0.11/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.11/0.12	% Command    : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 240 THM
0.11/0.32	% Computer : n018.cluster.edu
0.11/0.32	% Model    : x86_64 x86_64
0.11/0.32	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.11/0.32	% Memory   : 8042.1875MB
0.11/0.32	% OS       : Linux 3.10.0-693.el7.x86_64
0.11/0.32	% CPULimit   : 1920
0.11/0.32	% WCLimit    : 240
0.11/0.32	% DateTime   : Wed Jul 30 09:00:04 EDT 2025
0.11/0.32	% CPUTime    : 
0.19/0.46	Running higher-order theorem proving
0.19/0.49	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.rVDS4DcAjm/E---3.1_23407.p
0.89/0.61	# Version: 3.0.0-ho
0.89/0.61	# Preprocessing class: HSLMSMSSLLLCHSA.
0.89/0.61	# Scheduled 6 strats onto 8 cores with 240 seconds (1920 total)
0.89/0.61	# Starting lpo1_fix with 720s (3) cores
0.89/0.61	# Starting full_lambda_9 with 240s (1) cores
0.89/0.61	# Starting almost_fo_4 with 240s (1) cores
0.89/0.61	# Starting new_ho_9 with 240s (1) cores
0.89/0.61	# Starting pre_casc_4 with 240s (1) cores
0.89/0.61	# Starting ho_unfolding_6 with 240s (1) cores
0.89/0.61	# full_lambda_9 with pid 23486 completed with status 0
0.89/0.61	# Result found by full_lambda_9
0.89/0.61	# Preprocessing class: HSLMSMSSLLLCHSA.
0.89/0.61	# Scheduled 6 strats onto 8 cores with 240 seconds (1920 total)
0.89/0.61	# Starting lpo1_fix with 720s (3) cores
0.89/0.61	# Starting full_lambda_9 with 240s (1) cores
0.89/0.61	# SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
0.89/0.61	# Search class: HGHSM-FSLM32-DHSMMSBN
0.89/0.61	# partial match(1): HGHSM-FSLM32-MHSMMSBN
0.89/0.61	# Scheduled 12 strats onto 1 cores with 240 seconds (240 total)
0.89/0.61	# Starting full_lambda_5 with 20s (1) cores
0.89/0.61	# full_lambda_5 with pid 23492 completed with status 0
0.89/0.61	# Result found by full_lambda_5
0.89/0.61	# Preprocessing class: HSLMSMSSLLLCHSA.
0.89/0.61	# Scheduled 6 strats onto 8 cores with 240 seconds (1920 total)
0.89/0.61	# Starting lpo1_fix with 720s (3) cores
0.89/0.61	# Starting full_lambda_9 with 240s (1) cores
0.89/0.61	# SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
0.89/0.61	# Search class: HGHSM-FSLM32-DHSMMSBN
0.89/0.61	# partial match(1): HGHSM-FSLM32-MHSMMSBN
0.89/0.61	# Scheduled 12 strats onto 1 cores with 240 seconds (240 total)
0.89/0.61	# Starting full_lambda_5 with 20s (1) cores
0.89/0.61	# Preprocessing time       : 0.005 s
0.89/0.61	# Presaturation interreduction done
0.89/0.61	
0.89/0.61	# Proof found!
0.89/0.61	# SZS status Theorem
0.89/0.61	# SZS output start CNFRefutation
0.89/0.61	thf(decl_23, type, is_of: $i > ($i > $o) > $o).
0.89/0.61	thf(decl_24, type, all_of: ($i > $o) > ($i > $o) > $o).
0.89/0.61	thf(decl_26, type, in: $i > $i > $o).
0.89/0.61	thf(decl_62, type, imp: $o > $o > $o).
0.89/0.61	thf(decl_63, type, d_not: $o > $o).
0.89/0.61	thf(decl_66, type, l_ec: $o > $o > $o).
0.89/0.61	thf(decl_67, type, d_and: $o > $o > $o).
0.89/0.61	thf(decl_68, type, l_or: $o > $o > $o).
0.89/0.61	thf(decl_72, type, non: $i > ($i > $o) > $i > $o).
0.89/0.61	thf(decl_73, type, l_some: $i > ($i > $o) > $o).
0.89/0.61	thf(decl_74, type, or3: $o > $o > $o > $o).
0.89/0.61	thf(decl_75, type, and3: $o > $o > $o > $o).
0.89/0.61	thf(decl_76, type, ec3: $o > $o > $o > $o).
0.89/0.61	thf(decl_77, type, orec3: $o > $o > $o > $o).
0.89/0.61	thf(decl_78, type, e_is: $i > $i > $i > $o).
0.89/0.61	thf(decl_124, type, nat: $i).
0.89/0.61	thf(decl_125, type, n_is: $i > $i > $o).
0.89/0.61	thf(decl_128, type, n_some: ($i > $o) > $o).
0.89/0.61	thf(decl_143, type, n_pl: $i > $i > $i).
0.89/0.61	thf(decl_148, type, diffprop: $i > $i > $i > $o).
0.89/0.61	thf(decl_152, type, esk1_0: $i).
0.89/0.61	thf(decl_153, type, esk2_0: $i).
0.89/0.61	thf(decl_154, type, esk3_2: $i > $i > $i).
0.89/0.61	thf(decl_155, type, esk4_2: $i > $i > $i).
0.89/0.61	thf(def_d_not, axiom, ((d_not)=(^[X36:$o]:((imp @ ((X36)) @ (~($true)))))), file('/export/starexec/sandbox2/tmp/tmp.rVDS4DcAjm/E---3.1_23407.p', def_d_not)).
0.89/0.61	thf(def_imp, axiom, ((imp)=(^[X34:$o, X35:$o]:(((X34)=>(X35))))), file('/export/starexec/sandbox2/tmp/tmp.rVDS4DcAjm/E---3.1_23407.p', def_imp)).
0.89/0.61	thf(def_l_ec, axiom, ((l_ec)=(^[X38:$o, X39:$o]:((imp @ ((X38)) @ ((d_not @ ((X39)))))))), file('/export/starexec/sandbox2/tmp/tmp.rVDS4DcAjm/E---3.1_23407.p', def_l_ec)).
0.89/0.61	thf(def_d_and, axiom, ((d_and)=(^[X40:$o, X41:$o]:((d_not @ ((l_ec @ ((X40)) @ ((X41)))))))), file('/export/starexec/sandbox2/tmp/tmp.rVDS4DcAjm/E---3.1_23407.p', def_d_and)).
0.89/0.61	thf(def_all_of, axiom, ((all_of)=(^[X3:$i > $o, X2:$i > $o]:(![X4:$i]:(((is_of @ X4 @ X3)=>(X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.rVDS4DcAjm/E---3.1_23407.p', def_all_of)).
0.89/0.61	thf(def_is_of, axiom, ((is_of)=(^[X1:$i, X2:$i > $o]:((X2 @ X1)))), file('/export/starexec/sandbox2/tmp/tmp.rVDS4DcAjm/E---3.1_23407.p', def_is_of)).
0.89/0.61	thf(def_non, axiom, ((non)=(^[X1:$i, X2:$i > $o, X4:$i]:((d_not @ ((X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.rVDS4DcAjm/E---3.1_23407.p', def_non)).
0.89/0.61	thf(def_l_or, axiom, ((l_or)=(^[X42:$o]:(imp @ ((d_not @ ((X42))))))), file('/export/starexec/sandbox2/tmp/tmp.rVDS4DcAjm/E---3.1_23407.p', def_l_or)).
0.89/0.61	thf(def_and3, axiom, ((and3)=(^[X51:$o, X52:$o, X53:$o]:((d_and @ ((X51)) @ ((d_and @ ((X52)) @ ((X53)))))))), file('/export/starexec/sandbox2/tmp/tmp.rVDS4DcAjm/E---3.1_23407.p', def_and3)).
0.89/0.61	thf(def_e_is, axiom, ((e_is)=(^[X1:$i, X60:$i, X61:$i]:(((X60)=(X61))))), file('/export/starexec/sandbox2/tmp/tmp.rVDS4DcAjm/E---3.1_23407.p', def_e_is)).
0.89/0.61	thf(def_l_some, axiom, ((l_some)=(^[X1:$i, X2:$i > $o]:((d_not @ ((all_of @ (^[X4:$i]:((in @ X4 @ X1))) @ (non @ X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.rVDS4DcAjm/E---3.1_23407.p', def_l_some)).
0.89/0.61	thf(def_or3, axiom, ((or3)=(^[X48:$o, X49:$o, X50:$o]:((l_or @ ((X48)) @ ((l_or @ ((X49)) @ ((X50)))))))), file('/export/starexec/sandbox2/tmp/tmp.rVDS4DcAjm/E---3.1_23407.p', def_or3)).
0.89/0.61	thf(def_ec3, axiom, ((ec3)=(^[X54:$o, X55:$o, X56:$o]:((and3 @ ((l_ec @ ((X54)) @ ((X55)))) @ ((l_ec @ ((X55)) @ ((X56)))) @ ((l_ec @ ((X56)) @ ((X54)))))))), file('/export/starexec/sandbox2/tmp/tmp.rVDS4DcAjm/E---3.1_23407.p', def_ec3)).
0.89/0.61	thf(def_diffprop, axiom, ((diffprop)=(^[X1:$i, X183:$i, X4:$i]:((n_is @ X1 @ (n_pl @ X183 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.rVDS4DcAjm/E---3.1_23407.p', def_diffprop)).
0.89/0.61	thf(def_n_is, axiom, ((n_is)=(^[Z0/* 19 */:$i, Z1:$i]:(((Z0)=(Z1))))), file('/export/starexec/sandbox2/tmp/tmp.rVDS4DcAjm/E---3.1_23407.p', def_n_is)).
0.89/0.61	thf(def_orec3, axiom, ((orec3)=(^[X57:$o, X58:$o, X59:$o]:((d_and @ ((or3 @ ((X57)) @ ((X58)) @ ((X59)))) @ ((ec3 @ ((X57)) @ ((X58)) @ ((X59)))))))), file('/export/starexec/sandbox2/tmp/tmp.rVDS4DcAjm/E---3.1_23407.p', def_orec3)).
0.89/0.61	thf(def_n_some, axiom, ((n_some)=(^[Z0/* 3 */:$i > $o]:((((((![X325:$i]:(((((in @ X325 @ nat)))=>((((((Z0 @ X325)))=>(~($true))))))))))=>(~($true))))))), file('/export/starexec/sandbox2/tmp/tmp.rVDS4DcAjm/E---3.1_23407.p', def_n_some)).
0.89/0.61	thf(satz9a, conjecture, (all_of @ (^[X1:$i]:((in @ X1 @ nat))) @ (^[X1:$i]:((all_of @ (^[X201:$i]:((in @ X201 @ nat))) @ (^[X202:$i]:((or3 @ ((n_is @ X1 @ X202)) @ ((n_some @ (diffprop @ X1 @ X202))) @ ((n_some @ (diffprop @ X202 @ X1)))))))))), file('/export/starexec/sandbox2/tmp/tmp.rVDS4DcAjm/E---3.1_23407.p', satz9a)).
0.89/0.61	thf(satz9, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ nat))) @ (^[X1:$i]:((all_of @ (^[X187:$i]:((in @ X187 @ nat))) @ (^[X188:$i]:((orec3 @ ((n_is @ X1 @ X188)) @ ((n_some @ (^[X4:$i]:((n_is @ X1 @ (n_pl @ X188 @ X4)))))) @ ((n_some @ (^[X4:$i]:((n_is @ X188 @ (n_pl @ X1 @ X4))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.rVDS4DcAjm/E---3.1_23407.p', satz9)).
0.89/0.61	thf(c_0_19, plain, ((d_not)=(^[Z0/* 3 */:$o]:(((((Z0))=>(~($true))))))), inference(fof_simplification,[status(thm)],[def_d_not])).
0.89/0.61	thf(c_0_20, plain, ((imp)=(^[Z0/* 19 */:$o, Z1:$o]:(((Z0)=>(Z1))))), inference(fof_simplification,[status(thm)],[def_imp])).
0.89/0.61	thf(c_0_21, plain, ((l_ec)=(^[Z0/* 19 */:$o, Z1:$o]:(((((Z0))=>((((((Z1)))=>(~($true)))))))))), inference(fof_simplification,[status(thm)],[def_l_ec])).
0.89/0.61	thf(c_0_22, plain, ((d_not)=(^[Z0/* 3 */:$o]:(((((Z0))=>(~($true))))))), inference(apply_def,[status(thm)],[c_0_19, c_0_20])).
0.89/0.61	thf(c_0_23, plain, ((d_and)=(^[Z0/* 19 */:$o, Z1:$o]:((((((((((Z0)))=>(((((((Z1))))=>(~($true)))))))))=>(~($true))))))), inference(fof_simplification,[status(thm)],[def_d_and])).
0.89/0.61	thf(c_0_24, plain, ((l_ec)=(^[Z0/* 19 */:$o, Z1:$o]:(((((Z0))=>((((((Z1)))=>(~($true)))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_21, c_0_20]), c_0_22])).
0.89/0.61	thf(c_0_25, plain, ((all_of)=(^[Z0/* 19 */:$i > $o, Z1:$i > $o]:(![X4:$i]:((((Z0 @ X4))=>(Z1 @ X4)))))), inference(fof_simplification,[status(thm)],[def_all_of])).
0.89/0.61	thf(c_0_26, plain, ((is_of)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((Z1 @ Z0)))), inference(fof_simplification,[status(thm)],[def_is_of])).
0.89/0.61	thf(c_0_27, plain, ((non)=(^[Z0/* 19 */:$i, Z1:$i > $o, Z2:$i]:((((((Z1 @ Z2)))=>(~($true))))))), inference(fof_simplification,[status(thm)],[def_non])).
0.89/0.61	thf(c_0_28, plain, ((l_or)=(^[Z0/* 19 */:$o, Z1:$o]:((((((((Z0)))=>(~($true)))))=>(Z1))))), inference(fof_simplification,[status(thm)],[def_l_or])).
0.89/0.61	thf(c_0_29, plain, ((and3)=(^[Z0/* 19 */:$o, Z1:$o, Z2:$o]:(((((((((((Z0))))=>(((((((((((((((((Z1))))=>((((((((Z2)))))=>(~($true)))))))))=>(~($true))))))))=>(~($true)))))))))=>(~($true))))))), inference(fof_simplification,[status(thm)],[def_and3])).
0.89/0.61	thf(c_0_30, plain, ((d_and)=(^[Z0/* 19 */:$o, Z1:$o]:((((((((((Z0)))=>(((((((Z1))))=>(~($true)))))))))=>(~($true))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_23, c_0_24]), c_0_22])).
0.89/0.61	thf(c_0_31, plain, ((e_is)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:(((Z1)=(Z2))))), inference(fof_simplification,[status(thm)],[def_e_is])).
0.89/0.61	thf(c_0_32, plain, ((l_some)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((((((![X316:$i]:(((((in @ X316 @ Z0)))=>((((((Z1 @ X316)))=>(~($true))))))))))=>(~($true))))))), inference(fof_simplification,[status(thm)],[def_l_some])).
0.89/0.61	thf(c_0_33, plain, ((all_of)=(^[Z0/* 19 */:$i > $o, Z1:$i > $o]:(![X4:$i]:((((Z0 @ X4))=>(Z1 @ X4)))))), inference(apply_def,[status(thm)],[c_0_25, c_0_26])).
0.89/0.61	thf(c_0_34, plain, ((non)=(^[Z0/* 19 */:$i, Z1:$i > $o, Z2:$i]:((((((Z1 @ Z2)))=>(~($true))))))), inference(apply_def,[status(thm)],[c_0_27, c_0_22])).
0.89/0.61	thf(c_0_35, plain, ((or3)=(^[Z0/* 19 */:$o, Z1:$o, Z2:$o]:((((((((((Z0))))=>(~($true)))))=>((((((((((Z1))))=>(~($true)))))=>((Z2)))))))))), inference(fof_simplification,[status(thm)],[def_or3])).
0.89/0.61	thf(c_0_36, plain, ((l_or)=(^[Z0/* 19 */:$o, Z1:$o]:((((((((Z0)))=>(~($true)))))=>(Z1))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_28, c_0_20]), c_0_22])).
0.89/0.61	thf(c_0_37, plain, ((ec3)=(^[Z0/* 19 */:$o, Z1:$o, Z2:$o]:((((((((((((((((Z0)))=>(((((((Z1))))=>(~($true)))))))))))=>((((((((((((((((((((((Z1)))=>(((((((Z2))))=>(~($true)))))))))))=>(((((((((((((Z2)))=>(((((((Z0))))=>(~($true))))))))))))=>(~($true)))))))))=>(~($true))))))))=>(~($true)))))))))=>(~($true))))))), inference(fof_simplification,[status(thm)],[def_ec3])).
0.89/0.61	thf(c_0_38, plain, ((and3)=(^[Z0/* 19 */:$o, Z1:$o, Z2:$o]:(((((((((((Z0))))=>(((((((((((((((((Z1))))=>((((((((Z2)))))=>(~($true)))))))))=>(~($true))))))))=>(~($true)))))))))=>(~($true))))))), inference(apply_def,[status(thm)],[c_0_29, c_0_30])).
0.89/0.61	thf(c_0_39, plain, ((diffprop)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:((((Z0)=(n_pl @ Z1 @ Z2)))))), inference(fof_simplification,[status(thm)],[def_diffprop])).
0.89/0.61	thf(c_0_40, axiom, ((n_is)=(^[Z0/* 19 */:$i, Z1:$i]:(((Z0)=(Z1))))), inference(apply_def,[status(thm)],[def_n_is, c_0_31])).
0.89/0.61	thf(c_0_41, plain, ((l_some)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((((((![X316:$i]:(((((in @ X316 @ Z0)))=>((((((Z1 @ X316)))=>(~($true))))))))))=>(~($true))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_32, c_0_33]), c_0_34]), c_0_22])).
0.89/0.61	thf(c_0_42, plain, ((orec3)=(^[Z0/* 19 */:$o, Z1:$o, Z2:$o]:((((((((((((((((((((Z0)))))=>(~($true)))))=>(((((((((((Z1)))))=>(~($true)))))=>(((Z2)))))))))))=>(((((((((((((((((((((((Z0))))=>((((((((Z1)))))=>(~($true)))))))))))=>(((((((((((((((((((((((Z1))))=>((((((((Z2)))))=>(~($true)))))))))))=>((((((((((((((Z2))))=>((((((((Z0)))))=>(~($true))))))))))))=>(~($true)))))))))=>(~($true))))))))=>(~($true)))))))))=>(~($true))))))))=>(~($true)))))))))=>(~($true))))))), inference(fof_simplification,[status(thm)],[def_orec3])).
0.89/0.61	thf(c_0_43, plain, ((or3)=(^[Z0/* 19 */:$o, Z1:$o, Z2:$o]:((((((((((Z0))))=>(~($true)))))=>((((((((((Z1))))=>(~($true)))))=>((Z2)))))))))), inference(apply_def,[status(thm)],[c_0_35, c_0_36])).
0.89/0.61	thf(c_0_44, plain, ((ec3)=(^[Z0/* 19 */:$o, Z1:$o, Z2:$o]:((((((((((((((((Z0)))=>(((((((Z1))))=>(~($true)))))))))))=>((((((((((((((((((((((Z1)))=>(((((((Z2))))=>(~($true)))))))))))=>(((((((((((((Z2)))=>(((((((Z0))))=>(~($true))))))))))))=>(~($true)))))))))=>(~($true))))))))=>(~($true)))))))))=>(~($true))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_37, c_0_38]), c_0_24])).
0.89/0.61	thf(c_0_45, plain, ((diffprop)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:((((Z0)=(n_pl @ Z1 @ Z2)))))), inference(apply_def,[status(thm)],[c_0_39, c_0_40])).
0.89/0.61	thf(c_0_46, axiom, ((n_some)=(^[Z0/* 3 */:$i > $o]:((((((![X325:$i]:(((((in @ X325 @ nat)))=>((((((Z0 @ X325)))=>(~($true))))))))))=>(~($true))))))), inference(apply_def,[status(thm)],[def_n_some, c_0_41])).
0.89/0.61	thf(c_0_47, plain, ((orec3)=(^[Z0/* 19 */:$o, Z1:$o, Z2:$o]:((((((((((((((((((((Z0)))))=>(~($true)))))=>(((((((((((Z1)))))=>(~($true)))))=>(((Z2)))))))))))=>(((((((((((((((((((((((Z0))))=>((((((((Z1)))))=>(~($true)))))))))))=>(((((((((((((((((((((((Z1))))=>((((((((Z2)))))=>(~($true)))))))))))=>((((((((((((((Z2))))=>((((((((Z0)))))=>(~($true))))))))))))=>(~($true)))))))))=>(~($true))))))))=>(~($true)))))))))=>(~($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_30]), c_0_44])).
0.89/0.61	thf(c_0_48, negated_conjecture, ~(![X337:$i]:(((in @ X337 @ nat)=>![X336:$i]:(((in @ X336 @ nat)=>((((X337)=(X336))=>~($true))=>(((![X334:$i]:(((in @ X334 @ nat)=>(((X337)=(n_pl @ X336 @ X334))=>~($true))))=>~($true))=>~($true))=>(![X335:$i]:(((in @ X335 @ nat)=>(((X336)=(n_pl @ X337 @ X335))=>~($true))))=>~($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)],[inference(assume_negation,[status(cth)],[satz9a])]), c_0_43]), c_0_33]), c_0_40]), c_0_45]), c_0_46])).
0.89/0.61	thf(c_0_49, plain, ![X366:$i]:(((in @ X366 @ nat)=>![X365:$i]:(((in @ X365 @ nat)=>((((((X366)=(X365))=>~($true))=>(((![X363:$i]:(((in @ X363 @ nat)=>(((X366)=(n_pl @ X365 @ X363))=>~($true))))=>~($true))=>~($true))=>(![X364:$i]:(((in @ X364 @ nat)=>(((X365)=(n_pl @ X366 @ X364))=>~($true))))=>~($true))))=>((((((X366)=(X365))=>((![X363:$i]:(((in @ X363 @ nat)=>(((X366)=(n_pl @ X365 @ X363))=>~($true))))=>~($true))=>~($true)))=>(((((![X363:$i]:(((in @ X363 @ nat)=>(((X366)=(n_pl @ X365 @ X363))=>~($true))))=>~($true))=>((![X364:$i]:(((in @ X364 @ nat)=>(((X365)=(n_pl @ X366 @ X364))=>~($true))))=>~($true))=>~($true)))=>(((![X364:$i]:(((in @ X364 @ nat)=>(((X365)=(n_pl @ X366 @ X364))=>~($true))))=>~($true))=>(((X366)=(X365))=>~($true)))=>~($true)))=>~($true))=>~($true)))=>~($true))=>~($true)))=>~($true)))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz9]), c_0_33]), c_0_40]), c_0_46]), c_0_47])).
0.89/0.61	thf(c_0_50, negated_conjecture, ![X424:$i, X425:$i]:(((in @ esk1_0 @ nat)&((in @ esk2_0 @ nat)&((((esk1_0)!=(esk2_0))|~($true))&(((~(in @ X424 @ nat)|(((esk1_0)!=(n_pl @ esk2_0 @ X424))|~($true))|~($true))&(($true)|~($true)))&((~(in @ X425 @ nat)|(((esk2_0)!=(n_pl @ esk1_0 @ X425))|~($true)))&($true))))))), 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_48])])])])])])).
0.89/0.61	thf(c_0_51, plain, ![X454:$i, X455:$i, X458:$i, X459:$i, X460:$i, X461:$i]:((((((((in @ (esk4_2 @ X454 @ X455) @ nat)|~($true)|((in @ (esk3_2 @ X454 @ X455) @ nat)|~($true))|((X454)=(X455))|~($true)|~(in @ X455 @ nat)|~(in @ X454 @ nat))&((((X455)=(n_pl @ X454 @ (esk4_2 @ X454 @ X455)))|~($true)|((in @ (esk3_2 @ X454 @ X455) @ nat)|~($true))|((X454)=(X455))|~($true)|~(in @ X455 @ nat)|~(in @ X454 @ nat))&(($true)|~($true)|((in @ (esk3_2 @ X454 @ X455) @ nat)|~($true))|((X454)=(X455))|~($true)|~(in @ X455 @ nat)|~(in @ X454 @ nat))))&((((in @ (esk4_2 @ X454 @ X455) @ nat)|~($true)|(((X454)=(n_pl @ X455 @ (esk3_2 @ X454 @ X455)))|~($true))|((X454)=(X455))|~($true)|~(in @ X455 @ nat)|~(in @ X454 @ nat))&((((X455)=(n_pl @ X454 @ (esk4_2 @ X454 @ X455)))|~($true)|(((X454)=(n_pl @ X455 @ (esk3_2 @ X454 @ X455)))|~($true))|((X454)=(X455))|~($true)|~(in @ X455 @ nat)|~(in @ X454 @ nat))&(($true)|~($true)|(((X454)=(n_pl @ X455 @ (esk3_2 @ X454 @ X455)))|~($true))|((X454)=(X455))|~($true)|~(in @ X455 @ nat)|~(in @ X454 @ nat))))&(((in @ (esk4_2 @ X454 @ X455) @ nat)|~($true)|(($true)|~($true))|((X454)=(X455))|~($true)|~(in @ X455 @ nat)|~(in @ X454 @ nat))&((((X455)=(n_pl @ X454 @ (esk4_2 @ X454 @ X455)))|~($true)|(($true)|~($true))|((X454)=(X455))|~($true)|~(in @ X455 @ nat)|~(in @ X454 @ nat))&(($true)|~($true)|(($true)|~($true))|((X454)=(X455))|~($true)|~(in @ X455 @ nat)|~(in @ X454 @ nat))))))&(((in @ (esk4_2 @ X454 @ X455) @ nat)|~($true)|($true)|((X454)=(X455))|~($true)|~(in @ X455 @ nat)|~(in @ X454 @ nat))&((((X455)=(n_pl @ X454 @ (esk4_2 @ X454 @ X455)))|~($true)|($true)|((X454)=(X455))|~($true)|~(in @ X455 @ nat)|~(in @ X454 @ nat))&(($true)|~($true)|($true)|((X454)=(X455))|~($true)|~(in @ X455 @ nat)|~(in @ X454 @ nat)))))&(((((in @ (esk4_2 @ X454 @ X455) @ nat)|~($true)|((in @ (esk3_2 @ X454 @ X455) @ nat)|~($true))|($true)|~($true)|~(in @ X455 @ nat)|~(in @ X454 @ nat))&((((X455)=(n_pl @ X454 @ (esk4_2 @ X454 @ X455)))|~($true)|((in @ (esk3_2 @ X454 @ X455) @ nat)|~($true))|($true)|~($true)|~(in @ X455 @ nat)|~(in @ X454 @ nat))&(($true)|~($true)|((in @ (esk3_2 @ X454 @ X455) @ nat)|~($true))|($true)|~($true)|~(in @ X455 @ nat)|~(in @ X454 @ nat))))&((((in @ (esk4_2 @ X454 @ X455) @ nat)|~($true)|(((X454)=(n_pl @ X455 @ (esk3_2 @ X454 @ X455)))|~($true))|($true)|~($true)|~(in @ X455 @ nat)|~(in @ X454 @ nat))&((((X455)=(n_pl @ X454 @ (esk4_2 @ X454 @ X455)))|~($true)|(((X454)=(n_pl @ X455 @ (esk3_2 @ X454 @ X455)))|~($true))|($true)|~($true)|~(in @ X455 @ nat)|~(in @ X454 @ nat))&(($true)|~($true)|(((X454)=(n_pl @ X455 @ (esk3_2 @ X454 @ X455)))|~($true))|($true)|~($true)|~(in @ X455 @ nat)|~(in @ X454 @ nat))))&(((in @ (esk4_2 @ X454 @ X455) @ nat)|~($true)|(($true)|~($true))|($true)|~($true)|~(in @ X455 @ nat)|~(in @ X454 @ nat))&((((X455)=(n_pl @ X454 @ (esk4_2 @ X454 @ X455)))|~($true)|(($true)|~($true))|($true)|~($true)|~(in @ X455 @ nat)|~(in @ X454 @ nat))&(($true)|~($true)|(($true)|~($true))|($true)|~($true)|~(in @ X455 @ nat)|~(in @ X454 @ nat))))))&(((in @ (esk4_2 @ X454 @ X455) @ nat)|~($true)|($true)|($true)|~($true)|~(in @ X455 @ nat)|~(in @ X454 @ nat))&((((X455)=(n_pl @ X454 @ (esk4_2 @ X454 @ X455)))|~($true)|($true)|($true)|~($true)|~(in @ X455 @ nat)|~(in @ X454 @ nat))&(($true)|~($true)|($true)|($true)|~($true)|~(in @ X455 @ nat)|~(in @ X454 @ nat))))))&((((~(in @ X458 @ nat)|(((X454)!=(n_pl @ X455 @ X458))|~($true))|~($true)|((X454)!=(X455))|~($true)|~($true)|~(in @ X455 @ nat)|~(in @ X454 @ nat))&(($true)|~($true)|((X454)!=(X455))|~($true)|~($true)|~(in @ X455 @ nat)|~(in @ X454 @ nat)))&(((((~(in @ X460 @ nat)|(((X455)!=(n_pl @ X454 @ X460))|~($true))|~($true)|(~(in @ X459 @ nat)|(((X454)!=(n_pl @ X455 @ X459))|~($true)))|~($true)|~($true)|~($true)|~(in @ X455 @ nat)|~(in @ X454 @ nat))&(($true)|~($true)|(~(in @ X459 @ nat)|(((X454)!=(n_pl @ X455 @ X459))|~($true)))|~($true)|~($true)|~($true)|~(in @ X455 @ nat)|~(in @ X454 @ nat)))&((~(in @ X460 @ nat)|(((X455)!=(n_pl @ X454 @ X460))|~($true))|~($true)|($true)|~($true)|~($true)|~($true)|~(in @ X455 @ nat)|~(in @ X454 @ nat))&(($true)|~($true)|($true)|~($true)|~($true)|~($true)|~(in @ X455 @ nat)|~(in @ X454 @ nat))))&(((~(in @ X461 @ nat)|(((X455)!=(n_pl @ X454 @ X461))|~($true))|(((X454)!=(X455))|~($true))|~($true)|~($true)|~($true)|~(in @ X455 @ nat)|~(in @ X454 @ nat))&(($true)|(((X454)!=(X455))|~($true))|~($true)|~($true)|~($true)|~(in @ X455 @ nat)|~(in @ X454 @ nat)))&(($true)|~($true)|~($true)|~($true)|~(in @ X455 @ nat)|~(in @ X454 @ nat))))&(($true)|~($true)|~($true)|~(in @ X455 @ nat)|~(in @ X454 @ nat))))&(($true)|~($true)|~(in @ X455 @ nat)|~(in @ X454 @ nat))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_49])])])])])])).
0.89/0.61	thf(c_0_52, negated_conjecture, ![X1:$i]:((~((in @ X1 @ nat))|((esk1_0)!=(n_pl @ esk2_0 @ X1))|~(($true))|~(($true)))), inference(split_conjunct,[status(thm)],[c_0_50])).
0.89/0.61	thf(c_0_53, plain, ![X1:$i, X4:$i]:((((X1)=(n_pl @ X4 @ (esk4_2 @ X4 @ X1)))|((X4)=(n_pl @ X1 @ (esk3_2 @ X4 @ X1)))|((X4)=(X1))|~(($true))|~(($true))|~(($true))|~((in @ X1 @ nat))|~((in @ X4 @ nat)))), inference(split_conjunct,[status(thm)],[c_0_51])).
0.89/0.61	thf(c_0_54, negated_conjecture, (((esk1_0)!=(esk2_0))|~(($true))), inference(split_conjunct,[status(thm)],[c_0_50])).
0.89/0.61	thf(c_0_55, plain, ![X1:$i, X4:$i]:((((X1)=(n_pl @ X4 @ (esk4_2 @ X4 @ X1)))|(in @ (esk3_2 @ X4 @ X1) @ nat)|((X4)=(X1))|~(($true))|~(($true))|~(($true))|~((in @ X1 @ nat))|~((in @ X4 @ nat)))), inference(split_conjunct,[status(thm)],[c_0_51])).
0.89/0.61	thf(c_0_56, negated_conjecture, ![X1:$i]:((((esk1_0)!=(n_pl @ esk2_0 @ X1))|~((in @ X1 @ nat)))), inference(cn,[status(thm)],[c_0_52])).
0.89/0.61	thf(c_0_57, plain, ![X4:$i, X1:$i]:((((X1)=(X4))|((X4)=(n_pl @ X1 @ (esk3_2 @ X4 @ X1)))|((X1)=(n_pl @ X4 @ (esk4_2 @ X4 @ X1)))|~((in @ X4 @ nat))|~((in @ X1 @ nat)))), inference(cn,[status(thm)],[c_0_53])).
0.89/0.61	thf(c_0_58, negated_conjecture, (in @ esk2_0 @ nat), inference(split_conjunct,[status(thm)],[c_0_50])).
0.89/0.61	thf(c_0_59, negated_conjecture, (in @ esk1_0 @ nat), inference(split_conjunct,[status(thm)],[c_0_50])).
0.89/0.61	thf(c_0_60, negated_conjecture, ((esk2_0)!=(esk1_0)), inference(cn,[status(thm)],[c_0_54])).
0.89/0.61	thf(c_0_61, plain, ![X4:$i, X1:$i]:(((in @ (esk4_2 @ X1 @ X4) @ nat)|((X1)=(n_pl @ X4 @ (esk3_2 @ X1 @ X4)))|((X1)=(X4))|~(($true))|~(($true))|~(($true))|~((in @ X4 @ nat))|~((in @ X1 @ nat)))), inference(split_conjunct,[status(thm)],[c_0_51])).
0.89/0.61	thf(c_0_62, plain, ![X4:$i, X1:$i]:((((X1)=(X4))|((X1)=(n_pl @ X4 @ (esk4_2 @ X4 @ X1)))|(in @ (esk3_2 @ X4 @ X1) @ nat)|~((in @ X4 @ nat))|~((in @ X1 @ nat)))), inference(cn,[status(thm)],[c_0_55])).
0.89/0.61	thf(c_0_63, plain, ![X4:$i, X1:$i]:(((in @ (esk4_2 @ X1 @ X4) @ nat)|(in @ (esk3_2 @ X1 @ X4) @ nat)|((X1)=(X4))|~(($true))|~(($true))|~(($true))|~((in @ X4 @ nat))|~((in @ X1 @ nat)))), inference(split_conjunct,[status(thm)],[c_0_51])).
0.89/0.61	thf(c_0_64, negated_conjecture, ![X1:$i]:((~((in @ X1 @ nat))|((esk2_0)!=(n_pl @ esk1_0 @ X1))|~(($true)))), inference(split_conjunct,[status(thm)],[c_0_50])).
0.89/0.61	thf(c_0_65, negated_conjecture, (((n_pl @ esk1_0 @ (esk3_2 @ esk2_0 @ esk1_0))=(esk2_0))|~((in @ (esk4_2 @ esk2_0 @ esk1_0) @ nat))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56, c_0_57]), c_0_58])])]), c_0_59])]), c_0_60])).
0.89/0.61	thf(c_0_66, plain, ![X4:$i, X1:$i]:((((X1)=(X4))|((X1)=(n_pl @ X4 @ (esk3_2 @ X1 @ X4)))|(in @ (esk4_2 @ X1 @ X4) @ nat)|~((in @ X4 @ nat))|~((in @ X1 @ nat)))), inference(cn,[status(thm)],[c_0_61])).
0.89/0.61	thf(c_0_67, negated_conjecture, ((in @ (esk3_2 @ esk2_0 @ esk1_0) @ nat)|~((in @ (esk4_2 @ esk2_0 @ esk1_0) @ nat))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56, c_0_62]), c_0_58])])]), c_0_59])]), c_0_60])).
0.89/0.61	thf(c_0_68, plain, ![X4:$i, X1:$i]:((((X1)=(X4))|(in @ (esk3_2 @ X1 @ X4) @ nat)|(in @ (esk4_2 @ X1 @ X4) @ nat)|~((in @ X4 @ nat))|~((in @ X1 @ nat)))), inference(cn,[status(thm)],[c_0_63])).
0.89/0.61	thf(c_0_69, negated_conjecture, ![X1:$i]:((((esk2_0)!=(n_pl @ esk1_0 @ X1))|~((in @ X1 @ nat)))), inference(cn,[status(thm)],[c_0_64])).
0.89/0.61	thf(c_0_70, negated_conjecture, ((n_pl @ esk1_0 @ (esk3_2 @ esk2_0 @ esk1_0))=(esk2_0)), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65, c_0_66]), c_0_59]), c_0_58])]), c_0_60])).
0.89/0.61	thf(c_0_71, negated_conjecture, (in @ (esk3_2 @ esk2_0 @ esk1_0) @ nat), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67, c_0_68]), c_0_59]), c_0_58])]), c_0_60])).
0.89/0.61	thf(c_0_72, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69, c_0_70]), c_0_71])]), ['proof']).
0.89/0.61	# SZS output end CNFRefutation
0.89/0.61	# Parsed axioms                        : 338
0.89/0.61	# Removed by relevancy pruning/SinE    : 219
0.89/0.61	# Initial clauses                      : 202
0.89/0.61	# Removed in clause preprocessing      : 58
0.89/0.61	# Initial clauses in saturation        : 144
0.89/0.61	# Processed clauses                    : 333
0.89/0.61	# ...of these trivial                  : 5
0.89/0.61	# ...subsumed                          : 49
0.89/0.61	# ...remaining for further processing  : 279
0.89/0.61	# Other redundant clauses eliminated   : 27
0.89/0.61	# Clauses deleted for lack of memory   : 0
0.89/0.61	# Backward-subsumed                    : 1
0.89/0.61	# Backward-rewritten                   : 4
0.89/0.61	# Generated clauses                    : 770
0.89/0.61	# ...of the previous two non-redundant : 720
0.89/0.61	# ...aggressively subsumed             : 0
0.89/0.61	# Contextual simplify-reflections      : 3
0.89/0.61	# Paramodulations                      : 670
0.89/0.61	# Factorizations                       : 2
0.89/0.61	# NegExts                              : 0
0.89/0.61	# Equation resolutions                 : 32
0.89/0.61	# Disequality decompositions           : 0
0.89/0.61	# Total rewrite steps                  : 120
0.89/0.61	# ...of those cached                   : 102
0.89/0.61	# Propositional unsat checks           : 0
0.89/0.61	#    Propositional check models        : 0
0.89/0.61	#    Propositional check unsatisfiable : 0
0.89/0.61	#    Propositional clauses             : 0
0.89/0.61	#    Propositional clauses after purity: 0
0.89/0.61	#    Propositional unsat core size     : 0
0.89/0.61	#    Propositional preprocessing time  : 0.000
0.89/0.61	#    Propositional encoding time       : 0.000
0.89/0.61	#    Propositional solver time         : 0.000
0.89/0.61	#    Success case prop preproc time    : 0.000
0.89/0.61	#    Success case prop encoding time   : 0.000
0.89/0.61	#    Success case prop solver time     : 0.000
0.89/0.61	# Current number of processed clauses  : 141
0.89/0.61	#    Positive orientable unit clauses  : 35
0.89/0.61	#    Positive unorientable unit clauses: 7
0.89/0.61	#    Negative unit clauses             : 6
0.89/0.61	#    Non-unit-clauses                  : 93
0.89/0.61	# Current number of unprocessed clauses: 653
0.89/0.61	# ...number of literals in the above   : 2449
0.89/0.61	# Current number of archived formulas  : 0
0.89/0.61	# Current number of archived clauses   : 133
0.89/0.61	# Clause-clause subsumption calls (NU) : 4607
0.89/0.61	# Rec. Clause-clause subsumption calls : 1335
0.89/0.61	# Non-unit clause-clause subsumptions  : 41
0.89/0.61	# Unit Clause-clause subsumption calls : 134
0.89/0.61	# Rewrite failures with RHS unbound    : 32
0.89/0.61	# BW rewrite match attempts            : 30
0.89/0.61	# BW rewrite match successes           : 8
0.89/0.61	# Condensation attempts                : 0
0.89/0.61	# Condensation successes               : 0
0.89/0.61	# Termbank termtop insertions          : 50357
0.89/0.61	# Search garbage collected termcells   : 9927
0.89/0.61	
0.89/0.61	# -------------------------------------------------
0.89/0.61	# User time                : 0.069 s
0.89/0.61	# System time              : 0.009 s
0.89/0.61	# Total time               : 0.078 s
0.89/0.61	# Maximum resident set size: 4072 pages
0.89/0.61	
0.89/0.61	# -------------------------------------------------
0.89/0.61	# User time                : 0.079 s
0.89/0.61	# System time              : 0.010 s
0.89/0.61	# Total time               : 0.089 s
0.89/0.61	# Maximum resident set size: 2192 pages
0.89/0.61	% E exiting
0.89/0.61	% E exiting
0.89/0.62	EOF