TSTP Solution File: HWV028-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : HWV028-1 : TPTP v8.1.2. Released v2.5.0.
% 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 : n024.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 02:31:38 EDT 2023
% Result : Unsatisfiable 0.21s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HWV028-1 : TPTP v8.1.2. Released v2.5.0.
% 0.07/0.13 % 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 : n024.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 : Tue Aug 29 16:36:08 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.21/0.41 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.21/0.41
% 0.21/0.41 % SZS status Unsatisfiable
% 0.21/0.41
% 0.21/0.41 % SZS output start Proof
% 0.21/0.41 Take the following subset of the input axioms:
% 0.21/0.41 fof(axiom_1, axiom, ![X_0]: plus(X_0, n1)!=n0).
% 0.21/0.41 fof(axiom_13, axiom, ![Z_21, Y_20, X_19]: (~gt(Z_21, Y_20) | (gt(Z_21, X_19) | ~gt(Y_20, X_19)))).
% 0.21/0.41 fof(axiom_17, axiom, ![X_28]: ~gt(X_28, X_28)).
% 0.21/0.41 fof(axiom_21, axiom, ![X_t_32]: level(X_t_32)=int_level(X_t_32)).
% 0.21/0.41 fof(axiom_26, axiom, ![X_t_37]: (~p_Reset(X_t_37) | int_level(plus(X_t_37, n1))=n0)).
% 0.21/0.41 fof(axiom_29, axiom, ![X_t_37_2]: (~p_Reset(X_t_37_2) | ~p_Wr_error(plus(X_t_37_2, n1)))).
% 0.21/0.41 fof(axiom_30, axiom, ![X_t_37_2]: (~p_Reset(X_t_37_2) | ~p_Rd_error(plus(X_t_37_2, n1)))).
% 0.21/0.41 fof(axiom_31, axiom, ![X_k1_38, X_k2_39, X_t_37_2]: (~p_Reset(X_t_37_2) | ~p_Mem(X_k1_38, X_k2_39, plus(X_t_37_2, n1)))).
% 0.21/0.41 fof(axiom_32, axiom, ![X_k1_40, X_t_37_2]: (~p_Reset(X_t_37_2) | ~p_Data_out(X_k1_40, plus(X_t_37_2, n1)))).
% 0.21/0.41 fof(axiom_6, axiom, ![X_3, Y_4]: (~def_10(Y_4, X_3) | ~gt(X_3, Y_4))).
% 0.21/0.41 fof(axiom_7, axiom, ![X_3_2, Y_4_2]: (~def_10(Y_4_2, X_3_2) | X_3_2!=Y_4_2)).
% 0.21/0.41 fof(quest_1, negated_conjecture, p_Reset(t_139)).
% 0.21/0.41 fof(quest_2, negated_conjecture, gt(level(plus(t_139, n1)), fifo_length)).
% 0.21/0.41 fof(quest_3, negated_conjecture, gt(fifo_length, n0)).
% 0.21/0.41
% 0.21/0.41 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.41 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.41 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.41 fresh(y, y, x1...xn) = u
% 0.21/0.41 C => fresh(s, t, x1...xn) = v
% 0.21/0.41 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.41 variables of u and v.
% 0.21/0.41 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.41 input problem has no model of domain size 1).
% 0.21/0.41
% 0.21/0.41 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.41
% 0.21/0.41 Axiom 1 (axiom_21): level(X) = int_level(X).
% 0.21/0.41 Axiom 2 (quest_1): p_Reset(t_139) = true2.
% 0.21/0.41 Axiom 3 (quest_3): gt(fifo_length, n0) = true2.
% 0.21/0.41 Axiom 4 (axiom_26): fresh9(X, X, Y) = n0.
% 0.21/0.41 Axiom 5 (axiom_13): fresh15(X, X, Y, Z) = true2.
% 0.21/0.41 Axiom 6 (axiom_26): fresh9(p_Reset(X), true2, X) = int_level(plus(X, n1)).
% 0.21/0.41 Axiom 7 (axiom_13): fresh14(X, X, Y, Z, W) = gt(Y, W).
% 0.21/0.41 Axiom 8 (quest_2): gt(level(plus(t_139, n1)), fifo_length) = true2.
% 0.21/0.41 Axiom 9 (axiom_13): fresh14(gt(X, Y), true2, Z, X, Y) = fresh15(gt(Z, X), true2, Z, Y).
% 0.21/0.41
% 0.21/0.41 Goal 1 (axiom_17): gt(X, X) = true2.
% 0.21/0.41 The goal is true when:
% 0.21/0.41 X = n0
% 0.21/0.41
% 0.21/0.41 Proof:
% 0.21/0.41 gt(n0, n0)
% 0.21/0.41 = { by axiom 4 (axiom_26) R->L }
% 0.21/0.41 gt(fresh9(true2, true2, t_139), n0)
% 0.21/0.41 = { by axiom 2 (quest_1) R->L }
% 0.21/0.41 gt(fresh9(p_Reset(t_139), true2, t_139), n0)
% 0.21/0.41 = { by axiom 6 (axiom_26) }
% 0.21/0.41 gt(int_level(plus(t_139, n1)), n0)
% 0.21/0.41 = { by axiom 1 (axiom_21) R->L }
% 0.21/0.41 gt(level(plus(t_139, n1)), n0)
% 0.21/0.41 = { by axiom 7 (axiom_13) R->L }
% 0.21/0.41 fresh14(true2, true2, level(plus(t_139, n1)), fifo_length, n0)
% 0.21/0.41 = { by axiom 3 (quest_3) R->L }
% 0.21/0.41 fresh14(gt(fifo_length, n0), true2, level(plus(t_139, n1)), fifo_length, n0)
% 0.21/0.41 = { by axiom 9 (axiom_13) }
% 0.21/0.41 fresh15(gt(level(plus(t_139, n1)), fifo_length), true2, level(plus(t_139, n1)), n0)
% 0.21/0.41 = { by axiom 8 (quest_2) }
% 0.21/0.41 fresh15(true2, true2, level(plus(t_139, n1)), n0)
% 0.21/0.41 = { by axiom 5 (axiom_13) }
% 0.21/0.41 true2
% 0.21/0.41 % SZS output end Proof
% 0.21/0.41
% 0.21/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
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