0.03/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.12 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 240 THM 0.12/0.33 % Computer : n013.cluster.edu 0.12/0.33 % Model : x86_64 x86_64 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.33 % Memory : 8042.1875MB 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.33 % CPULimit : 1920 0.12/0.33 % WCLimit : 240 0.12/0.33 % DateTime : Wed Jul 30 09:35:49 EDT 2025 0.12/0.33 % CPUTime : 0.20/0.47 Running higher-order theorem proving 0.20/0.55 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.lBsOH5vCnP/E---3.1_5230.p 0.41/0.78 # Version: 3.0.0-ho 0.41/0.78 # Preprocessing class: HSLMSMSMLLLCHSA. 0.41/0.78 # Scheduled 5 strats onto 8 cores with 240 seconds (1920 total) 0.41/0.78 # Starting pre_casc_4 with 960s (4) cores 0.41/0.78 # Starting full_lambda_6 with 240s (1) cores 0.41/0.78 # Starting sh10 with 240s (1) cores 0.41/0.78 # Starting post_as_ho9 with 240s (1) cores 0.41/0.78 # Starting post_as_ho8 with 240s (1) cores 0.41/0.78 # post_as_ho9 with pid 5317 completed with status 0 0.41/0.78 # Result found by post_as_ho9 0.41/0.78 # Preprocessing class: HSLMSMSMLLLCHSA. 0.41/0.78 # Scheduled 5 strats onto 8 cores with 240 seconds (1920 total) 0.41/0.78 # Starting pre_casc_4 with 960s (4) cores 0.41/0.78 # Starting full_lambda_6 with 240s (1) cores 0.41/0.78 # Starting sh10 with 240s (1) cores 0.41/0.78 # Starting post_as_ho9 with 240s (1) cores 0.41/0.78 # SinE strategy is GSinE(CountFormulas,,true,1,0,2,20000,1.0,true) 0.41/0.78 # Search class: HGHNF-FFLS31-DHSMMFBN 0.41/0.78 # partial match(5): HGHSM-FSLS31-SHSMMSBN 0.41/0.78 # Scheduled 6 strats onto 1 cores with 240 seconds (240 total) 0.41/0.78 # Starting new_ho_10 with 130s (1) cores 0.41/0.78 # new_ho_10 with pid 5319 completed with status 0 0.41/0.78 # Result found by new_ho_10 0.41/0.78 # Preprocessing class: HSLMSMSMLLLCHSA. 0.41/0.78 # Scheduled 5 strats onto 8 cores with 240 seconds (1920 total) 0.41/0.78 # Starting pre_casc_4 with 960s (4) cores 0.41/0.78 # Starting full_lambda_6 with 240s (1) cores 0.41/0.78 # Starting sh10 with 240s (1) cores 0.41/0.78 # Starting post_as_ho9 with 240s (1) cores 0.41/0.78 # SinE strategy is GSinE(CountFormulas,,true,1,0,2,20000,1.0,true) 0.41/0.78 # Search class: HGHNF-FFLS31-DHSMMFBN 0.41/0.78 # partial match(5): HGHSM-FSLS31-SHSMMSBN 0.41/0.78 # Scheduled 6 strats onto 1 cores with 240 seconds (240 total) 0.41/0.78 # Starting new_ho_10 with 130s (1) cores 0.41/0.78 # Preprocessing time : 0.005 s 0.41/0.78 # Presaturation interreduction done 0.41/0.78 0.41/0.78 # Proof found! 0.41/0.78 # SZS status Theorem 0.41/0.78 # SZS output start CNFRefutation 0.41/0.78 thf(decl_23, type, is_of: $i > ($i > $o) > $o). 0.41/0.78 thf(decl_24, type, all_of: ($i > $o) > ($i > $o) > $o). 0.41/0.78 thf(decl_26, type, in: $i > $i > $o). 0.41/0.78 thf(decl_30, type, power: $i > $i). 0.41/0.78 thf(decl_43, type, d_Sep: $i > ($i > $o) > $i). 0.41/0.78 thf(decl_62, type, imp: $o > $o > $o). 0.41/0.78 thf(decl_63, type, d_not: $o > $o). 0.41/0.78 thf(decl_67, type, d_and: $o > $o > $o). 0.41/0.78 thf(decl_68, type, l_or: $o > $o > $o). 0.41/0.78 thf(decl_72, type, non: $i > ($i > $o) > $i > $o). 0.41/0.78 thf(decl_73, type, l_some: $i > ($i > $o) > $o). 0.41/0.78 thf(decl_75, type, and3: $o > $o > $o > $o). 0.41/0.78 thf(decl_78, type, e_is: $i > $i > $i > $o). 0.41/0.78 thf(decl_103, type, esti: $i > $i > $i > $o). 0.41/0.78 thf(decl_112, type, anec: $i > ($i > $i > $o) > $i > $o). 0.41/0.78 thf(decl_113, type, ect: $i > ($i > $i > $o) > $i). 0.41/0.78 thf(decl_116, type, ecect: $i > ($i > $i > $o) > $i > $i). 0.41/0.78 thf(decl_124, type, nat: $i). 0.41/0.78 thf(decl_125, type, n_is: $i > $i > $o). 0.41/0.78 thf(decl_149, type, d_29_ii: $i > $i > $o). 0.41/0.78 thf(decl_163, type, n_ts: $i > $i > $i). 0.41/0.78 thf(decl_177, type, pair1type: $i > $i). 0.41/0.78 thf(decl_190, type, frac: $i). 0.41/0.78 thf(decl_192, type, num: $i > $i). 0.41/0.78 thf(decl_193, type, den: $i > $i). 0.41/0.78 thf(decl_194, type, n_eq: $i > $i > $o). 0.41/0.78 thf(decl_195, type, moref: $i > $i > $o). 0.41/0.78 thf(decl_196, type, lessf: $i > $i > $o). 0.41/0.78 thf(decl_204, type, inf: $i > $i > $o). 0.41/0.78 thf(decl_205, type, rat: $i). 0.41/0.78 thf(decl_206, type, rt_is: $i > $i > $o). 0.41/0.78 thf(decl_213, type, class: $i > $i). 0.41/0.78 thf(decl_216, type, rt_more: $i > $i > $o). 0.41/0.78 thf(decl_218, type, rt_less: $i > $i > $o). 0.41/0.78 thf(decl_221, type, rt_lessis: $i > $i > $o). 0.41/0.78 thf(decl_222, type, esk1_0: $i). 0.41/0.78 thf(decl_223, type, esk2_0: $i). 0.41/0.78 thf(decl_224, type, esk3_0: $i). 0.41/0.78 thf(decl_225, type, esk4_0: $i). 0.41/0.78 thf(def_all_of, axiom, ((all_of)=(^[X3:$i > $o, X2:$i > $o]:(![X4:$i]:(((is_of @ X4 @ X3)=>(X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.lBsOH5vCnP/E---3.1_5230.p', def_all_of)). 0.41/0.78 thf(def_is_of, axiom, ((is_of)=(^[X1:$i, X2:$i > $o]:((X2 @ X1)))), file('/export/starexec/sandbox2/tmp/tmp.lBsOH5vCnP/E---3.1_5230.p', def_is_of)). 0.41/0.78 thf(def_d_not, axiom, ((d_not)=(^[X36:$o]:((imp @ ((X36)) @ (~($true)))))), file('/export/starexec/sandbox2/tmp/tmp.lBsOH5vCnP/E---3.1_5230.p', def_d_not)). 0.41/0.78 thf(def_imp, axiom, ((imp)=(^[X34:$o, X35:$o]:(((X34)=>(X35))))), file('/export/starexec/sandbox2/tmp/tmp.lBsOH5vCnP/E---3.1_5230.p', def_imp)). 0.41/0.78 thf(def_n_eq, axiom, ((n_eq)=(^[X1:$i, X218:$i]:((n_is @ (n_ts @ (num @ X1) @ (den @ X218)) @ (n_ts @ (num @ X218) @ (den @ X1)))))), file('/export/starexec/sandbox2/tmp/tmp.lBsOH5vCnP/E---3.1_5230.p', def_n_eq)). 0.41/0.78 thf(def_ect, axiom, ((ect)=(^[X1:$i, X95:$i > $i > $o]:(d_Sep @ (power @ X1) @ (anec @ X1 @ X95)))), file('/export/starexec/sandbox2/tmp/tmp.lBsOH5vCnP/E---3.1_5230.p', def_ect)). 0.41/0.78 thf(def_l_some, axiom, ((l_some)=(^[X1:$i, X2:$i > $o]:((d_not @ ((all_of @ (^[X4:$i]:((in @ X4 @ X1))) @ (non @ X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.lBsOH5vCnP/E---3.1_5230.p', def_l_some)). 0.41/0.78 thf(def_rat, axiom, ((rat)=(d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0)))))))), file('/export/starexec/sandbox2/tmp/tmp.lBsOH5vCnP/E---3.1_5230.p', def_rat)). 0.41/0.78 thf(def_frac, axiom, ((frac)=(pair1type @ nat)), file('/export/starexec/sandbox2/tmp/tmp.lBsOH5vCnP/E---3.1_5230.p', def_frac)). 0.41/0.78 thf(def_l_or, axiom, ((l_or)=(^[X42:$o]:(imp @ ((d_not @ ((X42))))))), file('/export/starexec/sandbox2/tmp/tmp.lBsOH5vCnP/E---3.1_5230.p', def_l_or)). 0.41/0.78 thf(def_rt_less, axiom, ((rt_less)=(^[X1:$i, X648:$i]:((l_some @ frac @ (^[X4:$i]:((l_some @ frac @ (^[X10:$i]:((and3 @ ((inf @ X4 @ (class @ X1))) @ ((inf @ X10 @ (class @ X648))) @ ((lessf @ X4 @ X10)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.lBsOH5vCnP/E---3.1_5230.p', def_rt_less)). 0.41/0.78 thf(def_class, axiom, ((class)=(ecect @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))), file('/export/starexec/sandbox2/tmp/tmp.lBsOH5vCnP/E---3.1_5230.p', def_class)). 0.41/0.78 thf(def_inf, axiom, ((inf)=(esti @ (pair1type @ nat))), file('/export/starexec/sandbox2/tmp/tmp.lBsOH5vCnP/E---3.1_5230.p', def_inf)). 0.41/0.78 thf(def_and3, axiom, ((and3)=(^[X51:$o, X52:$o, X53:$o]:((d_and @ ((X51)) @ ((d_and @ ((X52)) @ ((X53)))))))), file('/export/starexec/sandbox2/tmp/tmp.lBsOH5vCnP/E---3.1_5230.p', def_and3)). 0.41/0.78 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.lBsOH5vCnP/E---3.1_5230.p', def_rt_lessis)). 0.41/0.78 thf(def_rt_is, axiom, ((rt_is)=(e_is @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))))), file('/export/starexec/sandbox2/tmp/tmp.lBsOH5vCnP/E---3.1_5230.p', def_rt_is)). 0.41/0.78 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.lBsOH5vCnP/E---3.1_5230.p', def_rt_more)). 0.41/0.78 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.lBsOH5vCnP/E---3.1_5230.p', def_moref)). 0.41/0.78 thf(satz81d, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ rat))) @ (^[X1:$i]:((all_of @ (^[X660:$i]:((in @ X660 @ rat))) @ (^[X661:$i]:(((rt_lessis @ X1 @ X661)=>(d_not @ ((rt_more @ X1 @ X661)))))))))), file('/export/starexec/sandbox2/tmp/tmp.lBsOH5vCnP/E---3.1_5230.p', satz81d)). 0.41/0.78 thf(satz81g, conjecture, (all_of @ (^[X1:$i]:((in @ X1 @ rat))) @ (^[X1:$i]:((all_of @ (^[X654:$i]:((in @ X654 @ rat))) @ (^[X655:$i]:(((d_not @ ((rt_lessis @ X1 @ X655)))<=(rt_more @ X1 @ X655)))))))), file('/export/starexec/sandbox2/tmp/tmp.lBsOH5vCnP/E---3.1_5230.p', satz81g)). 0.41/0.78 thf(c_0_20, plain, ((all_of)=(^[Z0/* 19 */:$i > $o, Z1:$i > $o]:(![X4:$i]:((((Z0 @ X4))=>(Z1 @ X4)))))), inference(fof_simplification,[status(thm)],[def_all_of])). 0.41/0.78 thf(c_0_21, plain, ((is_of)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((Z1 @ Z0)))), inference(fof_simplification,[status(thm)],[def_is_of])). 0.41/0.78 thf(c_0_22, plain, ((d_not)=(^[Z0/* 3 */:$o]:(((((Z0))=>(~($true))))))), inference(fof_simplification,[status(thm)],[def_d_not])). 0.41/0.78 thf(c_0_23, plain, ((imp)=(^[Z0/* 19 */:$o, Z1:$o]:(((Z0)=>(Z1))))), inference(fof_simplification,[status(thm)],[def_imp])). 0.41/0.78 thf(c_0_24, plain, ((n_eq)=(^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0)))))), inference(fof_simplification,[status(thm)],[def_n_eq])). 0.41/0.78 thf(c_0_25, plain, ((ect)=(^[Z0/* 19 */:$i, Z1:$i > $i > $o]:(d_Sep @ (power @ Z0) @ (anec @ Z0 @ Z1)))), inference(fof_simplification,[status(thm)],[def_ect])). 0.41/0.78 thf(c_0_26, plain, ((l_some)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((((((![X682:$i]:(((((in @ X682 @ Z0)))=>(non @ Z0 @ Z1 @ X682))))))=>(~($true))))))), inference(fof_simplification,[status(thm)],[def_l_some])). 0.41/0.78 thf(c_0_27, plain, ((all_of)=(^[Z0/* 19 */:$i > $o, Z1:$i > $o]:(![X4:$i]:((((Z0 @ X4))=>(Z1 @ X4)))))), inference(apply_def,[status(thm)],[c_0_20, c_0_21])). 0.41/0.78 thf(c_0_28, plain, ((d_not)=(^[Z0/* 3 */:$o]:(((((Z0))=>(~($true))))))), inference(apply_def,[status(thm)],[c_0_22, c_0_23])). 0.41/0.78 thf(c_0_29, axiom, ((rat)=(d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0)))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[def_rat, c_0_24]), c_0_25]), def_frac])). 0.41/0.78 thf(c_0_30, plain, ((l_or)=(^[Z0/* 19 */:$o, Z1:$o]:((((((((Z0)))=>(~($true)))))=>(Z1))))), inference(fof_simplification,[status(thm)],[def_l_or])). 0.41/0.78 thf(c_0_31, plain, ((rt_less)=(^[Z0/* 19 */:$i, Z1:$i]:((((((![X686:$i]:(((((in @ X686 @ (pair1type @ nat))))=>(non @ (pair1type @ nat) @ (^[Z2/* 3 */:$i]:((((((![X685:$i]:(((((in @ X685 @ (pair1type @ nat))))=>(non @ (pair1type @ nat) @ (^[Z3/* 3 */:$i]:(((d_and @ (((esti @ (pair1type @ nat) @ Z2 @ (ecect @ (pair1type @ nat) @ (^[Z4/* 19 */:$i, Z5:$i]:((n_is @ (n_ts @ (num @ Z4) @ (den @ Z5)) @ (n_ts @ (num @ Z5) @ (den @ Z4))))) @ Z0)))) @ ((d_and @ (((esti @ (pair1type @ nat) @ Z3 @ (ecect @ (pair1type @ nat) @ (^[Z4/* 19 */:$i, Z5:$i]:((n_is @ (n_ts @ (num @ Z4) @ (den @ Z5)) @ (n_ts @ (num @ Z5) @ (den @ Z4))))) @ Z1)))) @ (((lessf @ Z2 @ Z3))))))))) @ X685))))))=>(~($true)))))) @ X686))))))=>(~($true))))))), inference(fof_simplification,[status(thm)],[def_rt_less])). 0.41/0.78 thf(c_0_32, axiom, ((class)=(ecect @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[def_class, c_0_24]), def_frac])). 0.41/0.78 thf(c_0_33, axiom, ((inf)=(esti @ (pair1type @ nat))), inference(apply_def,[status(thm)],[def_inf, def_frac])). 0.41/0.78 thf(c_0_34, plain, ((and3)=(^[Z0/* 19 */:$o, Z1:$o, Z2:$o]:((d_and @ ((Z0)) @ ((d_and @ ((Z1)) @ ((Z2)))))))), inference(fof_simplification,[status(thm)],[def_and3])). 0.41/0.78 thf(c_0_35, plain, ((l_some)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((((((![X682:$i]:(((((in @ X682 @ Z0)))=>(non @ Z0 @ Z1 @ X682))))))=>(~($true))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_26, c_0_27]), c_0_28])). 0.41/0.78 thf(c_0_36, plain, ((rt_lessis)=(^[Z0/* 19 */:$i, Z1:$i]:((((((((((((((![X687:$i]:(((((in @ X687 @ (pair1type @ nat))))=>(non @ (pair1type @ nat) @ (^[Z2/* 3 */:$i]:((((((![X688:$i]:(((((in @ X688 @ (pair1type @ nat))))=>(non @ (pair1type @ nat) @ (^[Z3/* 3 */:$i]:(((d_and @ (((esti @ (pair1type @ nat) @ Z2 @ (ecect @ (pair1type @ nat) @ (^[Z4/* 19 */:$i, Z5:$i]:((n_is @ (n_ts @ (num @ Z4) @ (den @ Z5)) @ (n_ts @ (num @ Z5) @ (den @ Z4))))) @ Z0)))) @ ((d_and @ (((esti @ (pair1type @ nat) @ Z3 @ (ecect @ (pair1type @ nat) @ (^[Z4/* 19 */:$i, Z5:$i]:((n_is @ (n_ts @ (num @ Z4) @ (den @ Z5)) @ (n_ts @ (num @ Z5) @ (den @ Z4))))) @ Z1)))) @ (((lessf @ Z2 @ Z3))))))))) @ X688))))))=>(~($true)))))) @ X687))))))=>(~($true)))))))=>(~($true)))))=>((e_is @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))))) @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[def_rt_lessis])). 0.41/0.78 thf(c_0_37, axiom, ((rt_is)=(e_is @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))))), inference(apply_def,[status(thm)],[def_rt_is, c_0_29])). 0.41/0.78 thf(c_0_38, plain, ((l_or)=(^[Z0/* 19 */:$o, Z1:$o]:((((((((Z0)))=>(~($true)))))=>(Z1))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_30, c_0_23]), c_0_28])). 0.41/0.78 thf(c_0_39, plain, ((rt_less)=(^[Z0/* 19 */:$i, Z1:$i]:((((((![X686:$i]:(((((in @ X686 @ (pair1type @ nat))))=>(non @ (pair1type @ nat) @ (^[Z2/* 3 */:$i]:((((((![X685:$i]:(((((in @ X685 @ (pair1type @ nat))))=>(non @ (pair1type @ nat) @ (^[Z3/* 3 */:$i]:(((d_and @ (((esti @ (pair1type @ nat) @ Z2 @ (ecect @ (pair1type @ nat) @ (^[Z4/* 19 */:$i, Z5:$i]:((n_is @ (n_ts @ (num @ Z4) @ (den @ Z5)) @ (n_ts @ (num @ Z5) @ (den @ Z4))))) @ Z0)))) @ ((d_and @ (((esti @ (pair1type @ nat) @ Z3 @ (ecect @ (pair1type @ nat) @ (^[Z4/* 19 */:$i, Z5:$i]:((n_is @ (n_ts @ (num @ Z4) @ (den @ Z5)) @ (n_ts @ (num @ Z5) @ (den @ Z4))))) @ Z1)))) @ (((lessf @ Z2 @ Z3))))))))) @ X685))))))=>(~($true)))))) @ X686))))))=>(~($true))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_31, def_frac]), c_0_32]), c_0_33]), c_0_34]), c_0_35])). 0.41/0.78 thf(c_0_40, plain, ((rt_more)=(^[Z0/* 19 */:$i, Z1:$i]:((((((![X684:$i]:(((((in @ X684 @ (pair1type @ nat))))=>(non @ (pair1type @ nat) @ (^[Z2/* 3 */:$i]:((((((![X683:$i]:(((((in @ X683 @ (pair1type @ nat))))=>(non @ (pair1type @ nat) @ (^[Z3/* 3 */:$i]:(((d_and @ (((esti @ (pair1type @ nat) @ Z2 @ (ecect @ (pair1type @ nat) @ (^[Z4/* 19 */:$i, Z5:$i]:((n_is @ (n_ts @ (num @ Z4) @ (den @ Z5)) @ (n_ts @ (num @ Z5) @ (den @ Z4))))) @ Z0)))) @ ((d_and @ (((esti @ (pair1type @ nat) @ Z3 @ (ecect @ (pair1type @ nat) @ (^[Z4/* 19 */:$i, Z5:$i]:((n_is @ (n_ts @ (num @ Z4) @ (den @ Z5)) @ (n_ts @ (num @ Z5) @ (den @ Z4))))) @ Z1)))) @ ((((d_29_ii @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2)))))))))))) @ X683))))))=>(~($true)))))) @ X684))))))=>(~($true))))))), inference(fof_simplification,[status(thm)],[def_rt_more])). 0.41/0.78 thf(c_0_41, plain, ((moref)=(^[Z0/* 19 */:$i, Z1:$i]:((d_29_ii @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0)))))), inference(fof_simplification,[status(thm)],[def_moref])). 0.41/0.78 thf(c_0_42, plain, ((rt_lessis)=(^[Z0/* 19 */:$i, Z1:$i]:((((((((((((((![X687:$i]:(((((in @ X687 @ (pair1type @ nat))))=>(non @ (pair1type @ nat) @ (^[Z2/* 3 */:$i]:((((((![X688:$i]:(((((in @ X688 @ (pair1type @ nat))))=>(non @ (pair1type @ nat) @ (^[Z3/* 3 */:$i]:(((d_and @ (((esti @ (pair1type @ nat) @ Z2 @ (ecect @ (pair1type @ nat) @ (^[Z4/* 19 */:$i, Z5:$i]:((n_is @ (n_ts @ (num @ Z4) @ (den @ Z5)) @ (n_ts @ (num @ Z5) @ (den @ Z4))))) @ Z0)))) @ ((d_and @ (((esti @ (pair1type @ nat) @ Z3 @ (ecect @ (pair1type @ nat) @ (^[Z4/* 19 */:$i, Z5:$i]:((n_is @ (n_ts @ (num @ Z4) @ (den @ Z5)) @ (n_ts @ (num @ Z5) @ (den @ Z4))))) @ Z1)))) @ (((lessf @ Z2 @ Z3))))))))) @ X688))))))=>(~($true)))))) @ X687))))))=>(~($true)))))))=>(~($true)))))=>((e_is @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))))) @ Z0 @ Z1))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_36, c_0_37]), c_0_38]), c_0_39])). 0.41/0.78 thf(c_0_43, plain, ((rt_more)=(^[Z0/* 19 */:$i, Z1:$i]:((((((![X684:$i]:(((((in @ X684 @ (pair1type @ nat))))=>(non @ (pair1type @ nat) @ (^[Z2/* 3 */:$i]:((((((![X683:$i]:(((((in @ X683 @ (pair1type @ nat))))=>(non @ (pair1type @ nat) @ (^[Z3/* 3 */:$i]:(((d_and @ (((esti @ (pair1type @ nat) @ Z2 @ (ecect @ (pair1type @ nat) @ (^[Z4/* 19 */:$i, Z5:$i]:((n_is @ (n_ts @ (num @ Z4) @ (den @ Z5)) @ (n_ts @ (num @ Z5) @ (den @ Z4))))) @ Z0)))) @ ((d_and @ (((esti @ (pair1type @ nat) @ Z3 @ (ecect @ (pair1type @ nat) @ (^[Z4/* 19 */:$i, Z5:$i]:((n_is @ (n_ts @ (num @ Z4) @ (den @ Z5)) @ (n_ts @ (num @ Z5) @ (den @ Z4))))) @ Z1)))) @ ((((d_29_ii @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2)))))))))))) @ X683))))))=>(~($true)))))) @ X684))))))=>(~($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(apply_def,[status(thm)],[c_0_40, def_frac]), c_0_32]), c_0_33]), c_0_41]), c_0_34]), c_0_35])). 0.41/0.78 thf(c_0_44, plain, ![X706:$i]:(((in @ X706 @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))))=>![X705:$i]:(((in @ X705 @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))))=>((((![X701:$i]:(((in @ X701 @ (pair1type @ nat))=>(non @ (pair1type @ nat) @ (^[Z0/* 10 */:$i]:((![X702:$i]:(((in @ X702 @ (pair1type @ nat))=>(non @ (pair1type @ nat) @ (^[Z1/* 3 */:$i]:((d_and @ ((esti @ (pair1type @ nat) @ Z0 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ X706))) @ ((d_and @ ((esti @ (pair1type @ nat) @ Z1 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ X705))) @ ((lessf @ Z0 @ Z1))))))) @ X702)))=>~($true)))) @ X701)))=>~($true))=>~($true))=>(e_is @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))) @ X706 @ X705))=>((![X703:$i]:(((in @ X703 @ (pair1type @ nat))=>(non @ (pair1type @ nat) @ (^[Z0/* 10 */:$i]:((![X704:$i]:(((in @ X704 @ (pair1type @ nat))=>(non @ (pair1type @ nat) @ (^[Z1/* 3 */:$i]:((d_and @ ((esti @ (pair1type @ nat) @ Z0 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ X706))) @ ((d_and @ ((esti @ (pair1type @ nat) @ Z1 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ X705))) @ ((d_29_ii @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))))) @ X704)))=>~($true)))) @ X703)))=>~($true))=>~($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)],[satz81d]), c_0_27]), c_0_29]), c_0_42]), c_0_28]), c_0_43])). 0.41/0.78 thf(c_0_45, negated_conjecture, ~(![X694:$i]:(((in @ X694 @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))))=>![X693:$i]:(((in @ X693 @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))))=>((![X691:$i]:(((in @ X691 @ (pair1type @ nat))=>(non @ (pair1type @ nat) @ (^[Z0/* 10 */:$i]:((![X692:$i]:(((in @ X692 @ (pair1type @ nat))=>(non @ (pair1type @ nat) @ (^[Z1/* 3 */:$i]:((d_and @ ((esti @ (pair1type @ nat) @ Z0 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ X694))) @ ((d_and @ ((esti @ (pair1type @ nat) @ Z1 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ X693))) @ ((d_29_ii @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))))) @ X692)))=>~($true)))) @ X691)))=>~($true))=>((((![X689:$i]:(((in @ X689 @ (pair1type @ nat))=>(non @ (pair1type @ nat) @ (^[Z0/* 10 */:$i]:((![X690:$i]:(((in @ X690 @ (pair1type @ nat))=>(non @ (pair1type @ nat) @ (^[Z1/* 3 */:$i]:((d_and @ ((esti @ (pair1type @ nat) @ Z0 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ X694))) @ ((d_and @ ((esti @ (pair1type @ nat) @ Z1 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ X693))) @ ((lessf @ Z0 @ Z1))))))) @ X690)))=>~($true)))) @ X689)))=>~($true))=>~($true))=>(e_is @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))) @ X694 @ X693))=>~($true)))))))), 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(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[satz81g])]), c_0_27]), c_0_29]), c_0_42]), c_0_28]), c_0_43])])). 0.41/0.78 thf(c_0_46, plain, ![X754:$i, X755:$i, X756:$i, X757:$i]:(((((~(in @ X757 @ (pair1type @ nat))|(non @ (pair1type @ nat) @ (^[Z0/* 10 */:$i]:((![X704:$i]:(((in @ X704 @ (pair1type @ nat))=>(non @ (pair1type @ nat) @ (^[Z1/* 3 */:$i]:((d_and @ ((esti @ (pair1type @ nat) @ Z0 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ X754))) @ ((d_and @ ((esti @ (pair1type @ nat) @ Z1 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ X755))) @ ((d_29_ii @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))))) @ X704)))=>~($true)))) @ X757)|~($true)|(~(in @ X756 @ (pair1type @ nat))|(non @ (pair1type @ nat) @ (^[Z0/* 10 */:$i]:((![X702:$i]:(((in @ X702 @ (pair1type @ nat))=>(non @ (pair1type @ nat) @ (^[Z1/* 3 */:$i]:((d_and @ ((esti @ (pair1type @ nat) @ Z0 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ X754))) @ ((d_and @ ((esti @ (pair1type @ nat) @ Z1 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ X755))) @ ((lessf @ Z0 @ Z1))))))) @ X702)))=>~($true)))) @ X756)|~($true))|~(in @ X755 @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))))|~(in @ X754 @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0)))))))))&(($true)|~($true)|(~(in @ X756 @ (pair1type @ nat))|(non @ (pair1type @ nat) @ (^[Z0/* 10 */:$i]:((![X702:$i]:(((in @ X702 @ (pair1type @ nat))=>(non @ (pair1type @ nat) @ (^[Z1/* 3 */:$i]:((d_and @ ((esti @ (pair1type @ nat) @ Z0 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ X754))) @ ((d_and @ ((esti @ (pair1type @ nat) @ Z1 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ X755))) @ ((lessf @ Z0 @ Z1))))))) @ X702)))=>~($true)))) @ X756)|~($true))|~(in @ X755 @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))))|~(in @ X754 @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))))))&((~(in @ X757 @ (pair1type @ nat))|(non @ (pair1type @ nat) @ (^[Z0/* 10 */:$i]:((![X704:$i]:(((in @ X704 @ (pair1type @ nat))=>(non @ (pair1type @ nat) @ (^[Z1/* 3 */:$i]:((d_and @ ((esti @ (pair1type @ nat) @ Z0 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ X754))) @ ((d_and @ ((esti @ (pair1type @ nat) @ Z1 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ X755))) @ ((d_29_ii @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))))) @ X704)))=>~($true)))) @ X757)|~($true)|(($true)|~($true))|~(in @ X755 @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))))|~(in @ X754 @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0)))))))))&(($true)|~($true)|(($true)|~($true))|~(in @ X755 @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))))|~(in @ X754 @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0)))))))))))&((~(in @ X757 @ (pair1type @ nat))|(non @ (pair1type @ nat) @ (^[Z0/* 10 */:$i]:((![X704:$i]:(((in @ X704 @ (pair1type @ nat))=>(non @ (pair1type @ nat) @ (^[Z1/* 3 */:$i]:((d_and @ ((esti @ (pair1type @ nat) @ Z0 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ X754))) @ ((d_and @ ((esti @ (pair1type @ nat) @ Z1 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ X755))) @ ((d_29_ii @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))))) @ X704)))=>~($true)))) @ X757)|~($true)|~(e_is @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))) @ X754 @ X755)|~(in @ X755 @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))))|~(in @ X754 @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0)))))))))&(($true)|~($true)|~(e_is @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))) @ X754 @ X755)|~(in @ X755 @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))))|~(in @ X754 @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0)))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])])])])])). 0.41/0.78 thf(c_0_47, negated_conjecture, ((in @ esk1_0 @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))))&((in @ esk2_0 @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))))&((((in @ esk3_0 @ (pair1type @ nat))|~($true))&(~(non @ (pair1type @ nat) @ (^[Z0/* 10 */:$i]:((![X692:$i]:(((in @ X692 @ (pair1type @ nat))=>(non @ (pair1type @ nat) @ (^[Z1/* 3 */:$i]:((d_and @ ((esti @ (pair1type @ nat) @ Z0 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ esk1_0))) @ ((d_and @ ((esti @ (pair1type @ nat) @ Z1 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ esk2_0))) @ ((d_29_ii @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))))) @ X692)))=>~($true)))) @ esk3_0)|~($true)))&(((((in @ esk4_0 @ (pair1type @ nat))|~($true)|(e_is @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))) @ esk1_0 @ esk2_0))&(~(non @ (pair1type @ nat) @ (^[Z0/* 10 */:$i]:((![X690:$i]:(((in @ X690 @ (pair1type @ nat))=>(non @ (pair1type @ nat) @ (^[Z1/* 3 */:$i]:((d_and @ ((esti @ (pair1type @ nat) @ Z0 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ esk1_0))) @ ((d_and @ ((esti @ (pair1type @ nat) @ Z1 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ esk2_0))) @ ((lessf @ Z0 @ Z1))))))) @ X690)))=>~($true)))) @ esk4_0)|~($true)|(e_is @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))) @ esk1_0 @ esk2_0)))&(($true)|(e_is @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))) @ esk1_0 @ esk2_0)))&($true))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])])])])). 0.41/0.78 thf(c_0_48, plain, ![X1:$i, X7:$i, X6:$i, X5:$i]:(((non @ (pair1type @ nat) @ (^[Z0/* 10 */:$i]:((![X799:$i]:(((in @ X799 @ (pair1type @ nat))=>(non @ (pair1type @ nat) @ (^[Z1/* 3 */:$i]:((d_and @ ((esti @ (pair1type @ nat) @ Z0 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ X5))) @ ((d_and @ ((esti @ (pair1type @ nat) @ Z1 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ X6))) @ ((d_29_ii @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))))) @ X799)))=>~(($true))))) @ X1)|(non @ (pair1type @ nat) @ (^[Z0/* 10 */:$i]:((![X800:$i]:(((in @ X800 @ (pair1type @ nat))=>(non @ (pair1type @ nat) @ (^[Z1/* 3 */:$i]:((d_and @ ((esti @ (pair1type @ nat) @ Z0 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ X5))) @ ((d_and @ ((esti @ (pair1type @ nat) @ Z1 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ X6))) @ ((lessf @ Z0 @ Z1))))))) @ X800)))=>~(($true))))) @ X7)|~((in @ X1 @ (pair1type @ nat)))|~(($true))|~((in @ X7 @ (pair1type @ nat)))|~(($true))|~((in @ X6 @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0)))))))))|~((in @ X5 @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))))))), inference(split_conjunct,[status(thm)],[c_0_46])). 0.41/0.78 thf(c_0_49, negated_conjecture, (~((non @ (pair1type @ nat) @ (^[Z0/* 10 */:$i]:((![X801:$i]:(((in @ X801 @ (pair1type @ nat))=>(non @ (pair1type @ nat) @ (^[Z1/* 3 */:$i]:((d_and @ ((esti @ (pair1type @ nat) @ Z0 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ esk1_0))) @ ((d_and @ ((esti @ (pair1type @ nat) @ Z1 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ esk2_0))) @ ((d_29_ii @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))))) @ X801)))=>~(($true))))) @ esk3_0))|~(($true))), inference(split_conjunct,[status(thm)],[c_0_47])). 0.41/0.78 thf(c_0_50, plain, ![X1:$i, X6:$i, X5:$i]:(((non @ (pair1type @ nat) @ (^[Z0/* 10 */:$i]:((![X802:$i]:(((in @ X802 @ (pair1type @ nat))=>(non @ (pair1type @ nat) @ (^[Z1/* 3 */:$i]:((d_and @ ((esti @ (pair1type @ nat) @ Z0 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ X5))) @ ((d_and @ ((esti @ (pair1type @ nat) @ Z1 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ X6))) @ ((d_29_ii @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))))) @ X802)))=>~(($true))))) @ X1)|~((in @ X1 @ (pair1type @ nat)))|~(($true))|~((e_is @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))) @ X5 @ X6))|~((in @ X6 @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0)))))))))|~((in @ X5 @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))))))), inference(split_conjunct,[status(thm)],[c_0_46])). 0.41/0.78 thf(c_0_51, plain, ![X1:$i, X7:$i, X6:$i, X5:$i]:(((non @ (pair1type @ nat) @ (^[Z0/* 10 */:$i]:((![X803:$i]:(((in @ X803 @ (pair1type @ nat))=>(non @ (pair1type @ nat) @ (^[Z1/* 3 */:$i]:((d_and @ ((esti @ (pair1type @ nat) @ Z0 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ X5))) @ ((d_and @ ((esti @ (pair1type @ nat) @ Z1 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ X6))) @ ((lessf @ Z0 @ Z1))))))) @ X803)))=>~(($true))))) @ X7)|(non @ (pair1type @ nat) @ (^[Z0/* 10 */:$i]:((![X804:$i]:(((in @ X804 @ (pair1type @ nat))=>(non @ (pair1type @ nat) @ (^[Z1/* 3 */:$i]:((d_and @ ((esti @ (pair1type @ nat) @ Z0 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ X5))) @ ((d_and @ ((esti @ (pair1type @ nat) @ Z1 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ X6))) @ ((d_29_ii @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))))) @ X804)))=>~(($true))))) @ X1)|~((in @ X7 @ (pair1type @ nat)))|~((in @ X1 @ (pair1type @ nat)))|~((in @ X6 @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0)))))))))|~((in @ X5 @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))))))), inference(cn,[status(thm)],[c_0_48])). 0.41/0.78 thf(c_0_52, negated_conjecture, ~((non @ (pair1type @ nat) @ (^[Z0/* 10 */:$i]:((![X805:$i]:(((in @ X805 @ (pair1type @ nat))=>(non @ (pair1type @ nat) @ (^[Z1/* 3 */:$i]:((d_and @ ((esti @ (pair1type @ nat) @ Z0 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ esk1_0))) @ ((d_and @ ((esti @ (pair1type @ nat) @ Z1 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ esk2_0))) @ ((d_29_ii @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))))) @ X805)))=>~(($true))))) @ esk3_0)), inference(cn,[status(thm)],[c_0_49])). 0.41/0.78 thf(c_0_53, plain, ![X1:$i, X5:$i, X6:$i]:(((non @ (pair1type @ nat) @ (^[Z0/* 10 */:$i]:((![X806:$i]:(((in @ X806 @ (pair1type @ nat))=>(non @ (pair1type @ nat) @ (^[Z1/* 3 */:$i]:((d_and @ ((esti @ (pair1type @ nat) @ Z0 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ X5))) @ ((d_and @ ((esti @ (pair1type @ nat) @ Z1 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ X6))) @ ((d_29_ii @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))))) @ X806)))=>~(($true))))) @ X1)|~((in @ X1 @ (pair1type @ nat)))|~((in @ X6 @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0)))))))))|~((in @ X5 @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0)))))))))|~((e_is @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))) @ X5 @ X6)))), inference(cn,[status(thm)],[c_0_50])). 0.41/0.78 thf(c_0_54, negated_conjecture, ((in @ esk3_0 @ (pair1type @ nat))|~(($true))), inference(split_conjunct,[status(thm)],[c_0_47])). 0.41/0.78 thf(c_0_55, plain, ![X1:$i, X4:$i, X6:$i, X5:$i]:(((non @ (pair1type @ nat) @ (^[Z0/* 7 */:$i]:(~(![X807:$i]:(((in @ X807 @ (pair1type @ nat))=>(non @ (pair1type @ nat) @ (^[Z1/* 3 */:$i]:((d_and @ ((esti @ (pair1type @ nat) @ Z0 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ X1))) @ ((d_and @ ((esti @ (pair1type @ nat) @ Z1 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ X4))) @ ((d_29_ii @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))))) @ X807)))))) @ X5)|(non @ (pair1type @ nat) @ (^[Z0/* 7 */:$i]:(~(![X808:$i]:(((in @ X808 @ (pair1type @ nat))=>(non @ (pair1type @ nat) @ (^[Z1/* 3 */:$i]:((d_and @ ((esti @ (pair1type @ nat) @ Z0 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ X1))) @ ((d_and @ ((esti @ (pair1type @ nat) @ Z1 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ X4))) @ ((lessf @ Z0 @ Z1))))))) @ X808)))))) @ X6)|~((in @ X4 @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0)))))))))|~((in @ X1 @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0)))))))))|~((in @ X6 @ (pair1type @ nat)))|~((in @ X5 @ (pair1type @ nat))))), inference(cn,[status(thm)],[c_0_51])). 0.41/0.78 thf(c_0_56, negated_conjecture, (in @ esk2_0 @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0)))))))), inference(split_conjunct,[status(thm)],[c_0_47])). 0.41/0.78 thf(c_0_57, negated_conjecture, ((in @ esk4_0 @ (pair1type @ nat))|(e_is @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))) @ esk1_0 @ esk2_0)|~(($true))), inference(split_conjunct,[status(thm)],[c_0_47])). 0.41/0.78 thf(c_0_58, negated_conjecture, ~((non @ (pair1type @ nat) @ (^[Z0/* 7 */:$i]:(~(![X809:$i]:(((in @ X809 @ (pair1type @ nat))=>(non @ (pair1type @ nat) @ (^[Z1/* 3 */:$i]:((d_and @ ((esti @ (pair1type @ nat) @ Z0 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ esk1_0))) @ ((d_and @ ((esti @ (pair1type @ nat) @ Z1 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ esk2_0))) @ ((d_29_ii @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))))) @ X809)))))) @ esk3_0)), inference(cn,[status(thm)],[c_0_52])). 0.41/0.78 thf(c_0_59, plain, ![X1:$i, X4:$i, X5:$i]:(((non @ (pair1type @ nat) @ (^[Z0/* 7 */:$i]:(~(![X810:$i]:(((in @ X810 @ (pair1type @ nat))=>(non @ (pair1type @ nat) @ (^[Z1/* 3 */:$i]:((d_and @ ((esti @ (pair1type @ nat) @ Z0 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ X1))) @ ((d_and @ ((esti @ (pair1type @ nat) @ Z1 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ X4))) @ ((d_29_ii @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))))) @ X810)))))) @ X5)|~((e_is @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))) @ X1 @ X4))|~((in @ X4 @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0)))))))))|~((in @ X1 @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0)))))))))|~((in @ X5 @ (pair1type @ nat))))), inference(cn,[status(thm)],[c_0_53])). 0.41/0.78 thf(c_0_60, negated_conjecture, (in @ esk1_0 @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0)))))))), inference(split_conjunct,[status(thm)],[c_0_47])). 0.41/0.78 thf(c_0_61, negated_conjecture, (in @ esk3_0 @ (pair1type @ nat)), inference(cn,[status(thm)],[c_0_54])). 0.41/0.78 thf(c_0_62, negated_conjecture, ![X1:$i, X5:$i, X4:$i]:(((non @ (pair1type @ nat) @ (^[Z0/* 7 */:$i]:(~(![X811:$i]:(((in @ X811 @ (pair1type @ nat))=>(non @ (pair1type @ nat) @ (^[Z1/* 3 */:$i]:((d_and @ ((esti @ (pair1type @ nat) @ Z0 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ X1))) @ ((d_and @ ((esti @ (pair1type @ nat) @ Z1 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ esk2_0))) @ ((d_29_ii @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))))) @ X811)))))) @ X4)|(non @ (pair1type @ nat) @ (^[Z0/* 7 */:$i]:(~(![X812:$i]:(((in @ X812 @ (pair1type @ nat))=>(non @ (pair1type @ nat) @ (^[Z1/* 3 */:$i]:((d_and @ ((esti @ (pair1type @ nat) @ Z0 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ X1))) @ ((d_and @ ((esti @ (pair1type @ nat) @ Z1 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ esk2_0))) @ ((lessf @ Z0 @ Z1))))))) @ X812)))))) @ X5)|~((in @ X1 @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0)))))))))|~((in @ X5 @ (pair1type @ nat)))|~((in @ X4 @ (pair1type @ nat))))), inference(spm,[status(thm)],[c_0_55, c_0_56])). 0.41/0.78 thf(c_0_63, negated_conjecture, ((in @ esk4_0 @ (pair1type @ nat))|(e_is @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))) @ esk1_0 @ esk2_0)), inference(cn,[status(thm)],[c_0_57])). 0.41/0.78 thf(c_0_64, negated_conjecture, ~((e_is @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))) @ esk1_0 @ esk2_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58, c_0_59]), c_0_56]), c_0_60]), c_0_61])])). 0.41/0.78 thf(c_0_65, negated_conjecture, ((e_is @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))) @ esk1_0 @ esk2_0)|~((non @ (pair1type @ nat) @ (^[Z0/* 10 */:$i]:((![X813:$i]:(((in @ X813 @ (pair1type @ nat))=>(non @ (pair1type @ nat) @ (^[Z1/* 3 */:$i]:((d_and @ ((esti @ (pair1type @ nat) @ Z0 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ esk1_0))) @ ((d_and @ ((esti @ (pair1type @ nat) @ Z1 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ esk2_0))) @ ((lessf @ Z0 @ Z1))))))) @ X813)))=>~(($true))))) @ esk4_0))|~(($true))), inference(split_conjunct,[status(thm)],[c_0_47])). 0.41/0.78 thf(c_0_66, negated_conjecture, ![X4:$i, X1:$i]:(((non @ (pair1type @ nat) @ (^[Z0/* 7 */:$i]:(~(![X814:$i]:(((in @ X814 @ (pair1type @ nat))=>(non @ (pair1type @ nat) @ (^[Z1/* 3 */:$i]:((d_and @ ((esti @ (pair1type @ nat) @ Z0 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ esk1_0))) @ ((d_and @ ((esti @ (pair1type @ nat) @ Z1 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ esk2_0))) @ ((d_29_ii @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))))) @ X814)))))) @ X1)|(non @ (pair1type @ nat) @ (^[Z0/* 7 */:$i]:(~(![X815:$i]:(((in @ X815 @ (pair1type @ nat))=>(non @ (pair1type @ nat) @ (^[Z1/* 3 */:$i]:((d_and @ ((esti @ (pair1type @ nat) @ Z0 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ esk1_0))) @ ((d_and @ ((esti @ (pair1type @ nat) @ Z1 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ esk2_0))) @ ((lessf @ Z0 @ Z1))))))) @ X815)))))) @ X4)|~((in @ X4 @ (pair1type @ nat)))|~((in @ X1 @ (pair1type @ nat))))), inference(spm,[status(thm)],[c_0_62, c_0_60])). 0.41/0.78 thf(c_0_67, negated_conjecture, (in @ esk4_0 @ (pair1type @ nat)), inference(sr,[status(thm)],[c_0_63, c_0_64])). 0.41/0.78 thf(c_0_68, negated_conjecture, ((e_is @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))) @ esk1_0 @ esk2_0)|~((non @ (pair1type @ nat) @ (^[Z0/* 10 */:$i]:((![X816:$i]:(((in @ X816 @ (pair1type @ nat))=>(non @ (pair1type @ nat) @ (^[Z1/* 3 */:$i]:((d_and @ ((esti @ (pair1type @ nat) @ Z0 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ esk1_0))) @ ((d_and @ ((esti @ (pair1type @ nat) @ Z1 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ esk2_0))) @ ((lessf @ Z0 @ Z1))))))) @ X816)))=>~(($true))))) @ esk4_0))), inference(cn,[status(thm)],[c_0_65])). 0.41/0.78 thf(c_0_69, negated_conjecture, ![X1:$i]:(((non @ (pair1type @ nat) @ (^[Z0/* 7 */:$i]:(~(![X817:$i]:(((in @ X817 @ (pair1type @ nat))=>(non @ (pair1type @ nat) @ (^[Z1/* 3 */:$i]:((d_and @ ((esti @ (pair1type @ nat) @ Z0 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ esk1_0))) @ ((d_and @ ((esti @ (pair1type @ nat) @ Z1 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ esk2_0))) @ ((d_29_ii @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))))) @ X817)))))) @ X1)|(non @ (pair1type @ nat) @ (^[Z0/* 7 */:$i]:(~(![X818:$i]:(((in @ X818 @ (pair1type @ nat))=>(non @ (pair1type @ nat) @ (^[Z1/* 3 */:$i]:((d_and @ ((esti @ (pair1type @ nat) @ Z0 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ esk1_0))) @ ((d_and @ ((esti @ (pair1type @ nat) @ Z1 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ esk2_0))) @ ((lessf @ Z0 @ Z1))))))) @ X818)))))) @ esk4_0)|~((in @ X1 @ (pair1type @ nat))))), inference(spm,[status(thm)],[c_0_66, c_0_67])). 0.41/0.78 thf(c_0_70, negated_conjecture, ((e_is @ (d_Sep @ (power @ (pair1type @ nat)) @ (anec @ (pair1type @ nat) @ (^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (n_ts @ (num @ Z0) @ (den @ Z1)) @ (n_ts @ (num @ Z1) @ (den @ Z0))))))) @ esk1_0 @ esk2_0)|~((non @ (pair1type @ nat) @ (^[Z0/* 7 */:$i]:(~(![X819:$i]:(((in @ X819 @ (pair1type @ nat))=>(non @ (pair1type @ nat) @ (^[Z1/* 3 */:$i]:((d_and @ ((esti @ (pair1type @ nat) @ Z0 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ esk1_0))) @ ((d_and @ ((esti @ (pair1type @ nat) @ Z1 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ esk2_0))) @ ((lessf @ Z0 @ Z1))))))) @ X819)))))) @ esk4_0))), inference(cn,[status(thm)],[c_0_68])). 0.41/0.78 thf(c_0_71, negated_conjecture, (non @ (pair1type @ nat) @ (^[Z0/* 7 */:$i]:(~(![X820:$i]:(((in @ X820 @ (pair1type @ nat))=>(non @ (pair1type @ nat) @ (^[Z1/* 3 */:$i]:((d_and @ ((esti @ (pair1type @ nat) @ Z0 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ esk1_0))) @ ((d_and @ ((esti @ (pair1type @ nat) @ Z1 @ (ecect @ (pair1type @ nat) @ (^[Z2/* 19 */:$i, Z3:$i]:((n_is @ (n_ts @ (num @ Z2) @ (den @ Z3)) @ (n_ts @ (num @ Z3) @ (den @ Z2))))) @ esk2_0))) @ ((lessf @ Z0 @ Z1))))))) @ X820)))))) @ esk4_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58, c_0_69]), c_0_61])])). 0.41/0.78 thf(c_0_72, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_70, c_0_71])]), c_0_64]), ['proof']). 0.41/0.78 # SZS output end CNFRefutation 0.41/0.78 # Parsed axioms : 697 0.41/0.78 # Removed by relevancy pruning/SinE : 655 0.41/0.78 # Initial clauses : 51 0.41/0.78 # Removed in clause preprocessing : 15 0.41/0.78 # Initial clauses in saturation : 36 0.41/0.78 # Processed clauses : 274 0.41/0.78 # ...of these trivial : 0 0.41/0.78 # ...subsumed : 58 0.41/0.78 # ...remaining for further processing : 216 0.41/0.78 # Other redundant clauses eliminated : 0 0.41/0.78 # Clauses deleted for lack of memory : 0 0.41/0.78 # Backward-subsumed : 1 0.41/0.78 # Backward-rewritten : 4 0.41/0.78 # Generated clauses : 897 0.41/0.78 # ...of the previous two non-redundant : 852 0.41/0.78 # ...aggressively subsumed : 0 0.41/0.78 # Contextual simplify-reflections : 13 0.41/0.78 # Paramodulations : 895 0.41/0.78 # Factorizations : 0 0.41/0.78 # NegExts : 0 0.41/0.78 # Equation resolutions : 0 0.41/0.78 # Disequality decompositions : 0 0.41/0.78 # Total rewrite steps : 239 0.41/0.78 # ...of those cached : 230 0.41/0.78 # Propositional unsat checks : 0 0.41/0.78 # Propositional check models : 0 0.41/0.78 # Propositional check unsatisfiable : 0 0.41/0.78 # Propositional clauses : 0 0.41/0.78 # Propositional clauses after purity: 0 0.41/0.78 # Propositional unsat core size : 0 0.41/0.78 # Propositional preprocessing time : 0.000 0.41/0.78 # Propositional encoding time : 0.000 0.41/0.78 # Propositional solver time : 0.000 0.41/0.78 # Success case prop preproc time : 0.000 0.41/0.78 # Success case prop encoding time : 0.000 0.41/0.78 # Success case prop solver time : 0.000 0.41/0.78 # Current number of processed clauses : 173 0.41/0.78 # Positive orientable unit clauses : 11 0.41/0.78 # Positive unorientable unit clauses: 0 0.41/0.78 # Negative unit clauses : 3 0.41/0.78 # Non-unit-clauses : 159 0.41/0.78 # Current number of unprocessed clauses: 645 0.41/0.78 # ...number of literals in the above : 4792 0.41/0.78 # Current number of archived formulas : 0 0.41/0.78 # Current number of archived clauses : 43 0.41/0.78 # Clause-clause subsumption calls (NU) : 21491 0.41/0.78 # Rec. Clause-clause subsumption calls : 3756 0.41/0.78 # Non-unit clause-clause subsumptions : 71 0.41/0.78 # Unit Clause-clause subsumption calls : 155 0.41/0.78 # Rewrite failures with RHS unbound : 0 0.41/0.78 # BW rewrite match attempts : 38 0.41/0.78 # BW rewrite match successes : 4 0.41/0.78 # Condensation attempts : 274 0.41/0.78 # Condensation successes : 0 0.41/0.78 # Termbank termtop insertions : 215903 0.41/0.78 # Search garbage collected termcells : 10313 0.41/0.78 0.41/0.78 # ------------------------------------------------- 0.41/0.78 # User time : 0.173 s 0.41/0.78 # System time : 0.010 s 0.41/0.78 # Total time : 0.183 s 0.41/0.78 # Maximum resident set size: 4280 pages 0.41/0.78 0.41/0.78 # ------------------------------------------------- 0.41/0.78 # User time : 0.193 s 0.41/0.78 # System time : 0.013 s 0.41/0.78 # Total time : 0.206 s 0.41/0.78 # Maximum resident set size: 3124 pages 0.41/0.78 % E exiting 0.41/0.78 % E exiting 0.41/0.78 EOF