%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LAT268-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:44:40 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.45s
% Output : Proof 0.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT268-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 14:09:29 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.45 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.10/0.45
% 0.10/0.45 % SZS status Unsatisfiable
% 0.10/0.45
% 0.10/0.45 % SZS output start Proof
% 0.10/0.45 Axiom 1 (cls_conjecture_1): c_in(v_x, v_S, t_a) = true.
% 0.10/0.45 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).
% 0.10/0.45 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).
% 0.10/0.45 Axiom 4 (cls_conjecture_0): c_lessequals(v_S, v_A, tc_set(t_a)) = true.
% 0.10/0.45 Axiom 5 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.10/0.45 Axiom 6 (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).
% 0.10/0.45 Axiom 7 (cls_Tarski_Oglb__dual__lub_0): c_Tarski_Oglb(X, Y, Z) = c_Tarski_Olub(X, c_Tarski_Odual(Y, Z), Z).
% 0.10/0.45 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.
% 0.10/0.45 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.
% 0.10/0.45 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.
% 0.10/0.45 Axiom 11 (cls_Tarski_OCL_Olub__upper_0): ifeq(c_in(X, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(Y, tc_Product__Type_Ounit)), true, ifeq(c_in(X, c_Tarski_OCompleteLattice, tc_Tarski_Opotype_Opotype__ext__type(Y, tc_Product__Type_Ounit)), true, ifeq(c_in(Z, W, Y), true, ifeq(c_lessequals(W, c_Tarski_Opotype_Opset(X, Y, tc_Product__Type_Ounit), tc_set(Y)), true, c_in(c_Pair(Z, c_Tarski_Olub(W, X, Y), Y, Y), c_Tarski_Opotype_Oorder(X, Y, tc_Product__Type_Ounit), tc_prod(Y, Y)), true), true), true), true) = true.
% 0.10/0.45
% 0.10/0.45 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.
% 0.10/0.45 Proof:
% 0.10/0.45 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))
% 0.10/0.45 = { by axiom 3 (cls_Tarski_Or_A_61_61_Aorder_Acl_0) }
% 0.10/0.45 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))
% 0.10/0.45 = { by axiom 5 (ifeq_axiom) R->L }
% 0.10/0.45 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)
% 0.10/0.45 = { by axiom 11 (cls_Tarski_OCL_Olub__upper_0) R->L }
% 0.10/0.45 ifeq(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(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(v_x, v_S, t_a), true, 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, 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)
% 0.10/0.45 = { by axiom 8 (cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0) }
% 0.10/0.45 ifeq(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(true, true, ifeq(c_in(v_x, v_S, t_a), true, 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, 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)
% 0.10/0.45 = { by axiom 9 (cls_Tarski_Odual_Acl_A_58_APartialOrder_0) }
% 0.10/0.45 ifeq(ifeq(true, true, ifeq(true, true, ifeq(c_in(v_x, v_S, t_a), true, 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, 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)
% 0.10/0.45 = { by axiom 5 (ifeq_axiom) }
% 0.10/0.45 ifeq(ifeq(true, true, ifeq(c_in(v_x, v_S, t_a), true, 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, 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)
% 0.10/0.45 = { by axiom 5 (ifeq_axiom) }
% 0.10/0.45 ifeq(ifeq(c_in(v_x, v_S, t_a), true, 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, 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)
% 0.10/0.45 = { by axiom 6 (cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0) }
% 0.10/0.45 ifeq(ifeq(c_in(v_x, v_S, t_a), true, ifeq(c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(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)
% 0.10/0.45 = { by axiom 2 (cls_Tarski_OA_A_61_61_Apset_Acl_0) R->L }
% 0.10/0.45 ifeq(ifeq(c_in(v_x, v_S, t_a), true, ifeq(c_lessequals(v_S, v_A, tc_set(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)
% 0.10/0.45 = { by axiom 7 (cls_Tarski_Oglb__dual__lub_0) R->L }
% 0.10/0.45 ifeq(ifeq(c_in(v_x, v_S, t_a), true, ifeq(c_lessequals(v_S, v_A, tc_set(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)
% 0.10/0.45 = { by axiom 1 (cls_conjecture_1) }
% 0.10/0.45 ifeq(ifeq(true, true, ifeq(c_lessequals(v_S, v_A, tc_set(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)
% 0.10/0.45 = { by axiom 5 (ifeq_axiom) }
% 0.10/0.45 ifeq(ifeq(c_lessequals(v_S, v_A, tc_set(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, 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)
% 0.10/0.45 = { by axiom 4 (cls_conjecture_0) }
% 0.10/0.45 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)
% 0.10/0.45 = { by axiom 5 (ifeq_axiom) }
% 0.10/0.45 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)
% 0.10/0.45 = { 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) }
% 0.10/0.45 true
% 0.10/0.45 % SZS output end Proof
% 0.10/0.45
% 0.10/0.45 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------