TSTP Solution File: SWV262-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SWV262-1 : TPTP v8.1.2. Released v3.2.0.
% 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 : n032.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 23:03:17 EDT 2023
% Result : Unsatisfiable 210.08s 27.13s
% Output : Proof 210.77s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.09 % Problem : SWV262-1 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.10 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Tue Aug 29 07:02:01 EDT 2023
% 0.10/0.30 % CPUTime :
% 210.08/27.13 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 210.08/27.13
% 210.08/27.13 % SZS status Unsatisfiable
% 210.08/27.13
% 210.77/27.13 % SZS output start Proof
% 210.77/27.13 Take the following subset of the input axioms:
% 210.77/27.13 fof(cls_Message_Oparts__Un_0, axiom, ![V_G, V_H]: c_Message_Oparts(c_union(V_G, V_H, tc_Message_Omsg))=c_union(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_Message_Omsg)).
% 210.77/27.13 fof(cls_Set_OUn__assoc_0, axiom, ![T_a, V_A, V_B, V_C]: c_union(c_union(V_A, V_B, T_a), V_C, T_a)=c_union(V_A, c_union(V_B, V_C, T_a), T_a)).
% 210.77/27.13 fof(cls_Set_OUn__empty__left_0, axiom, ![V_y, T_a2]: c_union(c_emptyset, V_y, T_a2)=V_y).
% 210.77/27.13 fof(cls_Set_OUn__insert__left_0, axiom, ![V_a, T_a2, V_B2, V_C2]: c_union(c_insert(V_a, V_B2, T_a2), V_C2, T_a2)=c_insert(V_a, c_union(V_B2, V_C2, T_a2), T_a2)).
% 210.77/27.13 fof(cls_conjecture_0, negated_conjecture, c_Message_Oparts(c_insert(v_X, c_insert(v_Y, v_H, tc_Message_Omsg), tc_Message_Omsg))!=c_union(c_union(c_Message_Oparts(c_insert(v_X, c_emptyset, tc_Message_Omsg)), c_Message_Oparts(c_insert(v_Y, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oparts(v_H), tc_Message_Omsg)).
% 210.77/27.13
% 210.77/27.13 Now clausify the problem and encode Horn clauses using encoding 3 of
% 210.77/27.13 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 210.77/27.13 We repeatedly replace C & s=t => u=v by the two clauses:
% 210.77/27.13 fresh(y, y, x1...xn) = u
% 210.77/27.13 C => fresh(s, t, x1...xn) = v
% 210.77/27.13 where fresh is a fresh function symbol and x1..xn are the free
% 210.77/27.13 variables of u and v.
% 210.77/27.13 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 210.77/27.13 input problem has no model of domain size 1).
% 210.77/27.13
% 210.77/27.13 The encoding turns the above axioms into the following unit equations and goals:
% 210.77/27.13
% 210.77/27.13 Axiom 1 (cls_Set_OUn__empty__left_0): c_union(c_emptyset, X, Y) = X.
% 210.77/27.13 Axiom 2 (cls_Message_Oparts__Un_0): c_Message_Oparts(c_union(X, Y, tc_Message_Omsg)) = c_union(c_Message_Oparts(X), c_Message_Oparts(Y), tc_Message_Omsg).
% 210.77/27.13 Axiom 3 (cls_Set_OUn__insert__left_0): c_union(c_insert(X, Y, Z), W, Z) = c_insert(X, c_union(Y, W, Z), Z).
% 210.77/27.13 Axiom 4 (cls_Set_OUn__assoc_0): c_union(c_union(X, Y, Z), W, Z) = c_union(X, c_union(Y, W, Z), Z).
% 210.77/27.13
% 210.77/27.13 Goal 1 (cls_conjecture_0): c_Message_Oparts(c_insert(v_X, c_insert(v_Y, v_H, tc_Message_Omsg), tc_Message_Omsg)) = c_union(c_union(c_Message_Oparts(c_insert(v_X, c_emptyset, tc_Message_Omsg)), c_Message_Oparts(c_insert(v_Y, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oparts(v_H), tc_Message_Omsg).
% 210.77/27.13 Proof:
% 210.77/27.13 c_Message_Oparts(c_insert(v_X, c_insert(v_Y, v_H, tc_Message_Omsg), tc_Message_Omsg))
% 210.77/27.13 = { by axiom 1 (cls_Set_OUn__empty__left_0) R->L }
% 210.77/27.13 c_Message_Oparts(c_insert(v_X, c_union(c_emptyset, c_insert(v_Y, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg))
% 210.77/27.13 = { by axiom 3 (cls_Set_OUn__insert__left_0) R->L }
% 210.77/27.13 c_Message_Oparts(c_union(c_insert(v_X, c_emptyset, tc_Message_Omsg), c_insert(v_Y, v_H, tc_Message_Omsg), tc_Message_Omsg))
% 210.77/27.13 = { by axiom 1 (cls_Set_OUn__empty__left_0) R->L }
% 210.77/27.13 c_Message_Oparts(c_union(c_insert(v_X, c_emptyset, tc_Message_Omsg), c_insert(v_Y, c_union(c_emptyset, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg))
% 210.77/27.13 = { by axiom 3 (cls_Set_OUn__insert__left_0) R->L }
% 210.77/27.13 c_Message_Oparts(c_union(c_insert(v_X, c_emptyset, tc_Message_Omsg), c_union(c_insert(v_Y, c_emptyset, tc_Message_Omsg), v_H, tc_Message_Omsg), tc_Message_Omsg))
% 210.77/27.13 = { by axiom 4 (cls_Set_OUn__assoc_0) R->L }
% 210.77/27.13 c_Message_Oparts(c_union(c_union(c_insert(v_X, c_emptyset, tc_Message_Omsg), c_insert(v_Y, c_emptyset, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg))
% 210.77/27.13 = { by axiom 2 (cls_Message_Oparts__Un_0) }
% 210.77/27.13 c_union(c_Message_Oparts(c_union(c_insert(v_X, c_emptyset, tc_Message_Omsg), c_insert(v_Y, c_emptyset, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Oparts(v_H), tc_Message_Omsg)
% 210.77/27.13 = { by axiom 2 (cls_Message_Oparts__Un_0) }
% 210.77/27.13 c_union(c_union(c_Message_Oparts(c_insert(v_X, c_emptyset, tc_Message_Omsg)), c_Message_Oparts(c_insert(v_Y, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oparts(v_H), tc_Message_Omsg)
% 210.77/27.13 % SZS output end Proof
% 210.77/27.13
% 210.77/27.13 RESULT: Unsatisfiable (the axioms are contradictory).
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