0.03/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.13 % Command : run_E %s %d THM 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 : 960 0.12/0.34 % WCLimit : 120 0.12/0.34 % DateTime : Tue Aug 9 04:35:30 EDT 2022 0.12/0.34 % CPUTime : 0.19/0.46 Running first-order on 8 cores theorem proving 0.19/0.46 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=120 /export/starexec/sandbox/benchmark/theBenchmark.p 0.19/0.46 # Version: 3.0pre003 0.85/0.59 # Preprocessing class: FSLSSLSSSSSNFFN. 0.85/0.59 # Scheduled 4 strats onto 8 cores with 120 seconds (960 total) 0.85/0.59 # Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 600s (5) cores 0.85/0.59 # Starting new_bool_3 with 120s (1) cores 0.85/0.59 # Starting new_bool_1 with 120s (1) cores 0.85/0.59 # Starting sh5l with 120s (1) cores 0.85/0.59 # H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with pid 30277 completed with status 0 0.85/0.59 # Result found by H----_102_C18_F1_PI_AE_CS_SP_PS_S2S 0.85/0.59 # Preprocessing class: FSLSSLSSSSSNFFN. 0.85/0.59 # Scheduled 4 strats onto 8 cores with 120 seconds (960 total) 0.85/0.59 # Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 600s (5) cores 0.85/0.59 # No SInE strategy applied 0.85/0.59 # Search class: FGUSF-FFMM21-MFFFFFNN 0.85/0.59 # Scheduled 7 strats onto 5 cores with 600 seconds (600 total) 0.85/0.59 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 270s (1) cores 0.85/0.59 # Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 61s (1) cores 0.85/0.59 # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 55s (1) cores 0.85/0.59 # Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 55s (1) cores 0.85/0.59 # Starting G-E--_208_C09_12_F1_SE_CS_SP_PS_S5PRR_S04AN with 55s (1) cores 0.85/0.59 # U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 30293 completed with status 0 0.85/0.59 # Result found by U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN 0.85/0.59 # Preprocessing class: FSLSSLSSSSSNFFN. 0.85/0.59 # Scheduled 4 strats onto 8 cores with 120 seconds (960 total) 0.85/0.59 # Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 600s (5) cores 0.85/0.59 # No SInE strategy applied 0.85/0.59 # Search class: FGUSF-FFMM21-MFFFFFNN 0.85/0.59 # Scheduled 7 strats onto 5 cores with 600 seconds (600 total) 0.85/0.59 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 270s (1) cores 0.85/0.59 # Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 61s (1) cores 0.85/0.59 # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 55s (1) cores 0.85/0.59 # Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 55s (1) cores 0.85/0.59 # Preprocessing time : 0.002 s 0.85/0.59 # Presaturation interreduction done 0.85/0.59 0.85/0.59 # Proof found! 0.85/0.59 # SZS status Theorem 0.85/0.59 # SZS output start CNFRefutation 0.85/0.59 tff(decl_22, type, and_1: $o). 0.85/0.59 tff(decl_23, type, and: ($i * $i) > $i). 0.85/0.59 tff(decl_24, type, implies: ($i * $i) > $i). 0.85/0.59 tff(decl_25, type, is_a_theorem: $i > $o). 0.85/0.59 tff(decl_26, type, modus_tollens: $o). 0.85/0.59 tff(decl_27, type, not: $i > $i). 0.85/0.59 tff(decl_28, type, and_2: $o). 0.85/0.59 tff(decl_29, type, or: ($i * $i) > $i). 0.85/0.59 tff(decl_30, type, or_3: $o). 0.85/0.59 tff(decl_31, type, and_3: $o). 0.85/0.59 tff(decl_32, type, equivalence_3: $o). 0.85/0.59 tff(decl_33, type, equiv: ($i * $i) > $i). 0.85/0.59 tff(decl_34, type, kn2: $o). 0.85/0.59 tff(decl_35, type, kn3: $o). 0.85/0.59 tff(decl_36, type, or_1: $o). 0.85/0.59 tff(decl_37, type, cn3: $o). 0.85/0.59 tff(decl_38, type, cn1: $o). 0.85/0.59 tff(decl_39, type, equivalence_1: $o). 0.85/0.59 tff(decl_40, type, substitution_of_equivalents: $o). 0.85/0.59 tff(decl_41, type, r5: $o). 0.85/0.59 tff(decl_42, type, r2: $o). 0.85/0.59 tff(decl_43, type, or_2: $o). 0.85/0.59 tff(decl_44, type, cn2: $o). 0.85/0.59 tff(decl_45, type, implies_2: $o). 0.85/0.59 tff(decl_46, type, r1: $o). 0.85/0.59 tff(decl_47, type, r3: $o). 0.85/0.59 tff(decl_48, type, r4: $o). 0.85/0.59 tff(decl_49, type, kn1: $o). 0.85/0.59 tff(decl_50, type, equivalence_2: $o). 0.85/0.59 tff(decl_51, type, modus_ponens: $o). 0.85/0.59 tff(decl_52, type, implies_1: $o). 0.85/0.59 tff(decl_53, type, implies_3: $o). 0.85/0.59 tff(decl_54, type, op_implies_and: $o). 0.85/0.59 tff(decl_55, type, op_implies_or: $o). 0.85/0.59 tff(decl_56, type, op_equiv: $o). 0.85/0.59 tff(decl_57, type, op_or: $o). 0.85/0.59 tff(decl_58, type, op_and: $o). 0.85/0.59 tff(decl_59, type, axiom_m7: $o). 0.85/0.59 tff(decl_60, type, possibly: $i > $i). 0.85/0.59 tff(decl_61, type, strict_implies: ($i * $i) > $i). 0.85/0.59 tff(decl_62, type, necessarily: $i > $i). 0.85/0.59 tff(decl_63, type, axiom_B: $o). 0.85/0.59 tff(decl_64, type, axiom_m4: $o). 0.85/0.59 tff(decl_65, type, axiom_m3: $o). 0.85/0.59 tff(decl_66, type, axiom_m1: $o). 0.85/0.59 tff(decl_67, type, substitution_strict_equiv: $o). 0.85/0.59 tff(decl_68, type, strict_equiv: ($i * $i) > $i). 0.85/0.59 tff(decl_69, type, axiom_K: $o). 0.85/0.59 tff(decl_70, type, axiom_4: $o). 0.85/0.59 tff(decl_71, type, axiom_5: $o). 0.85/0.59 tff(decl_72, type, axiom_s4: $o). 0.85/0.59 tff(decl_73, type, axiom_m6: $o). 0.85/0.59 tff(decl_74, type, axiom_m2: $o). 0.85/0.59 tff(decl_75, type, axiom_s3: $o). 0.85/0.59 tff(decl_76, type, necessitation: $o). 0.85/0.59 tff(decl_77, type, axiom_m8: $o). 0.85/0.59 tff(decl_78, type, axiom_m5: $o). 0.85/0.59 tff(decl_79, type, modus_ponens_strict_implies: $o). 0.85/0.59 tff(decl_80, type, axiom_s2: $o). 0.85/0.59 tff(decl_81, type, axiom_m9: $o). 0.85/0.59 tff(decl_82, type, axiom_M: $o). 0.85/0.59 tff(decl_83, type, axiom_s1: $o). 0.85/0.59 tff(decl_84, type, adjunction: $o). 0.85/0.59 tff(decl_85, type, axiom_m10: $o). 0.85/0.59 tff(decl_86, type, op_possibly: $o). 0.85/0.59 tff(decl_87, type, op_strict_equiv: $o). 0.85/0.59 tff(decl_88, type, op_necessarily: $o). 0.85/0.59 tff(decl_89, type, op_strict_implies: $o). 0.85/0.59 tff(decl_90, type, esk1_0: $i). 0.85/0.59 tff(decl_91, type, esk2_0: $i). 0.85/0.59 tff(decl_92, type, esk3_0: $i). 0.85/0.59 tff(decl_93, type, esk4_0: $i). 0.85/0.59 tff(decl_94, type, esk5_0: $i). 0.85/0.59 tff(decl_95, type, esk6_0: $i). 0.85/0.59 tff(decl_96, type, esk7_0: $i). 0.85/0.59 tff(decl_97, type, esk8_0: $i). 0.85/0.59 tff(decl_98, type, esk9_0: $i). 0.85/0.59 tff(decl_99, type, esk10_0: $i). 0.85/0.59 tff(decl_100, type, esk11_0: $i). 0.85/0.59 tff(decl_101, type, esk12_0: $i). 0.85/0.59 tff(decl_102, type, esk13_0: $i). 0.85/0.59 tff(decl_103, type, esk14_0: $i). 0.85/0.59 tff(decl_104, type, esk15_0: $i). 0.85/0.59 tff(decl_105, type, esk16_0: $i). 0.85/0.59 tff(decl_106, type, esk17_0: $i). 0.85/0.59 tff(decl_107, type, esk18_0: $i). 0.85/0.59 tff(decl_108, type, esk19_0: $i). 0.85/0.59 tff(decl_109, type, esk20_0: $i). 0.85/0.59 tff(decl_110, type, esk21_0: $i). 0.85/0.59 tff(decl_111, type, esk22_0: $i). 0.85/0.59 tff(decl_112, type, esk23_0: $i). 0.85/0.59 tff(decl_113, type, esk24_0: $i). 0.85/0.59 tff(decl_114, type, esk25_0: $i). 0.85/0.59 tff(decl_115, type, esk26_0: $i). 0.85/0.59 tff(decl_116, type, esk27_0: $i). 0.85/0.59 tff(decl_117, type, esk28_0: $i). 0.85/0.59 tff(decl_118, type, esk29_0: $i). 0.85/0.59 tff(decl_119, type, esk30_0: $i). 0.85/0.59 tff(decl_120, type, esk31_0: $i). 0.85/0.59 tff(decl_121, type, esk32_0: $i). 0.85/0.59 tff(decl_122, type, esk33_0: $i). 0.85/0.59 tff(decl_123, type, esk34_0: $i). 0.85/0.59 tff(decl_124, type, esk35_0: $i). 0.85/0.59 tff(decl_125, type, esk36_0: $i). 0.85/0.59 tff(decl_126, type, esk37_0: $i). 0.85/0.59 tff(decl_127, type, esk38_0: $i). 0.85/0.59 tff(decl_128, type, esk39_0: $i). 0.85/0.59 tff(decl_129, type, esk40_0: $i). 0.85/0.59 tff(decl_130, type, esk41_0: $i). 0.85/0.59 tff(decl_131, type, esk42_0: $i). 0.85/0.59 tff(decl_132, type, esk43_0: $i). 0.85/0.59 tff(decl_133, type, esk44_0: $i). 0.85/0.59 tff(decl_134, type, esk45_0: $i). 0.85/0.59 tff(decl_135, type, esk46_0: $i). 0.85/0.59 tff(decl_136, type, esk47_0: $i). 0.85/0.59 tff(decl_137, type, esk48_0: $i). 0.85/0.59 tff(decl_138, type, esk49_0: $i). 0.85/0.59 tff(decl_139, type, esk50_0: $i). 0.85/0.59 tff(decl_140, type, esk51_0: $i). 0.85/0.59 tff(decl_141, type, esk52_0: $i). 0.85/0.59 tff(decl_142, type, esk53_0: $i). 0.85/0.59 tff(decl_143, type, esk54_0: $i). 0.85/0.59 tff(decl_144, type, esk55_0: $i). 0.85/0.59 tff(decl_145, type, esk56_0: $i). 0.85/0.59 tff(decl_146, type, esk57_0: $i). 0.85/0.59 tff(decl_147, type, esk58_0: $i). 0.85/0.59 tff(decl_148, type, esk59_0: $i). 0.85/0.59 tff(decl_149, type, esk60_0: $i). 0.85/0.59 tff(decl_150, type, esk61_0: $i). 0.85/0.59 tff(decl_151, type, esk62_0: $i). 0.85/0.59 tff(decl_152, type, esk63_0: $i). 0.85/0.59 tff(decl_153, type, esk64_0: $i). 0.85/0.59 tff(decl_154, type, esk65_0: $i). 0.85/0.59 tff(decl_155, type, esk66_0: $i). 0.85/0.59 tff(decl_156, type, esk67_0: $i). 0.85/0.59 tff(decl_157, type, esk68_0: $i). 0.85/0.59 tff(decl_158, type, esk69_0: $i). 0.85/0.59 tff(decl_159, type, esk70_0: $i). 0.85/0.59 tff(decl_160, type, esk71_0: $i). 0.85/0.59 tff(decl_161, type, esk72_0: $i). 0.85/0.59 tff(decl_162, type, esk73_0: $i). 0.85/0.59 tff(decl_163, type, esk74_0: $i). 0.85/0.59 tff(decl_164, type, esk75_0: $i). 0.85/0.59 tff(decl_165, type, esk76_0: $i). 0.85/0.59 tff(decl_166, type, esk77_0: $i). 0.85/0.59 tff(decl_167, type, esk78_0: $i). 0.85/0.59 tff(decl_168, type, esk79_0: $i). 0.85/0.59 tff(decl_169, type, esk80_0: $i). 0.85/0.59 tff(decl_170, type, esk81_0: $i). 0.85/0.59 tff(decl_171, type, esk82_0: $i). 0.85/0.59 tff(decl_172, type, esk83_0: $i). 0.85/0.59 tff(decl_173, type, esk84_0: $i). 0.85/0.59 tff(decl_174, type, esk85_0: $i). 0.85/0.59 tff(decl_175, type, esk86_0: $i). 0.85/0.59 tff(decl_176, type, esk87_0: $i). 0.85/0.59 tff(decl_177, type, esk88_0: $i). 0.85/0.59 tff(decl_178, type, esk89_0: $i). 0.85/0.59 tff(decl_179, type, esk90_0: $i). 0.85/0.59 tff(decl_180, type, esk91_0: $i). 0.85/0.59 tff(decl_181, type, esk92_0: $i). 0.85/0.59 tff(decl_182, type, esk93_0: $i). 0.85/0.59 tff(decl_183, type, esk94_0: $i). 0.85/0.59 fof(op_implies_and, axiom, (![X1, X2]:(implies(X1,X2)=not(and(X1,not(X2))))<=op_implies_and), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax', op_implies_and)). 0.85/0.59 fof(op_or, axiom, (![X1, X2]:(not(and(not(X1),not(X2)))=or(X1,X2))<=op_or), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax', op_or)). 0.85/0.59 fof(modus_ponens, axiom, (modus_ponens<=>![X1, X2]:(((is_a_theorem(X1)&is_a_theorem(implies(X1,X2)))=>is_a_theorem(X2)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', modus_ponens)). 0.85/0.59 fof(implies_2, axiom, (![X1, X2]:(is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))))<=>implies_2), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', implies_2)). 0.85/0.59 fof(hilbert_op_implies_and, axiom, op_implies_and, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_op_implies_and)). 0.85/0.59 fof(op_equiv, axiom, (![X1, X2]:(equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1)))<=op_equiv), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax', op_equiv)). 0.85/0.59 fof(and_3, axiom, (and_3<=>![X1, X2]:(is_a_theorem(implies(X1,implies(X2,and(X1,X2)))))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', and_3)). 0.85/0.59 fof(hilbert_modus_ponens, axiom, modus_ponens, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_modus_ponens)). 0.85/0.59 fof(hilbert_implies_2, axiom, implies_2, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_implies_2)). 0.85/0.59 fof(or_3, axiom, (![X1, X2, X3]:(is_a_theorem(implies(implies(X1,X3),implies(implies(X2,X3),implies(or(X1,X2),X3)))))<=>or_3), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', or_3)). 0.85/0.59 fof(hilbert_op_or, axiom, op_or, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_op_or)). 0.85/0.59 fof(substitution_of_equivalents, axiom, (substitution_of_equivalents<=>![X1, X2]:((X2=X1<=is_a_theorem(equiv(X1,X2))))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', substitution_of_equivalents)). 0.85/0.59 fof(hilbert_and_3, axiom, and_3, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_and_3)). 0.85/0.59 fof(r1, axiom, (r1<=>![X4]:(is_a_theorem(implies(or(X4,X4),X4)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', r1)). 0.85/0.59 fof(hilbert_or_3, axiom, or_3, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_or_3)). 0.85/0.59 fof(implies_1, axiom, (![X1, X2]:(is_a_theorem(implies(X1,implies(X2,X1))))<=>implies_1), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', implies_1)). 0.85/0.59 fof(hilbert_op_equiv, axiom, op_equiv, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_op_equiv)). 0.85/0.59 fof(hilbert_implies_1, axiom, implies_1, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_implies_1)). 0.85/0.59 fof(op_possibly, axiom, (op_possibly=>![X1]:(possibly(X1)=not(necessarily(not(X1))))), file('/export/starexec/sandbox/benchmark/Axioms/LCL007+1.ax', op_possibly)). 0.85/0.59 fof(substitution_of_equivalents, axiom, substitution_of_equivalents, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', substitution_of_equivalents)). 0.85/0.59 fof(and_1, axiom, (and_1<=>![X1, X2]:(is_a_theorem(implies(and(X1,X2),X1)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', and_1)). 0.85/0.59 fof(axiom_5, axiom, (axiom_5<=>![X1]:(is_a_theorem(implies(possibly(X1),necessarily(possibly(X1)))))), file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax', axiom_5)). 0.85/0.59 fof(axiom_M, axiom, (axiom_M<=>![X1]:(is_a_theorem(implies(necessarily(X1),X1)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax', axiom_M)). 0.85/0.59 fof(km5_op_possibly, axiom, op_possibly, file('/export/starexec/sandbox/benchmark/Axioms/LCL007+2.ax', km5_op_possibly)). 0.85/0.59 fof(hilbert_and_1, axiom, and_1, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_and_1)). 0.85/0.59 fof(km5_axiom_5, axiom, axiom_5, file('/export/starexec/sandbox/benchmark/Axioms/LCL007+2.ax', km5_axiom_5)). 0.85/0.59 fof(km5_axiom_M, axiom, axiom_M, file('/export/starexec/sandbox/benchmark/Axioms/LCL007+2.ax', km5_axiom_M)). 0.85/0.59 fof(axiom_4, axiom, (axiom_4<=>![X1]:(is_a_theorem(implies(necessarily(X1),necessarily(necessarily(X1)))))), file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax', axiom_4)). 0.85/0.59 fof(km4b_axiom_4, conjecture, axiom_4, file('/export/starexec/sandbox/benchmark/theBenchmark.p', km4b_axiom_4)). 0.85/0.59 fof(c_0_29, plain, (op_implies_and=>![X1, X2]:(implies(X1,X2)=not(and(X1,not(X2))))), inference(fof_simplification,[status(thm)],[op_implies_and])). 0.85/0.59 fof(c_0_30, plain, (op_or=>![X1, X2]:(not(and(not(X1),not(X2)))=or(X1,X2))), inference(fof_simplification,[status(thm)],[op_or])). 0.85/0.59 fof(c_0_31, plain, ![X117, X118]:((~op_implies_and|implies(X117,X118)=not(and(X117,not(X118))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])])). 0.85/0.59 fof(c_0_32, plain, ![X103, X104]:(((~modus_ponens|(~is_a_theorem(X103)|~is_a_theorem(implies(X103,X104))|is_a_theorem(X104)))&(((is_a_theorem(esk49_0)|modus_ponens)&(is_a_theorem(implies(esk49_0,esk50_0))|modus_ponens))&(~is_a_theorem(esk50_0)|modus_ponens)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[modus_ponens])])])])])). 0.85/0.59 fof(c_0_33, plain, ![X83, X84]:(((~is_a_theorem(implies(implies(esk38_0,implies(esk38_0,esk39_0)),implies(esk38_0,esk39_0)))|implies_2)&(~implies_2|is_a_theorem(implies(implies(X83,implies(X83,X84)),implies(X83,X84)))))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[implies_2])])])])). 0.85/0.59 fof(c_0_34, plain, ![X123, X124]:((~op_or|not(and(not(X123),not(X124)))=or(X123,X124))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])])). 0.85/0.59 cnf(c_0_35, plain, (implies(X1,X2)=not(and(X1,not(X2)))|~op_implies_and), inference(split_conjunct,[status(thm)],[c_0_31])). 0.85/0.59 cnf(c_0_36, plain, (op_implies_and), inference(split_conjunct,[status(thm)],[hilbert_op_implies_and])). 0.85/0.59 fof(c_0_37, plain, (op_equiv=>![X1, X2]:(equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1)))), inference(fof_simplification,[status(thm)],[op_equiv])). 0.85/0.59 fof(c_0_38, plain, ![X25, X26]:(((~and_3|is_a_theorem(implies(X25,implies(X26,and(X25,X26)))))&(~is_a_theorem(implies(esk10_0,implies(esk11_0,and(esk10_0,esk11_0))))|and_3))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and_3])])])])). 0.85/0.59 cnf(c_0_39, plain, (is_a_theorem(X2)|~modus_ponens|~is_a_theorem(X1)|~is_a_theorem(implies(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_32])). 0.85/0.59 cnf(c_0_40, plain, (modus_ponens), inference(split_conjunct,[status(thm)],[hilbert_modus_ponens])). 0.85/0.59 cnf(c_0_41, plain, (is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))|~implies_2), inference(split_conjunct,[status(thm)],[c_0_33])). 0.85/0.59 cnf(c_0_42, plain, (implies_2), inference(split_conjunct,[status(thm)],[hilbert_implies_2])). 0.85/0.59 fof(c_0_43, plain, ![X22, X23, X24]:(((~is_a_theorem(implies(implies(esk7_0,esk9_0),implies(implies(esk8_0,esk9_0),implies(or(esk7_0,esk8_0),esk9_0))))|or_3)&(~or_3|is_a_theorem(implies(implies(X22,X24),implies(implies(X23,X24),implies(or(X22,X23),X24))))))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[or_3])])])])). 0.85/0.59 cnf(c_0_44, plain, (not(and(not(X1),not(X2)))=or(X1,X2)|~op_or), inference(split_conjunct,[status(thm)],[c_0_34])). 0.85/0.59 cnf(c_0_45, plain, (not(and(X1,not(X2)))=implies(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35, c_0_36])])). 0.85/0.59 cnf(c_0_46, plain, (op_or), inference(split_conjunct,[status(thm)],[hilbert_op_or])). 0.85/0.59 fof(c_0_47, plain, (substitution_of_equivalents<=>![X1, X2]:((is_a_theorem(equiv(X1,X2))=>X2=X1))), inference(fof_simplification,[status(thm)],[substitution_of_equivalents])). 0.85/0.59 fof(c_0_48, plain, ![X121, X122]:((~op_equiv|equiv(X121,X122)=and(implies(X121,X122),implies(X122,X121)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])])). 0.85/0.59 cnf(c_0_49, plain, (is_a_theorem(implies(X1,implies(X2,and(X1,X2))))|~and_3), inference(split_conjunct,[status(thm)],[c_0_38])). 0.85/0.59 cnf(c_0_50, plain, (and_3), inference(split_conjunct,[status(thm)],[hilbert_and_3])). 0.85/0.59 fof(c_0_51, plain, ![X85]:(((~r1|is_a_theorem(implies(or(X85,X85),X85)))&(~is_a_theorem(implies(or(esk40_0,esk40_0),esk40_0))|r1))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r1])])])])). 0.85/0.59 cnf(c_0_52, plain, (is_a_theorem(X1)|~is_a_theorem(implies(X2,X1))|~is_a_theorem(X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39, c_0_40])])). 0.85/0.59 cnf(c_0_53, plain, (is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41, c_0_42])])). 0.85/0.59 cnf(c_0_54, plain, (is_a_theorem(implies(implies(X1,X2),implies(implies(X3,X2),implies(or(X1,X3),X2))))|~or_3), inference(split_conjunct,[status(thm)],[c_0_43])). 0.85/0.59 cnf(c_0_55, plain, (or(X1,X2)=implies(not(X1),X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44, c_0_45]), c_0_46])])). 0.85/0.59 cnf(c_0_56, plain, (or_3), inference(split_conjunct,[status(thm)],[hilbert_or_3])). 0.85/0.59 fof(c_0_57, plain, ![X109, X110]:(((~is_a_theorem(implies(esk51_0,implies(esk52_0,esk51_0)))|implies_1)&(~implies_1|is_a_theorem(implies(X109,implies(X110,X109)))))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[implies_1])])])])). 0.85/0.59 fof(c_0_58, plain, ![X59, X60]:(((~substitution_of_equivalents|(~is_a_theorem(equiv(X59,X60))|X60=X59))&((is_a_theorem(equiv(esk27_0,esk28_0))|substitution_of_equivalents)&(esk28_0!=esk27_0|substitution_of_equivalents)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_47])])])])])). 0.85/0.59 cnf(c_0_59, plain, (equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))|~op_equiv), inference(split_conjunct,[status(thm)],[c_0_48])). 0.85/0.59 cnf(c_0_60, plain, (op_equiv), inference(split_conjunct,[status(thm)],[hilbert_op_equiv])). 0.85/0.59 cnf(c_0_61, plain, (is_a_theorem(implies(X1,implies(X2,and(X1,X2))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49, c_0_50])])). 0.85/0.59 cnf(c_0_62, plain, (is_a_theorem(implies(or(X1,X1),X1))|~r1), inference(split_conjunct,[status(thm)],[c_0_51])). 0.85/0.59 cnf(c_0_63, plain, (r1|~is_a_theorem(implies(or(esk40_0,esk40_0),esk40_0))), inference(split_conjunct,[status(thm)],[c_0_51])). 0.85/0.59 cnf(c_0_64, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(implies(X1,implies(X1,X2)))), inference(spm,[status(thm)],[c_0_52, c_0_53])). 0.85/0.59 cnf(c_0_65, plain, (is_a_theorem(implies(implies(X1,X2),implies(implies(X3,X2),implies(implies(not(X1),X3),X2))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54, c_0_55]), c_0_56])])). 0.85/0.59 cnf(c_0_66, plain, (is_a_theorem(implies(X1,implies(X2,X1)))|~implies_1), inference(split_conjunct,[status(thm)],[c_0_57])). 0.85/0.59 cnf(c_0_67, plain, (implies_1), inference(split_conjunct,[status(thm)],[hilbert_implies_1])). 0.85/0.59 fof(c_0_68, plain, ![X205]:((~op_possibly|possibly(X205)=not(necessarily(not(X205))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_possibly])])])). 0.85/0.59 cnf(c_0_69, plain, (X2=X1|~substitution_of_equivalents|~is_a_theorem(equiv(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_58])). 0.85/0.59 cnf(c_0_70, plain, (substitution_of_equivalents), inference(split_conjunct,[status(thm)],[substitution_of_equivalents])). 0.85/0.59 cnf(c_0_71, plain, (equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_59, c_0_60])])). 0.85/0.59 cnf(c_0_72, plain, (is_a_theorem(implies(X1,and(X2,X1)))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_52, c_0_61])). 0.85/0.59 fof(c_0_73, plain, ![X7, X8]:(((~and_1|is_a_theorem(implies(and(X7,X8),X7)))&(~is_a_theorem(implies(and(esk1_0,esk2_0),esk1_0))|and_1))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and_1])])])])). 0.85/0.59 cnf(c_0_74, plain, (is_a_theorem(implies(implies(not(X1),X1),X1))|~r1), inference(rw,[status(thm)],[c_0_62, c_0_55])). 0.85/0.59 cnf(c_0_75, plain, (r1|~is_a_theorem(implies(implies(not(esk40_0),esk40_0),esk40_0))), inference(rw,[status(thm)],[c_0_63, c_0_55])). 0.85/0.59 cnf(c_0_76, plain, (is_a_theorem(implies(implies(X1,X2),implies(implies(not(X1),X1),X2)))), inference(spm,[status(thm)],[c_0_64, c_0_65])). 0.85/0.59 cnf(c_0_77, plain, (is_a_theorem(implies(X1,implies(X2,X1)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_66, c_0_67])])). 0.85/0.59 fof(c_0_78, plain, ![X155]:(((~axiom_5|is_a_theorem(implies(possibly(X155),necessarily(possibly(X155)))))&(~is_a_theorem(implies(possibly(esk70_0),necessarily(possibly(esk70_0))))|axiom_5))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_5])])])])). 0.85/0.59 fof(c_0_79, plain, ![X191]:(((~axiom_M|is_a_theorem(implies(necessarily(X191),X191)))&(~is_a_theorem(implies(necessarily(esk88_0),esk88_0))|axiom_M))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_M])])])])). 0.85/0.59 cnf(c_0_80, plain, (possibly(X1)=not(necessarily(not(X1)))|~op_possibly), inference(split_conjunct,[status(thm)],[c_0_68])). 0.85/0.59 cnf(c_0_81, plain, (op_possibly), inference(split_conjunct,[status(thm)],[km5_op_possibly])). 0.85/0.59 cnf(c_0_82, plain, (X1=X2|~is_a_theorem(and(implies(X1,X2),implies(X2,X1)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_69, c_0_70]), c_0_71])])). 0.85/0.59 cnf(c_0_83, plain, (is_a_theorem(and(X1,X2))|~is_a_theorem(X2)|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_52, c_0_72])). 0.85/0.59 cnf(c_0_84, plain, (is_a_theorem(implies(and(X1,X2),X1))|~and_1), inference(split_conjunct,[status(thm)],[c_0_73])). 0.85/0.59 cnf(c_0_85, plain, (and_1), inference(split_conjunct,[status(thm)],[hilbert_and_1])). 0.85/0.59 cnf(c_0_86, plain, (is_a_theorem(implies(implies(not(X1),X1),X1))|~is_a_theorem(implies(implies(not(esk40_0),esk40_0),esk40_0))), inference(spm,[status(thm)],[c_0_74, c_0_75])). 0.85/0.59 cnf(c_0_87, plain, (is_a_theorem(implies(implies(not(X1),X1),X2))|~is_a_theorem(implies(X1,X2))), inference(spm,[status(thm)],[c_0_52, c_0_76])). 0.85/0.59 cnf(c_0_88, plain, (is_a_theorem(implies(X1,X1))), inference(spm,[status(thm)],[c_0_64, c_0_77])). 0.85/0.59 cnf(c_0_89, plain, (is_a_theorem(implies(possibly(X1),necessarily(possibly(X1))))|~axiom_5), inference(split_conjunct,[status(thm)],[c_0_78])). 0.85/0.59 cnf(c_0_90, plain, (axiom_5), inference(split_conjunct,[status(thm)],[km5_axiom_5])). 0.85/0.59 cnf(c_0_91, plain, (is_a_theorem(implies(necessarily(X1),X1))|~axiom_M), inference(split_conjunct,[status(thm)],[c_0_79])). 0.85/0.59 cnf(c_0_92, plain, (axiom_M), inference(split_conjunct,[status(thm)],[km5_axiom_M])). 0.85/0.59 cnf(c_0_93, plain, (not(necessarily(not(X1)))=possibly(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_80, c_0_81])])). 0.85/0.59 cnf(c_0_94, plain, (X1=X2|~is_a_theorem(implies(X2,X1))|~is_a_theorem(implies(X1,X2))), inference(spm,[status(thm)],[c_0_82, c_0_83])). 0.85/0.59 cnf(c_0_95, plain, (is_a_theorem(implies(X1,and(X1,X1)))), inference(spm,[status(thm)],[c_0_64, c_0_61])). 0.85/0.59 cnf(c_0_96, plain, (is_a_theorem(implies(and(X1,X2),X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_84, c_0_85])])). 0.85/0.59 cnf(c_0_97, plain, (is_a_theorem(implies(implies(not(X1),X1),X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86, c_0_87]), c_0_88])])). 0.85/0.59 cnf(c_0_98, plain, (is_a_theorem(implies(possibly(X1),necessarily(possibly(X1))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_89, c_0_90])])). 0.85/0.59 cnf(c_0_99, plain, (is_a_theorem(implies(necessarily(X1),X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_91, c_0_92])])). 0.85/0.59 cnf(c_0_100, plain, (not(and(X1,possibly(X2)))=implies(X1,necessarily(not(X2)))), inference(spm,[status(thm)],[c_0_45, c_0_93])). 0.85/0.59 cnf(c_0_101, plain, (and(X1,X1)=X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94, c_0_95]), c_0_96])])). 0.85/0.59 cnf(c_0_102, plain, (not(necessarily(implies(X1,X2)))=possibly(and(X1,not(X2)))), inference(spm,[status(thm)],[c_0_93, c_0_45])). 0.85/0.59 cnf(c_0_103, plain, (implies(not(X1),X1)=X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94, c_0_97]), c_0_77])])). 0.85/0.59 cnf(c_0_104, plain, (not(necessarily(possibly(X1)))=possibly(necessarily(not(X1)))), inference(spm,[status(thm)],[c_0_93, c_0_93])). 0.85/0.59 cnf(c_0_105, plain, (necessarily(possibly(X1))=possibly(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94, c_0_98]), c_0_99])])). 0.85/0.59 cnf(c_0_106, plain, (not(possibly(X1))=implies(possibly(X1),necessarily(not(X1)))), inference(spm,[status(thm)],[c_0_100, c_0_101])). 0.85/0.59 cnf(c_0_107, plain, (not(necessarily(X1))=possibly(not(X1))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102, c_0_103]), c_0_101])). 0.85/0.59 cnf(c_0_108, plain, (not(not(X1))=implies(not(X1),X1)), inference(spm,[status(thm)],[c_0_45, c_0_101])). 0.85/0.59 cnf(c_0_109, plain, (possibly(necessarily(not(X1)))=implies(possibly(X1),necessarily(not(X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_104, c_0_105]), c_0_106])). 0.85/0.59 cnf(c_0_110, plain, (implies(possibly(not(X1)),necessarily(X1))=necessarily(X1)), inference(spm,[status(thm)],[c_0_103, c_0_107])). 0.85/0.59 cnf(c_0_111, plain, (not(not(X1))=X1), inference(rw,[status(thm)],[c_0_108, c_0_103])). 0.85/0.59 fof(c_0_112, plain, ![X153]:(((~axiom_4|is_a_theorem(implies(necessarily(X153),necessarily(necessarily(X153)))))&(~is_a_theorem(implies(necessarily(esk69_0),necessarily(necessarily(esk69_0))))|axiom_4))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_4])])])])). 0.85/0.59 fof(c_0_113, negated_conjecture, ~axiom_4, inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[km4b_axiom_4])])). 0.85/0.59 cnf(c_0_114, plain, (necessarily(implies(possibly(X1),necessarily(not(X1))))=implies(possibly(X1),necessarily(not(X1)))), inference(spm,[status(thm)],[c_0_105, c_0_109])). 0.85/0.59 cnf(c_0_115, plain, (implies(possibly(X1),necessarily(not(X1)))=necessarily(not(X1))), inference(spm,[status(thm)],[c_0_110, c_0_111])). 0.85/0.59 cnf(c_0_116, plain, (axiom_4|~is_a_theorem(implies(necessarily(esk69_0),necessarily(necessarily(esk69_0))))), inference(split_conjunct,[status(thm)],[c_0_112])). 0.85/0.59 cnf(c_0_117, negated_conjecture, (~axiom_4), inference(split_conjunct,[status(thm)],[c_0_113])). 0.85/0.59 cnf(c_0_118, plain, (necessarily(necessarily(not(X1)))=necessarily(not(X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_114, c_0_115]), c_0_115])). 0.85/0.59 cnf(c_0_119, plain, (~is_a_theorem(implies(necessarily(esk69_0),necessarily(necessarily(esk69_0))))), inference(sr,[status(thm)],[c_0_116, c_0_117])). 0.85/0.59 cnf(c_0_120, plain, (necessarily(necessarily(X1))=necessarily(X1)), inference(spm,[status(thm)],[c_0_118, c_0_111])). 0.85/0.59 cnf(c_0_121, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119, c_0_120]), c_0_88])]), ['proof']). 0.85/0.59 # SZS output end CNFRefutation 0.85/0.59 # Parsed axioms : 82 0.85/0.59 # Removed by relevancy pruning/SinE : 0 0.85/0.59 # Initial clauses : 140 0.85/0.59 # Removed in clause preprocessing : 0 0.85/0.59 # Initial clauses in saturation : 140 0.85/0.59 # Processed clauses : 896 0.85/0.59 # ...of these trivial : 81 0.85/0.59 # ...subsumed : 368 0.85/0.59 # ...remaining for further processing : 447 0.85/0.59 # Other redundant clauses eliminated : 0 0.85/0.59 # Clauses deleted for lack of memory : 0 0.85/0.59 # Backward-subsumed : 7 0.85/0.59 # Backward-rewritten : 40 0.85/0.59 # Generated clauses : 7711 0.85/0.59 # ...of the previous two non-redundant : 5483 0.85/0.59 # ...aggressively subsumed : 0 0.85/0.59 # Contextual simplify-reflections : 2 0.85/0.59 # Paramodulations : 7711 0.85/0.59 # Factorizations : 0 0.85/0.59 # NegExts : 0 0.85/0.59 # Equation resolutions : 0 0.85/0.59 # Propositional unsat checks : 0 0.85/0.59 # Propositional check models : 0 0.85/0.59 # Propositional check unsatisfiable : 0 0.85/0.59 # Propositional clauses : 0 0.85/0.59 # Propositional clauses after purity: 0 0.85/0.59 # Propositional unsat core size : 0 0.85/0.59 # Propositional preprocessing time : 0.000 0.85/0.59 # Propositional encoding time : 0.000 0.85/0.59 # Propositional solver time : 0.000 0.85/0.59 # Success case prop preproc time : 0.000 0.85/0.59 # Success case prop encoding time : 0.000 0.85/0.59 # Success case prop solver time : 0.000 0.85/0.59 # Current number of processed clauses : 290 0.85/0.59 # Positive orientable unit clauses : 118 0.85/0.59 # Positive unorientable unit clauses: 6 0.85/0.59 # Negative unit clauses : 4 0.85/0.59 # Non-unit-clauses : 162 0.85/0.59 # Current number of unprocessed clauses: 4806 0.85/0.59 # ...number of literals in the above : 7450 0.85/0.59 # Current number of archived formulas : 0 0.85/0.59 # Current number of archived clauses : 157 0.85/0.59 # Clause-clause subsumption calls (NU) : 2873 0.85/0.59 # Rec. Clause-clause subsumption calls : 2642 0.85/0.59 # Non-unit clause-clause subsumptions : 288 0.85/0.59 # Unit Clause-clause subsumption calls : 748 0.85/0.59 # Rewrite failures with RHS unbound : 0 0.85/0.59 # BW rewrite match attempts : 1427 0.85/0.59 # BW rewrite match successes : 58 0.85/0.59 # Condensation attempts : 0 0.85/0.59 # Condensation successes : 0 0.85/0.59 # Termbank termtop insertions : 106337 0.85/0.59 0.85/0.59 # ------------------------------------------------- 0.85/0.59 # User time : 0.111 s 0.85/0.59 # System time : 0.011 s 0.85/0.59 # Total time : 0.122 s 0.85/0.59 # Maximum resident set size: 2240 pages 0.85/0.59 0.85/0.59 # ------------------------------------------------- 0.85/0.59 # User time : 0.527 s 0.85/0.59 # System time : 0.039 s 0.85/0.59 # Total time : 0.567 s 0.85/0.59 # Maximum resident set size: 1812 pages 0.85/0.59 EOF