TSTP Solution File: NUM851+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : NUM851+1 : 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 : n026.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 11:58:38 EDT 2023
% Result : Theorem 0.21s 0.50s
% 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 : NUM851+1 : TPTP v8.1.2. Released v4.1.0.
% 0.13/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 17:28:47 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.50 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.21/0.50
% 0.21/0.50 % SZS status Theorem
% 0.21/0.50
% 0.21/0.50 % SZS output start Proof
% 0.21/0.50 Take the following subset of the input axioms:
% 0.21/0.50 fof('ass(cond(270, 0), 0)', axiom, ![Vd418, Vd419]: vmul(Vd418, Vd419)=vmul(Vd419, Vd418)).
% 0.21/0.50 fof('ass(cond(281, 0), 0)', axiom, ![Vd432, Vd433, Vd434]: vmul(Vd432, vplus(Vd433, Vd434))=vplus(vmul(Vd432, Vd433), vmul(Vd432, Vd434))).
% 0.21/0.50 fof('ass(cond(61, 0), 0)', axiom, ![Vd78, Vd79]: vplus(Vd79, Vd78)=vplus(Vd78, Vd79)).
% 0.21/0.50 fof('holds(conseq_conjunct2(conseq(302)), 475, 1)', conjecture, vmul(vplus(vd471, vd473), vd469)=vplus(vmul(vd471, vd469), vmul(vd473, vd469))).
% 0.21/0.50
% 0.21/0.50 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.50 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.50 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.50 fresh(y, y, x1...xn) = u
% 0.21/0.50 C => fresh(s, t, x1...xn) = v
% 0.21/0.50 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.50 variables of u and v.
% 0.21/0.50 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.50 input problem has no model of domain size 1).
% 0.21/0.50
% 0.21/0.50 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.50
% 0.21/0.50 Axiom 1 (ass(cond(270, 0), 0)): vmul(X, Y) = vmul(Y, X).
% 0.21/0.50 Axiom 2 (ass(cond(61, 0), 0)): vplus(X, Y) = vplus(Y, X).
% 0.21/0.50 Axiom 3 (ass(cond(281, 0), 0)): vmul(X, vplus(Y, Z)) = vplus(vmul(X, Y), vmul(X, Z)).
% 0.21/0.50
% 0.21/0.50 Goal 1 (holds(conseq_conjunct2(conseq(302)), 475, 1)): vmul(vplus(vd471, vd473), vd469) = vplus(vmul(vd471, vd469), vmul(vd473, vd469)).
% 0.21/0.50 Proof:
% 0.21/0.50 vmul(vplus(vd471, vd473), vd469)
% 0.21/0.50 = { by axiom 1 (ass(cond(270, 0), 0)) }
% 0.21/0.50 vmul(vd469, vplus(vd471, vd473))
% 0.21/0.50 = { by axiom 2 (ass(cond(61, 0), 0)) }
% 0.21/0.50 vmul(vd469, vplus(vd473, vd471))
% 0.21/0.50 = { by axiom 3 (ass(cond(281, 0), 0)) }
% 0.21/0.50 vplus(vmul(vd469, vd473), vmul(vd469, vd471))
% 0.21/0.50 = { by axiom 1 (ass(cond(270, 0), 0)) }
% 0.21/0.50 vplus(vmul(vd473, vd469), vmul(vd469, vd471))
% 0.21/0.50 = { by axiom 1 (ass(cond(270, 0), 0)) }
% 0.21/0.50 vplus(vmul(vd473, vd469), vmul(vd471, vd469))
% 0.21/0.50 = { by axiom 2 (ass(cond(61, 0), 0)) R->L }
% 0.21/0.50 vplus(vmul(vd471, vd469), vmul(vd473, vd469))
% 0.21/0.50 % SZS output end Proof
% 0.21/0.50
% 0.21/0.50 RESULT: Theorem (the conjecture is true).
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