TSTP Solution File: SET077+1 by Goeland---1.0.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Goeland---1.0.0
% Problem  : SET077+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : goeland -dmt -presko -proof %s

% Computer : n019.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 : Tue Sep 20 04:15:15 EDT 2022

% Result   : Theorem 0.19s 0.49s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem    : SET077+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.04/0.13  % Command    : goeland -dmt -presko -proof %s
% 0.12/0.34  % Computer : n019.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Sat Sep  3 02:08:35 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.12/0.35  [DMT] DMT loaded with preskolemization
% 0.12/0.35  [EQ] equality loaded.
% 0.12/0.35  [0.000039s][1][MAIN] Problem : theBenchmark.p
% 0.12/0.36  Conjecture not found
% 0.12/0.36  Start search
% 0.12/0.36  nb_step : 1 - limit : 49
% 0.12/0.36  Launch Gotab with destructive = true
% 0.19/0.49  % SZS output start Proof for theBenchmark.p
% 0.19/0.49  [0] ALPHA_AND : ((! [X12_12] :  (subclass(X12_12, universal_class)) & ! [X13_13, Y14_14] :  ((=(X13_13, Y14_14) <=> (subclass(X13_13, Y14_14) & subclass(Y14_14, X13_13)))) & ! [X18_18, Y19_19] :  (member(unordered_pair(X18_18, Y19_19), universal_class)) & ! [X20_20] :  (=(singleton(X20_20), unordered_pair(X20_20, X20_20))) & ! [X21_21, Y22_22] :  (=(ordered_pair(X21_21, Y22_22), unordered_pair(singleton(X21_21), unordered_pair(X21_21, singleton(Y22_22))))) & ! [X27_27, Y28_28] :  (((member(X27_27, universal_class) & member(Y28_28, universal_class)) => (=(first(ordered_pair(X27_27, Y28_28)), X27_27) & =(second(ordered_pair(X27_27, Y28_28)), Y28_28)))) & ! [X29_29, Y30_30, Z31_31] :  ((member(Z31_31, cross_product(X29_29, Y30_30)) => =(Z31_31, ordered_pair(first(Z31_31), second(Z31_31))))) & subclass(element_relation, cross_product(universal_class, universal_class)) & ! [X39_39, XR40_40, Y41_41] :  (=(restrict(XR40_40, X39_39, Y41_41), intersection(XR40_40, cross_product(X39_39, Y41_41)))) & ! [X42_42] :  (~member(X42_42, null_class)) & ! [X49_49] :  (subclass(rotate(X49_49), cross_product(cross_product(universal_class, universal_class), universal_class))) & ! [X54_54] :  (subclass(flip(X54_54), cross_product(cross_product(universal_class, universal_class), universal_class))) & ! [X58_58] :  (=(successor(X58_58), union(X58_58, singleton(X58_58)))) & subclass(successor_relation, cross_product(universal_class, universal_class)) & ! [Y61_61] :  (=(inverse(Y61_61), domain_of(flip(cross_product(Y61_61, universal_class))))) & ! [Z62_62] :  (=(range_of(Z62_62), domain_of(inverse(Z62_62)))) & ! [X63_63, XR64_64] :  (=(image(XR64_64, X63_63), range_of(restrict(XR64_64, X63_63, universal_class)))) & ? [X66_66] :  (((member(X66_66, universal_class) & inductive(X66_66)) & ! [Y67_67] :  ((inductive(Y67_67) => subclass(X66_66, Y67_67))))) & ! [X71_71] :  ((member(X71_71, universal_class) => member(sum_class(X71_71), universal_class))) & ! [U74_74] :  ((member(U74_74, universal_class) => member(power_class(U74_74), universal_class))) & ! [XR75_75, YR76_76] :  (subclass(compose(YR76_76, XR75_75), cross_product(universal_class, universal_class))) & ! [X84_84, XF85_85] :  (((member(X84_84, universal_class) & function(XF85_85)) => member(image(XF85_85, X84_84), universal_class))) & ! [X89_89] :  ((~=(X89_89, null_class) => ? [U90_90] :  (((member(U90_90, universal_class) & member(U90_90, X89_89)) & disjoint(U90_90, X89_89))))) & ! [XF91_91, Y92_92] :  (=(apply(XF91_91, Y92_92), sum_class(image(XF91_91, singleton(Y92_92))))) & ? [XF93_93] :  ((function(XF93_93) & ! [Y94_94] :  ((member(Y94_94, universal_class) => (=(Y94_94, null_class) | member(apply(XF93_93, Y94_94), Y94_94))))))) & ~! [X95_95] :  (member(singleton(X95_95), universal_class)))
% 0.19/0.49  	-> [1] (! [X12_12] :  (subclass(X12_12, universal_class)) & ! [X13_13, Y14_14] :  ((=(X13_13, Y14_14) <=> (subclass(X13_13, Y14_14) & subclass(Y14_14, X13_13)))) & ! [X18_18, Y19_19] :  (member(unordered_pair(X18_18, Y19_19), universal_class)) & ! [X20_20] :  (=(singleton(X20_20), unordered_pair(X20_20, X20_20))) & ! [X21_21, Y22_22] :  (=(ordered_pair(X21_21, Y22_22), unordered_pair(singleton(X21_21), unordered_pair(X21_21, singleton(Y22_22))))) & ! [X27_27, Y28_28] :  (((member(X27_27, universal_class) & member(Y28_28, universal_class)) => (=(first(ordered_pair(X27_27, Y28_28)), X27_27) & =(second(ordered_pair(X27_27, Y28_28)), Y28_28)))) & ! [X29_29, Y30_30, Z31_31] :  ((member(Z31_31, cross_product(X29_29, Y30_30)) => =(Z31_31, ordered_pair(first(Z31_31), second(Z31_31))))) & subclass(element_relation, cross_product(universal_class, universal_class)) & ! [X39_39, XR40_40, Y41_41] :  (=(restrict(XR40_40, X39_39, Y41_41), intersection(XR40_40, cross_product(X39_39, Y41_41)))) & ! [X42_42] :  (~member(X42_42, null_class)) & ! [X49_49] :  (subclass(rotate(X49_49), cross_product(cross_product(universal_class, universal_class), universal_class))) & ! [X54_54] :  (subclass(flip(X54_54), cross_product(cross_product(universal_class, universal_class), universal_class))) & ! [X58_58] :  (=(successor(X58_58), union(X58_58, singleton(X58_58)))) & subclass(successor_relation, cross_product(universal_class, universal_class)) & ! [Y61_61] :  (=(inverse(Y61_61), domain_of(flip(cross_product(Y61_61, universal_class))))) & ! [Z62_62] :  (=(range_of(Z62_62), domain_of(inverse(Z62_62)))) & ! [X63_63, XR64_64] :  (=(image(XR64_64, X63_63), range_of(restrict(XR64_64, X63_63, universal_class)))) & ? [X66_66] :  (((member(X66_66, universal_class) & inductive(X66_66)) & ! [Y67_67] :  ((inductive(Y67_67) => subclass(X66_66, Y67_67))))) & ! [X71_71] :  ((member(X71_71, universal_class) => member(sum_class(X71_71), universal_class))) & ! [U74_74] :  ((member(U74_74, universal_class) => member(power_class(U74_74), universal_class))) & ! [XR75_75, YR76_76] :  (subclass(compose(YR76_76, XR75_75), cross_product(universal_class, universal_class))) & ! [X84_84, XF85_85] :  (((member(X84_84, universal_class) & function(XF85_85)) => member(image(XF85_85, X84_84), universal_class))) & ! [X89_89] :  ((~=(X89_89, null_class) => ? [U90_90] :  (((member(U90_90, universal_class) & member(U90_90, X89_89)) & disjoint(U90_90, X89_89))))) & ! [XF91_91, Y92_92] :  (=(apply(XF91_91, Y92_92), sum_class(image(XF91_91, singleton(Y92_92))))) & ? [XF93_93] :  ((function(XF93_93) & ! [Y94_94] :  ((member(Y94_94, universal_class) => (=(Y94_94, null_class) | member(apply(XF93_93, Y94_94), Y94_94))))))), ~! [X95_95] :  (member(singleton(X95_95), universal_class))
% 0.19/0.49  
% 0.19/0.49  [1] ALPHA_AND : (! [X12_12] :  (subclass(X12_12, universal_class)) & ! [X13_13, Y14_14] :  ((=(X13_13, Y14_14) <=> (subclass(X13_13, Y14_14) & subclass(Y14_14, X13_13)))) & ! [X18_18, Y19_19] :  (member(unordered_pair(X18_18, Y19_19), universal_class)) & ! [X20_20] :  (=(singleton(X20_20), unordered_pair(X20_20, X20_20))) & ! [X21_21, Y22_22] :  (=(ordered_pair(X21_21, Y22_22), unordered_pair(singleton(X21_21), unordered_pair(X21_21, singleton(Y22_22))))) & ! [X27_27, Y28_28] :  (((member(X27_27, universal_class) & member(Y28_28, universal_class)) => (=(first(ordered_pair(X27_27, Y28_28)), X27_27) & =(second(ordered_pair(X27_27, Y28_28)), Y28_28)))) & ! [X29_29, Y30_30, Z31_31] :  ((member(Z31_31, cross_product(X29_29, Y30_30)) => =(Z31_31, ordered_pair(first(Z31_31), second(Z31_31))))) & subclass(element_relation, cross_product(universal_class, universal_class)) & ! [X39_39, XR40_40, Y41_41] :  (=(restrict(XR40_40, X39_39, Y41_41), intersection(XR40_40, cross_product(X39_39, Y41_41)))) & ! [X42_42] :  (~member(X42_42, null_class)) & ! [X49_49] :  (subclass(rotate(X49_49), cross_product(cross_product(universal_class, universal_class), universal_class))) & ! [X54_54] :  (subclass(flip(X54_54), cross_product(cross_product(universal_class, universal_class), universal_class))) & ! [X58_58] :  (=(successor(X58_58), union(X58_58, singleton(X58_58)))) & subclass(successor_relation, cross_product(universal_class, universal_class)) & ! [Y61_61] :  (=(inverse(Y61_61), domain_of(flip(cross_product(Y61_61, universal_class))))) & ! [Z62_62] :  (=(range_of(Z62_62), domain_of(inverse(Z62_62)))) & ! [X63_63, XR64_64] :  (=(image(XR64_64, X63_63), range_of(restrict(XR64_64, X63_63, universal_class)))) & ? [X66_66] :  (((member(X66_66, universal_class) & inductive(X66_66)) & ! [Y67_67] :  ((inductive(Y67_67) => subclass(X66_66, Y67_67))))) & ! [X71_71] :  ((member(X71_71, universal_class) => member(sum_class(X71_71), universal_class))) & ! [U74_74] :  ((member(U74_74, universal_class) => member(power_class(U74_74), universal_class))) & ! [XR75_75, YR76_76] :  (subclass(compose(YR76_76, XR75_75), cross_product(universal_class, universal_class))) & ! [X84_84, XF85_85] :  (((member(X84_84, universal_class) & function(XF85_85)) => member(image(XF85_85, X84_84), universal_class))) & ! [X89_89] :  ((~=(X89_89, null_class) => ? [U90_90] :  (((member(U90_90, universal_class) & member(U90_90, X89_89)) & disjoint(U90_90, X89_89))))) & ! [XF91_91, Y92_92] :  (=(apply(XF91_91, Y92_92), sum_class(image(XF91_91, singleton(Y92_92))))) & ? [XF93_93] :  ((function(XF93_93) & ! [Y94_94] :  ((member(Y94_94, universal_class) => (=(Y94_94, null_class) | member(apply(XF93_93, Y94_94), Y94_94)))))))
% 0.19/0.49  	-> [2] ! [X12_12] :  (subclass(X12_12, universal_class)), ! [X13_13, Y14_14] :  ((=(X13_13, Y14_14) <=> (subclass(X13_13, Y14_14) & subclass(Y14_14, X13_13)))), ! [X18_18, Y19_19] :  (member(unordered_pair(X18_18, Y19_19), universal_class)), ! [X20_20] :  (=(singleton(X20_20), unordered_pair(X20_20, X20_20))), ! [X21_21, Y22_22] :  (=(ordered_pair(X21_21, Y22_22), unordered_pair(singleton(X21_21), unordered_pair(X21_21, singleton(Y22_22))))), ! [X27_27, Y28_28] :  (((member(X27_27, universal_class) & member(Y28_28, universal_class)) => (=(first(ordered_pair(X27_27, Y28_28)), X27_27) & =(second(ordered_pair(X27_27, Y28_28)), Y28_28)))), ! [X29_29, Y30_30, Z31_31] :  ((member(Z31_31, cross_product(X29_29, Y30_30)) => =(Z31_31, ordered_pair(first(Z31_31), second(Z31_31))))), subclass(element_relation, cross_product(universal_class, universal_class)), ! [X39_39, XR40_40, Y41_41] :  (=(restrict(XR40_40, X39_39, Y41_41), intersection(XR40_40, cross_product(X39_39, Y41_41)))), ! [X42_42] :  (~member(X42_42, null_class)), ! [X49_49] :  (subclass(rotate(X49_49), cross_product(cross_product(universal_class, universal_class), universal_class))), ! [X54_54] :  (subclass(flip(X54_54), cross_product(cross_product(universal_class, universal_class), universal_class))), ! [X58_58] :  (=(successor(X58_58), union(X58_58, singleton(X58_58)))), subclass(successor_relation, cross_product(universal_class, universal_class)), ! [Y61_61] :  (=(inverse(Y61_61), domain_of(flip(cross_product(Y61_61, universal_class))))), ! [Z62_62] :  (=(range_of(Z62_62), domain_of(inverse(Z62_62)))), ! [X63_63, XR64_64] :  (=(image(XR64_64, X63_63), range_of(restrict(XR64_64, X63_63, universal_class)))), ? [X66_66] :  (((member(X66_66, universal_class) & inductive(X66_66)) & ! [Y67_67] :  ((inductive(Y67_67) => subclass(X66_66, Y67_67))))), ! [X71_71] :  ((member(X71_71, universal_class) => member(sum_class(X71_71), universal_class))), ! [U74_74] :  ((member(U74_74, universal_class) => member(power_class(U74_74), universal_class))), ! [XR75_75, YR76_76] :  (subclass(compose(YR76_76, XR75_75), cross_product(universal_class, universal_class))), ! [X84_84, XF85_85] :  (((member(X84_84, universal_class) & function(XF85_85)) => member(image(XF85_85, X84_84), universal_class))), ! [X89_89] :  ((~=(X89_89, null_class) => ? [U90_90] :  (((member(U90_90, universal_class) & member(U90_90, X89_89)) & disjoint(U90_90, X89_89))))), ! [XF91_91, Y92_92] :  (=(apply(XF91_91, Y92_92), sum_class(image(XF91_91, singleton(Y92_92))))), ? [XF93_93] :  ((function(XF93_93) & ! [Y94_94] :  ((member(Y94_94, universal_class) => (=(Y94_94, null_class) | member(apply(XF93_93, Y94_94), Y94_94))))))
% 0.19/0.49  
% 0.19/0.49  [2] Rewrite : subclass(element_relation, cross_product(universal_class, universal_class))
% 0.19/0.49  	-> [3] ! [U11_11] :  ((member(U11_11, element_relation) => member(U11_11, cross_product(universal_class, universal_class))))
% 0.19/0.49  
% 0.19/0.49  [3] Rewrite : subclass(successor_relation, cross_product(universal_class, universal_class))
% 0.19/0.49  	-> [4] ! [U11_11] :  ((member(U11_11, successor_relation) => member(U11_11, cross_product(universal_class, universal_class))))
% 0.19/0.49  
% 0.19/0.49  [4] DELTA_NOT_FORALL : ~! [X95_95] :  (member(singleton(X95_95), universal_class))
% 0.19/0.49  	-> [5] ~member(singleton(skolem_X9595), universal_class)
% 0.19/0.49  
% 0.19/0.49  [5] DELTA_EXISTS : ? [X66_66] :  (((member(X66_66, universal_class) & inductive(X66_66)) & ! [Y67_67] :  ((inductive(Y67_67) => subclass(X66_66, Y67_67)))))
% 0.19/0.49  	-> [6] ((member(skolem_X6666, universal_class) & inductive(skolem_X6666)) & ! [Y67_67] :  ((inductive(Y67_67) => subclass(skolem_X6666, Y67_67))))
% 0.19/0.49  
% 0.19/0.49  [6] ALPHA_AND : ((member(skolem_X6666, universal_class) & inductive(skolem_X6666)) & ! [Y67_67] :  ((inductive(Y67_67) => subclass(skolem_X6666, Y67_67))))
% 0.19/0.49  	-> [7] (member(skolem_X6666, universal_class) & inductive(skolem_X6666)), ! [Y67_67] :  ((inductive(Y67_67) => subclass(skolem_X6666, Y67_67)))
% 0.19/0.49  
% 0.19/0.49  [7] ALPHA_AND : (member(skolem_X6666, universal_class) & inductive(skolem_X6666))
% 0.19/0.49  	-> [8] member(skolem_X6666, universal_class), inductive(skolem_X6666)
% 0.19/0.49  
% 0.19/0.49  [8] Rewrite : inductive(skolem_X6666)
% 0.19/0.49  	-> [9] (member(null_class, skolem_X6666) & subclass(image(successor_relation, skolem_X6666), skolem_X6666))
% 0.19/0.49  
% 0.19/0.49  [9] ALPHA_AND : (member(null_class, skolem_X6666) & subclass(image(successor_relation, skolem_X6666), skolem_X6666))
% 0.19/0.49  	-> [10] member(null_class, skolem_X6666), subclass(image(successor_relation, skolem_X6666), skolem_X6666)
% 0.19/0.49  
% 0.19/0.49  [10] Rewrite : subclass(image(successor_relation, skolem_X6666), skolem_X6666)
% 0.19/0.49  	-> [11] ! [U11_11] :  ((member(U11_11, image(successor_relation, skolem_X6666)) => member(U11_11, skolem_X6666)))
% 0.19/0.49  
% 0.19/0.49  [11] DELTA_EXISTS : ? [XF93_93] :  ((function(XF93_93) & ! [Y94_94] :  ((member(Y94_94, universal_class) => (=(Y94_94, null_class) | member(apply(XF93_93, Y94_94), Y94_94))))))
% 0.19/0.49  	-> [12] (function(skolem_XF9393) & ! [Y94_94] :  ((member(Y94_94, universal_class) => (=(Y94_94, null_class) | member(apply(skolem_XF9393, Y94_94), Y94_94)))))
% 0.19/0.49  
% 0.19/0.49  [12] ALPHA_AND : (function(skolem_XF9393) & ! [Y94_94] :  ((member(Y94_94, universal_class) => (=(Y94_94, null_class) | member(apply(skolem_XF9393, Y94_94), Y94_94)))))
% 0.19/0.49  	-> [13] function(skolem_XF9393), ! [Y94_94] :  ((member(Y94_94, universal_class) => (=(Y94_94, null_class) | member(apply(skolem_XF9393, Y94_94), Y94_94))))
% 0.19/0.49  
% 0.19/0.49  [13] Rewrite : function(skolem_XF9393)
% 0.19/0.49  	-> [14] (subclass(skolem_XF9393, cross_product(universal_class, universal_class)) & subclass(compose(skolem_XF9393, inverse(skolem_XF9393)), identity_relation))
% 0.19/0.49  
% 0.19/0.49  [14] ALPHA_AND : (subclass(skolem_XF9393, cross_product(universal_class, universal_class)) & subclass(compose(skolem_XF9393, inverse(skolem_XF9393)), identity_relation))
% 0.19/0.49  	-> [15] subclass(skolem_XF9393, cross_product(universal_class, universal_class)), subclass(compose(skolem_XF9393, inverse(skolem_XF9393)), identity_relation)
% 0.19/0.49  
% 0.19/0.49  [15] Rewrite : subclass(skolem_XF9393, cross_product(universal_class, universal_class))
% 0.19/0.49  	-> [16] ! [U11_11] :  ((member(U11_11, skolem_XF9393) => member(U11_11, cross_product(universal_class, universal_class))))
% 0.19/0.49  
% 0.19/0.49  [16] Rewrite : subclass(compose(skolem_XF9393, inverse(skolem_XF9393)), identity_relation)
% 0.19/0.49  	-> [17] ! [U11_11] :  ((member(U11_11, compose(skolem_XF9393, inverse(skolem_XF9393))) => member(U11_11, identity_relation)))
% 0.19/0.49  
% 0.19/0.49  [17] GAMMA_FORALL : ! [X12_12] :  (subclass(X12_12, universal_class))
% 0.19/0.49  	-> [18] subclass(X12_0_0, universal_class)
% 0.19/0.49  
% 0.19/0.49  [18] Rewrite : subclass(X12_0_0, universal_class)
% 0.19/0.49  	-> [19] ! [U11_11] :  ((member(U11_11, X12_0_0) => member(U11_11, universal_class)))
% 0.19/0.49  
% 0.19/0.49  [19] GAMMA_FORALL : ! [X13_13, Y14_14] :  ((=(X13_13, Y14_14) <=> (subclass(X13_13, Y14_14) & subclass(Y14_14, X13_13))))
% 0.19/0.49  	-> [20] (=(Y14_0_1, Y14_0_1) <=> (subclass(Y14_0_1, Y14_0_1) & subclass(Y14_0_1, Y14_0_1)))
% 0.19/0.49  
% 0.19/0.49  [20] BETA_EQUIV : (=(Y14_0_1, Y14_0_1) <=> (subclass(Y14_0_1, Y14_0_1) & subclass(Y14_0_1, Y14_0_1)))
% 0.19/0.49  	-> [21] ~=(Y14_0_1, Y14_0_1), ~(subclass(Y14_0_1, Y14_0_1) & subclass(Y14_0_1, Y14_0_1))
% 0.19/0.49  	-> [22] =(Y14_0_1, Y14_0_1), (subclass(Y14_0_1, Y14_0_1) & subclass(Y14_0_1, Y14_0_1))
% 0.19/0.49  
% 0.19/0.49  [21] CLOSURE : ~=(Y14_0_1, Y14_0_1)
% 0.19/0.49  
% 0.19/0.49  [23] Rewrite : subclass(Y14_0_1, Y14_0_1)
% 0.19/0.49  	-> [24] ! [U11_11] :  ((member(U11_11, Y14_0_1) => member(U11_11, Y14_0_1)))
% 0.19/0.49  
% 0.19/0.49  [24] GAMMA_FORALL : ! [X18_18, Y19_19] :  (member(unordered_pair(X18_18, Y19_19), universal_class))
% 0.19/0.49  	-> [25] member(unordered_pair(X18_0_2, Y19_0_2), universal_class)
% 0.19/0.49  
% 0.19/0.49  [25] GAMMA_FORALL : ! [X20_20] :  (=(singleton(X20_20), unordered_pair(X20_20, X20_20)))
% 0.19/0.49  	-> [26] =(singleton(X20_0_3), unordered_pair(X20_0_3, X20_0_3))
% 0.19/0.49  
% 0.19/0.49  [26] CLOSURE : =
% 0.19/0.49  
% 0.19/0.49  % SZS output end Proof for theBenchmark.p
% 0.19/0.49  [0.140635s][1][Res] 197 goroutines created
% 0.19/0.49  ==== Result ====
% 0.19/0.49  [0.140671s][1][Res] VALID
% 0.19/0.49  % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------