TSTP Solution File: COL124-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : COL124-2 : 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 : n005.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 : Wed Aug 30 18:32:17 EDT 2023
% Result : Unsatisfiable 0.21s 0.39s
% 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
% 0.00/0.13 % Problem : COL124-2 : TPTP v8.1.2. Released v3.2.0.
% 0.14/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.35 % Computer : n005.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sun Aug 27 04:57:53 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.39 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 0.21/0.39
% 0.21/0.39 % SZS status Unsatisfiable
% 0.21/0.39
% 0.21/0.40 % SZS output start Proof
% 0.21/0.40 Take the following subset of the input axioms:
% 0.21/0.40 fof(cls_Comb_OI__contract__E_0, axiom, ![V_z]: ~c_in(c_Pair(c_Comb_OI, V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))).
% 0.21/0.40 fof(cls_Comb_Ocontract_OK_0, axiom, ![V_x, V_y]: c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_y), V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))).
% 0.21/0.40 fof(cls_conjecture_0, negated_conjecture, ![V_V, V_U, V_W]: (c_in(c_Pair(V_V, v_x(V_U, V_V, V_W), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) | (~c_in(c_Pair(V_U, V_W, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) | ~c_in(c_Pair(V_U, V_V, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))).
% 0.21/0.40
% 0.21/0.40 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.40 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.40 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.40 fresh(y, y, x1...xn) = u
% 0.21/0.40 C => fresh(s, t, x1...xn) = v
% 0.21/0.40 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.40 variables of u and v.
% 0.21/0.40 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.40 input problem has no model of domain size 1).
% 0.21/0.40
% 0.21/0.40 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.40
% 0.21/0.40 Axiom 1 (cls_conjecture_0): fresh2(X, X, Y, Z, W) = true2.
% 0.21/0.40 Axiom 2 (cls_conjecture_0): fresh(X, X, Y, Z, W) = c_in(c_Pair(Y, v_x(Z, Y, W), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)).
% 0.21/0.40 Axiom 3 (cls_Comb_Ocontract_OK_0): c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, X), Y), X, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) = true2.
% 0.21/0.40 Axiom 4 (cls_conjecture_0): fresh(c_in(c_Pair(X, Y, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true2, Z, X, Y) = fresh2(c_in(c_Pair(X, Z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true2, Z, X, Y).
% 0.21/0.40
% 0.21/0.40 Goal 1 (cls_Comb_OI__contract__E_0): c_in(c_Pair(c_Comb_OI, X, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) = true2.
% 0.21/0.40 The goal is true when:
% 0.21/0.40 X = v_x(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, c_Comb_OI), X), c_Comb_OI, c_Comb_OI)
% 0.21/0.40
% 0.21/0.40 Proof:
% 0.21/0.40 c_in(c_Pair(c_Comb_OI, v_x(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, c_Comb_OI), X), c_Comb_OI, c_Comb_OI), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))
% 0.21/0.40 = { by axiom 2 (cls_conjecture_0) R->L }
% 0.21/0.40 fresh(true2, true2, c_Comb_OI, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, c_Comb_OI), X), c_Comb_OI)
% 0.21/0.40 = { by axiom 3 (cls_Comb_Ocontract_OK_0) R->L }
% 0.21/0.40 fresh(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, c_Comb_OI), X), c_Comb_OI, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true2, c_Comb_OI, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, c_Comb_OI), X), c_Comb_OI)
% 0.21/0.40 = { by axiom 4 (cls_conjecture_0) }
% 0.21/0.40 fresh2(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, c_Comb_OI), X), c_Comb_OI, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true2, c_Comb_OI, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, c_Comb_OI), X), c_Comb_OI)
% 0.21/0.40 = { by axiom 3 (cls_Comb_Ocontract_OK_0) }
% 0.21/0.40 fresh2(true2, true2, c_Comb_OI, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, c_Comb_OI), X), c_Comb_OI)
% 0.21/0.40 = { by axiom 1 (cls_conjecture_0) }
% 0.21/0.40 true2
% 0.21/0.40 % SZS output end Proof
% 0.21/0.40
% 0.21/0.40 RESULT: Unsatisfiable (the axioms are contradictory).
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