TSTP Solution File: GEO305+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GEO305+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 : 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 23:28:34 EDT 2023
% Result : Theorem 58.29s 7.79s
% Output : Proof 58.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO305+1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 22:29:14 EDT 2023
% 0.13/0.35 % CPUTime :
% 58.29/7.79 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 58.29/7.79
% 58.29/7.79 % SZS status Theorem
% 58.29/7.79
% 58.29/7.79 % SZS output start Proof
% 58.29/7.79 Take the following subset of the input axioms:
% 58.29/7.80 fof('and(holds(conjunct2(345), 1294, 0), and(pred(conjunct1(345), 9), and(pred(conjunct1(345), 8), and(pred(conjunct1(345), 7), and(qe(s3(plural(345))), and(qe(s2(plural(345))), qe(s1(plural(345)))))))))', axiom, vf(vd1287, vd1288)=vf(vd1287, vd1289) & (vd1288!=vd1289 & (vd1287!=vd1289 & (vd1287!=vd1288 & (?[Vd1293]: (vd1289=Vd1293 & rpoint(Vd1293)) & (?[Vd1292]: (vd1288=Vd1292 & rpoint(Vd1292)) & ?[Vd1291]: (vd1287=Vd1291 & rpoint(Vd1291)))))))).
% 58.29/7.80 fof('and(pred(conjunct2(348), 4), and(holds(conjunct2(348), 1304, 0), and(pred(conjunct2(348), 1), holds(conjunct1(348), 1301, 0))))', axiom, vd1302=vd1303 & (rR(vd1289, vd1287, vd1302) & (rpoint(vd1303) & rR(vd1288, vd1287, vd1299)))).
% 58.29/7.80 fof('pred(347, 0)', axiom, rline(vd1297)).
% 58.29/7.80 fof('pred(conjunct2(349), 0)', conjecture, ron(vd1302, vd1297)).
% 58.29/7.80 fof('pred(s1(plural(347)), 0)', axiom, ron(vd1287, vd1297)).
% 58.29/7.80 fof('pred(s2(plural(347)), 0)', axiom, ron(vd1289, vd1297)).
% 58.29/7.80 fof('qu(cond(axiom(83), 0), imp(cond(axiom(83), 0)))', axiom, ![Vd352, Vd353, Vd354, Vd359, Vd360]: ((Vd359=Vd360 & (ron(Vd353, Vd359) & (ron(Vd352, Vd359) & (rR(Vd353, Vd352, Vd354) & (rline(Vd360) & (?[Vd358]: (Vd354=Vd358 & rpoint(Vd358)) & (?[Vd357]: (Vd353=Vd357 & rpoint(Vd357)) & ?[Vd356]: (Vd352=Vd356 & rpoint(Vd356))))))))) => ron(Vd354, Vd359))).
% 58.29/7.80
% 58.29/7.80 Now clausify the problem and encode Horn clauses using encoding 3 of
% 58.29/7.80 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 58.29/7.80 We repeatedly replace C & s=t => u=v by the two clauses:
% 58.29/7.80 fresh(y, y, x1...xn) = u
% 58.29/7.80 C => fresh(s, t, x1...xn) = v
% 58.29/7.80 where fresh is a fresh function symbol and x1..xn are the free
% 58.29/7.80 variables of u and v.
% 58.29/7.80 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 58.29/7.80 input problem has no model of domain size 1).
% 58.29/7.80
% 58.29/7.80 The encoding turns the above axioms into the following unit equations and goals:
% 58.29/7.80
% 58.29/7.80 Axiom 1 (and(pred(conjunct2(348), 4), and(holds(conjunct2(348), 1304, 0), and(pred(conjunct2(348), 1), holds(conjunct1(348), 1301, 0))))): vd1302 = vd1303.
% 58.29/7.80 Axiom 2 (and(holds(conjunct2(345), 1294, 0), and(pred(conjunct1(345), 9), and(pred(conjunct1(345), 8), and(pred(conjunct1(345), 7), and(qe(s3(plural(345))), and(qe(s2(plural(345))), qe(s1(plural(345)))))))))): vd1289 = vd1293.
% 58.29/7.80 Axiom 3 (and(holds(conjunct2(345), 1294, 0), and(pred(conjunct1(345), 9), and(pred(conjunct1(345), 8), and(pred(conjunct1(345), 7), and(qe(s3(plural(345))), and(qe(s2(plural(345))), qe(s1(plural(345)))))))))_1): vd1287 = vd1291.
% 58.29/7.80 Axiom 4 (and(pred(conjunct2(348), 4), and(holds(conjunct2(348), 1304, 0), and(pred(conjunct2(348), 1), holds(conjunct1(348), 1301, 0))))_3): rpoint(vd1303) = true2.
% 58.29/7.80 Axiom 5 (and(holds(conjunct2(345), 1294, 0), and(pred(conjunct1(345), 9), and(pred(conjunct1(345), 8), and(pred(conjunct1(345), 7), and(qe(s3(plural(345))), and(qe(s2(plural(345))), qe(s1(plural(345)))))))))_4): rpoint(vd1293) = true2.
% 58.29/7.80 Axiom 6 (and(holds(conjunct2(345), 1294, 0), and(pred(conjunct1(345), 9), and(pred(conjunct1(345), 8), and(pred(conjunct1(345), 7), and(qe(s3(plural(345))), and(qe(s2(plural(345))), qe(s1(plural(345)))))))))_6): rpoint(vd1291) = true2.
% 58.29/7.80 Axiom 7 (pred(347, 0)): rline(vd1297) = true2.
% 58.29/7.80 Axiom 8 (pred(s1(plural(347)), 0)): ron(vd1287, vd1297) = true2.
% 58.29/7.80 Axiom 9 (pred(s2(plural(347)), 0)): ron(vd1289, vd1297) = true2.
% 58.29/7.80 Axiom 10 (and(pred(conjunct2(348), 4), and(holds(conjunct2(348), 1304, 0), and(pred(conjunct2(348), 1), holds(conjunct1(348), 1301, 0))))_1): rR(vd1289, vd1287, vd1302) = true2.
% 58.29/7.80 Axiom 11 (qu(cond(axiom(83), 0), imp(cond(axiom(83), 0)))): fresh462(X, X, Y, Z) = true2.
% 58.29/7.80 Axiom 12 (qu(cond(axiom(83), 0), imp(cond(axiom(83), 0)))): fresh460(X, X, Y, Z, W) = ron(Z, Y).
% 58.29/7.80 Axiom 13 (qu(cond(axiom(83), 0), imp(cond(axiom(83), 0)))): fresh461(X, X, Y, Z, W, V) = fresh462(ron(W, Y), true2, Y, Z).
% 58.29/7.80 Axiom 14 (qu(cond(axiom(83), 0), imp(cond(axiom(83), 0)))): fresh459(X, X, Y, Z, W, V) = fresh460(ron(V, Y), true2, Y, Z, W).
% 58.29/7.80 Axiom 15 (qu(cond(axiom(83), 0), imp(cond(axiom(83), 0)))): fresh458(X, X, Y, Z, W, V) = fresh459(rpoint(Z), true2, Y, Z, W, V).
% 58.29/7.80 Axiom 16 (qu(cond(axiom(83), 0), imp(cond(axiom(83), 0)))): fresh457(X, X, Y, Z, W, V) = fresh458(rpoint(W), true2, Y, Z, W, V).
% 58.29/7.80 Axiom 17 (qu(cond(axiom(83), 0), imp(cond(axiom(83), 0)))): fresh456(X, X, Y, Z, W, V) = fresh457(rpoint(V), true2, Y, Z, W, V).
% 58.29/7.80 Axiom 18 (qu(cond(axiom(83), 0), imp(cond(axiom(83), 0)))): fresh456(rline(X), true2, X, Y, Z, W) = fresh461(rR(Z, W, Y), true2, X, Y, Z, W).
% 58.29/7.80
% 58.29/7.80 Goal 1 (pred(conjunct2(349), 0)): ron(vd1302, vd1297) = true2.
% 58.29/7.80 Proof:
% 58.29/7.80 ron(vd1302, vd1297)
% 58.29/7.80 = { by axiom 12 (qu(cond(axiom(83), 0), imp(cond(axiom(83), 0)))) R->L }
% 58.29/7.80 fresh460(true2, true2, vd1297, vd1302, vd1289)
% 58.29/7.80 = { by axiom 8 (pred(s1(plural(347)), 0)) R->L }
% 58.29/7.80 fresh460(ron(vd1287, vd1297), true2, vd1297, vd1302, vd1289)
% 58.29/7.80 = { by axiom 14 (qu(cond(axiom(83), 0), imp(cond(axiom(83), 0)))) R->L }
% 58.29/7.80 fresh459(true2, true2, vd1297, vd1302, vd1289, vd1287)
% 58.29/7.80 = { by axiom 4 (and(pred(conjunct2(348), 4), and(holds(conjunct2(348), 1304, 0), and(pred(conjunct2(348), 1), holds(conjunct1(348), 1301, 0))))_3) R->L }
% 58.29/7.80 fresh459(rpoint(vd1303), true2, vd1297, vd1302, vd1289, vd1287)
% 58.29/7.80 = { by axiom 1 (and(pred(conjunct2(348), 4), and(holds(conjunct2(348), 1304, 0), and(pred(conjunct2(348), 1), holds(conjunct1(348), 1301, 0))))) R->L }
% 58.29/7.80 fresh459(rpoint(vd1302), true2, vd1297, vd1302, vd1289, vd1287)
% 58.29/7.80 = { by axiom 15 (qu(cond(axiom(83), 0), imp(cond(axiom(83), 0)))) R->L }
% 58.29/7.80 fresh458(true2, true2, vd1297, vd1302, vd1289, vd1287)
% 58.29/7.80 = { by axiom 5 (and(holds(conjunct2(345), 1294, 0), and(pred(conjunct1(345), 9), and(pred(conjunct1(345), 8), and(pred(conjunct1(345), 7), and(qe(s3(plural(345))), and(qe(s2(plural(345))), qe(s1(plural(345)))))))))_4) R->L }
% 58.29/7.80 fresh458(rpoint(vd1293), true2, vd1297, vd1302, vd1289, vd1287)
% 58.29/7.80 = { by axiom 2 (and(holds(conjunct2(345), 1294, 0), and(pred(conjunct1(345), 9), and(pred(conjunct1(345), 8), and(pred(conjunct1(345), 7), and(qe(s3(plural(345))), and(qe(s2(plural(345))), qe(s1(plural(345)))))))))) R->L }
% 58.29/7.80 fresh458(rpoint(vd1289), true2, vd1297, vd1302, vd1289, vd1287)
% 58.29/7.80 = { by axiom 16 (qu(cond(axiom(83), 0), imp(cond(axiom(83), 0)))) R->L }
% 58.29/7.80 fresh457(true2, true2, vd1297, vd1302, vd1289, vd1287)
% 58.29/7.80 = { by axiom 6 (and(holds(conjunct2(345), 1294, 0), and(pred(conjunct1(345), 9), and(pred(conjunct1(345), 8), and(pred(conjunct1(345), 7), and(qe(s3(plural(345))), and(qe(s2(plural(345))), qe(s1(plural(345)))))))))_6) R->L }
% 58.29/7.80 fresh457(rpoint(vd1291), true2, vd1297, vd1302, vd1289, vd1287)
% 58.29/7.80 = { by axiom 3 (and(holds(conjunct2(345), 1294, 0), and(pred(conjunct1(345), 9), and(pred(conjunct1(345), 8), and(pred(conjunct1(345), 7), and(qe(s3(plural(345))), and(qe(s2(plural(345))), qe(s1(plural(345)))))))))_1) R->L }
% 58.29/7.80 fresh457(rpoint(vd1287), true2, vd1297, vd1302, vd1289, vd1287)
% 58.29/7.80 = { by axiom 17 (qu(cond(axiom(83), 0), imp(cond(axiom(83), 0)))) R->L }
% 58.29/7.80 fresh456(true2, true2, vd1297, vd1302, vd1289, vd1287)
% 58.29/7.80 = { by axiom 7 (pred(347, 0)) R->L }
% 58.29/7.80 fresh456(rline(vd1297), true2, vd1297, vd1302, vd1289, vd1287)
% 58.29/7.80 = { by axiom 18 (qu(cond(axiom(83), 0), imp(cond(axiom(83), 0)))) }
% 58.29/7.80 fresh461(rR(vd1289, vd1287, vd1302), true2, vd1297, vd1302, vd1289, vd1287)
% 58.29/7.80 = { by axiom 10 (and(pred(conjunct2(348), 4), and(holds(conjunct2(348), 1304, 0), and(pred(conjunct2(348), 1), holds(conjunct1(348), 1301, 0))))_1) }
% 58.29/7.80 fresh461(true2, true2, vd1297, vd1302, vd1289, vd1287)
% 58.29/7.80 = { by axiom 13 (qu(cond(axiom(83), 0), imp(cond(axiom(83), 0)))) }
% 58.29/7.80 fresh462(ron(vd1289, vd1297), true2, vd1297, vd1302)
% 58.29/7.80 = { by axiom 9 (pred(s2(plural(347)), 0)) }
% 58.29/7.80 fresh462(true2, true2, vd1297, vd1302)
% 58.29/7.80 = { by axiom 11 (qu(cond(axiom(83), 0), imp(cond(axiom(83), 0)))) }
% 58.29/7.80 true2
% 58.29/7.80 % SZS output end Proof
% 58.29/7.80
% 58.29/7.80 RESULT: Theorem (the conjecture is true).
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