TSTP Solution File: SET975+1 by Goeland---1.0.0
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%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SET975+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n004.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 04:17:57 EDT 2022
% Result : Theorem 223.64s 30.28s
% Output : Proof 223.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET975+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : goeland -dmt -presko -proof %s
% 0.12/0.33 % Computer : n004.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 : Sat Sep 3 08:45:04 EDT 2022
% 0.12/0.33 % 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 Start search
% 0.12/0.34 nb_step : 1 - limit : 10
% 0.12/0.34 Launch Gotab with destructive = true
% 223.64/30.27 % SZS output start Proof for theBenchmark.p
% 223.64/30.28 [0] ALPHA_AND : (! [A4_4, B5_5] : ((in(A4_4, B5_5) => ~in(B5_5, A4_4))) & ! [A6_6, B7_7] : (=(unordered_pair(A6_6, B7_7), unordered_pair(B7_7, A6_6))) & ! [A8_8, B9_9] : ((=(B9_9, singleton(A8_8)) <=> ! [C10_10] : ((in(C10_10, B9_9) <=> =(C10_10, A8_8))))) & ! [A11_11, B12_12] : (=(ordered_pair(A11_11, B12_12), unordered_pair(unordered_pair(A11_11, B12_12), singleton(A11_11)))) & ! [A13_13, B14_14] : (~empty(ordered_pair(A13_13, B14_14))) & ? [A19_19] : (empty(A19_19)) & ? [A20_20] : (~empty(A20_20)) & ~! [A21_21, B22_22, C23_23, D24_24] : ((in(ordered_pair(A21_21, B22_22), cartesian_product2(singleton(C23_23), D24_24)) <=> (=(A21_21, C23_23) & in(B22_22, D24_24)))))
% 223.64/30.28 -> [1] ! [A4_4, B5_5] : ((in(A4_4, B5_5) => ~in(B5_5, A4_4))), ! [A6_6, B7_7] : (=(unordered_pair(A6_6, B7_7), unordered_pair(B7_7, A6_6))), ! [A8_8, B9_9] : ((=(B9_9, singleton(A8_8)) <=> ! [C10_10] : ((in(C10_10, B9_9) <=> =(C10_10, A8_8))))), ! [A11_11, B12_12] : (=(ordered_pair(A11_11, B12_12), unordered_pair(unordered_pair(A11_11, B12_12), singleton(A11_11)))), ! [A13_13, B14_14] : (~empty(ordered_pair(A13_13, B14_14))), ? [A19_19] : (empty(A19_19)), ? [A20_20] : (~empty(A20_20)), ~! [A21_21, B22_22, C23_23, D24_24] : ((in(ordered_pair(A21_21, B22_22), cartesian_product2(singleton(C23_23), D24_24)) <=> (=(A21_21, C23_23) & in(B22_22, D24_24))))
% 223.64/30.28
% 223.64/30.28 [1] DELTA_EXISTS : ? [A19_19] : (empty(A19_19))
% 223.64/30.28 -> [2] empty(skolem_A1919)
% 223.64/30.28
% 223.64/30.28 [2] DELTA_EXISTS : ? [A20_20] : (~empty(A20_20))
% 223.64/30.28 -> [3] ~empty(skolem_A2020)
% 223.64/30.28
% 223.64/30.28 [3] DELTA_NOT_FORALL : ~! [A21_21, B22_22, C23_23, D24_24] : ((in(ordered_pair(A21_21, B22_22), cartesian_product2(singleton(C23_23), D24_24)) <=> (=(A21_21, C23_23) & in(B22_22, D24_24))))
% 223.64/30.28 -> [4] ~(in(ordered_pair(skolem_A2121, skolem_B2222), cartesian_product2(singleton(skolem_C2323), skolem_D2424)) <=> (=(skolem_A2121, skolem_C2323) & in(skolem_B2222, skolem_D2424)))
% 223.64/30.28
% 223.64/30.28 [4] BETA_NOT_EQUIV : ~(in(ordered_pair(skolem_A2121, skolem_B2222), cartesian_product2(singleton(skolem_C2323), skolem_D2424)) <=> (=(skolem_A2121, skolem_C2323) & in(skolem_B2222, skolem_D2424)))
% 223.64/30.28 -> [5] ~in(ordered_pair(skolem_A2121, skolem_B2222), cartesian_product2(singleton(skolem_C2323), skolem_D2424)), (=(skolem_A2121, skolem_C2323) & in(skolem_B2222, skolem_D2424))
% 223.64/30.28 -> [6] in(ordered_pair(skolem_A2121, skolem_B2222), cartesian_product2(singleton(skolem_C2323), skolem_D2424)), ~(=(skolem_A2121, skolem_C2323) & in(skolem_B2222, skolem_D2424))
% 223.64/30.28
% 223.64/30.28 [5] Rewrite : ~in(ordered_pair(skolem_A2121, skolem_B2222), cartesian_product2(singleton(skolem_C2323), skolem_D2424))
% 223.64/30.28 -> [7] ~(in(skolem_A2121, singleton(skolem_C2323)) & in(skolem_B2222, skolem_D2424))
% 223.64/30.28
% 223.64/30.28 [7] ALPHA_AND : (=(skolem_A2121, skolem_C2323) & in(skolem_B2222, skolem_D2424))
% 223.64/30.28 -> [9] =(skolem_A2121, skolem_C2323), in(skolem_B2222, skolem_D2424)
% 223.64/30.28
% 223.64/30.28 [9] BETA_NOT_AND : ~(in(skolem_A2121, singleton(skolem_C2323)) & in(skolem_B2222, skolem_D2424))
% 223.64/30.28 -> [16] ~in(skolem_A2121, singleton(skolem_C2323))
% 223.64/30.28 -> [17] ~in(skolem_B2222, skolem_D2424)
% 223.64/30.28
% 223.64/30.28 [17] CLOSURE : ~in(skolem_B2222, skolem_D2424)
% 223.64/30.28
% 223.64/30.28 [16] GAMMA_FORALL : ! [A4_4, B5_5] : ((in(A4_4, B5_5) => ~in(B5_5, A4_4)))
% 223.64/30.28 -> [19] (in(skolem_B2222, skolem_D2424) => ~in(skolem_D2424, skolem_B2222))
% 223.64/30.28
% 223.64/30.28 [19] BETA_IMPLY : (in(skolem_B2222, skolem_D2424) => ~in(skolem_D2424, skolem_B2222))
% 223.64/30.28 -> [20] ~in(skolem_B2222, skolem_D2424)
% 223.64/30.28 -> [21] ~in(skolem_D2424, skolem_B2222)
% 223.64/30.28
% 223.64/30.28 [20] CLOSURE : =
% 223.64/30.28
% 223.64/30.28 [21] GAMMA_FORALL : ! [A6_6, B7_7] : (=(unordered_pair(A6_6, B7_7), unordered_pair(B7_7, A6_6)))
% 223.64/30.28 -> [25] =(unordered_pair(A6_1_1, B7_1_1), unordered_pair(B7_1_1, A6_1_1))
% 223.64/30.28
% 223.64/30.28 [25] GAMMA_FORALL : ! [A8_8, B9_9] : ((=(B9_9, singleton(A8_8)) <=> ! [C10_10] : ((in(C10_10, B9_9) <=> =(C10_10, A8_8)))))
% 223.64/30.28 -> [27] (=(singleton(skolem_C2323), singleton(skolem_C2323)) <=> ! [C10_10] : ((in(C10_10, singleton(skolem_C2323)) <=> =(C10_10, skolem_C2323))))
% 223.64/30.28
% 223.64/30.28 [27] BETA_EQUIV : (=(singleton(skolem_C2323), singleton(skolem_C2323)) <=> ! [C10_10] : ((in(C10_10, singleton(skolem_C2323)) <=> =(C10_10, skolem_C2323))))
% 223.64/30.28 -> [28] ~=(singleton(skolem_C2323), singleton(skolem_C2323)), ~! [C10_10] : ((in(C10_10, singleton(skolem_C2323)) <=> =(C10_10, skolem_C2323)))
% 223.64/30.28 -> [29] =(singleton(skolem_C2323), singleton(skolem_C2323)), ! [C10_10] : ((in(C10_10, singleton(skolem_C2323)) <=> =(C10_10, skolem_C2323)))
% 223.64/30.28
% 223.64/30.28 [28] DELTA_NOT_FORALL : ~! [C10_10] : ((in(C10_10, singleton(skolem_C2323)) <=> =(C10_10, skolem_C2323)))
% 223.64/30.28 -> [30] ~(in(skolem_C1010(singleton(skolem_C2323), skolem_C2323), singleton(skolem_C2323)) <=> =(skolem_C1010(singleton(skolem_C2323), skolem_C2323), skolem_C2323))
% 223.64/30.28
% 223.64/30.28 [30] CLOSURE : ~! [C10_10] : ((in(C10_10, singleton(skolem_C2323)) <=> =(C10_10, skolem_C2323)))
% 223.64/30.28
% 223.64/30.28 [35] BETA_EQUIV : (in(skolem_A2121, singleton(skolem_C2323)) <=> =(skolem_A2121, skolem_C2323))
% 223.64/30.28 -> [41] ~in(skolem_A2121, singleton(skolem_C2323)), ~=(skolem_A2121, skolem_C2323)
% 223.64/30.28 -> [42] in(skolem_A2121, singleton(skolem_C2323)), =(skolem_A2121, skolem_C2323)
% 223.64/30.28
% 223.64/30.28 [41] CLOSURE : =
% 223.64/30.28
% 223.64/30.28 [42] CLOSURE : =
% 223.64/30.28
% 223.64/30.28 [6] Rewrite : in(ordered_pair(skolem_A2121, skolem_B2222), cartesian_product2(singleton(skolem_C2323), skolem_D2424))
% 223.64/30.28 -> [8] (in(skolem_A2121, singleton(skolem_C2323)) & in(skolem_B2222, skolem_D2424))
% 223.64/30.28
% 223.64/30.28 [8] ALPHA_AND : (in(skolem_A2121, singleton(skolem_C2323)) & in(skolem_B2222, skolem_D2424))
% 223.64/30.28 -> [10] in(skolem_A2121, singleton(skolem_C2323)), in(skolem_B2222, skolem_D2424)
% 223.64/30.28
% 223.64/30.28 [10] BETA_NOT_AND : ~(=(skolem_A2121, skolem_C2323) & in(skolem_B2222, skolem_D2424))
% 223.64/30.28 -> [11] ~=(skolem_A2121, skolem_C2323)
% 223.64/30.28 -> [12] ~in(skolem_B2222, skolem_D2424)
% 223.64/30.28
% 223.64/30.28 [12] CLOSURE : ~in(skolem_B2222, skolem_D2424)
% 223.64/30.28
% 223.64/30.28 [11] GAMMA_FORALL : ! [A4_4, B5_5] : ((in(A4_4, B5_5) => ~in(B5_5, A4_4)))
% 223.64/30.28 -> [13] (in(skolem_B2222, skolem_D2424) => ~in(skolem_D2424, skolem_B2222))
% 223.64/30.28
% 223.64/30.28 [13] BETA_IMPLY : (in(skolem_B2222, skolem_D2424) => ~in(skolem_D2424, skolem_B2222))
% 223.64/30.28 -> [14] ~in(skolem_B2222, skolem_D2424)
% 223.64/30.28 -> [15] ~in(skolem_D2424, skolem_B2222)
% 223.64/30.28
% 223.64/30.28 [14] CLOSURE : ~in(skolem_B2222, skolem_D2424)
% 223.64/30.28
% 223.64/30.28 [15] GAMMA_FORALL : ! [A6_6, B7_7] : (=(unordered_pair(A6_6, B7_7), unordered_pair(B7_7, A6_6)))
% 223.64/30.28 -> [18] =(unordered_pair(A6_0_1, B7_0_1), unordered_pair(B7_0_1, A6_0_1))
% 223.64/30.28
% 223.64/30.28 [18] GAMMA_FORALL : ! [A8_8, B9_9] : ((=(B9_9, singleton(A8_8)) <=> ! [C10_10] : ((in(C10_10, B9_9) <=> =(C10_10, A8_8)))))
% 223.64/30.28 -> [22] (=(singleton(skolem_C2323), singleton(skolem_C2323)) <=> ! [C10_10] : ((in(C10_10, singleton(skolem_C2323)) <=> =(C10_10, skolem_C2323))))
% 223.64/30.28
% 223.64/30.28 [22] BETA_EQUIV : (=(singleton(skolem_C2323), singleton(skolem_C2323)) <=> ! [C10_10] : ((in(C10_10, singleton(skolem_C2323)) <=> =(C10_10, skolem_C2323))))
% 223.64/30.28 -> [23] ~=(singleton(skolem_C2323), singleton(skolem_C2323)), ~! [C10_10] : ((in(C10_10, singleton(skolem_C2323)) <=> =(C10_10, skolem_C2323)))
% 223.64/30.28 -> [24] =(singleton(skolem_C2323), singleton(skolem_C2323)), ! [C10_10] : ((in(C10_10, singleton(skolem_C2323)) <=> =(C10_10, skolem_C2323)))
% 223.64/30.28
% 223.64/30.28 [23] DELTA_NOT_FORALL : ~! [C10_10] : ((in(C10_10, singleton(skolem_C2323)) <=> =(C10_10, skolem_C2323)))
% 223.64/30.28 -> [26] ~(in(skolem_C1010(singleton(skolem_C2323), skolem_C2323), singleton(skolem_C2323)) <=> =(skolem_C1010(singleton(skolem_C2323), skolem_C2323), skolem_C2323))
% 223.64/30.28
% 223.64/30.28 [26] CLOSURE : ~! [C10_10] : ((in(C10_10, singleton(skolem_C2323)) <=> =(C10_10, skolem_C2323)))
% 223.64/30.28
% 223.64/30.28 [38] BETA_EQUIV : (in(skolem_A2121, singleton(skolem_C2323)) <=> =(skolem_A2121, skolem_C2323))
% 223.64/30.28 -> [43] ~in(skolem_A2121, singleton(skolem_C2323)), ~=(skolem_A2121, skolem_C2323)
% 223.64/30.28 -> [44] in(skolem_A2121, singleton(skolem_C2323)), =(skolem_A2121, skolem_C2323)
% 223.64/30.28
% 223.64/30.28 [43] CLOSURE : =
% 223.64/30.28
% 223.64/30.28 [44] CLOSURE : =
% 223.64/30.28
% 223.64/30.28 % SZS output end Proof for theBenchmark.p
% 223.64/30.28 [29.937737s][1][Res] 293462 goroutines created
% 223.64/30.28 ==== Result ====
% 223.64/30.28 [29.937775s][1][Res] VALID
% 223.64/30.28 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------