TSTP Solution File: SWV395+1 by Goeland---1.0.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SWV395+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n026.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 13:39:33 EDT 2022
% Result : Theorem 0.51s 0.62s
% Output : Proof 0.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWV395+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : goeland -dmt -presko -proof %s
% 0.12/0.33 % Computer : n026.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 03:05:09 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 [DMT] DMT loaded with preskolemization
% 0.12/0.33 [EQ] equality loaded.
% 0.12/0.33 [0.000037s][1][MAIN] Problem : theBenchmark.p
% 0.12/0.33 Conjecture not found
% 0.12/0.34 Conjecture not found
% 0.12/0.34 Conjecture not found
% 0.12/0.34 Start search
% 0.12/0.34 nb_step : 1 - limit : 41
% 0.12/0.34 Launch Gotab with destructive = true
% 0.51/0.62 % SZS output start Proof for theBenchmark.p
% 0.51/0.62 [0] ALPHA_AND : ((! [U4_4, V5_5, W6_6] : (((less_than(U4_4, V5_5) & less_than(V5_5, W6_6)) => less_than(U4_4, W6_6))) & ! [U7_7, V8_8] : ((less_than(U7_7, V8_8) | less_than(V8_8, U7_7))) & ! [U9_9] : (less_than(U9_9, U9_9)) & ! [U12_12] : (less_than(bottom, U12_12))) & (~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, X125_125] : ((((pair_in_list(create_slb, W124_124, X125_125) & strictly_less_than(W124_124, X125_125)) & ok(remove_cpq(triple(U122_122, create_slb, V123_123), W124_124))) => pair_in_list(remove_slb(create_slb, W124_124), W124_124, X125_125))))
% 0.51/0.62 -> [1] (! [U4_4, V5_5, W6_6] : (((less_than(U4_4, V5_5) & less_than(V5_5, W6_6)) => less_than(U4_4, W6_6))) & ! [U7_7, V8_8] : ((less_than(U7_7, V8_8) | less_than(V8_8, U7_7))) & ! [U9_9] : (less_than(U9_9, U9_9)) & ! [U12_12] : (less_than(bottom, U12_12))), (~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, X125_125] : ((((pair_in_list(create_slb, W124_124, X125_125) & strictly_less_than(W124_124, X125_125)) & ok(remove_cpq(triple(U122_122, create_slb, V123_123), W124_124))) => pair_in_list(remove_slb(create_slb, W124_124), W124_124, X125_125)))
% 0.51/0.62
% 0.51/0.62 [1] ALPHA_AND : (! [U4_4, V5_5, W6_6] : (((less_than(U4_4, V5_5) & less_than(V5_5, W6_6)) => less_than(U4_4, W6_6))) & ! [U7_7, V8_8] : ((less_than(U7_7, V8_8) | less_than(V8_8, U7_7))) & ! [U9_9] : (less_than(U9_9, U9_9)) & ! [U12_12] : (less_than(bottom, U12_12)))
% 0.51/0.62 -> [2] ! [U4_4, V5_5, W6_6] : (((less_than(U4_4, V5_5) & less_than(V5_5, W6_6)) => less_than(U4_4, W6_6))), ! [U7_7, V8_8] : ((less_than(U7_7, V8_8) | less_than(V8_8, U7_7))), ! [U9_9] : (less_than(U9_9, U9_9)), ! [U12_12] : (less_than(bottom, U12_12))
% 0.51/0.62
% 0.51/0.62 [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))))))
% 0.51/0.62 -> [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)))))
% 0.51/0.62
% 0.51/0.62 [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))))
% 0.51/0.62 -> [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)))
% 0.51/0.62
% 0.51/0.62 [4] DELTA_NOT_FORALL : ~! [U122_122, V123_123, W124_124, X125_125] : ((((pair_in_list(create_slb, W124_124, X125_125) & strictly_less_than(W124_124, X125_125)) & ok(remove_cpq(triple(U122_122, create_slb, V123_123), W124_124))) => pair_in_list(remove_slb(create_slb, W124_124), W124_124, X125_125)))
% 0.51/0.62 -> [5] ~(((pair_in_list(create_slb, skolem_W124124, skolem_X125125) & strictly_less_than(skolem_W124124, skolem_X125125)) & ok(remove_cpq(triple(skolem_U122122, create_slb, skolem_V123123), skolem_W124124))) => pair_in_list(remove_slb(create_slb, skolem_W124124), skolem_W124124, skolem_X125125))
% 0.51/0.62
% 0.51/0.62 [5] ALPHA_NOT_IMPLY : ~(((pair_in_list(create_slb, skolem_W124124, skolem_X125125) & strictly_less_than(skolem_W124124, skolem_X125125)) & ok(remove_cpq(triple(skolem_U122122, create_slb, skolem_V123123), skolem_W124124))) => pair_in_list(remove_slb(create_slb, skolem_W124124), skolem_W124124, skolem_X125125))
% 0.51/0.62 -> [6] ((pair_in_list(create_slb, skolem_W124124, skolem_X125125) & strictly_less_than(skolem_W124124, skolem_X125125)) & ok(remove_cpq(triple(skolem_U122122, create_slb, skolem_V123123), skolem_W124124))), ~pair_in_list(remove_slb(create_slb, skolem_W124124), skolem_W124124, skolem_X125125)
% 0.51/0.62
% 0.51/0.62 [6] ALPHA_AND : ((pair_in_list(create_slb, skolem_W124124, skolem_X125125) & strictly_less_than(skolem_W124124, skolem_X125125)) & ok(remove_cpq(triple(skolem_U122122, create_slb, skolem_V123123), skolem_W124124)))
% 0.51/0.62 -> [7] (pair_in_list(create_slb, skolem_W124124, skolem_X125125) & strictly_less_than(skolem_W124124, skolem_X125125)), ok(remove_cpq(triple(skolem_U122122, create_slb, skolem_V123123), skolem_W124124))
% 0.51/0.62
% 0.51/0.62 [7] ALPHA_AND : (pair_in_list(create_slb, skolem_W124124, skolem_X125125) & strictly_less_than(skolem_W124124, skolem_X125125))
% 0.51/0.62 -> [8] pair_in_list(create_slb, skolem_W124124, skolem_X125125), strictly_less_than(skolem_W124124, skolem_X125125)
% 0.51/0.62
% 0.51/0.62 [8] Rewrite : strictly_less_than(skolem_W124124, skolem_X125125)
% 0.51/0.62 -> [9] (less_than(skolem_W124124, skolem_X125125) & ~less_than(skolem_X125125, skolem_W124124))
% 0.51/0.62
% 0.51/0.62 [9] ALPHA_AND : (less_than(skolem_W124124, skolem_X125125) & ~less_than(skolem_X125125, skolem_W124124))
% 0.51/0.62 -> [10] less_than(skolem_W124124, skolem_X125125), ~less_than(skolem_X125125, skolem_W124124)
% 0.51/0.62
% 0.51/0.62 [10] GAMMA_FORALL : ! [U4_4, V5_5, W6_6] : (((less_than(U4_4, V5_5) & less_than(V5_5, W6_6)) => less_than(U4_4, W6_6)))
% 0.51/0.62 -> [11] ((less_than(skolem_X125125, skolem_W124124) & less_than(skolem_W124124, skolem_W124124)) => less_than(skolem_X125125, skolem_W124124))
% 0.51/0.62
% 0.51/0.62 [11] BETA_IMPLY : ((less_than(skolem_X125125, skolem_W124124) & less_than(skolem_W124124, skolem_W124124)) => less_than(skolem_X125125, skolem_W124124))
% 0.51/0.62 -> [12] ~(less_than(skolem_X125125, skolem_W124124) & less_than(skolem_W124124, skolem_W124124))
% 0.51/0.62 -> [13] less_than(skolem_X125125, skolem_W124124)
% 0.51/0.62
% 0.51/0.62 [13] CLOSURE : less_than(skolem_X125125, skolem_W124124)
% 0.51/0.62
% 0.51/0.62 [12] BETA_NOT_AND : ~(less_than(skolem_X125125, skolem_W124124) & less_than(skolem_W124124, skolem_W124124))
% 0.51/0.62 -> [20] ~less_than(skolem_X125125, skolem_W124124)
% 0.51/0.62 -> [21] ~less_than(skolem_W124124, skolem_W124124)
% 0.51/0.62
% 0.51/0.62 [21] GAMMA_FORALL : ! [U7_7, V8_8] : ((less_than(U7_7, V8_8) | less_than(V8_8, U7_7)))
% 0.51/0.62 -> [23] (less_than(skolem_X125125, skolem_W124124) | less_than(skolem_W124124, skolem_X125125))
% 0.51/0.62
% 0.51/0.62 [23] BETA_OR : (less_than(skolem_X125125, skolem_W124124) | less_than(skolem_W124124, skolem_X125125))
% 0.51/0.62 -> [26] less_than(skolem_X125125, skolem_W124124)
% 0.51/0.62 -> [27] less_than(skolem_W124124, skolem_X125125)
% 0.51/0.62
% 0.51/0.62 [26] CLOSURE : less_than(skolem_X125125, skolem_W124124)
% 0.51/0.62
% 0.51/0.62 [27] GAMMA_FORALL : ! [U9_9] : (less_than(U9_9, U9_9))
% 0.51/0.62 -> [29] less_than(U9_2_2, U9_2_2)
% 0.51/0.62
% 0.51/0.62 [29] CLOSURE : less_than(U9_2_2, U9_2_2)
% 0.51/0.62
% 0.51/0.62 [22] BETA_OR : (less_than(skolem_W124124, skolem_X125125) | less_than(skolem_X125125, skolem_W124124))
% 0.51/0.62 -> [30] less_than(skolem_W124124, skolem_X125125)
% 0.51/0.62 -> [31] less_than(skolem_X125125, skolem_W124124)
% 0.51/0.62
% 0.51/0.62 [31] CLOSURE : less_than(skolem_X125125, skolem_W124124)
% 0.51/0.62
% 0.51/0.62 [30] GAMMA_FORALL : ! [U9_9] : (less_than(U9_9, U9_9))
% 0.51/0.62 -> [32] less_than(U9_3_2, U9_3_2)
% 0.51/0.62
% 0.51/0.62 [32] GAMMA_FORALL : ! [U12_12] : (less_than(bottom, U12_12))
% 0.51/0.62 -> [33] less_than(bottom, U12_0_3)
% 0.51/0.62
% 0.51/0.62 [33] GAMMA_FORALL : ! [U14_14, V15_15, W16_16] : (isnonempty_slb(insert_slb(U14_14, pair(V15_15, W16_16))))
% 0.51/0.62 -> [34] isnonempty_slb(insert_slb(U14_0_4, pair(V15_0_4, W16_0_4)))
% 0.51/0.62
% 0.51/0.62 [34] GAMMA_FORALL : ! [U17_17] : (~contains_slb(create_slb, U17_17))
% 0.51/0.62 -> [35] ~contains_slb(create_slb, U17_0_5)
% 0.51/0.62
% 0.51/0.62 [35] GAMMA_FORALL : ! [U22_22, V23_23] : (~pair_in_list(create_slb, U22_22, V23_23))
% 0.51/0.62 -> [36] ~pair_in_list(create_slb, U22_0_6, V23_0_6)
% 0.51/0.62
% 0.51/0.62 [36] CLOSURE : ~pair_in_list(create_slb, U22_0_6, V23_0_6)
% 0.51/0.62
% 0.51/0.62 % SZS output end Proof for theBenchmark.p
% 0.51/0.62 [0.290652s][1][Res] 439 goroutines created
% 0.51/0.62 ==== Result ====
% 0.51/0.62 [0.290688s][1][Res] VALID
% 0.51/0.62 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------