TSTP Solution File: NUM840+2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUM840+2 : TPTP v8.1.2. Released v4.1.0.
% 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 : n023.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 11:58:33 EDT 2023
% Result : Theorem 18.08s 2.61s
% Output : Proof 18.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM840+2 : TPTP v8.1.2. Released v4.1.0.
% 0.03/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Aug 25 08:28:42 EDT 2023
% 0.12/0.33 % CPUTime :
% 18.08/2.61 Command-line arguments: --no-flatten-goal
% 18.08/2.61
% 18.08/2.61 % SZS status Theorem
% 18.08/2.61
% 18.08/2.62 % SZS output start Proof
% 18.08/2.62 Take the following subset of the input axioms:
% 18.08/2.62 fof('ass(cond(140, 0), 0)', axiom, ![Vd208, Vd209]: (greater(Vd208, Vd209) => less(Vd209, Vd208))).
% 18.08/2.62 fof('ass(cond(33, 0), 0)', axiom, ![Vd46, Vd47, Vd48]: vplus(vplus(Vd46, Vd47), Vd48)=vplus(Vd46, vplus(Vd47, Vd48))).
% 18.08/2.62 fof('ass(cond(61, 0), 0)', axiom, ![Vd78, Vd79]: vplus(Vd79, Vd78)=vplus(Vd78, Vd79)).
% 18.08/2.62 fof('ass(cond(81, 0), 0)', axiom, ![Vd104, Vd105]: (Vd104!=Vd105 => ![Vd107]: vplus(Vd107, Vd104)!=vplus(Vd107, Vd105))).
% 18.08/2.62 fof('def(cond(conseq(axiom(3)), 11), 1)', axiom, ![Vd193, Vd194]: (greater(Vd194, Vd193) <=> ?[Vd196]: Vd194=vplus(Vd193, Vd196))).
% 18.08/2.62 fof('def(cond(conseq(axiom(3)), 12), 1)', axiom, ![Vd198, Vd199]: (less(Vd199, Vd198) <=> ?[Vd201]: Vd198=vplus(Vd199, Vd201))).
% 18.08/2.62 fof('holds(antec(conjunct2(conjunct2(204))), 335, 0)', axiom, less(vplus(vd328, vd330), vplus(vd329, vd330))).
% 18.08/2.62 fof('holds(conseq(conjunct2(conjunct2(204))), 336, 0)', conjecture, less(vd328, vd329)).
% 18.08/2.62
% 18.08/2.62 Now clausify the problem and encode Horn clauses using encoding 3 of
% 18.08/2.62 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 18.08/2.62 We repeatedly replace C & s=t => u=v by the two clauses:
% 18.08/2.62 fresh(y, y, x1...xn) = u
% 18.08/2.62 C => fresh(s, t, x1...xn) = v
% 18.08/2.62 where fresh is a fresh function symbol and x1..xn are the free
% 18.08/2.62 variables of u and v.
% 18.08/2.62 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 18.08/2.62 input problem has no model of domain size 1).
% 18.08/2.62
% 18.08/2.62 The encoding turns the above axioms into the following unit equations and goals:
% 18.08/2.62
% 18.08/2.62 Axiom 1 (ass(cond(61, 0), 0)): vplus(X, Y) = vplus(Y, X).
% 18.08/2.62 Axiom 2 (ass(cond(81, 0), 0)): fresh(X, X, Y, Z) = Z.
% 18.08/2.62 Axiom 3 (ass(cond(140, 0), 0)): fresh10(X, X, Y, Z) = true2.
% 18.08/2.62 Axiom 4 (def(cond(conseq(axiom(3)), 11), 1)): fresh5(X, X, Y, Z) = true2.
% 18.08/2.62 Axiom 5 (def(cond(conseq(axiom(3)), 12), 1)_1): fresh3(X, X, Y, Z) = Y.
% 18.08/2.62 Axiom 6 (def(cond(conseq(axiom(3)), 11), 1)_1): fresh2(X, X, Y, Z) = Z.
% 18.08/2.62 Axiom 7 (ass(cond(33, 0), 0)): vplus(vplus(X, Y), Z) = vplus(X, vplus(Y, Z)).
% 18.08/2.62 Axiom 8 (ass(cond(140, 0), 0)): fresh10(greater(X, Y), true2, X, Y) = less(Y, X).
% 18.08/2.62 Axiom 9 (def(cond(conseq(axiom(3)), 11), 1)): fresh5(X, vplus(Y, Z), Y, X) = greater(X, Y).
% 18.08/2.62 Axiom 10 (def(cond(conseq(axiom(3)), 12), 1)_1): fresh3(less(X, Y), true2, Y, X) = vplus(X, vd201(Y, X)).
% 18.08/2.62 Axiom 11 (def(cond(conseq(axiom(3)), 11), 1)_1): fresh2(greater(X, Y), true2, Y, X) = vplus(Y, vd196(Y, X)).
% 18.08/2.62 Axiom 12 (holds(antec(conjunct2(conjunct2(204))), 335, 0)): less(vplus(vd328, vd330), vplus(vd329, vd330)) = true2.
% 18.08/2.62 Axiom 13 (ass(cond(81, 0), 0)): fresh(vplus(X, Y), vplus(X, Z), Y, Z) = Y.
% 18.08/2.62
% 18.08/2.62 Lemma 14: greater(vplus(X, Y), X) = true2.
% 18.08/2.62 Proof:
% 18.08/2.62 greater(vplus(X, Y), X)
% 18.08/2.62 = { by axiom 9 (def(cond(conseq(axiom(3)), 11), 1)) R->L }
% 18.08/2.62 fresh5(vplus(X, Y), vplus(X, Y), X, vplus(X, Y))
% 18.08/2.62 = { by axiom 4 (def(cond(conseq(axiom(3)), 11), 1)) }
% 18.08/2.62 true2
% 18.08/2.62
% 18.08/2.62 Lemma 15: vplus(X, vd196(X, vplus(X, Y))) = vplus(X, Y).
% 18.08/2.62 Proof:
% 18.08/2.62 vplus(X, vd196(X, vplus(X, Y)))
% 18.08/2.62 = { by axiom 11 (def(cond(conseq(axiom(3)), 11), 1)_1) R->L }
% 18.08/2.62 fresh2(greater(vplus(X, Y), X), true2, X, vplus(X, Y))
% 18.08/2.62 = { by lemma 14 }
% 18.08/2.62 fresh2(true2, true2, X, vplus(X, Y))
% 18.08/2.62 = { by axiom 6 (def(cond(conseq(axiom(3)), 11), 1)_1) }
% 18.08/2.62 vplus(X, Y)
% 18.08/2.62
% 18.08/2.62 Lemma 16: vd196(X, vplus(X, Y)) = Y.
% 18.08/2.62 Proof:
% 18.08/2.62 vd196(X, vplus(X, Y))
% 18.08/2.62 = { by axiom 2 (ass(cond(81, 0), 0)) R->L }
% 18.08/2.62 fresh(vplus(X, Y), vplus(X, Y), Y, vd196(X, vplus(X, Y)))
% 18.08/2.62 = { by lemma 15 R->L }
% 18.08/2.62 fresh(vplus(X, Y), vplus(X, vd196(X, vplus(X, Y))), Y, vd196(X, vplus(X, Y)))
% 18.08/2.62 = { by axiom 13 (ass(cond(81, 0), 0)) }
% 18.08/2.62 Y
% 18.08/2.62
% 18.08/2.62 Lemma 17: vd196(X, vplus(Y, X)) = Y.
% 18.08/2.62 Proof:
% 18.08/2.62 vd196(X, vplus(Y, X))
% 18.08/2.62 = { by axiom 1 (ass(cond(61, 0), 0)) R->L }
% 18.08/2.62 vd196(X, vplus(X, Y))
% 18.08/2.62 = { by lemma 16 }
% 18.08/2.62 Y
% 18.08/2.62
% 18.08/2.62 Goal 1 (holds(conseq(conjunct2(conjunct2(204))), 336, 0)): less(vd328, vd329) = true2.
% 18.08/2.62 Proof:
% 18.08/2.62 less(vd328, vd329)
% 18.08/2.62 = { by axiom 8 (ass(cond(140, 0), 0)) R->L }
% 18.08/2.62 fresh10(greater(vd329, vd328), true2, vd329, vd328)
% 18.08/2.62 = { by lemma 17 R->L }
% 18.08/2.62 fresh10(greater(vd329, vd196(vd201(vplus(vd329, vd330), vplus(vd328, vd330)), vplus(vd328, vd201(vplus(vd329, vd330), vplus(vd328, vd330))))), true2, vd329, vd328)
% 18.08/2.62 = { by lemma 17 R->L }
% 18.08/2.62 fresh10(greater(vd196(vd330, vplus(vd329, vd330)), vd196(vd201(vplus(vd329, vd330), vplus(vd328, vd330)), vplus(vd328, vd201(vplus(vd329, vd330), vplus(vd328, vd330))))), true2, vd329, vd328)
% 18.08/2.62 = { by axiom 5 (def(cond(conseq(axiom(3)), 12), 1)_1) R->L }
% 18.08/2.62 fresh10(greater(vd196(vd330, fresh3(true2, true2, vplus(vd329, vd330), vplus(vd328, vd330))), vd196(vd201(vplus(vd329, vd330), vplus(vd328, vd330)), vplus(vd328, vd201(vplus(vd329, vd330), vplus(vd328, vd330))))), true2, vd329, vd328)
% 18.08/2.62 = { by axiom 12 (holds(antec(conjunct2(conjunct2(204))), 335, 0)) R->L }
% 18.08/2.62 fresh10(greater(vd196(vd330, fresh3(less(vplus(vd328, vd330), vplus(vd329, vd330)), true2, vplus(vd329, vd330), vplus(vd328, vd330))), vd196(vd201(vplus(vd329, vd330), vplus(vd328, vd330)), vplus(vd328, vd201(vplus(vd329, vd330), vplus(vd328, vd330))))), true2, vd329, vd328)
% 18.08/2.62 = { by axiom 10 (def(cond(conseq(axiom(3)), 12), 1)_1) }
% 18.08/2.62 fresh10(greater(vd196(vd330, vplus(vplus(vd328, vd330), vd201(vplus(vd329, vd330), vplus(vd328, vd330)))), vd196(vd201(vplus(vd329, vd330), vplus(vd328, vd330)), vplus(vd328, vd201(vplus(vd329, vd330), vplus(vd328, vd330))))), true2, vd329, vd328)
% 18.08/2.62 = { by axiom 7 (ass(cond(33, 0), 0)) }
% 18.08/2.62 fresh10(greater(vd196(vd330, vplus(vd328, vplus(vd330, vd201(vplus(vd329, vd330), vplus(vd328, vd330))))), vd196(vd201(vplus(vd329, vd330), vplus(vd328, vd330)), vplus(vd328, vd201(vplus(vd329, vd330), vplus(vd328, vd330))))), true2, vd329, vd328)
% 18.08/2.62 = { by axiom 1 (ass(cond(61, 0), 0)) R->L }
% 18.08/2.62 fresh10(greater(vd196(vd330, vplus(vplus(vd330, vd201(vplus(vd329, vd330), vplus(vd328, vd330))), vd328)), vd196(vd201(vplus(vd329, vd330), vplus(vd328, vd330)), vplus(vd328, vd201(vplus(vd329, vd330), vplus(vd328, vd330))))), true2, vd329, vd328)
% 18.08/2.62 = { by axiom 7 (ass(cond(33, 0), 0)) }
% 18.08/2.62 fresh10(greater(vd196(vd330, vplus(vd330, vplus(vd201(vplus(vd329, vd330), vplus(vd328, vd330)), vd328))), vd196(vd201(vplus(vd329, vd330), vplus(vd328, vd330)), vplus(vd328, vd201(vplus(vd329, vd330), vplus(vd328, vd330))))), true2, vd329, vd328)
% 18.08/2.62 = { by axiom 1 (ass(cond(61, 0), 0)) }
% 18.08/2.62 fresh10(greater(vd196(vd330, vplus(vd330, vplus(vd328, vd201(vplus(vd329, vd330), vplus(vd328, vd330))))), vd196(vd201(vplus(vd329, vd330), vplus(vd328, vd330)), vplus(vd328, vd201(vplus(vd329, vd330), vplus(vd328, vd330))))), true2, vd329, vd328)
% 18.08/2.62 = { by lemma 16 }
% 18.08/2.62 fresh10(greater(vplus(vd328, vd201(vplus(vd329, vd330), vplus(vd328, vd330))), vd196(vd201(vplus(vd329, vd330), vplus(vd328, vd330)), vplus(vd328, vd201(vplus(vd329, vd330), vplus(vd328, vd330))))), true2, vd329, vd328)
% 18.08/2.63 = { by axiom 1 (ass(cond(61, 0), 0)) R->L }
% 18.08/2.63 fresh10(greater(vplus(vd328, vd201(vplus(vd329, vd330), vplus(vd328, vd330))), vd196(vd201(vplus(vd329, vd330), vplus(vd328, vd330)), vplus(vd201(vplus(vd329, vd330), vplus(vd328, vd330)), vd328))), true2, vd329, vd328)
% 18.08/2.63 = { by axiom 1 (ass(cond(61, 0), 0)) R->L }
% 18.08/2.63 fresh10(greater(vplus(vd201(vplus(vd329, vd330), vplus(vd328, vd330)), vd328), vd196(vd201(vplus(vd329, vd330), vplus(vd328, vd330)), vplus(vd201(vplus(vd329, vd330), vplus(vd328, vd330)), vd328))), true2, vd329, vd328)
% 18.08/2.63 = { by lemma 15 R->L }
% 18.08/2.63 fresh10(greater(vplus(vd201(vplus(vd329, vd330), vplus(vd328, vd330)), vd196(vd201(vplus(vd329, vd330), vplus(vd328, vd330)), vplus(vd201(vplus(vd329, vd330), vplus(vd328, vd330)), vd328))), vd196(vd201(vplus(vd329, vd330), vplus(vd328, vd330)), vplus(vd201(vplus(vd329, vd330), vplus(vd328, vd330)), vd328))), true2, vd329, vd328)
% 18.08/2.63 = { by axiom 1 (ass(cond(61, 0), 0)) R->L }
% 18.08/2.63 fresh10(greater(vplus(vd196(vd201(vplus(vd329, vd330), vplus(vd328, vd330)), vplus(vd201(vplus(vd329, vd330), vplus(vd328, vd330)), vd328)), vd201(vplus(vd329, vd330), vplus(vd328, vd330))), vd196(vd201(vplus(vd329, vd330), vplus(vd328, vd330)), vplus(vd201(vplus(vd329, vd330), vplus(vd328, vd330)), vd328))), true2, vd329, vd328)
% 18.08/2.63 = { by lemma 14 }
% 18.08/2.63 fresh10(true2, true2, vd329, vd328)
% 18.08/2.63 = { by axiom 3 (ass(cond(140, 0), 0)) }
% 18.08/2.63 true2
% 18.08/2.63 % SZS output end Proof
% 18.08/2.63
% 18.08/2.63 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------