TSTP Solution File: NUM841+2 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : NUM841+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 : 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 : Thu Aug 31 11:58:34 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
% 0.08/0.13 % Problem : NUM841+2 : TPTP v8.1.2. Released v4.1.0.
% 0.08/0.14 % 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 : Fri Aug 25 15:46:08 EDT 2023
% 0.15/0.35 % 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(189, 0), 0)', axiom, ![Vd295, Vd296]: greater(vplus(Vd295, Vd296), Vd295)).
% 0.21/0.50 fof('ass(cond(33, 0), 0)', axiom, ![Vd46, Vd47, Vd48]: vplus(vplus(Vd46, Vd47), Vd48)=vplus(Vd46, vplus(Vd47, Vd48))).
% 0.21/0.50 fof('ass(cond(61, 0), 0)', axiom, ![Vd78, Vd79]: vplus(Vd79, Vd78)=vplus(Vd78, Vd79)).
% 0.21/0.50 fof('ass(cond(goal(193), 0), 2)', axiom, ![Vd301, Vd302, Vd303]: (greater(Vd301, Vd302) => greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))).
% 0.21/0.50 fof('def(cond(conseq(axiom(3)), 11), 1)', axiom, ![Vd193, Vd194]: (greater(Vd194, Vd193) <=> ?[Vd196]: Vd194=vplus(Vd193, Vd196))).
% 0.21/0.50 fof('holds(214, 352, 0)', conjecture, greater(vplus(vd344, vd347), vplus(vd345, vd348))).
% 0.21/0.50 fof('holds(conjunct1(211), 346, 0)', axiom, greater(vd344, vd345)).
% 0.21/0.50 fof('holds(conjunct2(211), 349, 0)', axiom, greater(vd347, vd348)).
% 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 (holds(conjunct1(211), 346, 0)): greater(vd344, vd345) = true2.
% 0.21/0.50 Axiom 2 (holds(conjunct2(211), 349, 0)): greater(vd347, vd348) = true2.
% 0.21/0.50 Axiom 3 (ass(cond(61, 0), 0)): vplus(X, Y) = vplus(Y, X).
% 0.21/0.50 Axiom 4 (def(cond(conseq(axiom(3)), 11), 1)_1): fresh2(X, X, Y, Z) = Z.
% 0.21/0.50 Axiom 5 (ass(cond(189, 0), 0)): greater(vplus(X, Y), X) = true2.
% 0.21/0.50 Axiom 6 (ass(cond(33, 0), 0)): vplus(vplus(X, Y), Z) = vplus(X, vplus(Y, Z)).
% 0.21/0.50 Axiom 7 (ass(cond(goal(193), 0), 2)): fresh6(X, X, Y, Z, W) = true2.
% 0.21/0.50 Axiom 8 (def(cond(conseq(axiom(3)), 11), 1)_1): fresh2(greater(X, Y), true2, Y, X) = vplus(Y, vd196(Y, X)).
% 0.21/0.50 Axiom 9 (ass(cond(goal(193), 0), 2)): fresh6(greater(X, Y), true2, X, Y, Z) = greater(vplus(X, Z), vplus(Y, Z)).
% 0.21/0.50
% 0.21/0.50 Goal 1 (holds(214, 352, 0)): greater(vplus(vd344, vd347), vplus(vd345, vd348)) = true2.
% 0.21/0.50 Proof:
% 0.21/0.50 greater(vplus(vd344, vd347), vplus(vd345, vd348))
% 0.21/0.50 = { by axiom 4 (def(cond(conseq(axiom(3)), 11), 1)_1) R->L }
% 0.21/0.50 greater(vplus(vd344, fresh2(true2, true2, vd348, vd347)), vplus(vd345, vd348))
% 0.21/0.50 = { by axiom 2 (holds(conjunct2(211), 349, 0)) R->L }
% 0.21/0.50 greater(vplus(vd344, fresh2(greater(vd347, vd348), true2, vd348, vd347)), vplus(vd345, vd348))
% 0.21/0.50 = { by axiom 8 (def(cond(conseq(axiom(3)), 11), 1)_1) }
% 0.21/0.50 greater(vplus(vd344, vplus(vd348, vd196(vd348, vd347))), vplus(vd345, vd348))
% 0.21/0.50 = { by axiom 6 (ass(cond(33, 0), 0)) R->L }
% 0.21/0.50 greater(vplus(vplus(vd344, vd348), vd196(vd348, vd347)), vplus(vd345, vd348))
% 0.21/0.50 = { by axiom 3 (ass(cond(61, 0), 0)) R->L }
% 0.21/0.50 greater(vplus(vd196(vd348, vd347), vplus(vd344, vd348)), vplus(vd345, vd348))
% 0.21/0.50 = { by axiom 6 (ass(cond(33, 0), 0)) R->L }
% 0.21/0.50 greater(vplus(vplus(vd196(vd348, vd347), vd344), vd348), vplus(vd345, vd348))
% 0.21/0.50 = { by axiom 9 (ass(cond(goal(193), 0), 2)) R->L }
% 0.21/0.50 fresh6(greater(vplus(vd196(vd348, vd347), vd344), vd345), true2, vplus(vd196(vd348, vd347), vd344), vd345, vd348)
% 0.21/0.50 = { by axiom 4 (def(cond(conseq(axiom(3)), 11), 1)_1) R->L }
% 0.21/0.50 fresh6(greater(vplus(vd196(vd348, vd347), fresh2(true2, true2, vd345, vd344)), vd345), true2, vplus(vd196(vd348, vd347), vd344), vd345, vd348)
% 0.21/0.50 = { by axiom 1 (holds(conjunct1(211), 346, 0)) R->L }
% 0.21/0.50 fresh6(greater(vplus(vd196(vd348, vd347), fresh2(greater(vd344, vd345), true2, vd345, vd344)), vd345), true2, vplus(vd196(vd348, vd347), vd344), vd345, vd348)
% 0.21/0.50 = { by axiom 8 (def(cond(conseq(axiom(3)), 11), 1)_1) }
% 0.21/0.50 fresh6(greater(vplus(vd196(vd348, vd347), vplus(vd345, vd196(vd345, vd344))), vd345), true2, vplus(vd196(vd348, vd347), vd344), vd345, vd348)
% 0.21/0.50 = { by axiom 6 (ass(cond(33, 0), 0)) R->L }
% 0.21/0.50 fresh6(greater(vplus(vplus(vd196(vd348, vd347), vd345), vd196(vd345, vd344)), vd345), true2, vplus(vd196(vd348, vd347), vd344), vd345, vd348)
% 0.21/0.50 = { by axiom 3 (ass(cond(61, 0), 0)) R->L }
% 0.21/0.50 fresh6(greater(vplus(vd196(vd345, vd344), vplus(vd196(vd348, vd347), vd345)), vd345), true2, vplus(vd196(vd348, vd347), vd344), vd345, vd348)
% 0.21/0.50 = { by axiom 6 (ass(cond(33, 0), 0)) R->L }
% 0.21/0.50 fresh6(greater(vplus(vplus(vd196(vd345, vd344), vd196(vd348, vd347)), vd345), vd345), true2, vplus(vd196(vd348, vd347), vd344), vd345, vd348)
% 0.21/0.50 = { by axiom 3 (ass(cond(61, 0), 0)) R->L }
% 0.21/0.50 fresh6(greater(vplus(vd345, vplus(vd196(vd345, vd344), vd196(vd348, vd347))), vd345), true2, vplus(vd196(vd348, vd347), vd344), vd345, vd348)
% 0.21/0.50 = { by axiom 5 (ass(cond(189, 0), 0)) }
% 0.21/0.50 fresh6(true2, true2, vplus(vd196(vd348, vd347), vd344), vd345, vd348)
% 0.21/0.50 = { by axiom 7 (ass(cond(goal(193), 0), 2)) }
% 0.21/0.50 true2
% 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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