TSTP Solution File: LAT268-10 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT268-10 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n015.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 Aug 31 06:28:02 EDT 2023
% Result : Unsatisfiable 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT268-10 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 07:52:50 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.38 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.20/0.38
% 0.20/0.38 % SZS status Unsatisfiable
% 0.20/0.38
% 0.20/0.39 % SZS output start Proof
% 0.20/0.39 Axiom 1 (cls_conjecture_1): c_in(v_x, v_S, t_a) = true.
% 0.20/0.39 Axiom 2 (cls_Tarski_OA_A_61_61_Apset_Acl_0): v_A = c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit).
% 0.20/0.39 Axiom 3 (cls_Tarski_Or_A_61_61_Aorder_Acl_0): v_r = c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit).
% 0.20/0.39 Axiom 4 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.20/0.39 Axiom 5 (cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0): c_Tarski_Opotype_Opset(c_Tarski_Odual(X, Y), Y, tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(X, Y, tc_Product__Type_Ounit).
% 0.20/0.39 Axiom 6 (cls_conjecture_0): c_lessequals(v_S, v_A, tc_set(t_a)) = true.
% 0.20/0.39 Axiom 7 (cls_Tarski_Oglb__dual__lub_0): c_Tarski_Oglb(X, Y, Z) = c_Tarski_Olub(X, c_Tarski_Odual(Y, Z), Z).
% 0.20/0.39 Axiom 8 (cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0): c_in(c_Tarski_Odual(v_cl, t_a), c_Tarski_OCompleteLattice, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)) = true.
% 0.20/0.39 Axiom 9 (cls_Tarski_Odual_Acl_A_58_APartialOrder_0): c_in(c_Tarski_Odual(v_cl, t_a), c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)) = true.
% 0.20/0.39 Axiom 10 (cls_Tarski_O_Ix1_M_Ay1_J_A_58_Aorder_A_Idual_Acl_J_A_61_61_A_Iy1_M_Ax1_J_A_58_Aorder_Acl_0): ifeq(c_in(c_Pair(X, Y, Z, Z), c_Tarski_Opotype_Oorder(c_Tarski_Odual(W, Z), Z, tc_Product__Type_Ounit), tc_prod(Z, Z)), true, c_in(c_Pair(Y, X, Z, Z), c_Tarski_Opotype_Oorder(W, Z, tc_Product__Type_Ounit), tc_prod(Z, Z)), true) = true.
% 0.20/0.39 Axiom 11 (cls_Tarski_OCL_Olub__upper_0): ifeq(c_lessequals(X, c_Tarski_Opotype_Opset(Y, Z, tc_Product__Type_Ounit), tc_set(Z)), true, ifeq(c_in(Y, c_Tarski_OCompleteLattice, tc_Tarski_Opotype_Opotype__ext__type(Z, tc_Product__Type_Ounit)), true, ifeq(c_in(Y, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(Z, tc_Product__Type_Ounit)), true, ifeq(c_in(W, X, Z), true, c_in(c_Pair(W, c_Tarski_Olub(X, Y, Z), Z, Z), c_Tarski_Opotype_Oorder(Y, Z, tc_Product__Type_Ounit), tc_prod(Z, Z)), true), true), true), true) = true.
% 0.20/0.39
% 0.20/0.39 Goal 1 (cls_conjecture_2): c_in(c_Pair(c_Tarski_Oglb(v_S, v_cl, t_a), v_x, t_a, t_a), v_r, tc_prod(t_a, t_a)) = true.
% 0.20/0.39 Proof:
% 0.20/0.39 c_in(c_Pair(c_Tarski_Oglb(v_S, v_cl, t_a), v_x, t_a, t_a), v_r, tc_prod(t_a, t_a))
% 0.20/0.39 = { by axiom 3 (cls_Tarski_Or_A_61_61_Aorder_Acl_0) }
% 0.20/0.39 c_in(c_Pair(c_Tarski_Oglb(v_S, v_cl, t_a), v_x, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))
% 0.20/0.39 = { by axiom 4 (ifeq_axiom) R->L }
% 0.20/0.39 ifeq(true, true, c_in(c_Pair(c_Tarski_Oglb(v_S, v_cl, t_a), v_x, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)), true)
% 0.20/0.39 = { by axiom 11 (cls_Tarski_OCL_Olub__upper_0) R->L }
% 0.20/0.39 ifeq(ifeq(c_lessequals(v_S, c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl, t_a), t_a, tc_Product__Type_Ounit), tc_set(t_a)), true, ifeq(c_in(c_Tarski_Odual(v_cl, t_a), c_Tarski_OCompleteLattice, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), true, ifeq(c_in(c_Tarski_Odual(v_cl, t_a), c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), true, ifeq(c_in(v_x, v_S, t_a), true, c_in(c_Pair(v_x, c_Tarski_Olub(v_S, c_Tarski_Odual(v_cl, t_a), t_a), t_a, t_a), c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl, t_a), t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)), true), true), true), true), true, c_in(c_Pair(c_Tarski_Oglb(v_S, v_cl, t_a), v_x, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)), true)
% 0.20/0.39 = { by axiom 8 (cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0) }
% 0.20/0.39 ifeq(ifeq(c_lessequals(v_S, c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl, t_a), t_a, tc_Product__Type_Ounit), tc_set(t_a)), true, ifeq(true, true, ifeq(c_in(c_Tarski_Odual(v_cl, t_a), c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), true, ifeq(c_in(v_x, v_S, t_a), true, c_in(c_Pair(v_x, c_Tarski_Olub(v_S, c_Tarski_Odual(v_cl, t_a), t_a), t_a, t_a), c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl, t_a), t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)), true), true), true), true), true, c_in(c_Pair(c_Tarski_Oglb(v_S, v_cl, t_a), v_x, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)), true)
% 0.20/0.39 = { by axiom 5 (cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0) }
% 0.20/0.39 ifeq(ifeq(c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), true, ifeq(true, true, ifeq(c_in(c_Tarski_Odual(v_cl, t_a), c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), true, ifeq(c_in(v_x, v_S, t_a), true, c_in(c_Pair(v_x, c_Tarski_Olub(v_S, c_Tarski_Odual(v_cl, t_a), t_a), t_a, t_a), c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl, t_a), t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)), true), true), true), true), true, c_in(c_Pair(c_Tarski_Oglb(v_S, v_cl, t_a), v_x, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)), true)
% 0.20/0.39 = { by axiom 2 (cls_Tarski_OA_A_61_61_Apset_Acl_0) R->L }
% 0.20/0.39 ifeq(ifeq(c_lessequals(v_S, v_A, tc_set(t_a)), true, ifeq(true, true, ifeq(c_in(c_Tarski_Odual(v_cl, t_a), c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), true, ifeq(c_in(v_x, v_S, t_a), true, c_in(c_Pair(v_x, c_Tarski_Olub(v_S, c_Tarski_Odual(v_cl, t_a), t_a), t_a, t_a), c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl, t_a), t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)), true), true), true), true), true, c_in(c_Pair(c_Tarski_Oglb(v_S, v_cl, t_a), v_x, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)), true)
% 0.20/0.39 = { by axiom 4 (ifeq_axiom) }
% 0.20/0.39 ifeq(ifeq(c_lessequals(v_S, v_A, tc_set(t_a)), true, ifeq(c_in(c_Tarski_Odual(v_cl, t_a), c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), true, ifeq(c_in(v_x, v_S, t_a), true, c_in(c_Pair(v_x, c_Tarski_Olub(v_S, c_Tarski_Odual(v_cl, t_a), t_a), t_a, t_a), c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl, t_a), t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)), true), true), true), true, c_in(c_Pair(c_Tarski_Oglb(v_S, v_cl, t_a), v_x, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)), true)
% 0.20/0.39 = { by axiom 9 (cls_Tarski_Odual_Acl_A_58_APartialOrder_0) }
% 0.20/0.39 ifeq(ifeq(c_lessequals(v_S, v_A, tc_set(t_a)), true, ifeq(true, true, ifeq(c_in(v_x, v_S, t_a), true, c_in(c_Pair(v_x, c_Tarski_Olub(v_S, c_Tarski_Odual(v_cl, t_a), t_a), t_a, t_a), c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl, t_a), t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)), true), true), true), true, c_in(c_Pair(c_Tarski_Oglb(v_S, v_cl, t_a), v_x, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)), true)
% 0.20/0.39 = { by axiom 4 (ifeq_axiom) }
% 0.20/0.39 ifeq(ifeq(c_lessequals(v_S, v_A, tc_set(t_a)), true, ifeq(c_in(v_x, v_S, t_a), true, c_in(c_Pair(v_x, c_Tarski_Olub(v_S, c_Tarski_Odual(v_cl, t_a), t_a), t_a, t_a), c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl, t_a), t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)), true), true), true, c_in(c_Pair(c_Tarski_Oglb(v_S, v_cl, t_a), v_x, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)), true)
% 0.20/0.39 = { by axiom 7 (cls_Tarski_Oglb__dual__lub_0) R->L }
% 0.20/0.39 ifeq(ifeq(c_lessequals(v_S, v_A, tc_set(t_a)), true, ifeq(c_in(v_x, v_S, t_a), true, c_in(c_Pair(v_x, c_Tarski_Oglb(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl, t_a), t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)), true), true), true, c_in(c_Pair(c_Tarski_Oglb(v_S, v_cl, t_a), v_x, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)), true)
% 0.20/0.39 = { by axiom 1 (cls_conjecture_1) }
% 0.20/0.39 ifeq(ifeq(c_lessequals(v_S, v_A, tc_set(t_a)), true, ifeq(true, true, c_in(c_Pair(v_x, c_Tarski_Oglb(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl, t_a), t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)), true), true), true, c_in(c_Pair(c_Tarski_Oglb(v_S, v_cl, t_a), v_x, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)), true)
% 0.20/0.39 = { by axiom 6 (cls_conjecture_0) }
% 0.20/0.39 ifeq(ifeq(true, true, ifeq(true, true, c_in(c_Pair(v_x, c_Tarski_Oglb(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl, t_a), t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)), true), true), true, c_in(c_Pair(c_Tarski_Oglb(v_S, v_cl, t_a), v_x, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)), true)
% 0.20/0.39 = { by axiom 4 (ifeq_axiom) }
% 0.20/0.39 ifeq(ifeq(true, true, c_in(c_Pair(v_x, c_Tarski_Oglb(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl, t_a), t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)), true), true, c_in(c_Pair(c_Tarski_Oglb(v_S, v_cl, t_a), v_x, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)), true)
% 0.20/0.39 = { by axiom 4 (ifeq_axiom) }
% 0.20/0.39 ifeq(c_in(c_Pair(v_x, c_Tarski_Oglb(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl, t_a), t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)), true, c_in(c_Pair(c_Tarski_Oglb(v_S, v_cl, t_a), v_x, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)), true)
% 0.20/0.39 = { by axiom 10 (cls_Tarski_O_Ix1_M_Ay1_J_A_58_Aorder_A_Idual_Acl_J_A_61_61_A_Iy1_M_Ax1_J_A_58_Aorder_Acl_0) }
% 0.20/0.39 true
% 0.20/0.39 % SZS output end Proof
% 0.20/0.39
% 0.20/0.39 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------