0.00/0.02	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.04	% Command  : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM
0.10/0.36	% Computer : n016.cluster.edu
0.10/0.36	% Model    : x86_64 x86_64
0.10/0.36	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.10/0.36	% Memory   : 8046.5625MB
0.10/0.36	% OS       : Linux 6.8.0-71-generic
0.10/0.36	% CPULimit : 1440
0.10/0.36	% WCLimit  : 180
0.10/0.36	% DateTime : Mon Jul 27 13:38:37 UTC 2026
0.10/0.36	% CPUTime  : 
0.10/0.36	Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM
0.13/0.40	Running higher-order theorem proving
0.13/0.44	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=180 /export/starexec/sandbox2/tmp/tmp.wvh4OKvgP2/E---3.1_1392267.p
0.20/0.55	% Version: 3.5.1-ho
0.20/0.55	% Preprocessing class: HSLMSMSSLLLCHSA.
0.20/0.55	% Scheduled 6 strats onto 8 cores with 180 seconds (1440 total)
0.20/0.55	% Starting lpo1_fix with 540s (3) cores
0.20/0.55	% Starting full_lambda_9 with 180s (1) cores
0.20/0.55	% Starting almost_fo_4 with 180s (1) cores
0.20/0.55	% Starting new_ho_9 with 180s (1) cores
0.20/0.55	% Starting pre_casc_4 with 180s (1) cores
0.20/0.55	% Starting ho_unfolding_6 with 180s (1) cores
0.20/0.55	% pre_casc_4 with pid 1392284 completed with status 0
0.20/0.55	% Result found by pre_casc_4
0.20/0.55	% Preprocessing class: HSLMSMSSLLLCHSA.
0.20/0.55	% Scheduled 6 strats onto 8 cores with 180 seconds (1440 total)
0.20/0.55	% Starting lpo1_fix with 540s (3) cores
0.20/0.55	% Starting full_lambda_9 with 180s (1) cores
0.20/0.55	% Starting almost_fo_4 with 180s (1) cores
0.20/0.55	% Starting new_ho_9 with 180s (1) cores
0.20/0.55	% Starting pre_casc_4 with 180s (1) cores
0.20/0.55	% (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
0.20/0.55	% SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
0.20/0.55	% Search class: HGHSM-FFMM31-DHSMMSBN
0.20/0.55	% partial match(2): HGHSM-FFMM31-SHSSMSBN
0.20/0.55	% Scheduled 7 strats onto 1 cores with 180 seconds (180 total)
0.20/0.55	% Starting SubtermCWHack with 17s (1) cores
0.20/0.55	% SubtermCWHack with pid 1392286 completed with status 0
0.20/0.55	% Result found by SubtermCWHack
0.20/0.55	% Preprocessing class: HSLMSMSSLLLCHSA.
0.20/0.55	% Scheduled 6 strats onto 8 cores with 180 seconds (1440 total)
0.20/0.55	% Starting lpo1_fix with 540s (3) cores
0.20/0.55	% Starting full_lambda_9 with 180s (1) cores
0.20/0.55	% Starting almost_fo_4 with 180s (1) cores
0.20/0.55	% Starting new_ho_9 with 180s (1) cores
0.20/0.55	% Starting pre_casc_4 with 180s (1) cores
0.20/0.55	% (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
0.20/0.55	% SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
0.20/0.55	% Search class: HGHSM-FFMM31-DHSMMSBN
0.20/0.55	% partial match(2): HGHSM-FFMM31-SHSSMSBN
0.20/0.55	% Scheduled 7 strats onto 1 cores with 180 seconds (180 total)
0.20/0.55	% Starting SubtermCWHack with 17s (1) cores
0.20/0.55	% Preprocessing time       : 0.004 s
0.20/0.55	
0.20/0.55	% Proof found!
0.20/0.55	% SZS status Theorem
0.20/0.55	% SZS output start CNFRefutation
0.20/0.55	thf(decl_23, type, is_of: $i > ($i > $o) > $o).
0.20/0.55	thf(decl_24, type, all_of: ($i > $o) > ($i > $o) > $o).
0.20/0.55	thf(decl_26, type, in: $i > $i > $o).
0.20/0.55	thf(decl_62, type, imp: $o > $o > $o).
0.20/0.55	thf(decl_63, type, d_not: $o > $o).
0.20/0.55	thf(decl_68, type, l_or: $o > $o > $o).
0.20/0.55	thf(decl_72, type, non: $i > ($i > $o) > $i > $o).
0.20/0.55	thf(decl_73, type, l_some: $i > ($i > $o) > $o).
0.20/0.55	thf(decl_74, type, or3: $o > $o > $o > $o).
0.20/0.55	thf(decl_78, type, e_is: $i > $i > $i > $o).
0.20/0.55	thf(decl_124, type, nat: $i).
0.20/0.55	thf(decl_125, type, n_is: $i > $i > $o).
0.20/0.55	thf(decl_128, type, n_some: ($i > $o) > $o).
0.20/0.55	thf(decl_143, type, n_pl: $i > $i > $i).
0.20/0.55	thf(decl_148, type, diffprop: $i > $i > $i > $o).
0.20/0.55	thf(decl_149, type, d_29_ii: $i > $i > $o).
0.20/0.55	thf(decl_150, type, iii: $i > $i > $o).
0.20/0.55	thf(decl_153, type, lessis: $i > $i > $o).
0.20/0.55	thf(decl_154, type, esk1_0: $i).
0.20/0.55	thf(decl_155, type, esk2_0: $i).
0.20/0.55	thf(decl_160, type, esk7_2: $i > $i > $i).
0.20/0.55	thf(decl_161, type, esk8_2: $i > $i > $i).
0.20/0.55	thf(def_d_not, axiom, ((d_not)=(^[X36:$o]:((imp @ ((X36)) @ (~($true)))))), file('/export/starexec/sandbox2/tmp/tmp.wvh4OKvgP2/E---3.1_1392267.p', def_d_not)).
0.20/0.55	thf(def_imp, axiom, ((imp)=(^[X34:$o, X35:$o]:((((X34))=>((X35)))))), file('/export/starexec/sandbox2/tmp/tmp.wvh4OKvgP2/E---3.1_1392267.p', def_imp)).
0.20/0.55	thf(def_all_of, axiom, ((all_of)=(^[X3:$i > $o, X2:$i > $o]:(![X4:$i]:((((is_of @ X4 @ X3))=>((X2 @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.wvh4OKvgP2/E---3.1_1392267.p', def_all_of)).
0.20/0.55	thf(def_is_of, axiom, ((is_of)=(^[X1:$i, X2:$i > $o]:((X2 @ X1)))), file('/export/starexec/sandbox2/tmp/tmp.wvh4OKvgP2/E---3.1_1392267.p', def_is_of)).
0.20/0.55	thf(def_e_is, axiom, ((e_is)=(^[X1:$i, X60:$i, X61:$i]:(((X60)=(X61))))), file('/export/starexec/sandbox2/tmp/tmp.wvh4OKvgP2/E---3.1_1392267.p', def_e_is)).
0.20/0.55	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.wvh4OKvgP2/E---3.1_1392267.p', def_l_some)).
0.20/0.55	thf(def_diffprop, axiom, ((diffprop)=(^[X1:$i, X183:$i, X4:$i]:((n_is @ X1 @ (n_pl @ X183 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.wvh4OKvgP2/E---3.1_1392267.p', def_diffprop)).
0.20/0.55	thf(def_n_is, axiom, ((n_is)=(^[Z0:$i, Z1:$i]:(((Z0)=(Z1))))), file('/export/starexec/sandbox2/tmp/tmp.wvh4OKvgP2/E---3.1_1392267.p', def_n_is)).
0.20/0.55	thf(def_l_or, axiom, ((l_or)=(^[X42:$o]:(imp @ ((d_not @ ((X42))))))), file('/export/starexec/sandbox2/tmp/tmp.wvh4OKvgP2/E---3.1_1392267.p', def_l_or)).
0.20/0.55	thf(def_iii, axiom, ((iii)=(^[X1:$i, X185:$i]:((n_some @ (diffprop @ X185 @ X1))))), file('/export/starexec/sandbox2/tmp/tmp.wvh4OKvgP2/E---3.1_1392267.p', def_iii)).
0.20/0.55	thf(def_n_some, axiom, ((n_some)=(^[Z0:$i > $o]:(((((((![X297:$i]:((((((in @ X297 @ nat))))=>((non @ nat @ Z0 @ X297))))))))=>((~($true)))))))), file('/export/starexec/sandbox2/tmp/tmp.wvh4OKvgP2/E---3.1_1392267.p', def_n_some)).
0.20/0.55	thf(def_or3, axiom, ((or3)=(^[X48:$o, X49:$o, X50:$o]:((l_or @ ((X48)) @ ((l_or @ ((X49)) @ ((X50)))))))), file('/export/starexec/sandbox2/tmp/tmp.wvh4OKvgP2/E---3.1_1392267.p', def_or3)).
0.20/0.55	thf(def_d_29_ii, axiom, ((d_29_ii)=(^[X1:$i, X184:$i]:((n_some @ (diffprop @ X1 @ X184))))), file('/export/starexec/sandbox2/tmp/tmp.wvh4OKvgP2/E---3.1_1392267.p', def_d_29_ii)).
0.20/0.55	thf(def_lessis, axiom, ((lessis)=(^[X1:$i, X188:$i]:((l_or @ ((iii @ X1 @ X188)) @ ((n_is @ X1 @ X188)))))), file('/export/starexec/sandbox2/tmp/tmp.wvh4OKvgP2/E---3.1_1392267.p', def_lessis)).
0.20/0.55	thf(satz10e, conjecture, (all_of @ (^[X1:$i]:((in @ X1 @ nat))) @ (^[X1:$i]:((all_of @ (^[X228:$i]:((in @ X228 @ nat))) @ (^[X229:$i]:((((d_not @ ((d_29_ii @ X1 @ X229))))=>((lessis @ X1 @ X229))))))))), file('/export/starexec/sandbox2/tmp/tmp.wvh4OKvgP2/E---3.1_1392267.p', satz10e)).
0.20/0.55	thf(satz9a, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ nat))) @ (^[X1:$i]:((all_of @ (^[X195:$i]:((in @ X195 @ nat))) @ (^[X196:$i]:((or3 @ ((n_is @ X1 @ X196)) @ ((n_some @ (diffprop @ X1 @ X196))) @ ((n_some @ (diffprop @ X196 @ X1)))))))))), file('/export/starexec/sandbox2/tmp/tmp.wvh4OKvgP2/E---3.1_1392267.p', satz9a)).
0.20/0.55	thf(c_0_16, plain, ((d_not)=(^[Z0:$o]:((((((Z0)))=>((~($true)))))))), inference(fof_simplification,[status(thm)],[def_d_not])).
0.20/0.55	thf(c_0_17, plain, ((imp)=(^[Z0:$o, Z1:$o]:((((Z0))=>((Z1)))))), inference(fof_simplification,[status(thm)],[def_imp])).
0.20/0.55	thf(c_0_18, plain, ((all_of)=(^[Z0:$i > $o, Z1:$i > $o]:(![X4:$i]:(((((Z0 @ X4)))=>((Z1 @ X4))))))), inference(fof_simplification,[status(thm)],[def_all_of])).
0.20/0.55	thf(c_0_19, plain, ((is_of)=(^[Z0:$i, Z1:$i > $o]:((Z1 @ Z0)))), inference(fof_simplification,[status(thm)],[def_is_of])).
0.20/0.55	thf(c_0_20, plain, ((e_is)=(^[Z0:$i, Z1:$i, Z2:$i]:(((Z1)=(Z2))))), inference(fof_simplification,[status(thm)],[def_e_is])).
0.20/0.55	thf(c_0_21, plain, ((l_some)=(^[Z0:$i, Z1:$i > $o]:(((((((![X296:$i]:((((((in @ X296 @ Z0))))=>((non @ Z0 @ Z1 @ X296))))))))=>((~($true)))))))), inference(fof_simplification,[status(thm)],[def_l_some])).
0.20/0.55	thf(c_0_22, plain, ((d_not)=(^[Z0:$o]:((((((Z0)))=>((~($true)))))))), inference(apply_def,[status(thm)],[c_0_16, c_0_17])).
0.20/0.55	thf(c_0_23, plain, ((all_of)=(^[Z0:$i > $o, Z1:$i > $o]:(![X4:$i]:(((((Z0 @ X4)))=>((Z1 @ X4))))))), inference(apply_def,[status(thm)],[c_0_18, c_0_19])).
0.20/0.55	thf(c_0_24, plain, ((diffprop)=(^[Z0:$i, Z1:$i, Z2:$i]:((((Z0)=(n_pl @ Z1 @ Z2)))))), inference(fof_simplification,[status(thm)],[def_diffprop])).
0.20/0.55	thf(c_0_25, axiom, ((n_is)=(^[Z0:$i, Z1:$i]:(((Z0)=(Z1))))), inference(apply_def,[status(thm)],[def_n_is, c_0_20])).
0.20/0.55	thf(c_0_26, plain, ((l_some)=(^[Z0:$i, Z1:$i > $o]:(((((((![X296:$i]:((((((in @ X296 @ Z0))))=>((non @ Z0 @ Z1 @ X296))))))))=>((~($true)))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_21, c_0_22]), c_0_23])).
0.20/0.55	thf(c_0_27, plain, ((l_or)=(^[Z0:$o, Z1:$o]:((((((((((Z0))))=>((~($true)))))))=>((Z1)))))), inference(fof_simplification,[status(thm)],[def_l_or])).
0.20/0.55	thf(c_0_28, plain, ((iii)=(^[Z0:$i, Z1:$i]:(((((((![X299:$i]:((((((in @ X299 @ nat))))=>((non @ nat @ (^[Z2:$i]:((((Z1)=(n_pl @ Z0 @ Z2))))) @ X299))))))))=>((~($true)))))))), inference(fof_simplification,[status(thm)],[def_iii])).
0.20/0.55	thf(c_0_29, plain, ((diffprop)=(^[Z0:$i, Z1:$i, Z2:$i]:((((Z0)=(n_pl @ Z1 @ Z2)))))), inference(apply_def,[status(thm)],[c_0_24, c_0_25])).
0.20/0.55	thf(c_0_30, axiom, ((n_some)=(^[Z0:$i > $o]:(((((((![X297:$i]:((((((in @ X297 @ nat))))=>((non @ nat @ Z0 @ X297))))))))=>((~($true)))))))), inference(apply_def,[status(thm)],[def_n_some, c_0_26])).
0.20/0.55	thf(c_0_31, plain, ((or3)=(^[Z0:$o, Z1:$o, Z2:$o]:((((((((((((Z0)))))=>((~($true)))))))=>(((((((((((((Z1)))))=>((~($true)))))))=>(((Z2)))))))))))), inference(fof_simplification,[status(thm)],[def_or3])).
0.20/0.55	thf(c_0_32, plain, ((l_or)=(^[Z0:$o, Z1:$o]:((((((((((Z0))))=>((~($true)))))))=>((Z1)))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_27, c_0_17]), c_0_22])).
0.20/0.55	thf(c_0_33, plain, ((d_29_ii)=(^[Z0:$i, Z1:$i]:(((((((![X298:$i]:((((((in @ X298 @ nat))))=>((non @ nat @ (^[Z2:$i]:((((Z0)=(n_pl @ Z1 @ Z2))))) @ X298))))))))=>((~($true)))))))), inference(fof_simplification,[status(thm)],[def_d_29_ii])).
0.20/0.55	thf(c_0_34, plain, ((lessis)=(^[Z0:$i, Z1:$i]:(((((((((((((((((![X300:$i]:((((((in @ X300 @ nat))))=>((non @ nat @ (^[Z2:$i]:((((Z1)=(n_pl @ Z0 @ Z2))))) @ X300))))))))=>((~($true)))))))))=>((~($true)))))))=>(((((Z0)=(Z1)))))))))), inference(fof_simplification,[status(thm)],[def_lessis])).
0.20/0.55	thf(c_0_35, plain, ((iii)=(^[Z0:$i, Z1:$i]:(((((((![X299:$i]:((((((in @ X299 @ nat))))=>((non @ nat @ (^[Z2:$i]:((((Z1)=(n_pl @ Z0 @ Z2))))) @ X299))))))))=>((~($true)))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_28, c_0_29]), c_0_30])).
0.20/0.55	thf(c_0_36, plain, ((or3)=(^[Z0:$o, Z1:$o, Z2:$o]:((((((((((((Z0)))))=>((~($true)))))))=>(((((((((((((Z1)))))=>((~($true)))))))=>(((Z2)))))))))))), inference(apply_def,[status(thm)],[c_0_31, c_0_32])).
0.20/0.55	thf(c_0_37, negated_conjecture, ~((all_of @ (^[X1:$i]:((in @ X1 @ nat))) @ (^[X1:$i]:((all_of @ (^[X228:$i]:((in @ X228 @ nat))) @ (^[X229:$i]:((((d_not @ ((d_29_ii @ X1 @ X229))))=>((lessis @ X1 @ X229)))))))))), inference(assume_negation,[status(cth)],[satz10e])).
0.20/0.55	thf(c_0_38, plain, ((d_29_ii)=(^[Z0:$i, Z1:$i]:(((((((![X298:$i]:((((((in @ X298 @ nat))))=>((non @ nat @ (^[Z2:$i]:((((Z0)=(n_pl @ Z1 @ Z2))))) @ X298))))))))=>((~($true)))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_33, c_0_29]), c_0_30])).
0.20/0.55	thf(c_0_39, plain, ((lessis)=(^[Z0:$i, Z1:$i]:(((((((((((((((((![X300:$i]:((((((in @ X300 @ nat))))=>((non @ nat @ (^[Z2:$i]:((((Z1)=(n_pl @ Z0 @ Z2))))) @ X300))))))))=>((~($true)))))))))=>((~($true)))))))=>(((((Z0)=(Z1)))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_34, c_0_35]), c_0_25]), c_0_32])).
0.20/0.55	thf(c_0_40, plain, ![X325:$i]:(((in @ X325 @ nat)=>![X324:$i]:(((in @ X324 @ nat)=>((((X325)=(X324))=>~($true))=>(((![X322:$i]:(((in @ X322 @ nat)=>(non @ nat @ (^[Z0:$i]:(((X325)=(n_pl @ X324 @ Z0)))) @ X322)))=>~($true))=>~($true))=>(![X323:$i]:(((in @ X323 @ nat)=>(non @ nat @ (^[Z0:$i]:(((X324)=(n_pl @ X325 @ Z0)))) @ X323)))=>~($true)))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz9a]), c_0_36]), c_0_29]), c_0_30]), c_0_25]), c_0_23])).
0.20/0.55	thf(c_0_41, negated_conjecture, ~(![X304:$i]:(((in @ X304 @ nat)=>![X303:$i]:(((in @ X303 @ nat)=>(((![X301:$i]:(((in @ X301 @ nat)=>(non @ nat @ (^[Z0:$i]:(((X304)=(n_pl @ X303 @ Z0)))) @ X301)))=>~($true))=>~($true))=>(((![X302:$i]:(((in @ X302 @ nat)=>(non @ nat @ (^[Z0:$i]:(((X303)=(n_pl @ X304 @ Z0)))) @ X302)))=>~($true))=>~($true))=>((X304)=(X303))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_37]), c_0_38]), c_0_22]), c_0_39]), c_0_23])).
0.20/0.55	thf(c_0_42, plain, ![X418:$i, X419:$i]:(((((((in @ (esk8_2 @ X418 @ X419) @ nat)|~($true)|((in @ (esk7_2 @ X418 @ X419) @ nat)|~($true))|((X418)=(X419))|~(in @ X419 @ nat)|~(in @ X418 @ nat))&(~(non @ nat @ (^[Z0:$i]:(((X419)=(n_pl @ X418 @ Z0)))) @ (esk8_2 @ X418 @ X419))|~($true)|((in @ (esk7_2 @ X418 @ X419) @ nat)|~($true))|((X418)=(X419))|~(in @ X419 @ nat)|~(in @ X418 @ nat)))&(((in @ (esk8_2 @ X418 @ X419) @ nat)|~($true)|(~(non @ nat @ (^[Z0:$i]:(((X418)=(n_pl @ X419 @ Z0)))) @ (esk7_2 @ X418 @ X419))|~($true))|((X418)=(X419))|~(in @ X419 @ nat)|~(in @ X418 @ nat))&(~(non @ nat @ (^[Z0:$i]:(((X419)=(n_pl @ X418 @ Z0)))) @ (esk8_2 @ X418 @ X419))|~($true)|(~(non @ nat @ (^[Z0:$i]:(((X418)=(n_pl @ X419 @ Z0)))) @ (esk7_2 @ X418 @ X419))|~($true))|((X418)=(X419))|~(in @ X419 @ nat)|~(in @ X418 @ nat))))&(((in @ (esk8_2 @ X418 @ X419) @ nat)|~($true)|($true)|((X418)=(X419))|~(in @ X419 @ nat)|~(in @ X418 @ nat))&(~(non @ nat @ (^[Z0:$i]:(((X419)=(n_pl @ X418 @ Z0)))) @ (esk8_2 @ X418 @ X419))|~($true)|($true)|((X418)=(X419))|~(in @ X419 @ nat)|~(in @ X418 @ nat))))&(((((in @ (esk8_2 @ X418 @ X419) @ nat)|~($true)|((in @ (esk7_2 @ X418 @ X419) @ nat)|~($true))|($true)|~(in @ X419 @ nat)|~(in @ X418 @ nat))&(~(non @ nat @ (^[Z0:$i]:(((X419)=(n_pl @ X418 @ Z0)))) @ (esk8_2 @ X418 @ X419))|~($true)|((in @ (esk7_2 @ X418 @ X419) @ nat)|~($true))|($true)|~(in @ X419 @ nat)|~(in @ X418 @ nat)))&(((in @ (esk8_2 @ X418 @ X419) @ nat)|~($true)|(~(non @ nat @ (^[Z0:$i]:(((X418)=(n_pl @ X419 @ Z0)))) @ (esk7_2 @ X418 @ X419))|~($true))|($true)|~(in @ X419 @ nat)|~(in @ X418 @ nat))&(~(non @ nat @ (^[Z0:$i]:(((X419)=(n_pl @ X418 @ Z0)))) @ (esk8_2 @ X418 @ X419))|~($true)|(~(non @ nat @ (^[Z0:$i]:(((X418)=(n_pl @ X419 @ Z0)))) @ (esk7_2 @ X418 @ X419))|~($true))|($true)|~(in @ X419 @ nat)|~(in @ X418 @ nat))))&(((in @ (esk8_2 @ X418 @ X419) @ nat)|~($true)|($true)|($true)|~(in @ X419 @ nat)|~(in @ X418 @ nat))&(~(non @ nat @ (^[Z0:$i]:(((X419)=(n_pl @ X418 @ Z0)))) @ (esk8_2 @ X418 @ X419))|~($true)|($true)|($true)|~(in @ X419 @ nat)|~(in @ X418 @ nat)))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])])])])])])).
0.20/0.55	thf(c_0_43, negated_conjecture, ![X393:$i, X394:$i]:(((in @ esk1_0 @ nat)&((in @ esk2_0 @ nat)&(((~(in @ X393 @ nat)|(non @ nat @ (^[Z0:$i]:(((esk1_0)=(n_pl @ esk2_0 @ Z0)))) @ X393)|~($true))&(($true)|~($true)))&(((~(in @ X394 @ nat)|(non @ nat @ (^[Z0:$i]:(((esk2_0)=(n_pl @ esk1_0 @ Z0)))) @ X394)|~($true))&(($true)|~($true)))&((esk1_0)!=(esk2_0))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])])])])])])).
0.20/0.55	thf(c_0_44, plain, ![X1:$i, X4:$i]:(((in @ (esk7_2 @ X4 @ X1) @ nat)|((X4)=(X1))|~((non @ nat @ (^[Z0:$i]:(((X1)=(n_pl @ X4 @ Z0)))) @ (esk8_2 @ X4 @ X1)))|~(($true))|~(($true))|~((in @ X1 @ nat))|~((in @ X4 @ nat)))), inference(split_conjunct,[status(thm)],[c_0_42])).
0.20/0.55	thf(c_0_45, negated_conjecture, ![X1:$i]:(((non @ nat @ (^[Z0:$i]:(((esk1_0)=(n_pl @ esk2_0 @ Z0)))) @ X1)|~((in @ X1 @ nat))|~(($true)))), inference(split_conjunct,[status(thm)],[c_0_43])).
0.20/0.55	thf(c_0_46, plain, ![X4:$i, X1:$i]:((((X1)=(X4))|(in @ (esk7_2 @ X4 @ X1) @ nat)|~((in @ X4 @ nat))|~((in @ X1 @ nat))|~((non @ nat @ (^[Z0:$i]:(((X1)=(n_pl @ X4 @ Z0)))) @ (esk8_2 @ X4 @ X1))))), inference(cn,[status(thm)],[c_0_44])).
0.20/0.55	thf(c_0_47, negated_conjecture, ![X1:$i]:(((non @ nat @ (^[Z0:$i]:(((esk1_0)=(n_pl @ esk2_0 @ Z0)))) @ X1)|~((in @ X1 @ nat)))), inference(cn,[status(thm)],[c_0_45])).
0.20/0.55	thf(c_0_48, negated_conjecture, (in @ esk2_0 @ nat), inference(split_conjunct,[status(thm)],[c_0_43])).
0.20/0.55	thf(c_0_49, negated_conjecture, (in @ esk1_0 @ nat), inference(split_conjunct,[status(thm)],[c_0_43])).
0.20/0.55	thf(c_0_50, negated_conjecture, ((esk1_0)!=(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_43])).
0.20/0.55	thf(c_0_51, plain, ![X4:$i, X1:$i]:(((in @ (esk8_2 @ X1 @ X4) @ nat)|(in @ (esk7_2 @ X1 @ X4) @ nat)|((X1)=(X4))|~(($true))|~(($true))|~((in @ X4 @ nat))|~((in @ X1 @ nat)))), inference(split_conjunct,[status(thm)],[c_0_42])).
0.20/0.55	thf(c_0_52, plain, ![X1:$i, X4:$i]:((((X4)=(X1))|~((non @ nat @ (^[Z0:$i]:(((X1)=(n_pl @ X4 @ Z0)))) @ (esk8_2 @ X4 @ X1)))|~(($true))|~((non @ nat @ (^[Z0:$i]:(((X4)=(n_pl @ X1 @ Z0)))) @ (esk7_2 @ X4 @ X1)))|~(($true))|~((in @ X1 @ nat))|~((in @ X4 @ nat)))), inference(split_conjunct,[status(thm)],[c_0_42])).
0.20/0.55	thf(c_0_53, negated_conjecture, ![X1:$i]:(((non @ nat @ (^[Z0:$i]:(((esk2_0)=(n_pl @ esk1_0 @ Z0)))) @ X1)|~((in @ X1 @ nat))|~(($true)))), inference(split_conjunct,[status(thm)],[c_0_43])).
0.20/0.55	thf(c_0_54, negated_conjecture, ((in @ (esk7_2 @ esk2_0 @ esk1_0) @ nat)|~((in @ (esk8_2 @ esk2_0 @ esk1_0) @ nat))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46, c_0_47]), c_0_48]), c_0_49])]), c_0_50])).
0.20/0.55	thf(c_0_55, plain, ![X4:$i, X1:$i]:((((X1)=(X4))|(in @ (esk7_2 @ X1 @ X4) @ nat)|(in @ (esk8_2 @ X1 @ X4) @ nat)|~((in @ X4 @ nat))|~((in @ X1 @ nat)))), inference(cn,[status(thm)],[c_0_51])).
0.20/0.55	thf(c_0_56, plain, ![X4:$i, X1:$i]:(((in @ (esk8_2 @ X1 @ X4) @ nat)|((X1)=(X4))|~(($true))|~((non @ nat @ (^[Z0:$i]:(((X1)=(n_pl @ X4 @ Z0)))) @ (esk7_2 @ X1 @ X4)))|~(($true))|~((in @ X4 @ nat))|~((in @ X1 @ nat)))), inference(split_conjunct,[status(thm)],[c_0_42])).
0.20/0.55	thf(c_0_57, plain, ![X4:$i, X1:$i]:((((X1)=(X4))|~((in @ X4 @ nat))|~((in @ X1 @ nat))|~((non @ nat @ (^[Z0:$i]:(((X4)=(n_pl @ X1 @ Z0)))) @ (esk7_2 @ X4 @ X1)))|~((non @ nat @ (^[Z0:$i]:(((X1)=(n_pl @ X4 @ Z0)))) @ (esk8_2 @ X4 @ X1))))), inference(cn,[status(thm)],[c_0_52])).
0.20/0.55	thf(c_0_58, negated_conjecture, ![X1:$i]:(((non @ nat @ (^[Z0:$i]:(((esk2_0)=(n_pl @ esk1_0 @ Z0)))) @ X1)|~((in @ X1 @ nat)))), inference(cn,[status(thm)],[c_0_53])).
0.20/0.55	thf(c_0_59, negated_conjecture, (in @ (esk7_2 @ esk2_0 @ esk1_0) @ nat), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54, c_0_55]), c_0_49]), c_0_48])]), c_0_50])).
0.20/0.55	thf(c_0_60, plain, ![X1:$i, X4:$i]:((((X1)=(X4))|(in @ (esk8_2 @ X1 @ X4) @ nat)|~((in @ X4 @ nat))|~((in @ X1 @ nat))|~((non @ nat @ (^[Z0:$i]:(((X1)=(n_pl @ X4 @ Z0)))) @ (esk7_2 @ X1 @ X4))))), inference(cn,[status(thm)],[c_0_56])).
0.20/0.55	thf(c_0_61, negated_conjecture, ~((non @ nat @ (^[Z0:$i]:(((esk1_0)=(n_pl @ esk2_0 @ Z0)))) @ (esk8_2 @ esk2_0 @ esk1_0))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57, c_0_58]), c_0_48]), c_0_49]), c_0_59])]), c_0_50])).
0.20/0.55	thf(c_0_62, negated_conjecture, (in @ (esk8_2 @ esk2_0 @ esk1_0) @ nat), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_58]), c_0_49]), c_0_48]), c_0_59])]), c_0_50])).
0.20/0.55	thf(c_0_63, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61, c_0_47]), c_0_62])]), ['proof']).
0.20/0.55	% SZS output end CNFRefutation
0.20/0.55	% Parsed axioms                        : 353
0.20/0.55	% Removed by relevancy pruning/SinE    : 277
0.20/0.55	% Initial clauses                      : 141
0.20/0.55	% Removed in clause preprocessing      : 33
0.20/0.55	% Initial clauses in saturation        : 108
0.20/0.55	% Processed clauses                    : 519
0.20/0.55	% ...of these trivial                  : 43
0.20/0.55	% ...subsumed                          : 189
0.20/0.55	% ...remaining for further processing  : 287
0.20/0.55	% Other redundant clauses eliminated   : 24
0.20/0.55	% Clauses deleted for lack of memory   : 0
0.20/0.55	% Backward-subsumed                    : 3
0.20/0.55	% Backward-rewritten                   : 18
0.20/0.55	% Generated clauses                    : 1489
0.20/0.55	% ...of the previous two non-redundant : 1254
0.20/0.55	% ...aggressively subsumed             : 0
0.20/0.55	% Contextual simplify-reflections      : 3
0.20/0.55	% Paramodulations                      : 1459
0.20/0.55	% Factorizations                       : 2
0.20/0.55	% NegExts                              : 0
0.20/0.55	% Equation resolutions                 : 26
0.20/0.55	% Disequality decompositions           : 0
0.20/0.55	% Total rewrite steps                  : 347
0.20/0.55	% ...of those cached                   : 270
0.20/0.55	% Propositional unsat checks           : 0
0.20/0.55	%    Propositional check models        : 0
0.20/0.55	%    Propositional check unsatisfiable : 0
0.20/0.55	%    Propositional clauses             : 0
0.20/0.55	%    Propositional clauses after purity: 0
0.20/0.55	%    Propositional unsat core size     : 0
0.20/0.55	%    Propositional preprocessing time  : 0.000
0.20/0.55	%    Propositional encoding time       : 0.000
0.20/0.55	%    Propositional solver time         : 0.000
0.20/0.55	%    Success case prop preproc time    : 0.000
0.20/0.55	%    Success case prop encoding time   : 0.000
0.20/0.55	%    Success case prop solver time     : 0.000
0.20/0.55	% Current number of processed clauses  : 264
0.20/0.55	%    Positive orientable unit clauses  : 63
0.20/0.55	%    Positive unorientable unit clauses: 0
0.20/0.55	%    Negative unit clauses             : 23
0.20/0.55	%    Non-unit-clauses                  : 178
0.20/0.55	% Current number of unprocessed clauses: 832
0.20/0.55	% ...number of literals in the above   : 2802
0.20/0.55	% Current number of archived formulas  : 0
0.20/0.55	% Current number of archived clauses   : 21
0.20/0.55	% Clause-clause subsumption calls (NU) : 4743
0.20/0.55	% Rec. Clause-clause subsumption calls : 2470
0.20/0.55	% Non-unit clause-clause subsumptions  : 110
0.20/0.55	% Unit Clause-clause subsumption calls : 287
0.20/0.55	% Rewrite failures with RHS unbound    : 0
0.20/0.55	% BW rewrite match attempts            : 281
0.20/0.55	% BW rewrite match successes           : 17
0.20/0.55	% Condensation attempts                : 0
0.20/0.55	% Condensation successes               : 0
0.20/0.55	% Termbank termtop insertions          : 48186
0.20/0.55	% Search garbage collected termcells   : 7647
0.20/0.55	
0.20/0.55	% -------------------------------------------------
0.20/0.55	% User time                : 0.069 s
0.20/0.55	% System time              : 0.008 s
0.20/0.55	% Total time               : 0.077 s
0.20/0.55	% Maximum resident set size: 5128 pages
0.20/0.55	
0.20/0.55	% -------------------------------------------------
0.20/0.55	% User time                : 0.077 s
0.20/0.55	% System time              : 0.015 s
0.20/0.55	% Total time               : 0.092 s
0.20/0.55	% Maximum resident set size: 5376 pages
0.20/0.55	% E exiting
0.20/0.55	EOF