TSTP Solution File: SWV385+1 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SWV385+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 13:39:31 EDT 2022
% Result : Theorem 0.18s 0.49s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV385+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : goeland -dmt -presko -proof %s
% 0.12/0.33 % Computer : n001.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 : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Sep 4 03:10:27 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 [DMT] DMT loaded with preskolemization
% 0.12/0.34 [EQ] equality loaded.
% 0.12/0.34 [0.000037s][1][MAIN] Problem : theBenchmark.p
% 0.12/0.34 Conjecture not found
% 0.12/0.35 Conjecture not found
% 0.12/0.35 Conjecture not found
% 0.12/0.35 Start search
% 0.12/0.35 nb_step : 1 - limit : 43
% 0.12/0.35 Launch Gotab with destructive = true
% 0.18/0.48 % SZS output start Proof for theBenchmark.p
% 0.18/0.48 [0] ALPHA_AND : ((! [U3_3, V4_4, W5_5] : (((less_than(U3_3, V4_4) & less_than(V4_4, W5_5)) => less_than(U3_3, W5_5))) & ! [U6_6, V7_7] : ((less_than(U6_6, V7_7) | less_than(V7_7, U6_6))) & ! [U8_8] : (less_than(U8_8, U8_8)) & ! [U11_11] : (less_than(bottom, U11_11))) & (~isnonempty_slb(create_slb) & ! [U14_14, V15_15, W16_16] : (isnonempty_slb(insert_slb(U14_14, pair(V15_15, W16_16)))) & ! [U17_17] : (~contains_slb(create_slb, U17_17)) & ! [U22_22, V23_23] : (~pair_in_list(create_slb, U22_22, V23_23)) & ! [U29_29, V30_30, W31_31] : (=(remove_slb(insert_slb(U29_29, pair(V30_30, W31_31)), V30_30), U29_29)) & ! [U32_32, V33_33, W34_34, X35_35] : (((~=(V33_33, W34_34) & contains_slb(U32_32, W34_34)) => =(remove_slb(insert_slb(U32_32, pair(V33_33, X35_35)), W34_34), insert_slb(remove_slb(U32_32, W34_34), pair(V33_33, X35_35))))) & ! [U36_36, V37_37, W38_38] : (=(lookup_slb(insert_slb(U36_36, pair(V37_37, W38_38)), V37_37), W38_38)) & ! [U39_39, V40_40, W41_41, X42_42] : (((~=(V40_40, W41_41) & contains_slb(U39_39, W41_41)) => =(lookup_slb(insert_slb(U39_39, pair(V40_40, X42_42)), W41_41), lookup_slb(U39_39, W41_41)))) & ! [U43_43] : (=(update_slb(create_slb, U43_43), create_slb)) & ! [U44_44, V45_45, W46_46, X47_47] : ((strictly_less_than(X47_47, W46_46) => =(update_slb(insert_slb(U44_44, pair(V45_45, X47_47)), W46_46), insert_slb(update_slb(U44_44, W46_46), pair(V45_45, W46_46))))) & ! [U48_48, V49_49, W50_50, X51_51] : ((less_than(W50_50, X51_51) => =(update_slb(insert_slb(U48_48, pair(V49_49, X51_51)), W50_50), insert_slb(update_slb(U48_48, W50_50), pair(V49_49, X51_51)))))) & (! [U52_52] : (succ_cpq(U52_52, U52_52)) & ! [U53_53, V54_54, W55_55] : ((succ_cpq(U53_53, V54_54) => succ_cpq(U53_53, insert_cpq(V54_54, W55_55)))) & ! [U56_56, V57_57, W58_58] : ((succ_cpq(U56_56, V57_57) => succ_cpq(U56_56, remove_cpq(V57_57, W58_58)))) & ! [U59_59, V60_60] : ((succ_cpq(U59_59, V60_60) => succ_cpq(U59_59, findmin_cpq_eff(V60_60)))) & ! [U61_61, V62_62] : ((succ_cpq(U61_61, V62_62) => succ_cpq(U61_61, removemin_cpq_eff(V62_62)))) & ! [U63_63, V64_64] : (check_cpq(triple(U63_63, create_slb, V64_64))) & ! [U65_65, V66_66, W67_67, X68_68, Y69_69] : ((less_than(Y69_69, X68_68) => (check_cpq(triple(U65_65, insert_slb(V66_66, pair(X68_68, Y69_69)), W67_67)) <=> check_cpq(triple(U65_65, V66_66, W67_67))))) & ! [U70_70, V71_71, W72_72, X73_73, Y74_74] : ((strictly_less_than(X73_73, Y74_74) => (check_cpq(triple(U70_70, insert_slb(V71_71, pair(X73_73, Y74_74)), W72_72)) <=> $false))) & ! [U75_75, V76_76, W77_77, X78_78] : ((contains_cpq(triple(U75_75, V76_76, W77_77), X78_78) <=> contains_slb(V76_76, X78_78))) & ! [U79_79, V80_80] : ((ok(triple(U79_79, V80_80, bad)) <=> $false)) & ! [U81_81, V82_82, W83_83] : ((~ok(triple(U81_81, V82_82, W83_83)) => =(W83_83, bad))) & ! [U84_84, V85_85, W86_86, X87_87] : (=(insert_cpq(triple(U84_84, V85_85, W86_86), X87_87), triple(insert_pqp(U84_84, X87_87), insert_slb(V85_85, pair(X87_87, bottom)), W86_86))) & ! [U88_88, V89_89, W90_90, X91_91] : ((~contains_slb(V89_89, X91_91) => =(remove_cpq(triple(U88_88, V89_89, W90_90), X91_91), triple(U88_88, V89_89, bad)))) & ! [U92_92, V93_93, W94_94, X95_95] : (((contains_slb(V93_93, X95_95) & less_than(lookup_slb(V93_93, X95_95), X95_95)) => =(remove_cpq(triple(U92_92, V93_93, W94_94), X95_95), triple(remove_pqp(U92_92, X95_95), remove_slb(V93_93, X95_95), W94_94)))) & ! [U96_96, V97_97, W98_98, X99_99] : (((contains_slb(V97_97, X99_99) & strictly_less_than(X99_99, lookup_slb(V97_97, X99_99))) => =(remove_cpq(triple(U96_96, V97_97, W98_98), X99_99), triple(remove_pqp(U96_96, X99_99), remove_slb(V97_97, X99_99), bad)))) & ! [U100_100, V101_101] : (=(findmin_cpq_eff(triple(U100_100, create_slb, V101_101)), triple(U100_100, create_slb, bad))) & ! [U102_102, V103_103, W104_104, X105_105] : (((~=(V103_103, create_slb) & ~contains_slb(V103_103, findmin_pqp_res(U102_102))) => =(findmin_cpq_eff(triple(U102_102, V103_103, W104_104)), triple(U102_102, update_slb(V103_103, findmin_pqp_res(U102_102)), bad)))) & ! [U106_106, V107_107, W108_108, X109_109] : ((((~=(V107_107, create_slb) & contains_slb(V107_107, findmin_pqp_res(U106_106))) & strictly_less_than(findmin_pqp_res(U106_106), lookup_slb(V107_107, findmin_pqp_res(U106_106)))) => =(findmin_cpq_eff(triple(U106_106, V107_107, W108_108)), triple(U106_106, update_slb(V107_107, findmin_pqp_res(U106_106)), bad)))) & ! [U110_110, V111_111, W112_112, X113_113] : ((((~=(V111_111, create_slb) & contains_slb(V111_111, findmin_pqp_res(U110_110))) & less_than(lookup_slb(V111_111, findmin_pqp_res(U110_110)), findmin_pqp_res(U110_110))) => =(findmin_cpq_eff(triple(U110_110, V111_111, W112_112)), triple(U110_110, update_slb(V111_111, findmin_pqp_res(U110_110)), W112_112)))) & ! [U114_114, V115_115] : (=(findmin_cpq_res(triple(U114_114, create_slb, V115_115)), bottom)) & ! [U116_116, V117_117, W118_118, X119_119] : ((~=(V117_117, create_slb) => =(findmin_cpq_res(triple(U116_116, V117_117, W118_118)), findmin_pqp_res(U116_116)))) & ! [U120_120] : (=(removemin_cpq_eff(U120_120), remove_cpq(findmin_cpq_eff(U120_120), findmin_cpq_res(U120_120)))) & ! [U121_121] : (=(removemin_cpq_res(U121_121), findmin_cpq_res(U121_121)))) & ! [U122_122, V123_123, W124_124] : ((~ok(triple(U122_122, V123_123, W124_124)) => ~ok(im_succ_cpq(triple(U122_122, V123_123, W124_124))))) & ! [U125_125, V126_126, W127_127] : ((~check_cpq(triple(U125_125, V126_126, W127_127)) => (~check_cpq(im_succ_cpq(triple(U125_125, V126_126, W127_127))) | ~ok(im_succ_cpq(triple(U125_125, V126_126, W127_127)))))) & ~! [U128_128, V129_129, W130_130] : (((~check_cpq(triple(U128_128, V129_129, W130_130)) | ~ok(triple(U128_128, V129_129, W130_130))) => (~check_cpq(im_succ_cpq(triple(U128_128, V129_129, W130_130))) | ~ok(im_succ_cpq(triple(U128_128, V129_129, W130_130)))))))
% 0.18/0.48 -> [1] (! [U3_3, V4_4, W5_5] : (((less_than(U3_3, V4_4) & less_than(V4_4, W5_5)) => less_than(U3_3, W5_5))) & ! [U6_6, V7_7] : ((less_than(U6_6, V7_7) | less_than(V7_7, U6_6))) & ! [U8_8] : (less_than(U8_8, U8_8)) & ! [U11_11] : (less_than(bottom, U11_11))), (~isnonempty_slb(create_slb) & ! [U14_14, V15_15, W16_16] : (isnonempty_slb(insert_slb(U14_14, pair(V15_15, W16_16)))) & ! [U17_17] : (~contains_slb(create_slb, U17_17)) & ! [U22_22, V23_23] : (~pair_in_list(create_slb, U22_22, V23_23)) & ! [U29_29, V30_30, W31_31] : (=(remove_slb(insert_slb(U29_29, pair(V30_30, W31_31)), V30_30), U29_29)) & ! [U32_32, V33_33, W34_34, X35_35] : (((~=(V33_33, W34_34) & contains_slb(U32_32, W34_34)) => =(remove_slb(insert_slb(U32_32, pair(V33_33, X35_35)), W34_34), insert_slb(remove_slb(U32_32, W34_34), pair(V33_33, X35_35))))) & ! [U36_36, V37_37, W38_38] : (=(lookup_slb(insert_slb(U36_36, pair(V37_37, W38_38)), V37_37), W38_38)) & ! [U39_39, V40_40, W41_41, X42_42] : (((~=(V40_40, W41_41) & contains_slb(U39_39, W41_41)) => =(lookup_slb(insert_slb(U39_39, pair(V40_40, X42_42)), W41_41), lookup_slb(U39_39, W41_41)))) & ! [U43_43] : (=(update_slb(create_slb, U43_43), create_slb)) & ! [U44_44, V45_45, W46_46, X47_47] : ((strictly_less_than(X47_47, W46_46) => =(update_slb(insert_slb(U44_44, pair(V45_45, X47_47)), W46_46), insert_slb(update_slb(U44_44, W46_46), pair(V45_45, W46_46))))) & ! [U48_48, V49_49, W50_50, X51_51] : ((less_than(W50_50, X51_51) => =(update_slb(insert_slb(U48_48, pair(V49_49, X51_51)), W50_50), insert_slb(update_slb(U48_48, W50_50), pair(V49_49, X51_51)))))), (! [U52_52] : (succ_cpq(U52_52, U52_52)) & ! [U53_53, V54_54, W55_55] : ((succ_cpq(U53_53, V54_54) => succ_cpq(U53_53, insert_cpq(V54_54, W55_55)))) & ! [U56_56, V57_57, W58_58] : ((succ_cpq(U56_56, V57_57) => succ_cpq(U56_56, remove_cpq(V57_57, W58_58)))) & ! [U59_59, V60_60] : ((succ_cpq(U59_59, V60_60) => succ_cpq(U59_59, findmin_cpq_eff(V60_60)))) & ! [U61_61, V62_62] : ((succ_cpq(U61_61, V62_62) => succ_cpq(U61_61, removemin_cpq_eff(V62_62)))) & ! [U63_63, V64_64] : (check_cpq(triple(U63_63, create_slb, V64_64))) & ! [U65_65, V66_66, W67_67, X68_68, Y69_69] : ((less_than(Y69_69, X68_68) => (check_cpq(triple(U65_65, insert_slb(V66_66, pair(X68_68, Y69_69)), W67_67)) <=> check_cpq(triple(U65_65, V66_66, W67_67))))) & ! [U70_70, V71_71, W72_72, X73_73, Y74_74] : ((strictly_less_than(X73_73, Y74_74) => (check_cpq(triple(U70_70, insert_slb(V71_71, pair(X73_73, Y74_74)), W72_72)) <=> $false))) & ! [U75_75, V76_76, W77_77, X78_78] : ((contains_cpq(triple(U75_75, V76_76, W77_77), X78_78) <=> contains_slb(V76_76, X78_78))) & ! [U79_79, V80_80] : ((ok(triple(U79_79, V80_80, bad)) <=> $false)) & ! [U81_81, V82_82, W83_83] : ((~ok(triple(U81_81, V82_82, W83_83)) => =(W83_83, bad))) & ! [U84_84, V85_85, W86_86, X87_87] : (=(insert_cpq(triple(U84_84, V85_85, W86_86), X87_87), triple(insert_pqp(U84_84, X87_87), insert_slb(V85_85, pair(X87_87, bottom)), W86_86))) & ! [U88_88, V89_89, W90_90, X91_91] : ((~contains_slb(V89_89, X91_91) => =(remove_cpq(triple(U88_88, V89_89, W90_90), X91_91), triple(U88_88, V89_89, bad)))) & ! [U92_92, V93_93, W94_94, X95_95] : (((contains_slb(V93_93, X95_95) & less_than(lookup_slb(V93_93, X95_95), X95_95)) => =(remove_cpq(triple(U92_92, V93_93, W94_94), X95_95), triple(remove_pqp(U92_92, X95_95), remove_slb(V93_93, X95_95), W94_94)))) & ! [U96_96, V97_97, W98_98, X99_99] : (((contains_slb(V97_97, X99_99) & strictly_less_than(X99_99, lookup_slb(V97_97, X99_99))) => =(remove_cpq(triple(U96_96, V97_97, W98_98), X99_99), triple(remove_pqp(U96_96, X99_99), remove_slb(V97_97, X99_99), bad)))) & ! [U100_100, V101_101] : (=(findmin_cpq_eff(triple(U100_100, create_slb, V101_101)), triple(U100_100, create_slb, bad))) & ! [U102_102, V103_103, W104_104, X105_105] : (((~=(V103_103, create_slb) & ~contains_slb(V103_103, findmin_pqp_res(U102_102))) => =(findmin_cpq_eff(triple(U102_102, V103_103, W104_104)), triple(U102_102, update_slb(V103_103, findmin_pqp_res(U102_102)), bad)))) & ! [U106_106, V107_107, W108_108, X109_109] : ((((~=(V107_107, create_slb) & contains_slb(V107_107, findmin_pqp_res(U106_106))) & strictly_less_than(findmin_pqp_res(U106_106), lookup_slb(V107_107, findmin_pqp_res(U106_106)))) => =(findmin_cpq_eff(triple(U106_106, V107_107, W108_108)), triple(U106_106, update_slb(V107_107, findmin_pqp_res(U106_106)), bad)))) & ! [U110_110, V111_111, W112_112, X113_113] : ((((~=(V111_111, create_slb) & contains_slb(V111_111, findmin_pqp_res(U110_110))) & less_than(lookup_slb(V111_111, findmin_pqp_res(U110_110)), findmin_pqp_res(U110_110))) => =(findmin_cpq_eff(triple(U110_110, V111_111, W112_112)), triple(U110_110, update_slb(V111_111, findmin_pqp_res(U110_110)), W112_112)))) & ! [U114_114, V115_115] : (=(findmin_cpq_res(triple(U114_114, create_slb, V115_115)), bottom)) & ! [U116_116, V117_117, W118_118, X119_119] : ((~=(V117_117, create_slb) => =(findmin_cpq_res(triple(U116_116, V117_117, W118_118)), findmin_pqp_res(U116_116)))) & ! [U120_120] : (=(removemin_cpq_eff(U120_120), remove_cpq(findmin_cpq_eff(U120_120), findmin_cpq_res(U120_120)))) & ! [U121_121] : (=(removemin_cpq_res(U121_121), findmin_cpq_res(U121_121)))), ! [U122_122, V123_123, W124_124] : ((~ok(triple(U122_122, V123_123, W124_124)) => ~ok(im_succ_cpq(triple(U122_122, V123_123, W124_124))))), ! [U125_125, V126_126, W127_127] : ((~check_cpq(triple(U125_125, V126_126, W127_127)) => (~check_cpq(im_succ_cpq(triple(U125_125, V126_126, W127_127))) | ~ok(im_succ_cpq(triple(U125_125, V126_126, W127_127)))))), ~! [U128_128, V129_129, W130_130] : (((~check_cpq(triple(U128_128, V129_129, W130_130)) | ~ok(triple(U128_128, V129_129, W130_130))) => (~check_cpq(im_succ_cpq(triple(U128_128, V129_129, W130_130))) | ~ok(im_succ_cpq(triple(U128_128, V129_129, W130_130))))))
% 0.18/0.48
% 0.18/0.48 [1] ALPHA_AND : (! [U3_3, V4_4, W5_5] : (((less_than(U3_3, V4_4) & less_than(V4_4, W5_5)) => less_than(U3_3, W5_5))) & ! [U6_6, V7_7] : ((less_than(U6_6, V7_7) | less_than(V7_7, U6_6))) & ! [U8_8] : (less_than(U8_8, U8_8)) & ! [U11_11] : (less_than(bottom, U11_11)))
% 0.18/0.48 -> [2] ! [U3_3, V4_4, W5_5] : (((less_than(U3_3, V4_4) & less_than(V4_4, W5_5)) => less_than(U3_3, W5_5))), ! [U6_6, V7_7] : ((less_than(U6_6, V7_7) | less_than(V7_7, U6_6))), ! [U8_8] : (less_than(U8_8, U8_8)), ! [U11_11] : (less_than(bottom, U11_11))
% 0.18/0.48
% 0.18/0.48 [2] ALPHA_AND : (~isnonempty_slb(create_slb) & ! [U14_14, V15_15, W16_16] : (isnonempty_slb(insert_slb(U14_14, pair(V15_15, W16_16)))) & ! [U17_17] : (~contains_slb(create_slb, U17_17)) & ! [U22_22, V23_23] : (~pair_in_list(create_slb, U22_22, V23_23)) & ! [U29_29, V30_30, W31_31] : (=(remove_slb(insert_slb(U29_29, pair(V30_30, W31_31)), V30_30), U29_29)) & ! [U32_32, V33_33, W34_34, X35_35] : (((~=(V33_33, W34_34) & contains_slb(U32_32, W34_34)) => =(remove_slb(insert_slb(U32_32, pair(V33_33, X35_35)), W34_34), insert_slb(remove_slb(U32_32, W34_34), pair(V33_33, X35_35))))) & ! [U36_36, V37_37, W38_38] : (=(lookup_slb(insert_slb(U36_36, pair(V37_37, W38_38)), V37_37), W38_38)) & ! [U39_39, V40_40, W41_41, X42_42] : (((~=(V40_40, W41_41) & contains_slb(U39_39, W41_41)) => =(lookup_slb(insert_slb(U39_39, pair(V40_40, X42_42)), W41_41), lookup_slb(U39_39, W41_41)))) & ! [U43_43] : (=(update_slb(create_slb, U43_43), create_slb)) & ! [U44_44, V45_45, W46_46, X47_47] : ((strictly_less_than(X47_47, W46_46) => =(update_slb(insert_slb(U44_44, pair(V45_45, X47_47)), W46_46), insert_slb(update_slb(U44_44, W46_46), pair(V45_45, W46_46))))) & ! [U48_48, V49_49, W50_50, X51_51] : ((less_than(W50_50, X51_51) => =(update_slb(insert_slb(U48_48, pair(V49_49, X51_51)), W50_50), insert_slb(update_slb(U48_48, W50_50), pair(V49_49, X51_51))))))
% 0.18/0.48 -> [3] ~isnonempty_slb(create_slb), ! [U14_14, V15_15, W16_16] : (isnonempty_slb(insert_slb(U14_14, pair(V15_15, W16_16)))), ! [U17_17] : (~contains_slb(create_slb, U17_17)), ! [U22_22, V23_23] : (~pair_in_list(create_slb, U22_22, V23_23)), ! [U29_29, V30_30, W31_31] : (=(remove_slb(insert_slb(U29_29, pair(V30_30, W31_31)), V30_30), U29_29)), ! [U32_32, V33_33, W34_34, X35_35] : (((~=(V33_33, W34_34) & contains_slb(U32_32, W34_34)) => =(remove_slb(insert_slb(U32_32, pair(V33_33, X35_35)), W34_34), insert_slb(remove_slb(U32_32, W34_34), pair(V33_33, X35_35))))), ! [U36_36, V37_37, W38_38] : (=(lookup_slb(insert_slb(U36_36, pair(V37_37, W38_38)), V37_37), W38_38)), ! [U39_39, V40_40, W41_41, X42_42] : (((~=(V40_40, W41_41) & contains_slb(U39_39, W41_41)) => =(lookup_slb(insert_slb(U39_39, pair(V40_40, X42_42)), W41_41), lookup_slb(U39_39, W41_41)))), ! [U43_43] : (=(update_slb(create_slb, U43_43), create_slb)), ! [U44_44, V45_45, W46_46, X47_47] : ((strictly_less_than(X47_47, W46_46) => =(update_slb(insert_slb(U44_44, pair(V45_45, X47_47)), W46_46), insert_slb(update_slb(U44_44, W46_46), pair(V45_45, W46_46))))), ! [U48_48, V49_49, W50_50, X51_51] : ((less_than(W50_50, X51_51) => =(update_slb(insert_slb(U48_48, pair(V49_49, X51_51)), W50_50), insert_slb(update_slb(U48_48, W50_50), pair(V49_49, X51_51)))))
% 0.18/0.48
% 0.18/0.48 [3] ALPHA_AND : (! [U52_52] : (succ_cpq(U52_52, U52_52)) & ! [U53_53, V54_54, W55_55] : ((succ_cpq(U53_53, V54_54) => succ_cpq(U53_53, insert_cpq(V54_54, W55_55)))) & ! [U56_56, V57_57, W58_58] : ((succ_cpq(U56_56, V57_57) => succ_cpq(U56_56, remove_cpq(V57_57, W58_58)))) & ! [U59_59, V60_60] : ((succ_cpq(U59_59, V60_60) => succ_cpq(U59_59, findmin_cpq_eff(V60_60)))) & ! [U61_61, V62_62] : ((succ_cpq(U61_61, V62_62) => succ_cpq(U61_61, removemin_cpq_eff(V62_62)))) & ! [U63_63, V64_64] : (check_cpq(triple(U63_63, create_slb, V64_64))) & ! [U65_65, V66_66, W67_67, X68_68, Y69_69] : ((less_than(Y69_69, X68_68) => (check_cpq(triple(U65_65, insert_slb(V66_66, pair(X68_68, Y69_69)), W67_67)) <=> check_cpq(triple(U65_65, V66_66, W67_67))))) & ! [U70_70, V71_71, W72_72, X73_73, Y74_74] : ((strictly_less_than(X73_73, Y74_74) => (check_cpq(triple(U70_70, insert_slb(V71_71, pair(X73_73, Y74_74)), W72_72)) <=> $false))) & ! [U75_75, V76_76, W77_77, X78_78] : ((contains_cpq(triple(U75_75, V76_76, W77_77), X78_78) <=> contains_slb(V76_76, X78_78))) & ! [U79_79, V80_80] : ((ok(triple(U79_79, V80_80, bad)) <=> $false)) & ! [U81_81, V82_82, W83_83] : ((~ok(triple(U81_81, V82_82, W83_83)) => =(W83_83, bad))) & ! [U84_84, V85_85, W86_86, X87_87] : (=(insert_cpq(triple(U84_84, V85_85, W86_86), X87_87), triple(insert_pqp(U84_84, X87_87), insert_slb(V85_85, pair(X87_87, bottom)), W86_86))) & ! [U88_88, V89_89, W90_90, X91_91] : ((~contains_slb(V89_89, X91_91) => =(remove_cpq(triple(U88_88, V89_89, W90_90), X91_91), triple(U88_88, V89_89, bad)))) & ! [U92_92, V93_93, W94_94, X95_95] : (((contains_slb(V93_93, X95_95) & less_than(lookup_slb(V93_93, X95_95), X95_95)) => =(remove_cpq(triple(U92_92, V93_93, W94_94), X95_95), triple(remove_pqp(U92_92, X95_95), remove_slb(V93_93, X95_95), W94_94)))) & ! [U96_96, V97_97, W98_98, X99_99] : (((contains_slb(V97_97, X99_99) & strictly_less_than(X99_99, lookup_slb(V97_97, X99_99))) => =(remove_cpq(triple(U96_96, V97_97, W98_98), X99_99), triple(remove_pqp(U96_96, X99_99), remove_slb(V97_97, X99_99), bad)))) & ! [U100_100, V101_101] : (=(findmin_cpq_eff(triple(U100_100, create_slb, V101_101)), triple(U100_100, create_slb, bad))) & ! [U102_102, V103_103, W104_104, X105_105] : (((~=(V103_103, create_slb) & ~contains_slb(V103_103, findmin_pqp_res(U102_102))) => =(findmin_cpq_eff(triple(U102_102, V103_103, W104_104)), triple(U102_102, update_slb(V103_103, findmin_pqp_res(U102_102)), bad)))) & ! [U106_106, V107_107, W108_108, X109_109] : ((((~=(V107_107, create_slb) & contains_slb(V107_107, findmin_pqp_res(U106_106))) & strictly_less_than(findmin_pqp_res(U106_106), lookup_slb(V107_107, findmin_pqp_res(U106_106)))) => =(findmin_cpq_eff(triple(U106_106, V107_107, W108_108)), triple(U106_106, update_slb(V107_107, findmin_pqp_res(U106_106)), bad)))) & ! [U110_110, V111_111, W112_112, X113_113] : ((((~=(V111_111, create_slb) & contains_slb(V111_111, findmin_pqp_res(U110_110))) & less_than(lookup_slb(V111_111, findmin_pqp_res(U110_110)), findmin_pqp_res(U110_110))) => =(findmin_cpq_eff(triple(U110_110, V111_111, W112_112)), triple(U110_110, update_slb(V111_111, findmin_pqp_res(U110_110)), W112_112)))) & ! [U114_114, V115_115] : (=(findmin_cpq_res(triple(U114_114, create_slb, V115_115)), bottom)) & ! [U116_116, V117_117, W118_118, X119_119] : ((~=(V117_117, create_slb) => =(findmin_cpq_res(triple(U116_116, V117_117, W118_118)), findmin_pqp_res(U116_116)))) & ! [U120_120] : (=(removemin_cpq_eff(U120_120), remove_cpq(findmin_cpq_eff(U120_120), findmin_cpq_res(U120_120)))) & ! [U121_121] : (=(removemin_cpq_res(U121_121), findmin_cpq_res(U121_121))))
% 0.18/0.48 -> [4] ! [U52_52] : (succ_cpq(U52_52, U52_52)), ! [U53_53, V54_54, W55_55] : ((succ_cpq(U53_53, V54_54) => succ_cpq(U53_53, insert_cpq(V54_54, W55_55)))), ! [U56_56, V57_57, W58_58] : ((succ_cpq(U56_56, V57_57) => succ_cpq(U56_56, remove_cpq(V57_57, W58_58)))), ! [U59_59, V60_60] : ((succ_cpq(U59_59, V60_60) => succ_cpq(U59_59, findmin_cpq_eff(V60_60)))), ! [U61_61, V62_62] : ((succ_cpq(U61_61, V62_62) => succ_cpq(U61_61, removemin_cpq_eff(V62_62)))), ! [U63_63, V64_64] : (check_cpq(triple(U63_63, create_slb, V64_64))), ! [U65_65, V66_66, W67_67, X68_68, Y69_69] : ((less_than(Y69_69, X68_68) => (check_cpq(triple(U65_65, insert_slb(V66_66, pair(X68_68, Y69_69)), W67_67)) <=> check_cpq(triple(U65_65, V66_66, W67_67))))), ! [U70_70, V71_71, W72_72, X73_73, Y74_74] : ((strictly_less_than(X73_73, Y74_74) => (check_cpq(triple(U70_70, insert_slb(V71_71, pair(X73_73, Y74_74)), W72_72)) <=> $false))), ! [U75_75, V76_76, W77_77, X78_78] : ((contains_cpq(triple(U75_75, V76_76, W77_77), X78_78) <=> contains_slb(V76_76, X78_78))), ! [U79_79, V80_80] : ((ok(triple(U79_79, V80_80, bad)) <=> $false)), ! [U81_81, V82_82, W83_83] : ((~ok(triple(U81_81, V82_82, W83_83)) => =(W83_83, bad))), ! [U84_84, V85_85, W86_86, X87_87] : (=(insert_cpq(triple(U84_84, V85_85, W86_86), X87_87), triple(insert_pqp(U84_84, X87_87), insert_slb(V85_85, pair(X87_87, bottom)), W86_86))), ! [U88_88, V89_89, W90_90, X91_91] : ((~contains_slb(V89_89, X91_91) => =(remove_cpq(triple(U88_88, V89_89, W90_90), X91_91), triple(U88_88, V89_89, bad)))), ! [U92_92, V93_93, W94_94, X95_95] : (((contains_slb(V93_93, X95_95) & less_than(lookup_slb(V93_93, X95_95), X95_95)) => =(remove_cpq(triple(U92_92, V93_93, W94_94), X95_95), triple(remove_pqp(U92_92, X95_95), remove_slb(V93_93, X95_95), W94_94)))), ! [U96_96, V97_97, W98_98, X99_99] : (((contains_slb(V97_97, X99_99) & strictly_less_than(X99_99, lookup_slb(V97_97, X99_99))) => =(remove_cpq(triple(U96_96, V97_97, W98_98), X99_99), triple(remove_pqp(U96_96, X99_99), remove_slb(V97_97, X99_99), bad)))), ! [U100_100, V101_101] : (=(findmin_cpq_eff(triple(U100_100, create_slb, V101_101)), triple(U100_100, create_slb, bad))), ! [U102_102, V103_103, W104_104, X105_105] : (((~=(V103_103, create_slb) & ~contains_slb(V103_103, findmin_pqp_res(U102_102))) => =(findmin_cpq_eff(triple(U102_102, V103_103, W104_104)), triple(U102_102, update_slb(V103_103, findmin_pqp_res(U102_102)), bad)))), ! [U106_106, V107_107, W108_108, X109_109] : ((((~=(V107_107, create_slb) & contains_slb(V107_107, findmin_pqp_res(U106_106))) & strictly_less_than(findmin_pqp_res(U106_106), lookup_slb(V107_107, findmin_pqp_res(U106_106)))) => =(findmin_cpq_eff(triple(U106_106, V107_107, W108_108)), triple(U106_106, update_slb(V107_107, findmin_pqp_res(U106_106)), bad)))), ! [U110_110, V111_111, W112_112, X113_113] : ((((~=(V111_111, create_slb) & contains_slb(V111_111, findmin_pqp_res(U110_110))) & less_than(lookup_slb(V111_111, findmin_pqp_res(U110_110)), findmin_pqp_res(U110_110))) => =(findmin_cpq_eff(triple(U110_110, V111_111, W112_112)), triple(U110_110, update_slb(V111_111, findmin_pqp_res(U110_110)), W112_112)))), ! [U114_114, V115_115] : (=(findmin_cpq_res(triple(U114_114, create_slb, V115_115)), bottom)), ! [U116_116, V117_117, W118_118, X119_119] : ((~=(V117_117, create_slb) => =(findmin_cpq_res(triple(U116_116, V117_117, W118_118)), findmin_pqp_res(U116_116)))), ! [U120_120] : (=(removemin_cpq_eff(U120_120), remove_cpq(findmin_cpq_eff(U120_120), findmin_cpq_res(U120_120)))), ! [U121_121] : (=(removemin_cpq_res(U121_121), findmin_cpq_res(U121_121)))
% 0.18/0.48
% 0.18/0.48 [4] DELTA_NOT_FORALL : ~! [U128_128, V129_129, W130_130] : (((~check_cpq(triple(U128_128, V129_129, W130_130)) | ~ok(triple(U128_128, V129_129, W130_130))) => (~check_cpq(im_succ_cpq(triple(U128_128, V129_129, W130_130))) | ~ok(im_succ_cpq(triple(U128_128, V129_129, W130_130))))))
% 0.18/0.48 -> [5] ~((~check_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130)) | ~ok(triple(skolem_U128128, skolem_V129129, skolem_W130130))) => (~check_cpq(im_succ_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130))) | ~ok(im_succ_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130)))))
% 0.18/0.48
% 0.18/0.48 [5] ALPHA_NOT_IMPLY : ~((~check_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130)) | ~ok(triple(skolem_U128128, skolem_V129129, skolem_W130130))) => (~check_cpq(im_succ_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130))) | ~ok(im_succ_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130)))))
% 0.18/0.48 -> [6] (~check_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130)) | ~ok(triple(skolem_U128128, skolem_V129129, skolem_W130130))), ~(~check_cpq(im_succ_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130))) | ~ok(im_succ_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130))))
% 0.18/0.48
% 0.18/0.48 [6] ALPHA_NOT_OR : ~(~check_cpq(im_succ_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130))) | ~ok(im_succ_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130))))
% 0.18/0.48 -> [7] ~~check_cpq(im_succ_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130))), ~~ok(im_succ_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130)))
% 0.18/0.48
% 0.18/0.48 [7] ALPHA_NOT_NOT : ~~check_cpq(im_succ_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130)))
% 0.18/0.48 -> [8] check_cpq(im_succ_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130)))
% 0.18/0.48
% 0.18/0.48 [8] ALPHA_NOT_NOT : ~~ok(im_succ_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130)))
% 0.18/0.48 -> [9] ok(im_succ_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130)))
% 0.18/0.48
% 0.18/0.48 [9] BETA_OR : (~check_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130)) | ~ok(triple(skolem_U128128, skolem_V129129, skolem_W130130)))
% 0.18/0.48 -> [10] ~check_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130))
% 0.18/0.48 -> [11] ~ok(triple(skolem_U128128, skolem_V129129, skolem_W130130))
% 0.18/0.48
% 0.18/0.48 [11] GAMMA_FORALL : ! [U122_122, V123_123, W124_124] : ((~ok(triple(U122_122, V123_123, W124_124)) => ~ok(im_succ_cpq(triple(U122_122, V123_123, W124_124)))))
% 0.18/0.48 -> [13] (~ok(triple(skolem_U128128, skolem_V129129, skolem_W130130)) => ~ok(im_succ_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130))))
% 0.18/0.48
% 0.18/0.48 [13] BETA_IMPLY : (~ok(triple(skolem_U128128, skolem_V129129, skolem_W130130)) => ~ok(im_succ_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130))))
% 0.18/0.48 -> [16] ~~ok(triple(skolem_U128128, skolem_V129129, skolem_W130130))
% 0.18/0.48 -> [17] ~ok(im_succ_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130)))
% 0.18/0.48
% 0.18/0.48 [17] CLOSURE : ~ok(im_succ_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130)))
% 0.18/0.48
% 0.18/0.48 [16] ALPHA_NOT_NOT : ~~ok(triple(skolem_U128128, skolem_V129129, skolem_W130130))
% 0.18/0.48 -> [19] ok(triple(skolem_U128128, skolem_V129129, skolem_W130130))
% 0.18/0.48
% 0.18/0.48 [19] CLOSURE : ok(triple(skolem_U128128, skolem_V129129, skolem_W130130))
% 0.18/0.48
% 0.18/0.48 [10] GAMMA_FORALL : ! [U122_122, V123_123, W124_124] : ((~ok(triple(U122_122, V123_123, W124_124)) => ~ok(im_succ_cpq(triple(U122_122, V123_123, W124_124)))))
% 0.18/0.48 -> [12] (~ok(triple(skolem_U128128, skolem_V129129, skolem_W130130)) => ~ok(im_succ_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130))))
% 0.18/0.48
% 0.18/0.48 [12] BETA_IMPLY : (~ok(triple(skolem_U128128, skolem_V129129, skolem_W130130)) => ~ok(im_succ_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130))))
% 0.18/0.48 -> [14] ~~ok(triple(skolem_U128128, skolem_V129129, skolem_W130130))
% 0.18/0.48 -> [15] ~ok(im_succ_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130)))
% 0.18/0.48
% 0.18/0.48 [15] CLOSURE : ~ok(im_succ_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130)))
% 0.18/0.48
% 0.18/0.48 [14] ALPHA_NOT_NOT : ~~ok(triple(skolem_U128128, skolem_V129129, skolem_W130130))
% 0.18/0.48 -> [18] ok(triple(skolem_U128128, skolem_V129129, skolem_W130130))
% 0.18/0.48
% 0.18/0.48 [18] GAMMA_FORALL : ! [U125_125, V126_126, W127_127] : ((~check_cpq(triple(U125_125, V126_126, W127_127)) => (~check_cpq(im_succ_cpq(triple(U125_125, V126_126, W127_127))) | ~ok(im_succ_cpq(triple(U125_125, V126_126, W127_127))))))
% 0.18/0.48 -> [20] (~check_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130)) => (~check_cpq(im_succ_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130))) | ~ok(im_succ_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130)))))
% 0.18/0.49
% 0.18/0.49 [20] BETA_IMPLY : (~check_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130)) => (~check_cpq(im_succ_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130))) | ~ok(im_succ_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130)))))
% 0.18/0.49 -> [21] ~~check_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130))
% 0.18/0.49 -> [22] (~check_cpq(im_succ_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130))) | ~ok(im_succ_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130))))
% 0.18/0.49
% 0.18/0.49 [21] ALPHA_NOT_NOT : ~~check_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130))
% 0.18/0.49 -> [23] check_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130))
% 0.18/0.49
% 0.18/0.49 [23] CLOSURE : check_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130))
% 0.18/0.49
% 0.18/0.49 [22] BETA_OR : (~check_cpq(im_succ_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130))) | ~ok(im_succ_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130))))
% 0.18/0.49 -> [24] ~check_cpq(im_succ_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130)))
% 0.18/0.49 -> [25] ~ok(im_succ_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130)))
% 0.18/0.49
% 0.18/0.49 [24] CLOSURE : ~check_cpq(im_succ_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130)))
% 0.18/0.49
% 0.18/0.49 [25] CLOSURE : ~ok(im_succ_cpq(triple(skolem_U128128, skolem_V129129, skolem_W130130)))
% 0.18/0.49
% 0.18/0.49 % SZS output end Proof for theBenchmark.p
% 0.18/0.49 [0.143304s][1][Res] 77 goroutines created
% 0.18/0.49 ==== Result ====
% 0.18/0.49 [0.143362s][1][Res] VALID
% 0.18/0.49 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------