TSTP Solution File: SET978+1 by Goeland---1.0.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SET978+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n011.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 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET978+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : goeland -dmt -presko -proof %s
% 0.13/0.33 % Computer : n011.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Sep 3 08:46:58 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 [DMT] DMT loaded with preskolemization
% 0.13/0.34 [EQ] equality loaded.
% 0.13/0.34 [0.000049s][1][MAIN] Problem : theBenchmark.p
% 0.13/0.34 Start search
% 0.13/0.34 nb_step : 1 - limit : 6
% 0.13/0.34 Launch Gotab with destructive = true
% 0.13/0.40 % SZS output start Proof for theBenchmark.p
% 0.19/0.40 [0] ALPHA_AND : (? [A4_4] : (empty(A4_4)) & ? [A5_5] : (~empty(A5_5)) & ! [A6_6, B7_7] : ((disjoint(A6_6, B7_7) => disjoint(B7_7, A6_6))) & ! [A8_8, B9_9, C10_10, D11_11] : (((disjoint(A8_8, B9_9) | disjoint(C10_10, D11_11)) => disjoint(cartesian_product2(A8_8, C10_10), cartesian_product2(B9_9, D11_11)))) & ! [A16_16, B17_17] : ((~=(A16_16, B17_17) => disjoint(singleton(A16_16), singleton(B17_17)))) & ~! [A12_12, B13_13, C14_14, D15_15] : ((~=(A12_12, B13_13) => (disjoint(cartesian_product2(singleton(A12_12), C14_14), cartesian_product2(singleton(B13_13), D15_15)) & disjoint(cartesian_product2(C14_14, singleton(A12_12)), cartesian_product2(D15_15, singleton(B13_13)))))))
% 0.19/0.40 -> [1] ? [A4_4] : (empty(A4_4)), ? [A5_5] : (~empty(A5_5)), ! [A6_6, B7_7] : ((disjoint(A6_6, B7_7) => disjoint(B7_7, A6_6))), ! [A8_8, B9_9, C10_10, D11_11] : (((disjoint(A8_8, B9_9) | disjoint(C10_10, D11_11)) => disjoint(cartesian_product2(A8_8, C10_10), cartesian_product2(B9_9, D11_11)))), ! [A16_16, B17_17] : ((~=(A16_16, B17_17) => disjoint(singleton(A16_16), singleton(B17_17)))), ~! [A12_12, B13_13, C14_14, D15_15] : ((~=(A12_12, B13_13) => (disjoint(cartesian_product2(singleton(A12_12), C14_14), cartesian_product2(singleton(B13_13), D15_15)) & disjoint(cartesian_product2(C14_14, singleton(A12_12)), cartesian_product2(D15_15, singleton(B13_13))))))
% 0.19/0.40
% 0.19/0.40 [1] DELTA_EXISTS : ? [A4_4] : (empty(A4_4))
% 0.19/0.40 -> [2] empty(skolem_A44)
% 0.19/0.40
% 0.19/0.40 [2] DELTA_EXISTS : ? [A5_5] : (~empty(A5_5))
% 0.19/0.40 -> [3] ~empty(skolem_A55)
% 0.19/0.40
% 0.19/0.40 [3] DELTA_NOT_FORALL : ~! [A12_12, B13_13, C14_14, D15_15] : ((~=(A12_12, B13_13) => (disjoint(cartesian_product2(singleton(A12_12), C14_14), cartesian_product2(singleton(B13_13), D15_15)) & disjoint(cartesian_product2(C14_14, singleton(A12_12)), cartesian_product2(D15_15, singleton(B13_13))))))
% 0.19/0.40 -> [4] ~(~=(skolem_A1212, skolem_B1313) => (disjoint(cartesian_product2(singleton(skolem_A1212), skolem_C1414), cartesian_product2(singleton(skolem_B1313), skolem_D1515)) & disjoint(cartesian_product2(skolem_C1414, singleton(skolem_A1212)), cartesian_product2(skolem_D1515, singleton(skolem_B1313)))))
% 0.19/0.40
% 0.19/0.40 [4] ALPHA_NOT_IMPLY : ~(~=(skolem_A1212, skolem_B1313) => (disjoint(cartesian_product2(singleton(skolem_A1212), skolem_C1414), cartesian_product2(singleton(skolem_B1313), skolem_D1515)) & disjoint(cartesian_product2(skolem_C1414, singleton(skolem_A1212)), cartesian_product2(skolem_D1515, singleton(skolem_B1313)))))
% 0.19/0.40 -> [5] ~=(skolem_A1212, skolem_B1313), ~(disjoint(cartesian_product2(singleton(skolem_A1212), skolem_C1414), cartesian_product2(singleton(skolem_B1313), skolem_D1515)) & disjoint(cartesian_product2(skolem_C1414, singleton(skolem_A1212)), cartesian_product2(skolem_D1515, singleton(skolem_B1313))))
% 0.19/0.40
% 0.19/0.40 [5] BETA_NOT_AND : ~(disjoint(cartesian_product2(singleton(skolem_A1212), skolem_C1414), cartesian_product2(singleton(skolem_B1313), skolem_D1515)) & disjoint(cartesian_product2(skolem_C1414, singleton(skolem_A1212)), cartesian_product2(skolem_D1515, singleton(skolem_B1313))))
% 0.19/0.40 -> [6] ~disjoint(cartesian_product2(singleton(skolem_A1212), skolem_C1414), cartesian_product2(singleton(skolem_B1313), skolem_D1515))
% 0.19/0.40 -> [7] ~disjoint(cartesian_product2(skolem_C1414, singleton(skolem_A1212)), cartesian_product2(skolem_D1515, singleton(skolem_B1313)))
% 0.19/0.40
% 0.19/0.40 [6] GAMMA_FORALL : ! [A6_6, B7_7] : ((disjoint(A6_6, B7_7) => disjoint(B7_7, A6_6)))
% 0.19/0.40 -> [8] (disjoint(cartesian_product2(singleton(skolem_B1313), skolem_D1515), cartesian_product2(singleton(skolem_A1212), skolem_C1414)) => disjoint(cartesian_product2(singleton(skolem_A1212), skolem_C1414), cartesian_product2(singleton(skolem_B1313), skolem_D1515)))
% 0.19/0.40
% 0.19/0.40 [8] BETA_IMPLY : (disjoint(cartesian_product2(singleton(skolem_B1313), skolem_D1515), cartesian_product2(singleton(skolem_A1212), skolem_C1414)) => disjoint(cartesian_product2(singleton(skolem_A1212), skolem_C1414), cartesian_product2(singleton(skolem_B1313), skolem_D1515)))
% 0.19/0.40 -> [10] ~disjoint(cartesian_product2(singleton(skolem_B1313), skolem_D1515), cartesian_product2(singleton(skolem_A1212), skolem_C1414))
% 0.19/0.40 -> [11] disjoint(cartesian_product2(singleton(skolem_A1212), skolem_C1414), cartesian_product2(singleton(skolem_B1313), skolem_D1515))
% 0.19/0.40
% 0.19/0.40 [11] CLOSURE : disjoint(cartesian_product2(singleton(skolem_A1212), skolem_C1414), cartesian_product2(singleton(skolem_B1313), skolem_D1515))
% 0.19/0.40
% 0.19/0.40 [10] GAMMA_FORALL : ! [A8_8, B9_9, C10_10, D11_11] : (((disjoint(A8_8, B9_9) | disjoint(C10_10, D11_11)) => disjoint(cartesian_product2(A8_8, C10_10), cartesian_product2(B9_9, D11_11))))
% 0.19/0.40 -> [14] ((disjoint(singleton(skolem_A1212), singleton(skolem_B1313)) | disjoint(skolem_C1414, skolem_D1515)) => disjoint(cartesian_product2(singleton(skolem_A1212), skolem_C1414), cartesian_product2(singleton(skolem_B1313), skolem_D1515)))
% 0.19/0.40
% 0.19/0.40 [14] BETA_IMPLY : ((disjoint(singleton(skolem_A1212), singleton(skolem_B1313)) | disjoint(skolem_C1414, skolem_D1515)) => disjoint(cartesian_product2(singleton(skolem_A1212), skolem_C1414), cartesian_product2(singleton(skolem_B1313), skolem_D1515)))
% 0.19/0.40 -> [15] ~(disjoint(singleton(skolem_A1212), singleton(skolem_B1313)) | disjoint(skolem_C1414, skolem_D1515))
% 0.19/0.40 -> [16] disjoint(cartesian_product2(singleton(skolem_A1212), skolem_C1414), cartesian_product2(singleton(skolem_B1313), skolem_D1515))
% 0.19/0.40
% 0.19/0.40 [16] CLOSURE : disjoint(cartesian_product2(singleton(skolem_A1212), skolem_C1414), cartesian_product2(singleton(skolem_B1313), skolem_D1515))
% 0.19/0.40
% 0.19/0.40 [22] BETA_IMPLY : (~=(skolem_A1212, skolem_B1313) => disjoint(singleton(skolem_A1212), singleton(skolem_B1313)))
% 0.19/0.40 -> [33] ~~=(skolem_A1212, skolem_B1313)
% 0.19/0.40 -> [34] disjoint(singleton(skolem_A1212), singleton(skolem_B1313))
% 0.19/0.40
% 0.19/0.40 [34] CLOSURE : disjoint(singleton(skolem_A1212), singleton(skolem_B1313))
% 0.19/0.40
% 0.19/0.40 [33] ALPHA_NOT_NOT : ~~=(skolem_A1212, skolem_B1313)
% 0.19/0.40 -> [35] =(skolem_A1212, skolem_B1313)
% 0.19/0.40
% 0.19/0.40 [35] CLOSURE : =
% 0.19/0.40
% 0.19/0.40 [7] GAMMA_FORALL : ! [A6_6, B7_7] : ((disjoint(A6_6, B7_7) => disjoint(B7_7, A6_6)))
% 0.19/0.40 -> [9] (disjoint(cartesian_product2(skolem_D1515, singleton(skolem_B1313)), cartesian_product2(skolem_C1414, singleton(skolem_A1212))) => disjoint(cartesian_product2(skolem_C1414, singleton(skolem_A1212)), cartesian_product2(skolem_D1515, singleton(skolem_B1313))))
% 0.19/0.40
% 0.19/0.40 [9] BETA_IMPLY : (disjoint(cartesian_product2(skolem_D1515, singleton(skolem_B1313)), cartesian_product2(skolem_C1414, singleton(skolem_A1212))) => disjoint(cartesian_product2(skolem_C1414, singleton(skolem_A1212)), cartesian_product2(skolem_D1515, singleton(skolem_B1313))))
% 0.19/0.40 -> [12] ~disjoint(cartesian_product2(skolem_D1515, singleton(skolem_B1313)), cartesian_product2(skolem_C1414, singleton(skolem_A1212)))
% 0.19/0.40 -> [13] disjoint(cartesian_product2(skolem_C1414, singleton(skolem_A1212)), cartesian_product2(skolem_D1515, singleton(skolem_B1313)))
% 0.19/0.40
% 0.19/0.40 [13] CLOSURE : disjoint(cartesian_product2(skolem_C1414, singleton(skolem_A1212)), cartesian_product2(skolem_D1515, singleton(skolem_B1313)))
% 0.19/0.40
% 0.19/0.40 [12] GAMMA_FORALL : ! [A8_8, B9_9, C10_10, D11_11] : (((disjoint(A8_8, B9_9) | disjoint(C10_10, D11_11)) => disjoint(cartesian_product2(A8_8, C10_10), cartesian_product2(B9_9, D11_11))))
% 0.19/0.40 -> [17] ((disjoint(skolem_C1414, skolem_D1515) | disjoint(singleton(skolem_A1212), singleton(skolem_B1313))) => disjoint(cartesian_product2(skolem_C1414, singleton(skolem_A1212)), cartesian_product2(skolem_D1515, singleton(skolem_B1313))))
% 0.19/0.40
% 0.19/0.40 [17] BETA_IMPLY : ((disjoint(skolem_C1414, skolem_D1515) | disjoint(singleton(skolem_A1212), singleton(skolem_B1313))) => disjoint(cartesian_product2(skolem_C1414, singleton(skolem_A1212)), cartesian_product2(skolem_D1515, singleton(skolem_B1313))))
% 0.19/0.40 -> [18] ~(disjoint(skolem_C1414, skolem_D1515) | disjoint(singleton(skolem_A1212), singleton(skolem_B1313)))
% 0.19/0.40 -> [19] disjoint(cartesian_product2(skolem_C1414, singleton(skolem_A1212)), cartesian_product2(skolem_D1515, singleton(skolem_B1313)))
% 0.19/0.40
% 0.19/0.40 [19] CLOSURE : disjoint(cartesian_product2(skolem_C1414, singleton(skolem_A1212)), cartesian_product2(skolem_D1515, singleton(skolem_B1313)))
% 0.19/0.40
% 0.19/0.40 [23] BETA_IMPLY : (~=(skolem_A1212, skolem_B1313) => disjoint(singleton(skolem_A1212), singleton(skolem_B1313)))
% 0.19/0.40 -> [30] ~~=(skolem_A1212, skolem_B1313)
% 0.19/0.40 -> [31] disjoint(singleton(skolem_A1212), singleton(skolem_B1313))
% 0.19/0.40
% 0.19/0.40 [31] CLOSURE : disjoint(singleton(skolem_A1212), singleton(skolem_B1313))
% 0.19/0.40
% 0.19/0.40 [30] ALPHA_NOT_NOT : ~~=(skolem_A1212, skolem_B1313)
% 0.19/0.40 -> [32] =(skolem_A1212, skolem_B1313)
% 0.19/0.40
% 0.19/0.40 [32] CLOSURE : =
% 0.19/0.40
% 0.19/0.40 % SZS output end Proof for theBenchmark.p
% 0.19/0.40 [0.066076s][1][Res] 151 goroutines created
% 0.19/0.40 ==== Result ====
% 0.19/0.40 [0.066124s][1][Res] VALID
% 0.19/0.40 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------