TSTP Solution File: SET095+4 by Goeland---1.0.0
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%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SET095+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n003.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 04:15:22 EDT 2022
% Result : Theorem 0.20s 0.54s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET095+4 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : goeland -dmt -presko -proof %s
% 0.14/0.35 % Computer : n003.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Sep 3 02:19:10 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 [DMT] DMT loaded with preskolemization
% 0.14/0.36 [EQ] equality loaded.
% 0.14/0.36 [0.000092s][1][MAIN] Problem : theBenchmark.p
% 0.14/0.36 Conjecture not found
% 0.14/0.36 Start search
% 0.14/0.36 nb_step : 1 - limit : 15
% 0.14/0.36 Launch Gotab with destructive = true
% 0.20/0.54 % SZS output start Proof for theBenchmark.p
% 0.20/0.54 [0] ALPHA_AND : ((! [X10_10, A11_11] : ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11))) & ! [X18_18] : (~member(X18_18, empty_set)) & ! [X22_22, A23_23] : ((member(X22_22, singleton(A23_23)) <=> =(X22_22, A23_23)))) & ~! [A33_33, X34_34] : ((member(X34_34, A33_33) => subset(singleton(X34_34), A33_33))))
% 0.20/0.54 -> [1] (! [X10_10, A11_11] : ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11))) & ! [X18_18] : (~member(X18_18, empty_set)) & ! [X22_22, A23_23] : ((member(X22_22, singleton(A23_23)) <=> =(X22_22, A23_23)))), ~! [A33_33, X34_34] : ((member(X34_34, A33_33) => subset(singleton(X34_34), A33_33)))
% 0.20/0.54
% 0.20/0.54 [1] ALPHA_AND : (! [X10_10, A11_11] : ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11))) & ! [X18_18] : (~member(X18_18, empty_set)) & ! [X22_22, A23_23] : ((member(X22_22, singleton(A23_23)) <=> =(X22_22, A23_23))))
% 0.20/0.54 -> [2] ! [X10_10, A11_11] : ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11))), ! [X18_18] : (~member(X18_18, empty_set)), ! [X22_22, A23_23] : ((member(X22_22, singleton(A23_23)) <=> =(X22_22, A23_23)))
% 0.20/0.54
% 0.20/0.54 [2] DELTA_NOT_FORALL : ~! [A33_33, X34_34] : ((member(X34_34, A33_33) => subset(singleton(X34_34), A33_33)))
% 0.20/0.54 -> [3] ~(member(skolem_X3434, skolem_A3333) => subset(singleton(skolem_X3434), skolem_A3333))
% 0.20/0.54
% 0.20/0.54 [3] ALPHA_NOT_IMPLY : ~(member(skolem_X3434, skolem_A3333) => subset(singleton(skolem_X3434), skolem_A3333))
% 0.20/0.54 -> [4] member(skolem_X3434, skolem_A3333), ~subset(singleton(skolem_X3434), skolem_A3333)
% 0.20/0.54
% 0.20/0.54 [4] Rewrite : ~subset(singleton(skolem_X3434), skolem_A3333)
% 0.20/0.54 -> [5] ~(member(skolem_X77(singleton(skolem_X3434), skolem_A3333), singleton(skolem_X3434)) => member(skolem_X77(singleton(skolem_X3434), skolem_A3333), skolem_A3333))
% 0.20/0.54
% 0.20/0.54 [5] ALPHA_NOT_IMPLY : ~(member(skolem_X77(singleton(skolem_X3434), skolem_A3333), singleton(skolem_X3434)) => member(skolem_X77(singleton(skolem_X3434), skolem_A3333), skolem_A3333))
% 0.20/0.54 -> [6] member(skolem_X77(singleton(skolem_X3434), skolem_A3333), singleton(skolem_X3434)), ~member(skolem_X77(singleton(skolem_X3434), skolem_A3333), skolem_A3333)
% 0.20/0.54
% 0.20/0.54 [6] GAMMA_FORALL : ! [X10_10, A11_11] : ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11)))
% 0.20/0.54 -> [7] (member(X10_0_0, power_set(X10_0_0)) <=> subset(X10_0_0, X10_0_0))
% 0.20/0.54
% 0.20/0.54 [7] BETA_EQUIV : (member(X10_0_0, power_set(X10_0_0)) <=> subset(X10_0_0, X10_0_0))
% 0.20/0.54 -> [8] ~member(X10_0_0, power_set(X10_0_0)), ~subset(X10_0_0, X10_0_0)
% 0.20/0.54 -> [9] member(X10_0_0, power_set(X10_0_0)), subset(X10_0_0, X10_0_0)
% 0.20/0.54
% 0.20/0.54 [8] Rewrite : ~subset(X10_0_0, X10_0_0)
% 0.20/0.54 -> [10] ~(member(skolem_X77(X10_0_0, X10_0_0), X10_0_0) => member(skolem_X77(X10_0_0, X10_0_0), X10_0_0))
% 0.20/0.54
% 0.20/0.54 [10] ALPHA_NOT_IMPLY : ~(member(skolem_X77(X10_0_0, X10_0_0), X10_0_0) => member(skolem_X77(X10_0_0, X10_0_0), X10_0_0))
% 0.20/0.54 -> [12] member(skolem_X77(X10_0_0, X10_0_0), X10_0_0), ~member(skolem_X77(X10_0_0, X10_0_0), X10_0_0)
% 0.20/0.54
% 0.20/0.54 [12] CLOSURE : ~member(skolem_X77(X10_0_0, X10_0_0), X10_0_0)
% 0.20/0.54
% 0.20/0.54 [9] Rewrite : subset(X10_0_0, X10_0_0)
% 0.20/0.54 -> [11] ! [X7_7] : ((member(X7_7, X10_0_0) => member(X7_7, X10_0_0)))
% 0.20/0.54
% 0.20/0.54 [11] GAMMA_FORALL : ! [X18_18] : (~member(X18_18, empty_set))
% 0.20/0.54 -> [13] ~member(X18_0_1, empty_set)
% 0.20/0.54
% 0.20/0.54 [13] GAMMA_FORALL : ! [X22_22, A23_23] : ((member(X22_22, singleton(A23_23)) <=> =(X22_22, A23_23)))
% 0.20/0.54 -> [14] (member(skolem_X77(singleton(skolem_X3434), skolem_A3333), singleton(skolem_X3434)) <=> =(skolem_X77(singleton(skolem_X3434), skolem_A3333), skolem_X3434))
% 0.20/0.54
% 0.20/0.54 [14] BETA_EQUIV : (member(skolem_X77(singleton(skolem_X3434), skolem_A3333), singleton(skolem_X3434)) <=> =(skolem_X77(singleton(skolem_X3434), skolem_A3333), skolem_X3434))
% 0.20/0.54 -> [15] ~member(skolem_X77(singleton(skolem_X3434), skolem_A3333), singleton(skolem_X3434)), ~=(skolem_X77(singleton(skolem_X3434), skolem_A3333), skolem_X3434)
% 0.20/0.54 -> [16] member(skolem_X77(singleton(skolem_X3434), skolem_A3333), singleton(skolem_X3434)), =(skolem_X77(singleton(skolem_X3434), skolem_A3333), skolem_X3434)
% 0.20/0.54
% 0.20/0.54 [15] CLOSURE : ~=(skolem_X77(singleton(skolem_X3434), skolem_A3333), skolem_X3434)
% 0.20/0.54
% 0.20/0.54 [16] CLOSURE : =
% 0.20/0.54
% 0.20/0.54 % SZS output end Proof for theBenchmark.p
% 0.20/0.54 [0.187048s][1][Res] 464 goroutines created
% 0.20/0.54 ==== Result ====
% 0.20/0.54 [0.187090s][1][Res] VALID
% 0.20/0.54 % SZS status Theorem for theBenchmark.p
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