TSTP Solution File: SWV139+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV139+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 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 : n006.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 23:02:43 EDT 2023
% Result : Theorem 2.27s 0.70s
% Output : Proof 2.27s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV139+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.13/0.13 % 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 : n006.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
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 08:40:36 EDT 2023
% 0.14/0.34 % CPUTime :
% 2.27/0.70 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 2.27/0.70
% 2.27/0.70 % SZS status Theorem
% 2.27/0.70
% 2.27/0.70 % SZS output start Proof
% 2.27/0.70 Take the following subset of the input axioms:
% 2.27/0.71 fof(gauss_array_0009, conjecture, (leq(tptp_float_0_001, pv1341) & (leq(n1, loopcounter) & ((~leq(tptp_float_0_001, pv1341) => leq(n0, s_best7)) & ((~leq(tptp_float_0_001, pv1341) => leq(n0, s_sworst7)) & ((~leq(tptp_float_0_001, pv1341) => leq(n0, s_worst7)) & ((~leq(tptp_float_0_001, pv1341) => leq(s_best7, n3)) & ((~leq(tptp_float_0_001, pv1341) => leq(s_sworst7, n3)) & ((~leq(tptp_float_0_001, pv1341) => leq(s_worst7, n3)) & ((gt(loopcounter, n0) => leq(n0, s_best7)) & ((gt(loopcounter, n0) => leq(n0, s_sworst7)) & ((gt(loopcounter, n0) => leq(n0, s_worst7)) & ((gt(loopcounter, n0) => leq(s_best7, n3)) & ((gt(loopcounter, n0) => leq(s_sworst7, n3)) & (gt(loopcounter, n0) => leq(s_worst7, n3))))))))))))))) => leq(n0, s_best7)).
% 2.27/0.71 fof(leq_succ_gt, axiom, ![X, Y]: (leq(succ(X), Y) => gt(Y, X))).
% 2.27/0.71 fof(successor_1, axiom, succ(n0)=n1).
% 2.27/0.71
% 2.27/0.71 Now clausify the problem and encode Horn clauses using encoding 3 of
% 2.27/0.71 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 2.27/0.71 We repeatedly replace C & s=t => u=v by the two clauses:
% 2.27/0.71 fresh(y, y, x1...xn) = u
% 2.27/0.71 C => fresh(s, t, x1...xn) = v
% 2.27/0.71 where fresh is a fresh function symbol and x1..xn are the free
% 2.27/0.71 variables of u and v.
% 2.27/0.71 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 2.27/0.71 input problem has no model of domain size 1).
% 2.27/0.71
% 2.27/0.71 The encoding turns the above axioms into the following unit equations and goals:
% 2.27/0.71
% 2.27/0.71 Axiom 1 (successor_1): succ(n0) = n1.
% 2.27/0.71 Axiom 2 (gauss_array_0009_3): leq(n1, loopcounter) = true3.
% 2.27/0.71 Axiom 3 (gauss_array_0009_8): fresh40(X, X) = true3.
% 2.27/0.71 Axiom 4 (gauss_array_0009_8): fresh40(gt(loopcounter, n0), true3) = leq(n0, s_best7).
% 2.27/0.71 Axiom 5 (leq_succ_gt): fresh31(X, X, Y, Z) = true3.
% 2.27/0.71 Axiom 6 (leq_succ_gt): fresh31(leq(succ(X), Y), true3, X, Y) = gt(Y, X).
% 2.27/0.71
% 2.27/0.71 Goal 1 (gauss_array_0009_14): leq(n0, s_best7) = true3.
% 2.27/0.71 Proof:
% 2.27/0.71 leq(n0, s_best7)
% 2.27/0.71 = { by axiom 4 (gauss_array_0009_8) R->L }
% 2.27/0.71 fresh40(gt(loopcounter, n0), true3)
% 2.27/0.71 = { by axiom 6 (leq_succ_gt) R->L }
% 2.27/0.71 fresh40(fresh31(leq(succ(n0), loopcounter), true3, n0, loopcounter), true3)
% 2.27/0.71 = { by axiom 1 (successor_1) }
% 2.27/0.71 fresh40(fresh31(leq(n1, loopcounter), true3, n0, loopcounter), true3)
% 2.27/0.71 = { by axiom 2 (gauss_array_0009_3) }
% 2.27/0.71 fresh40(fresh31(true3, true3, n0, loopcounter), true3)
% 2.27/0.71 = { by axiom 5 (leq_succ_gt) }
% 2.27/0.71 fresh40(true3, true3)
% 2.27/0.71 = { by axiom 3 (gauss_array_0009_8) }
% 2.27/0.71 true3
% 2.27/0.71 % SZS output end Proof
% 2.27/0.71
% 2.27/0.71 RESULT: Theorem (the conjecture is true).
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