TSTP Solution File: COL105-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : COL105-2 : 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 : n007.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 18:32:09 EDT 2023
% Result : Unsatisfiable 0.14s 0.38s
% Output : Proof 0.14s
% 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 : COL105-2 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n007.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 04:55:42 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.38 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.14/0.38
% 0.14/0.38 % SZS status Unsatisfiable
% 0.14/0.38
% 0.14/0.38 % SZS output start Proof
% 0.14/0.38 Take the following subset of the input axioms:
% 0.14/0.38 fof(cls_Comb_Oparcontract_Ointros__1_0, axiom, ![V_x]: c_in(c_Pair(V_x, V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))).
% 0.14/0.38 fof(cls_conjecture_0, negated_conjecture, c_in(c_Pair(v_x, v_xb, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))).
% 0.14/0.38 fof(cls_conjecture_1, negated_conjecture, ![V_U]: (~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) | ~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))).
% 0.14/0.38
% 0.14/0.38 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.14/0.38 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.14/0.38 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.14/0.38 fresh(y, y, x1...xn) = u
% 0.14/0.38 C => fresh(s, t, x1...xn) = v
% 0.14/0.38 where fresh is a fresh function symbol and x1..xn are the free
% 0.14/0.38 variables of u and v.
% 0.14/0.38 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.14/0.38 input problem has no model of domain size 1).
% 0.14/0.38
% 0.14/0.38 The encoding turns the above axioms into the following unit equations and goals:
% 0.14/0.38
% 0.14/0.38 Axiom 1 (cls_Comb_Oparcontract_Ointros__1_0): c_in(c_Pair(X, X, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) = true2.
% 0.14/0.39 Axiom 2 (cls_conjecture_0): c_in(c_Pair(v_x, v_xb, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) = true2.
% 0.14/0.39
% 0.14/0.39 Goal 1 (cls_conjecture_1): tuple(c_in(c_Pair(v_x, X, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), c_in(c_Pair(v_xb, X, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) = tuple(true2, true2).
% 0.14/0.39 The goal is true when:
% 0.14/0.39 X = v_xb
% 0.14/0.39
% 0.14/0.39 Proof:
% 0.14/0.39 tuple(c_in(c_Pair(v_x, v_xb, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), c_in(c_Pair(v_xb, v_xb, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))
% 0.14/0.39 = { by axiom 1 (cls_Comb_Oparcontract_Ointros__1_0) }
% 0.14/0.39 tuple(c_in(c_Pair(v_x, v_xb, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true2)
% 0.14/0.39 = { by axiom 2 (cls_conjecture_0) }
% 0.14/0.39 tuple(true2, true2)
% 0.14/0.39 % SZS output end Proof
% 0.14/0.39
% 0.14/0.39 RESULT: Unsatisfiable (the axioms are contradictory).
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