitution_of_equivalents)).
% 3.75/0.87 cnf(i_0_65, plain, (modus_tollens)).
% 3.75/0.87 cnf(i_0_66, plain, (implies_1)).
% 3.75/0.87 cnf(i_0_67, plain, (implies_2)).
% 3.75/0.87 cnf(i_0_68, plain, (implies_3)).
% 3.75/0.87 cnf(i_0_69, plain, (and_1)).
% 3.75/0.87 cnf(i_0_70, plain, (and_2)).
% 3.75/0.87 cnf(i_0_71, plain, (and_3)).
% 3.75/0.87 cnf(i_0_72, plain, (or_1)).
% 3.75/0.87 cnf(i_0_73, plain, (or_2)).
% 3.75/0.87 cnf(i_0_74, plain, (or_3)).
% 3.75/0.87 cnf(i_0_75, plain, (equivalence_1)).
% 3.75/0.87 cnf(i_0_76, plain, (equivalence_2)).
% 3.75/0.87 cnf(i_0_77, plain, (equivalence_3)).
% 3.75/0.87 cnf(i_0_61, plain, (op_or)).
% 3.75/0.87 cnf(i_0_62, plain, (op_implies_and)).
% 3.75/0.87 cnf(i_0_63, plain, (op_equiv)).
% 3.75/0.87 cnf(i_0_136, plain, (necessitation)).
% 3.75/0.87 cnf(i_0_137, plain, (axiom_K)).
% 3.75/0.87 cnf(i_0_138, plain, (axiom_M)).
% 3.75/0.87 cnf(i_0_139, plain, (axiom_5)).
% 3.75/0.87 cnf(i_0_135, plain, (op_possibly)).
% 3.75/0.87 cnf(i_0_143, plain, (op_strict_implies)).
% 3.75/0.87 cnf(i_0_145, plain, (op_strict_equiv)).
% 3.75/0.87 cnf(i_0_142, plain, (op_implies)).
% 3.75/0.87 cnf(i_0_131, plain, (not(necessarily(not(X1)))=possibly(X1))).
% 3.75/0.87 cnf(i_0_96, plain, (is_a_theorem(implies(necessarily(X1),X1)))).
% 3.75/0.87 cnf(i_0_133, plain, (necessarily(implies(X1,X2))=strict_implies(X1,X2))).
% 3.75/0.87 cnf(i_0_11, plain, (is_a_theorem(implies(X1,implies(X2,X1))))).
% 3.75/0.87 cnf(i_0_25, plain, (is_a_theorem(implies(X1,or(X2,X1))))).
% 3.75/0.87 cnf(i_0_48, plain, (r2)).
% 3.75/0.87 cnf(i_0_23, plain, (is_a_theorem(implies(X1,or(X1,X2))))).
% 3.75/0.87 cnf(i_0_19, plain, (is_a_theorem(implies(and(X1,X2),X2)))).
% 3.75/0.87 cnf(i_0_58, plain, (not(and(X1,not(X2)))=implies(X1,X2))).
% 3.75/0.87 cnf(i_0_17, plain, (is_a_theorem(implies(and(X1,X2),X1)))).
% 3.75/0.87 cnf(i_0_36, plain, (kn2)).
% 3.75/0.87 cnf(i_0_102, plain, (is_a_theorem(implies(possibly(X1),necessarily(possibly(X1)))))).
% 3.75/0.87 cnf(i_0_56, plain, (implies(not(X1),X2)=or(X1,X2))).
% 3.75/0.87 cnf(i_0_42, plain, (cn2)).
% 3.75/0.87 cnf(i_0_31, plain, (is_a_theorem(implies(equiv(X1,X2),implies(X2,X1))))).
% 3.75/0.87 cnf(i_0_29, plain, (is_a_theorem(implies(equiv(X1,X2),implies(X1,X2))))).
% 3.75/0.87 cnf(i_0_21, plain, (is_a_theorem(implies(X1,implies(X2,and(X1,X2)))))).
% 3.75/0.87 cnf(i_0_134, plain, (and(strict_implies(X1,X2),strict_implies(X2,X1))=strict_equiv(X1,X2))).
% 3.75/0.87 cnf(i_0_9, plain, (is_a_theorem(implies(or(X1,not(X2)),implies(X2,X1))))).
% 3.75/0.87 cnf(i_0_13, plain, (is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))))).
% 3.75/0.87 cnf(i_0_94, plain, (is_a_theorem(implies(strict_implies(X1,X2),implies(necessarily(X1),necessarily(X2)))))).
% 3.75/0.87 cnf(i_0_15, plain, (is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))))).
% 3.75/0.87 cnf(i_0_33, plain, (is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X1),equiv(X1,X2)))))).
% 3.75/0.87 cnf(i_0_40, plain, (cn1)).
% 3.75/0.87 cnf(i_0_27, plain, (is_a_theorem(implies(implies(X1,X2),implies(implies(X3,X2),implies(or(X1,X3),X2)))))).
% 3.75/0.87 cnf(i_0_60, plain, (equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1)))).
% 3.75/0.87 cnf(i_0_146, negated_conjecture, (~axiom_m1)).
% 3.75/0.87 cnf(i_0_111, plain, (~is_a_theorem(strict_implies(and(esk77_0,esk78_0),and(esk78_0,esk77_0))))).
% 3.75/0.87 cnf(i_0_90, plain, (substitution_strict_equiv|esk62_0!=esk61_0)).
% 3.75/0.87 cnf(i_0_82, plain, (modus_ponens_strict_implies|~is_a_theorem(esk58_0))).
% 3.75/0.87 cnf(i_0_84, plain, (modus_ponens_strict_implies|is_a_theorem(esk57_0))).
% 3.75/0.87 cnf(i_0_88, plain, (adjunction|is_a_theorem(esk59_0))).
% 3.75/0.87 cnf(i_0_87, plain, (adjunction|is_a_theorem(esk60_0))).
% 3.75/0.87 cnf(i_0_86, plain, (adjunction|~is_a_theorem(and(esk59_0,esk60_0)))).
% 3.75/0.87 cnf(i_0_121, plain, (axiom_m6|~is_a_theorem(strict_implies(esk88_0,possibly(esk88_0))))).
% 3.75/0.87 cnf(i_0_81, plain, (is_a_theorem(necessarily(X1))|~is_a_theorem(X1))).
% 3.75/0.87 cnf(i_0_99, plain, (axiom_B|~is_a_theorem(implies(esk67_0,necessarily(possibly(esk67_0)))))).
% 3.75/0.87 cnf(i_0_83, plain, (modus_ponens_strict_implies|is_a_theorem(strict_implies(esk57_0,esk58_0)))).
% 3.75/0.87 cnf(i_0_7, plain, (X1=X2|~is_a_theorem(equiv(X1,X2)))).
% 3.75/0.87 cnf(i_0_92, plain, (X1=X2|~substitution_strict_equiv|~is_a_theorem(strict_equiv(X1,X2)))).
% 3.75/0.87 cnf(i_0_34, plain, (kn1|~is_a_theorem(implies(esk33_0,and(esk33_0,esk33_0))))).
% 3.75/0.87 cnf(i_0_91, plain, (substitution_strict_equiv|is_a_theorem(strict_equiv(esk61_0,esk62_0)))).
% 3.75/0.87 cnf(i_0_117, plain, (axiom_m4|~is_a_theorem(strict_implies(esk84_0,and(esk84_0,esk84_0))))).
% 3.75/0.87 cnf(i_0_132, plain, (not(possibly(not(X1)))=necessarily(X1)|~op_necessarily)).
% 3.75/0.87 cnf(i_0_46, plain, (r1|~is_a_theorem(implies(or(esk45_0,esk45_0),esk45_0)))).
% 3.75/0.87 cnf(i_0_113, plain, (axiom_m2|~is_a_theorem(strict_implies(and(esk79_0,esk80_0),esk79_0)))).
% 3.75/0.87 cnf(i_0_4, plain, (is_a_theorem(X1)|~is_a_theorem(implies(X2,X1))|~is_a_theorem(X2))).
% 3.75/0.87 cnf(i_0_122, plain, (is_a_theorem(strict_implies(X1,possibly(X1)))|~axiom_m6)).
% 3.75/0.87 cnf(i_0_97, plain, (axiom_4|~is_a_theorem(implies(necessarily(esk66_0),necessarily(necessarily(esk66_0)))))).
% 3.75/0.87 cnf(i_0_109, plain, (axiom_s4|~is_a_theorem(strict_implies(necessarily(esk76_0),necessarily(necessarily(esk76_0)))))).
% 3.75/0.87 cnf(i_0_59, plain, (or(not(X1),X2)=implies(X1,X2)|~op_implies_or)).
% 3.75/0.87 cnf(i_0_85, plain, (is_a_theorem(X1)|~modus_ponens_strict_implies|~is_a_theorem(strict_implies(X2,X1))|~is_a_theorem(X2))).
% 3.75/0.87 cnf(i_0_129, plain, (axiom_m10|~is_a_theorem(strict_implies(possibly(esk94_0),necessarily(possibly(esk94_0)))))).
% 3.75/0.87 cnf(i_0_127, plain, (axiom_m9|~is_a_theorem(strict_implies(possibly(possibly(esk93_0)),possibly(esk93_0))))).
% 3.75/0.87 cnf(i_0_100, plain, (is_a_theorem(implies(X1,necessarily(possibly(X1))))|~axiom_B)).
% 3.75/0.87 cnf(i_0_123, plain, (axiom_m7|~is_a_theorem(strict_implies(possibly(and(esk89_0,esk90_0)),esk89_0)))).
% 3.75/0.87 cnf(i_0_89, plain, (is_a_theorem(and(X1,X2))|~adjunction|~is_a_theorem(X2)|~is_a_theorem(X1))).
% 3.75/0.87 cnf(i_0_50, plain, (r3|~is_a_theorem(implies(or(esk48_0,esk49_0),or(esk49_0,esk48_0))))).
% 3.75/0.87 cnf(i_0_35, plain, (is_a_theorem(implies(X1,and(X1,X1)))|~kn1)).
% 3.75/0.87 cnf(i_0_118, plain, (is_a_theorem(strict_implies(X1,and(X1,X1)))|~axiom_m4)).
% 3.75/0.87 cnf(i_0_47, plain, (is_a_theorem(implies(or(X1,X1),X1))|~r1)).
% 3.75/0.87 cnf(i_0_114, plain, (is_a_theorem(strict_implies(and(X1,X2),X1))|~axiom_m2)).
% 3.75/0.87 cnf(i_0_125, plain, (axiom_m8|~is_a_theorem(strict_implies(strict_implies(esk91_0,esk92_0),strict_implies(possibly(esk91_0),possibly(esk92_0)))))).
% 3.75/0.87 cnf(i_0_98, plain, (is_a_theorem(implies(necessarily(X1),necessarily(necessarily(X1))))|~axiom_4)).
% 3.75/0.87 cnf(i_0_110, plain, (is_a_theorem(strict_implies(necessarily(X1),necessarily(necessarily(X1))))|~axiom_s4)).
% 3.75/0.87 cnf(i_0_130, plain, (is_a_theorem(strict_implies(possibly(X1),necessarily(possibly(X1))))|~axiom_m10)).
% 3.75/0.87 cnf(i_0_57, plain, (not(or(not(X1),not(X2)))=and(X1,X2)|~op_and)).
% 3.75/0.87 cnf(i_0_128, plain, (is_a_theorem(strict_implies(possibly(possibly(X1)),possibly(X1)))|~axiom_m9)).
% 3.75/0.87 cnf(i_0_124, plain, (is_a_theorem(strict_implies(possibly(and(X1,X2)),X1))|~axiom_m7)).
% 3.75/0.87 cnf(i_0_105, plain, (axiom_s2|~is_a_theorem(strict_implies(possibly(and(esk72_0,esk73_0)),and(possibly(esk72_0),possibly(esk73_0)))))).
% 3.75/0.87 cnf(i_0_45, plain, (is_a_theorem(implies(or(X1,X1),X1))|~cn3)).
% 3.75/0.87 cnf(i_0_51, plain, (is_a_theorem(implies(or(X1,X2),or(X2,X1)))|~r3)).
% 3.75/0.87 cnf(i_0_44, plain, (cn3|~is_a_theorem(implies(or(esk44_0,esk44_0),esk44_0)))).
% 3.75/0.87 cnf(i_0_107, plain, (axiom_s3|~is_a_theorem(strict_implies(strict_implies(esk74_0,esk75_0),strict_implies(not(possibly(esk75_0)),not(possibly(esk74_0))))))).
% 3.75/0.87 cnf(i_0_126, plain, (is_a_theorem(strict_implies(strict_implies(X1,X2),strict_implies(possibly(X1),possibly(X2))))|~axiom_m8)).
% 3.75/0.87 cnf(i_0_54, plain, (r5|~is_a_theorem(implies(implies(esk54_0,esk55_0),implies(or(esk53_0,esk54_0),or(esk53_0,esk55_0)))))).
% 3.75/0.87 cnf(i_0_52, plain, (r4|~is_a_theorem(implies(or(esk50_0,or(esk51_0,esk52_0)),or(esk51_0,or(esk50_0,esk52_0)))))).
% 3.75/0.87 cnf(i_0_115, plain, (axiom_m3|~is_a_theorem(strict_implies(and(and(esk81_0,esk82_0),esk83_0),and(esk81_0,and(esk82_0,esk83_0)))))).
% 3.75/0.87 cnf(i_0_119, plain, (axiom_m5|~is_a_theorem(strict_implies(and(strict_implies(esk85_0,esk86_0),strict_implies(esk86_0,esk87_0)),strict_implies(esk85_0,esk87_0))))).
% 3.75/0.87 cnf(i_0_38, plain, (kn3|~is_a_theorem(implies(implies(esk36_0,esk37_0),or(and(esk37_0,esk38_0),not(and(esk38_0,esk36_0))))))).
% 3.75/0.87 cnf(i_0_106, plain, (is_a_theorem(strict_implies(possibly(and(X1,X2)),and(possibly(X1),possibly(X2))))|~axiom_s2)).
% 3.75/0.87 cnf(i_0_103, plain, (axiom_s1|~is_a_theorem(implies(and(strict_implies(esk69_0,esk70_0),strict_implies(esk70_0,esk71_0)),strict_implies(esk69_0,esk71_0))))).
% 3.75/0.87 cnf(i_0_108, plain, (is_a_theorem(strict_implies(strict_implies(X1,X2),strict_implies(not(possibly(X2)),not(possibly(X1)))))|~axiom_s3)).
% 3.75/0.87 cnf(i_0_55, plain, (is_a_theorem(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2))))|~r5)).
% 3.75/0.87 cnf(i_0_53, plain, (is_a_theorem(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3))))|~r4)).
% 3.75/0.87 cnf(i_0_116, plain, (is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3))))|~axiom_m3)).
% 3.75/0.87 cnf(i_0_120, plain, (is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3)))|~axiom_m5)).
% 3.75/0.87 cnf(i_0_39, plain, (is_a_theorem(implies(implies(X1,X2),or(and(X2,X3),not(and(X3,X1)))))|~kn3)).
% 3.75/0.87 cnf(i_0_104, plain, (is_a_theorem(implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3)))|~axiom_s1)).
% 3.75/0.87 cnf(i_0_276, plain, (X211=X211)).
% 3.75/0.87 # End listing active clauses. There is an equivalent clause to each of these in the clausification!
% 3.75/0.87 # Begin printing tableau
% 3.75/0.87 # Found 5 steps
% 3.75/0.87 cnf(i_0_119, plain, (axiom_m5|~is_a_theorem(strict_implies(and(strict_implies(esk85_0,esk86_0),strict_implies(esk86_0,esk87_0)),strict_implies(esk85_0,esk87_0)))), inference(start_rule)).
% 3.75/0.87 cnf(i_0_450, plain, (axiom_m5), inference(extension_rule, [i_0_120])).
% 3.75/0.87 cnf(i_0_1081, plain, (is_a_theorem(strict_implies(and(strict_implies(X7,X3),strict_implies(X3,X8)),strict_implies(X7,X8)))), inference(extension_rule, [i_0_81])).
% 3.75/0.87 cnf(i_0_451, plain, (~is_a_theorem(strict_implies(and(strict_implies(esk85_0,esk86_0),strict_implies(esk86_0,esk87_0)),strict_implies(esk85_0,esk87_0)))), inference(etableau_closure_rule, [i_0_451, ...])).
% 3.75/0.87 cnf(i_0_1097, plain, (is_a_theorem(necessarily(strict_implies(and(strict_implies(X7,X3),strict_implies(X3,X8)),strict_implies(X7,X8))))), inference(etableau_closure_rule, [i_0_1097, ...])).
% 3.75/0.87 # End printing tableau
% 3.75/0.87 # SZS output end
% 3.75/0.87 # Branches closed with saturation will be marked with an "s"
% 3.97/0.87 # Child (8266) has found a proof.
% 3.97/0.87
% 3.97/0.87 # Proof search is over...
% 3.97/0.87 # Freeing feature tree
%------------------------------------------------------------------------------