0.06/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.12 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 240 THM 0.11/0.33 % Computer : n018.cluster.edu 0.11/0.33 % Model : x86_64 x86_64 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.33 % Memory : 8042.1875MB 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.33 % CPULimit : 1920 0.11/0.33 % WCLimit : 240 0.11/0.33 % DateTime : Wed Jul 30 08:55:34 EDT 2025 0.11/0.33 % CPUTime : 0.18/0.46 Running higher-order theorem proving 0.18/0.50 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=240 /export/starexec/sandbox2/tmp/tmp.wwvFOgLG2D/E---3.1_20079.p 3.80/1.08 # Version: 3.0.0-ho 3.80/1.08 # Preprocessing class: HSLMSMSMLLLCHSA. 3.80/1.08 # Scheduled 5 strats onto 8 cores with 240 seconds (1920 total) 3.80/1.08 # Starting pre_casc_4 with 960s (4) cores 3.80/1.08 # Starting full_lambda_6 with 240s (1) cores 3.80/1.08 # Starting sh10 with 240s (1) cores 3.80/1.08 # Starting post_as_ho9 with 240s (1) cores 3.80/1.08 # Starting post_as_ho8 with 240s (1) cores 3.80/1.08 # full_lambda_6 with pid 20158 completed with status 0 3.80/1.08 # Result found by full_lambda_6 3.80/1.08 # Preprocessing class: HSLMSMSMLLLCHSA. 3.80/1.08 # Scheduled 5 strats onto 8 cores with 240 seconds (1920 total) 3.80/1.08 # Starting pre_casc_4 with 960s (4) cores 3.80/1.08 # Starting full_lambda_6 with 240s (1) cores 3.80/1.08 # SinE strategy is GSinE(CountTerms,hypos,4,,4,20000,1.0,true) 3.80/1.08 # Search class: HGHSM-FSLM32-DHSMMFBN 3.80/1.08 # partial match(2): HGHSM-FSLM32-MHSMMSBN 3.80/1.08 # Scheduled 12 strats onto 1 cores with 240 seconds (240 total) 3.80/1.08 # Starting full_lambda_5 with 20s (1) cores 3.80/1.08 # full_lambda_5 with pid 20163 completed with status 0 3.80/1.08 # Result found by full_lambda_5 3.80/1.08 # Preprocessing class: HSLMSMSMLLLCHSA. 3.80/1.08 # Scheduled 5 strats onto 8 cores with 240 seconds (1920 total) 3.80/1.08 # Starting pre_casc_4 with 960s (4) cores 3.80/1.08 # Starting full_lambda_6 with 240s (1) cores 3.80/1.08 # SinE strategy is GSinE(CountTerms,hypos,4,,4,20000,1.0,true) 3.80/1.08 # Search class: HGHSM-FSLM32-DHSMMFBN 3.80/1.08 # partial match(2): HGHSM-FSLM32-MHSMMSBN 3.80/1.08 # Scheduled 12 strats onto 1 cores with 240 seconds (240 total) 3.80/1.08 # Starting full_lambda_5 with 20s (1) cores 3.80/1.08 # Preprocessing time : 0.011 s 3.80/1.08 # Presaturation interreduction done 3.80/1.08 3.80/1.08 # Proof found! 3.80/1.08 # SZS status Theorem 3.80/1.08 # SZS output start CNFRefutation 3.80/1.08 thf(decl_23, type, is_of: $i > ($i > $o) > $o). 3.80/1.08 thf(decl_24, type, all_of: ($i > $o) > ($i > $o) > $o). 3.80/1.08 thf(decl_26, type, in: $i > $i > $o). 3.80/1.08 thf(decl_62, type, imp: $o > $o > $o). 3.80/1.08 thf(decl_63, type, d_not: $o > $o). 3.80/1.08 thf(decl_66, type, l_ec: $o > $o > $o). 3.80/1.08 thf(decl_67, type, d_and: $o > $o > $o). 3.80/1.08 thf(decl_68, type, l_or: $o > $o > $o). 3.80/1.08 thf(decl_73, type, l_some: $i > ($i > $o) > $o). 3.80/1.08 thf(decl_74, type, or3: $o > $o > $o > $o). 3.80/1.08 thf(decl_75, type, and3: $o > $o > $o > $o). 3.80/1.08 thf(decl_78, type, e_is: $i > $i > $i > $o). 3.80/1.08 thf(decl_103, type, esti: $i > $i > $i > $o). 3.80/1.08 thf(decl_124, type, nat: $i). 3.80/1.08 thf(decl_125, type, n_is: $i > $i > $o). 3.80/1.08 thf(decl_128, type, n_some: ($i > $o) > $o). 3.80/1.08 thf(decl_143, type, n_pl: $i > $i > $i). 3.80/1.08 thf(decl_148, type, diffprop: $i > $i > $i > $o). 3.80/1.08 thf(decl_149, type, d_29_ii: $i > $i > $o). 3.80/1.08 thf(decl_150, type, iii: $i > $i > $o). 3.80/1.08 thf(decl_163, type, n_ts: $i > $i > $i). 3.80/1.08 thf(decl_190, type, frac: $i). 3.80/1.08 thf(decl_192, type, num: $i > $i). 3.80/1.08 thf(decl_193, type, den: $i > $i). 3.80/1.08 thf(decl_195, type, moref: $i > $i > $o). 3.80/1.08 thf(decl_196, type, lessf: $i > $i > $o). 3.80/1.08 thf(decl_204, type, inf: $i > $i > $o). 3.80/1.08 thf(decl_205, type, rat: $i). 3.80/1.08 thf(decl_206, type, rt_is: $i > $i > $o). 3.80/1.08 thf(decl_213, type, class: $i > $i). 3.80/1.08 thf(decl_216, type, rt_more: $i > $i > $o). 3.80/1.08 thf(decl_218, type, rt_less: $i > $i > $o). 3.80/1.08 thf(decl_221, type, rt_lessis: $i > $i > $o). 3.80/1.08 thf(decl_222, type, esk1_0: $i). 3.80/1.08 thf(decl_223, type, esk2_0: $i). 3.80/1.08 thf(def_d_not, axiom, ((d_not)=(^[X36:$o]:((imp @ ((X36)) @ (~($true)))))), file('/export/starexec/sandbox2/tmp/tmp.wwvFOgLG2D/E---3.1_20079.p', def_d_not)). 3.80/1.08 thf(def_imp, axiom, ((imp)=(^[X34:$o, X35:$o]:(((X34)=>(X35))))), file('/export/starexec/sandbox2/tmp/tmp.wwvFOgLG2D/E---3.1_20079.p', def_imp)). 3.80/1.08 thf(def_e_is, axiom, ((e_is)=(^[X1:$i, X60:$i, X61:$i]:(((X60)=(X61))))), file('/export/starexec/sandbox2/tmp/tmp.wwvFOgLG2D/E---3.1_20079.p', def_e_is)). 3.80/1.08 thf(def_l_ec, axiom, ((l_ec)=(^[X38:$o, X39:$o]:((imp @ ((X38)) @ ((d_not @ ((X39)))))))), file('/export/starexec/sandbox2/tmp/tmp.wwvFOgLG2D/E---3.1_20079.p', def_l_ec)). 3.80/1.08 thf(def_diffprop, axiom, ((diffprop)=(^[X1:$i, X183:$i, X4:$i]:((n_is @ X1 @ (n_pl @ X183 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.wwvFOgLG2D/E---3.1_20079.p', def_diffprop)). 3.80/1.08 thf(def_n_is, axiom, ((n_is)=(^[Z0/* 19 */:$i, Z1:$i]:(((Z0)=(Z1))))), file('/export/starexec/sandbox2/tmp/tmp.wwvFOgLG2D/E---3.1_20079.p', def_n_is)). 3.80/1.08 thf(def_d_and, axiom, ((d_and)=(^[X40:$o, X41:$o]:((d_not @ ((l_ec @ ((X40)) @ ((X41)))))))), file('/export/starexec/sandbox2/tmp/tmp.wwvFOgLG2D/E---3.1_20079.p', def_d_and)). 3.80/1.08 thf(def_iii, axiom, ((iii)=(^[X1:$i, X185:$i]:((n_some @ (diffprop @ X185 @ X1))))), file('/export/starexec/sandbox2/tmp/tmp.wwvFOgLG2D/E---3.1_20079.p', def_iii)). 3.80/1.08 thf(def_esti, axiom, ((esti)=(^[X1:$i]:(in))), file('/export/starexec/sandbox2/tmp/tmp.wwvFOgLG2D/E---3.1_20079.p', def_esti)). 3.80/1.08 thf(def_and3, axiom, ((and3)=(^[X51:$o, X52:$o, X53:$o]:((d_and @ ((X51)) @ ((d_and @ ((X52)) @ ((X53)))))))), file('/export/starexec/sandbox2/tmp/tmp.wwvFOgLG2D/E---3.1_20079.p', def_and3)). 3.80/1.08 thf(def_lessf, axiom, ((lessf)=(^[X1:$i, X220:$i]:((iii @ (n_ts @ (num @ X1) @ (den @ X220)) @ (n_ts @ (num @ X220) @ (den @ X1)))))), file('/export/starexec/sandbox2/tmp/tmp.wwvFOgLG2D/E---3.1_20079.p', def_lessf)). 3.80/1.08 thf(def_n_some, axiom, ((n_some)=(l_some @ nat)), file('/export/starexec/sandbox2/tmp/tmp.wwvFOgLG2D/E---3.1_20079.p', def_n_some)). 3.80/1.08 thf(def_d_29_ii, axiom, ((d_29_ii)=(^[X1:$i, X184:$i]:((n_some @ (diffprop @ X1 @ X184))))), file('/export/starexec/sandbox2/tmp/tmp.wwvFOgLG2D/E---3.1_20079.p', def_d_29_ii)). 3.80/1.08 thf(def_rt_less, axiom, ((rt_less)=(^[X1:$i, X648:$i]:((l_some @ frac @ (^[X4:$i]:((l_some @ frac @ (^[X10:$i]:((and3 @ ((inf @ X4 @ (class @ X1))) @ ((inf @ X10 @ (class @ X648))) @ ((lessf @ X4 @ X10)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.wwvFOgLG2D/E---3.1_20079.p', def_rt_less)). 3.80/1.08 thf(def_inf, axiom, ((inf)=(in)), file('/export/starexec/sandbox2/tmp/tmp.wwvFOgLG2D/E---3.1_20079.p', def_inf)). 3.80/1.08 thf(def_l_or, axiom, ((l_or)=(^[X42:$o]:(imp @ ((d_not @ ((X42))))))), file('/export/starexec/sandbox2/tmp/tmp.wwvFOgLG2D/E---3.1_20079.p', def_l_or)). 3.80/1.08 thf(def_moref, axiom, ((moref)=(^[X1:$i, X219:$i]:((d_29_ii @ (n_ts @ (num @ X1) @ (den @ X219)) @ (n_ts @ (num @ X219) @ (den @ X1)))))), file('/export/starexec/sandbox2/tmp/tmp.wwvFOgLG2D/E---3.1_20079.p', def_moref)). 3.80/1.08 thf(def_rt_lessis, axiom, ((rt_lessis)=(^[X1:$i, X651:$i]:((l_or @ ((rt_less @ X1 @ X651)) @ ((rt_is @ X1 @ X651)))))), file('/export/starexec/sandbox2/tmp/tmp.wwvFOgLG2D/E---3.1_20079.p', def_rt_lessis)). 3.80/1.08 thf(def_rt_is, axiom, ((rt_is)=(^[Z0/* 19 */:$i, Z1:$i]:(((Z0)=(Z1))))), file('/export/starexec/sandbox2/tmp/tmp.wwvFOgLG2D/E---3.1_20079.p', def_rt_is)). 3.80/1.08 thf(def_rt_more, axiom, ((rt_more)=(^[X1:$i, X646:$i]:((l_some @ frac @ (^[X4:$i]:((l_some @ frac @ (^[X10:$i]:((and3 @ ((inf @ X4 @ (class @ X1))) @ ((inf @ X10 @ (class @ X646))) @ ((moref @ X4 @ X10)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.wwvFOgLG2D/E---3.1_20079.p', def_rt_more)). 3.80/1.08 thf(def_all_of, axiom, ((all_of)=(^[X3:$i > $o, X2:$i > $o]:(![X4:$i]:(((is_of @ X4 @ X3)=>(X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.wwvFOgLG2D/E---3.1_20079.p', def_all_of)). 3.80/1.08 thf(def_is_of, axiom, ((is_of)=(^[X1:$i, X2:$i > $o]:((X2 @ X1)))), file('/export/starexec/sandbox2/tmp/tmp.wwvFOgLG2D/E---3.1_20079.p', def_is_of)). 3.80/1.08 thf(def_or3, axiom, ((or3)=(^[X48:$o, X49:$o, X50:$o]:((l_or @ ((X48)) @ ((l_or @ ((X49)) @ ((X50)))))))), file('/export/starexec/sandbox2/tmp/tmp.wwvFOgLG2D/E---3.1_20079.p', def_or3)). 3.80/1.08 thf(satz81e, conjecture, (all_of @ (^[X1:$i]:((in @ X1 @ rat))) @ (^[X1:$i]:((all_of @ (^[X664:$i]:((in @ X664 @ rat))) @ (^[X665:$i]:(((rt_lessis @ X1 @ X665)<=(d_not @ ((rt_more @ X1 @ X665)))))))))), file('/export/starexec/sandbox2/tmp/tmp.wwvFOgLG2D/E---3.1_20079.p', satz81e)). 3.80/1.08 thf(satz81a, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ rat))) @ (^[X1:$i]:((all_of @ (^[X666:$i]:((in @ X666 @ rat))) @ (^[X667:$i]:((or3 @ ((rt_is @ X1 @ X667)) @ ((rt_more @ X1 @ X667)) @ ((rt_less @ X1 @ X667))))))))), file('/export/starexec/sandbox2/tmp/tmp.wwvFOgLG2D/E---3.1_20079.p', satz81a)). 3.80/1.08 thf(c_0_25, plain, ((d_not)=(^[Z0/* 3 */:$o]:(((((Z0))=>(~($true))))))), inference(fof_simplification,[status(thm)],[def_d_not])). 3.80/1.08 thf(c_0_26, plain, ((imp)=(^[Z0/* 19 */:$o, Z1:$o]:(((Z0)=>(Z1))))), inference(fof_simplification,[status(thm)],[def_imp])). 3.80/1.08 thf(c_0_27, plain, ((e_is)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:(((Z1)=(Z2))))), inference(fof_simplification,[status(thm)],[def_e_is])). 3.80/1.08 thf(c_0_28, plain, ((l_ec)=(^[Z0/* 19 */:$o, Z1:$o]:(((((Z0))=>((((((Z1)))=>(~($true)))))))))), inference(fof_simplification,[status(thm)],[def_l_ec])). 3.80/1.08 thf(c_0_29, plain, ((d_not)=(^[Z0/* 3 */:$o]:(((((Z0))=>(~($true))))))), inference(apply_def,[status(thm)],[c_0_25, c_0_26])). 3.80/1.08 thf(c_0_30, plain, ((diffprop)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:((((Z0)=(n_pl @ Z1 @ Z2)))))), inference(fof_simplification,[status(thm)],[def_diffprop])). 3.80/1.08 thf(c_0_31, axiom, ((n_is)=(^[Z0/* 19 */:$i, Z1:$i]:(((Z0)=(Z1))))), inference(apply_def,[status(thm)],[def_n_is, c_0_27])). 3.80/1.08 thf(c_0_32, plain, ((d_and)=(^[Z0/* 19 */:$o, Z1:$o]:((((((((((Z0)))=>(((((((Z1))))=>(~($true)))))))))=>(~($true))))))), inference(fof_simplification,[status(thm)],[def_d_and])). 3.80/1.08 thf(c_0_33, plain, ((l_ec)=(^[Z0/* 19 */:$o, Z1:$o]:(((((Z0))=>((((((Z1)))=>(~($true)))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_28, c_0_29]), c_0_26])). 3.80/1.08 thf(c_0_34, plain, ((iii)=(^[Z0/* 19 */:$i, Z1:$i]:((l_some @ nat @ (^[Z2/* 3 */:$i]:((((Z1)=(n_pl @ Z0 @ Z2))))))))), inference(fof_simplification,[status(thm)],[def_iii])). 3.80/1.08 thf(c_0_35, plain, ((diffprop)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:((((Z0)=(n_pl @ Z1 @ Z2)))))), inference(apply_def,[status(thm)],[c_0_30, c_0_31])). 3.80/1.08 thf(c_0_36, plain, ((esti)=(^[Z0/* 26 */:$i]:(in))), inference(fof_simplification,[status(thm)],[def_esti])). 3.80/1.08 thf(c_0_37, plain, ((and3)=(^[Z0/* 19 */:$o, Z1:$o, Z2:$o]:(((((((((((Z0))))=>(((((((((((((((((Z1))))=>((((((((Z2)))))=>(~($true)))))))))=>(~($true))))))))=>(~($true)))))))))=>(~($true))))))), inference(fof_simplification,[status(thm)],[def_and3])). 3.80/1.08 thf(c_0_38, plain, ((d_and)=(^[Z0/* 19 */:$o, Z1:$o]:((((((((((Z0)))=>(((((((Z1))))=>(~($true)))))))))=>(~($true))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_32, c_0_29]), c_0_33])). 3.80/1.08 thf(c_0_39, plain, ((lessf)=(^[Z0/* 19 */:$i, Z1:$i]:(((l_some @ nat @ (^[Z2/* 3 */:$i]:((((n_ts @ (num @ Z1) @ (den @ Z0))=(n_pl @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ Z2)))))))))), inference(fof_simplification,[status(thm)],[def_lessf])). 3.80/1.08 thf(c_0_40, plain, ((iii)=(^[Z0/* 19 */:$i, Z1:$i]:((l_some @ nat @ (^[Z2/* 3 */:$i]:((((Z1)=(n_pl @ Z0 @ Z2))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_34, def_n_some]), c_0_35])). 3.80/1.08 thf(c_0_41, plain, ((d_29_ii)=(^[Z0/* 19 */:$i, Z1:$i]:((l_some @ nat @ (^[Z2/* 3 */:$i]:((((Z0)=(n_pl @ Z1 @ Z2))))))))), inference(fof_simplification,[status(thm)],[def_d_29_ii])). 3.80/1.08 thf(c_0_42, plain, ((rt_less)=(^[Z0/* 19 */:$i, Z1:$i]:((l_some @ frac @ (^[Z2/* 3 */:$i]:((l_some @ frac @ (^[Z3/* 3 */:$i]:((((((((((((in @ Z2 @ (class @ Z0))))))=>((((((((((((((((((in @ Z3 @ (class @ Z1))))))=>((((((((((l_some @ nat @ (^[Z4/* 3 */:$i]:((((n_ts @ (num @ Z3) @ (den @ Z2))=(n_pl @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ Z4))))))))))))=>(~($true)))))))))=>(~($true))))))))=>(~($true)))))))))=>(~($true))))))))))))), inference(fof_simplification,[status(thm)],[def_rt_less])). 3.80/1.08 thf(c_0_43, axiom, ((inf)=(in)), inference(apply_def,[status(thm)],[def_inf, c_0_36])). 3.80/1.08 thf(c_0_44, plain, ((and3)=(^[Z0/* 19 */:$o, Z1:$o, Z2:$o]:(((((((((((Z0))))=>(((((((((((((((((Z1))))=>((((((((Z2)))))=>(~($true)))))))))=>(~($true))))))))=>(~($true)))))))))=>(~($true))))))), inference(apply_def,[status(thm)],[c_0_37, c_0_38])). 3.80/1.08 thf(c_0_45, plain, ((lessf)=(^[Z0/* 19 */:$i, Z1:$i]:(((l_some @ nat @ (^[Z2/* 3 */:$i]:((((n_ts @ (num @ Z1) @ (den @ Z0))=(n_pl @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ Z2)))))))))), inference(apply_def,[status(thm)],[c_0_39, c_0_40])). 3.80/1.08 thf(c_0_46, plain, ((l_or)=(^[Z0/* 19 */:$o, Z1:$o]:((((((((Z0)))=>(~($true)))))=>(Z1))))), inference(fof_simplification,[status(thm)],[def_l_or])). 3.80/1.08 thf(c_0_47, plain, ((moref)=(^[Z0/* 19 */:$i, Z1:$i]:(((l_some @ nat @ (^[Z2/* 3 */:$i]:((((n_ts @ (num @ Z0) @ (den @ Z1))=(n_pl @ (n_ts @ (num @ Z1) @ (den @ Z0)) @ Z2)))))))))), inference(fof_simplification,[status(thm)],[def_moref])). 3.80/1.08 thf(c_0_48, plain, ((d_29_ii)=(^[Z0/* 19 */:$i, Z1:$i]:((l_some @ nat @ (^[Z2/* 3 */:$i]:((((Z0)=(n_pl @ Z1 @ Z2))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_41, def_n_some]), c_0_35])). 3.80/1.08 thf(c_0_49, plain, ((rt_lessis)=(^[Z0/* 19 */:$i, Z1:$i]:(((((((((((l_some @ frac @ (^[Z2/* 3 */:$i]:((l_some @ frac @ (^[Z3/* 3 */:$i]:((((((((((((in @ Z2 @ (class @ Z0))))))=>((((((((((((((((((in @ Z3 @ (class @ Z1))))))=>((((((((((l_some @ nat @ (^[Z4/* 3 */:$i]:((((n_ts @ (num @ Z3) @ (den @ Z2))=(n_pl @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ Z4))))))))))))=>(~($true)))))))))=>(~($true))))))))=>(~($true)))))))))=>(~($true))))))))))))))=>(~($true)))))=>((((Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[def_rt_lessis])). 3.80/1.08 thf(c_0_50, plain, ((rt_less)=(^[Z0/* 19 */:$i, Z1:$i]:((l_some @ frac @ (^[Z2/* 3 */:$i]:((l_some @ frac @ (^[Z3/* 3 */:$i]:((((((((((((in @ Z2 @ (class @ Z0))))))=>((((((((((((((((((in @ Z3 @ (class @ Z1))))))=>((((((((((l_some @ nat @ (^[Z4/* 3 */:$i]:((((n_ts @ (num @ Z3) @ (den @ Z2))=(n_pl @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ Z4))))))))))))=>(~($true)))))))))=>(~($true))))))))=>(~($true)))))))))=>(~($true))))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_42, c_0_43]), c_0_44]), c_0_45])). 3.80/1.08 thf(c_0_51, axiom, ((rt_is)=(^[Z0/* 19 */:$i, Z1:$i]:(((Z0)=(Z1))))), inference(apply_def,[status(thm)],[def_rt_is, c_0_27])). 3.80/1.08 thf(c_0_52, plain, ((l_or)=(^[Z0/* 19 */:$o, Z1:$o]:((((((((Z0)))=>(~($true)))))=>(Z1))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_46, c_0_29]), c_0_26])). 3.80/1.08 thf(c_0_53, plain, ((rt_more)=(^[Z0/* 19 */:$i, Z1:$i]:((l_some @ frac @ (^[Z2/* 3 */:$i]:((l_some @ frac @ (^[Z3/* 3 */:$i]:((((((((((((in @ Z2 @ (class @ Z0))))))=>((((((((((((((((((in @ Z3 @ (class @ Z1))))))=>((((((((((l_some @ nat @ (^[Z4/* 3 */:$i]:((((n_ts @ (num @ Z2) @ (den @ Z3))=(n_pl @ (n_ts @ (num @ Z3) @ (den @ Z2)) @ Z4))))))))))))=>(~($true)))))))))=>(~($true))))))))=>(~($true)))))))))=>(~($true))))))))))))), inference(fof_simplification,[status(thm)],[def_rt_more])). 3.80/1.08 thf(c_0_54, plain, ((moref)=(^[Z0/* 19 */:$i, Z1:$i]:(((l_some @ nat @ (^[Z2/* 3 */:$i]:((((n_ts @ (num @ Z0) @ (den @ Z1))=(n_pl @ (n_ts @ (num @ Z1) @ (den @ Z0)) @ Z2)))))))))), inference(apply_def,[status(thm)],[c_0_47, c_0_48])). 3.80/1.08 thf(c_0_55, plain, ((all_of)=(^[Z0/* 19 */:$i > $o, Z1:$i > $o]:(![X4:$i]:((((Z0 @ X4))=>(Z1 @ X4)))))), inference(fof_simplification,[status(thm)],[def_all_of])). 3.80/1.08 thf(c_0_56, plain, ((is_of)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((Z1 @ Z0)))), inference(fof_simplification,[status(thm)],[def_is_of])). 3.80/1.08 thf(c_0_57, plain, ((rt_lessis)=(^[Z0/* 19 */:$i, Z1:$i]:(((((((((((l_some @ frac @ (^[Z2/* 3 */:$i]:((l_some @ frac @ (^[Z3/* 3 */:$i]:((((((((((((in @ Z2 @ (class @ Z0))))))=>((((((((((((((((((in @ Z3 @ (class @ Z1))))))=>((((((((((l_some @ nat @ (^[Z4/* 3 */:$i]:((((n_ts @ (num @ Z3) @ (den @ Z2))=(n_pl @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ Z4))))))))))))=>(~($true)))))))))=>(~($true))))))))=>(~($true)))))))))=>(~($true))))))))))))))=>(~($true)))))=>((((Z0)=(Z1))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_49, c_0_50]), c_0_51]), c_0_52])). 3.80/1.08 thf(c_0_58, plain, ((rt_more)=(^[Z0/* 19 */:$i, Z1:$i]:((l_some @ frac @ (^[Z2/* 3 */:$i]:((l_some @ frac @ (^[Z3/* 3 */:$i]:((((((((((((in @ Z2 @ (class @ Z0))))))=>((((((((((((((((((in @ Z3 @ (class @ Z1))))))=>((((((((((l_some @ nat @ (^[Z4/* 3 */:$i]:((((n_ts @ (num @ Z2) @ (den @ Z3))=(n_pl @ (n_ts @ (num @ Z3) @ (den @ Z2)) @ Z4))))))))))))=>(~($true)))))))))=>(~($true))))))))=>(~($true)))))))))=>(~($true))))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_53, c_0_43]), c_0_44]), c_0_54])). 3.80/1.08 thf(c_0_59, plain, ((all_of)=(^[Z0/* 19 */:$i > $o, Z1:$i > $o]:(![X4:$i]:((((Z0 @ X4))=>(Z1 @ X4)))))), inference(apply_def,[status(thm)],[c_0_55, c_0_56])). 3.80/1.08 thf(c_0_60, plain, ((or3)=(^[Z0/* 19 */:$o, Z1:$o, Z2:$o]:((((((((((Z0))))=>(~($true)))))=>((((((((((Z1))))=>(~($true)))))=>((Z2)))))))))), inference(fof_simplification,[status(thm)],[def_or3])). 3.80/1.08 thf(c_0_61, negated_conjecture, ~(![X773:$i]:(((in @ X773 @ rat)=>![X772:$i]:(((in @ X772 @ rat)=>(((l_some @ frac @ (^[Z0/* 3 */:$i]:((l_some @ frac @ (^[Z1/* 10 */:$i]:((((in @ Z0 @ (class @ X773))=>((((in @ Z1 @ (class @ X772))=>((l_some @ nat @ (^[Z2/* 3 */:$i]:(((n_ts @ (num @ Z0) @ (den @ Z1))=(n_pl @ (n_ts @ (num @ Z1) @ (den @ Z0)) @ Z2)))))=>~($true)))=>~($true))=>~($true)))=>~($true))))))))=>~($true))=>(((l_some @ frac @ (^[Z0/* 3 */:$i]:((l_some @ frac @ (^[Z1/* 10 */:$i]:((((in @ Z0 @ (class @ X773))=>((((in @ Z1 @ (class @ X772))=>((l_some @ nat @ (^[Z2/* 3 */:$i]:(((n_ts @ (num @ Z1) @ (den @ Z0))=(n_pl @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ Z2)))))=>~($true)))=>~($true))=>~($true)))=>~($true))))))))=>~($true))=>((X773)=(X772))))))))), inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[satz81e])]), c_0_29]), c_0_57]), c_0_58]), c_0_59])])). 3.80/1.08 thf(c_0_62, plain, ((or3)=(^[Z0/* 19 */:$o, Z1:$o, Z2:$o]:((((((((((Z0))))=>(~($true)))))=>((((((((((Z1))))=>(~($true)))))=>((Z2)))))))))), inference(apply_def,[status(thm)],[c_0_60, c_0_52])). 3.80/1.08 thf(c_0_63, negated_conjecture, ((in @ esk1_0 @ rat)&((in @ esk2_0 @ rat)&((~(l_some @ frac @ (^[Z0/* 3 */:$i]:((l_some @ frac @ (^[Z1/* 10 */:$i]:((((in @ Z0 @ (class @ esk1_0))=>((((in @ Z1 @ (class @ esk2_0))=>((l_some @ nat @ (^[Z2/* 3 */:$i]:(((n_ts @ (num @ Z0) @ (den @ Z1))=(n_pl @ (n_ts @ (num @ Z1) @ (den @ Z0)) @ Z2)))))=>~($true)))=>~($true))=>~($true)))=>~($true))))))))|~($true))&((~(l_some @ frac @ (^[Z0/* 3 */:$i]:((l_some @ frac @ (^[Z1/* 10 */:$i]:((((in @ Z0 @ (class @ esk1_0))=>((((in @ Z1 @ (class @ esk2_0))=>((l_some @ nat @ (^[Z2/* 3 */:$i]:(((n_ts @ (num @ Z1) @ (den @ Z0))=(n_pl @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ Z2)))))=>~($true)))=>~($true))=>~($true)))=>~($true))))))))|~($true))&((esk1_0)!=(esk2_0)))))), inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_61])])])])). 3.80/1.08 thf(c_0_64, plain, ![X815:$i]:(((in @ X815 @ rat)=>![X814:$i]:(((in @ X814 @ rat)=>((((X815)=(X814))=>~($true))=>(((l_some @ frac @ (^[Z0/* 3 */:$i]:((l_some @ frac @ (^[Z1/* 10 */:$i]:((((in @ Z0 @ (class @ X815))=>((((in @ Z1 @ (class @ X814))=>((l_some @ nat @ (^[Z2/* 3 */:$i]:(((n_ts @ (num @ Z0) @ (den @ Z1))=(n_pl @ (n_ts @ (num @ Z1) @ (den @ Z0)) @ Z2)))))=>~($true)))=>~($true))=>~($true)))=>~($true))))))))=>~($true))=>(l_some @ frac @ (^[Z0/* 3 */:$i]:((l_some @ frac @ (^[Z1/* 10 */:$i]:((((in @ Z0 @ (class @ X815))=>((((in @ Z1 @ (class @ X814))=>((l_some @ nat @ (^[Z2/* 3 */:$i]:(((n_ts @ (num @ Z1) @ (den @ Z0))=(n_pl @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ Z2)))))=>~($true)))=>~($true))=>~($true)))=>~($true)))))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz81a]), c_0_50]), c_0_62]), c_0_51]), c_0_58]), c_0_59])). 3.80/1.08 thf(c_0_65, negated_conjecture, (~((l_some @ frac @ (^[Z0/* 3 */:$i]:((l_some @ frac @ (^[Z1/* 10 */:$i]:((((in @ Z0 @ (class @ esk1_0))=>((((in @ Z1 @ (class @ esk2_0))=>((l_some @ nat @ (^[Z2/* 3 */:$i]:(((n_ts @ (num @ Z0) @ (den @ Z1))=(n_pl @ (n_ts @ (num @ Z1) @ (den @ Z0)) @ Z2)))))=>~(($true))))=>~(($true)))=>~(($true))))=>~(($true))))))))))|~(($true))), inference(split_conjunct,[status(thm)],[c_0_63])). 3.80/1.08 thf(c_0_66, plain, ![X1476:$i, X1477:$i]:(((((l_some @ frac @ (^[Z0/* 3 */:$i]:((l_some @ frac @ (^[Z1/* 10 */:$i]:((((in @ Z0 @ (class @ X1476))=>((((in @ Z1 @ (class @ X1477))=>((l_some @ nat @ (^[Z2/* 3 */:$i]:(((n_ts @ (num @ Z0) @ (den @ Z1))=(n_pl @ (n_ts @ (num @ Z1) @ (den @ Z0)) @ Z2)))))=>~($true)))=>~($true))=>~($true)))=>~($true))))))))|(l_some @ frac @ (^[Z0/* 3 */:$i]:((l_some @ frac @ (^[Z1/* 10 */:$i]:((((in @ Z0 @ (class @ X1476))=>((((in @ Z1 @ (class @ X1477))=>((l_some @ nat @ (^[Z2/* 3 */:$i]:(((n_ts @ (num @ Z1) @ (den @ Z0))=(n_pl @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ Z2)))))=>~($true)))=>~($true))=>~($true)))=>~($true))))))))|((X1476)=(X1477))|~(in @ X1477 @ rat)|~(in @ X1476 @ rat))&(($true)|(l_some @ frac @ (^[Z0/* 3 */:$i]:((l_some @ frac @ (^[Z1/* 10 */:$i]:((((in @ Z0 @ (class @ X1476))=>((((in @ Z1 @ (class @ X1477))=>((l_some @ nat @ (^[Z2/* 3 */:$i]:(((n_ts @ (num @ Z1) @ (den @ Z0))=(n_pl @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ Z2)))))=>~($true)))=>~($true))=>~($true)))=>~($true))))))))|((X1476)=(X1477))|~(in @ X1477 @ rat)|~(in @ X1476 @ rat)))&(((l_some @ frac @ (^[Z0/* 3 */:$i]:((l_some @ frac @ (^[Z1/* 10 */:$i]:((((in @ Z0 @ (class @ X1476))=>((((in @ Z1 @ (class @ X1477))=>((l_some @ nat @ (^[Z2/* 3 */:$i]:(((n_ts @ (num @ Z0) @ (den @ Z1))=(n_pl @ (n_ts @ (num @ Z1) @ (den @ Z0)) @ Z2)))))=>~($true)))=>~($true))=>~($true)))=>~($true))))))))|(l_some @ frac @ (^[Z0/* 3 */:$i]:((l_some @ frac @ (^[Z1/* 10 */:$i]:((((in @ Z0 @ (class @ X1476))=>((((in @ Z1 @ (class @ X1477))=>((l_some @ nat @ (^[Z2/* 3 */:$i]:(((n_ts @ (num @ Z1) @ (den @ Z0))=(n_pl @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ Z2)))))=>~($true)))=>~($true))=>~($true)))=>~($true))))))))|($true)|~(in @ X1477 @ rat)|~(in @ X1476 @ rat))&(($true)|(l_some @ frac @ (^[Z0/* 3 */:$i]:((l_some @ frac @ (^[Z1/* 10 */:$i]:((((in @ Z0 @ (class @ X1476))=>((((in @ Z1 @ (class @ X1477))=>((l_some @ nat @ (^[Z2/* 3 */:$i]:(((n_ts @ (num @ Z1) @ (den @ Z0))=(n_pl @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ Z2)))))=>~($true)))=>~($true))=>~($true)))=>~($true))))))))|($true)|~(in @ X1477 @ rat)|~(in @ X1476 @ rat))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_64])])])])])). 3.80/1.08 thf(c_0_67, negated_conjecture, (~((l_some @ frac @ (^[Z0/* 3 */:$i]:((l_some @ frac @ (^[Z1/* 10 */:$i]:((((in @ Z0 @ (class @ esk1_0))=>((((in @ Z1 @ (class @ esk2_0))=>((l_some @ nat @ (^[Z2/* 3 */:$i]:(((n_ts @ (num @ Z1) @ (den @ Z0))=(n_pl @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ Z2)))))=>~(($true))))=>~(($true)))=>~(($true))))=>~(($true))))))))))|~(($true))), inference(split_conjunct,[status(thm)],[c_0_63])). 3.80/1.08 thf(c_0_68, negated_conjecture, ~((l_some @ frac @ (^[Z0/* 3 */:$i]:((l_some @ frac @ (^[Z1/* 10 */:$i]:((((in @ Z0 @ (class @ esk1_0))=>((((in @ Z1 @ (class @ esk2_0))=>((l_some @ nat @ (^[Z2/* 3 */:$i]:(((n_ts @ (num @ Z0) @ (den @ Z1))=(n_pl @ (n_ts @ (num @ Z1) @ (den @ Z0)) @ Z2)))))=>~(($true))))=>~(($true)))=>~(($true))))=>~(($true)))))))))), inference(cn,[status(thm)],[c_0_65])). 3.80/1.08 thf(c_0_69, plain, ![X4:$i, X1:$i]:(((l_some @ frac @ (^[Z0/* 3 */:$i]:((l_some @ frac @ (^[Z1/* 10 */:$i]:((((in @ Z0 @ (class @ X1))=>((((in @ Z1 @ (class @ X4))=>((l_some @ nat @ (^[Z2/* 3 */:$i]:(((n_ts @ (num @ Z0) @ (den @ Z1))=(n_pl @ (n_ts @ (num @ Z1) @ (den @ Z0)) @ Z2)))))=>~(($true))))=>~(($true)))=>~(($true))))=>~(($true)))))))))|(l_some @ frac @ (^[Z0/* 3 */:$i]:((l_some @ frac @ (^[Z1/* 10 */:$i]:((((in @ Z0 @ (class @ X1))=>((((in @ Z1 @ (class @ X4))=>((l_some @ nat @ (^[Z2/* 3 */:$i]:(((n_ts @ (num @ Z1) @ (den @ Z0))=(n_pl @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ Z2)))))=>~(($true))))=>~(($true)))=>~(($true))))=>~(($true)))))))))|((X1)=(X4))|~((in @ X4 @ rat))|~((in @ X1 @ rat)))), inference(split_conjunct,[status(thm)],[c_0_66])). 3.80/1.08 thf(c_0_70, negated_conjecture, ~((l_some @ frac @ (^[Z0/* 3 */:$i]:((l_some @ frac @ (^[Z1/* 10 */:$i]:((((in @ Z0 @ (class @ esk1_0))=>((((in @ Z1 @ (class @ esk2_0))=>((l_some @ nat @ (^[Z2/* 3 */:$i]:(((n_ts @ (num @ Z1) @ (den @ Z0))=(n_pl @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ Z2)))))=>~(($true))))=>~(($true)))=>~(($true))))=>~(($true)))))))))), inference(cn,[status(thm)],[c_0_67])). 3.80/1.08 thf(c_0_71, negated_conjecture, ~((l_some @ frac @ (^[Z0/* 3 */:$i]:((l_some @ frac @ (^[Z1/* 7 */:$i]:(~(((in @ Z0 @ (class @ esk1_0))=>((in @ Z1 @ (class @ esk2_0))=>~((l_some @ nat @ (^[Z2/* 3 */:$i]:(((n_ts @ (num @ Z0) @ (den @ Z1))=(n_pl @ (n_ts @ (num @ Z1) @ (den @ Z0)) @ Z2)))))))))))))))), inference(cn,[status(thm)],[c_0_68])). 3.80/1.08 thf(c_0_72, plain, ![X4:$i, X1:$i]:((((X1)=(X4))|(l_some @ frac @ (^[Z0/* 3 */:$i]:((l_some @ frac @ (^[Z1/* 7 */:$i]:(~(((in @ Z0 @ (class @ X1))=>((in @ Z1 @ (class @ X4))=>~((l_some @ nat @ (^[Z2/* 3 */:$i]:(((n_ts @ (num @ Z0) @ (den @ Z1))=(n_pl @ (n_ts @ (num @ Z1) @ (den @ Z0)) @ Z2)))))))))))))))|(l_some @ frac @ (^[Z0/* 3 */:$i]:((l_some @ frac @ (^[Z1/* 7 */:$i]:(~(((in @ Z0 @ (class @ X1))=>((in @ Z1 @ (class @ X4))=>~((l_some @ nat @ (^[Z2/* 3 */:$i]:(((n_ts @ (num @ Z1) @ (den @ Z0))=(n_pl @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ Z2)))))))))))))))|~((in @ X4 @ rat))|~((in @ X1 @ rat)))), inference(cn,[status(thm)],[c_0_69])). 3.80/1.08 thf(c_0_73, negated_conjecture, (in @ esk2_0 @ rat), inference(split_conjunct,[status(thm)],[c_0_63])). 3.80/1.08 thf(c_0_74, negated_conjecture, (in @ esk1_0 @ rat), inference(split_conjunct,[status(thm)],[c_0_63])). 3.80/1.08 thf(c_0_75, negated_conjecture, ((esk1_0)!=(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_63])). 3.80/1.08 thf(c_0_76, negated_conjecture, ~((l_some @ frac @ (^[Z0/* 3 */:$i]:((l_some @ frac @ (^[Z1/* 7 */:$i]:(~(((in @ Z0 @ (class @ esk1_0))=>((in @ Z1 @ (class @ esk2_0))=>~((l_some @ nat @ (^[Z2/* 3 */:$i]:(((n_ts @ (num @ Z1) @ (den @ Z0))=(n_pl @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ Z2)))))))))))))))), inference(cn,[status(thm)],[c_0_70])). 3.80/1.08 thf(c_0_77, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71, c_0_72]), c_0_73]), c_0_74])]), c_0_75]), c_0_76]), ['proof']). 3.80/1.08 # SZS output end CNFRefutation 3.80/1.08 # Parsed axioms : 695 3.80/1.08 # Removed by relevancy pruning/SinE : 358 3.80/1.08 # Initial clauses : 575 3.80/1.08 # Removed in clause preprocessing : 191 3.80/1.08 # Initial clauses in saturation : 384 3.80/1.08 # Processed clauses : 747 3.80/1.08 # ...of these trivial : 0 3.80/1.08 # ...subsumed : 273 3.80/1.08 # ...remaining for further processing : 474 3.80/1.08 # Other redundant clauses eliminated : 50 3.80/1.08 # Clauses deleted for lack of memory : 0 3.80/1.08 # Backward-subsumed : 4 3.80/1.08 # Backward-rewritten : 1 3.80/1.08 # Generated clauses : 4437 3.80/1.08 # ...of the previous two non-redundant : 4381 3.80/1.08 # ...aggressively subsumed : 0 3.80/1.08 # Contextual simplify-reflections : 0 3.80/1.08 # Paramodulations : 1536 3.80/1.08 # Factorizations : 0 3.80/1.08 # NegExts : 0 3.80/1.08 # Equation resolutions : 69 3.80/1.08 # Disequality decompositions : 0 3.80/1.08 # Total rewrite steps : 162 3.80/1.08 # ...of those cached : 151 3.80/1.08 # Propositional unsat checks : 0 3.80/1.08 # Propositional check models : 0 3.80/1.08 # Propositional check unsatisfiable : 0 3.80/1.08 # Propositional clauses : 0 3.80/1.08 # Propositional clauses after purity: 0 3.80/1.08 # Propositional unsat core size : 0 3.80/1.08 # Propositional preprocessing time : 0.000 3.80/1.08 # Propositional encoding time : 0.000 3.80/1.08 # Propositional solver time : 0.000 3.80/1.08 # Success case prop preproc time : 0.000 3.80/1.08 # Success case prop encoding time : 0.000 3.80/1.08 # Success case prop solver time : 0.000 3.80/1.08 # Current number of processed clauses : 242 3.80/1.08 # Positive orientable unit clauses : 24 3.80/1.08 # Positive unorientable unit clauses: 5 3.80/1.08 # Negative unit clauses : 30 3.80/1.08 # Non-unit-clauses : 183 3.80/1.08 # Current number of unprocessed clauses: 4099 3.80/1.08 # ...number of literals in the above : 32220 3.80/1.08 # Current number of archived formulas : 0 3.80/1.08 # Current number of archived clauses : 190 3.80/1.08 # Clause-clause subsumption calls (NU) : 43394 3.80/1.08 # Rec. Clause-clause subsumption calls : 4306 3.80/1.08 # Non-unit clause-clause subsumptions : 235 3.80/1.08 # Unit Clause-clause subsumption calls : 546 3.80/1.08 # Rewrite failures with RHS unbound : 52 3.80/1.08 # BW rewrite match attempts : 28 3.80/1.08 # BW rewrite match successes : 5 3.80/1.08 # Condensation attempts : 0 3.80/1.08 # Condensation successes : 0 3.80/1.08 # Termbank termtop insertions : 338823 3.80/1.08 # Search garbage collected termcells : 57271 3.80/1.08 3.80/1.08 # ------------------------------------------------- 3.80/1.08 # User time : 0.516 s 3.80/1.08 # System time : 0.017 s 3.80/1.08 # Total time : 0.532 s 3.80/1.08 # Maximum resident set size: 11332 pages 3.80/1.08 3.80/1.08 # ------------------------------------------------- 3.80/1.08 # User time : 0.533 s 3.80/1.08 # System time : 0.020 s 3.80/1.08 # Total time : 0.554 s 3.80/1.08 # Maximum resident set size: 3124 pages 3.80/1.08 % E exiting 3.80/1.08 % E exiting 3.80/1.08 EOF