TSTP Solution File: SYN180-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN180-1 : TPTP v8.1.2. Released v1.1.0.
% 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 : n025.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 : Fri Sep 1 03:33:29 EDT 2023
% Result : Unsatisfiable 32.04s 4.58s
% Output : Proof 33.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN180-1 : TPTP v8.1.2. Released v1.1.0.
% 0.00/0.13 % 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 : n025.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 : Sat Aug 26 19:48:38 EDT 2023
% 0.14/0.34 % CPUTime :
% 32.04/4.58 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 32.04/4.58
% 32.04/4.58 % SZS status Unsatisfiable
% 32.04/4.58
% 33.11/4.60 % SZS output start Proof
% 33.11/4.60 Take the following subset of the input axioms:
% 33.11/4.60 fof(axiom_1, axiom, s0(d)).
% 33.11/4.60 fof(axiom_13, axiom, r0(e)).
% 33.11/4.60 fof(axiom_17, axiom, ![X]: q0(X, d)).
% 33.11/4.60 fof(axiom_19, axiom, ![Y, X2]: m0(X2, d, Y)).
% 33.11/4.60 fof(axiom_28, axiom, k0(e)).
% 33.11/4.60 fof(prove_this, negated_conjecture, ~q4(a, e)).
% 33.11/4.60 fof(rule_090, axiom, p1(e, e, e) | (~r0(e) | ~k0(e))).
% 33.11/4.60 fof(rule_117, axiom, q1(d, d, d) | (~k0(e) | ~s0(d))).
% 33.11/4.60 fof(rule_122, axiom, ![G, H]: (q1(G, G, G) | ~m0(G, H, G))).
% 33.11/4.60 fof(rule_124, axiom, ![D, E]: (r1(D) | (~q0(D, E) | (~s0(d) | ~q1(d, E, d))))).
% 33.11/4.60 fof(rule_154, axiom, ![A2]: (p2(A2, A2, A2) | ~q1(A2, A2, A2))).
% 33.11/4.60 fof(rule_181, axiom, ![I]: (q2(I, I, I) | ~p1(I, I, I))).
% 33.11/4.60 fof(rule_187, axiom, ![C, F, D2, E2]: (q2(C, D2, C) | (~r1(D2) | (~m0(E2, F, C) | (~k0(D2) | ~q2(D2, D2, D2)))))).
% 33.11/4.60 fof(rule_205, axiom, ![E2, F2]: (k3(E2, E2, E2) | ~p2(F2, E2, E2))).
% 33.11/4.60 fof(rule_238, axiom, ![I2]: (m3(I2, I2, I2) | ~p2(I2, I2, I2))).
% 33.11/4.60 fof(rule_295, axiom, ![B, C2, D2, E2, F2]: (q4(B, C2) | (~k3(D2, D2, B) | (~q2(E2, C2, B) | ~m3(E2, F2, E2))))).
% 33.11/4.60
% 33.11/4.60 Now clausify the problem and encode Horn clauses using encoding 3 of
% 33.11/4.60 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 33.11/4.60 We repeatedly replace C & s=t => u=v by the two clauses:
% 33.11/4.60 fresh(y, y, x1...xn) = u
% 33.11/4.60 C => fresh(s, t, x1...xn) = v
% 33.11/4.60 where fresh is a fresh function symbol and x1..xn are the free
% 33.11/4.60 variables of u and v.
% 33.11/4.60 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 33.11/4.60 input problem has no model of domain size 1).
% 33.11/4.60
% 33.11/4.60 The encoding turns the above axioms into the following unit equations and goals:
% 33.11/4.60
% 33.11/4.60 Axiom 1 (axiom_17): q0(X, d) = true.
% 33.11/4.60 Axiom 2 (axiom_13): r0(e) = true.
% 33.11/4.60 Axiom 3 (axiom_1): s0(d) = true.
% 33.11/4.60 Axiom 4 (axiom_28): k0(e) = true.
% 33.11/4.60 Axiom 5 (rule_090): fresh320(X, X) = true.
% 33.11/4.60 Axiom 6 (rule_117): fresh285(X, X) = true.
% 33.11/4.60 Axiom 7 (axiom_19): m0(X, d, Y) = true.
% 33.11/4.60 Axiom 8 (rule_117): fresh286(X, X) = q1(d, d, d).
% 33.11/4.60 Axiom 9 (rule_090): fresh321(X, X) = p1(e, e, e).
% 33.11/4.60 Axiom 10 (rule_124): fresh593(X, X, Y) = true.
% 33.11/4.60 Axiom 11 (rule_090): fresh321(k0(e), true) = fresh320(r0(e), true).
% 33.11/4.60 Axiom 12 (rule_117): fresh286(k0(e), true) = fresh285(s0(d), true).
% 33.11/4.60 Axiom 13 (rule_122): fresh279(X, X, Y) = true.
% 33.11/4.60 Axiom 14 (rule_124): fresh276(X, X, Y) = r1(Y).
% 33.11/4.60 Axiom 15 (rule_154): fresh241(X, X, Y) = true.
% 33.11/4.60 Axiom 16 (rule_181): fresh200(X, X, Y) = true.
% 33.11/4.60 Axiom 17 (rule_205): fresh170(X, X, Y) = true.
% 33.11/4.60 Axiom 18 (rule_238): fresh129(X, X, Y) = true.
% 33.11/4.60 Axiom 19 (rule_124): fresh592(X, X, Y, Z) = fresh593(s0(d), true, Y).
% 33.11/4.60 Axiom 20 (rule_187): fresh545(X, X, Y, Z) = true.
% 33.11/4.60 Axiom 21 (rule_295): fresh463(X, X, Y, Z) = true.
% 33.11/4.60 Axiom 22 (rule_122): fresh279(m0(X, Y, X), true, X) = q1(X, X, X).
% 33.11/4.60 Axiom 23 (rule_154): fresh241(q1(X, X, X), true, X) = p2(X, X, X).
% 33.11/4.60 Axiom 24 (rule_181): fresh200(p1(X, X, X), true, X) = q2(X, X, X).
% 33.11/4.60 Axiom 25 (rule_205): fresh170(p2(X, Y, Y), true, Y) = k3(Y, Y, Y).
% 33.11/4.60 Axiom 26 (rule_238): fresh129(p2(X, X, X), true, X) = m3(X, X, X).
% 33.11/4.60 Axiom 27 (rule_295): fresh51(X, X, Y, Z, W) = q4(Y, Z).
% 33.11/4.60 Axiom 28 (rule_124): fresh592(q1(d, X, d), true, Y, X) = fresh276(q0(Y, X), true, Y).
% 33.11/4.60 Axiom 29 (rule_187): fresh544(X, X, Y, Z, W, V) = fresh545(m0(W, V, Y), true, Y, Z).
% 33.11/4.60 Axiom 30 (rule_187): fresh543(X, X, Y, Z, W, V) = q2(Y, Z, Y).
% 33.11/4.60 Axiom 31 (rule_295): fresh462(X, X, Y, Z, W, V) = fresh463(q2(W, Z, Y), true, Y, Z).
% 33.11/4.60 Axiom 32 (rule_187): fresh542(X, X, Y, Z, W, V) = fresh543(k0(Z), true, Y, Z, W, V).
% 33.11/4.60 Axiom 33 (rule_187): fresh542(q2(X, X, X), true, Y, X, Z, W) = fresh544(r1(X), true, Y, X, Z, W).
% 33.11/4.60 Axiom 34 (rule_295): fresh462(m3(X, Y, X), true, Z, W, X, V) = fresh51(k3(V, V, Z), true, Z, W, X).
% 33.11/4.60
% 33.11/4.60 Lemma 35: p2(X, X, X) = true.
% 33.11/4.60 Proof:
% 33.11/4.60 p2(X, X, X)
% 33.11/4.60 = { by axiom 23 (rule_154) R->L }
% 33.11/4.60 fresh241(q1(X, X, X), true, X)
% 33.11/4.60 = { by axiom 22 (rule_122) R->L }
% 33.11/4.60 fresh241(fresh279(m0(X, d, X), true, X), true, X)
% 33.11/4.60 = { by axiom 7 (axiom_19) }
% 33.11/4.60 fresh241(fresh279(true, true, X), true, X)
% 33.11/4.60 = { by axiom 13 (rule_122) }
% 33.11/4.60 fresh241(true, true, X)
% 33.11/4.60 = { by axiom 15 (rule_154) }
% 33.11/4.60 true
% 33.11/4.60
% 33.11/4.60 Goal 1 (prove_this): q4(a, e) = true.
% 33.11/4.60 Proof:
% 33.11/4.60 q4(a, e)
% 33.11/4.60 = { by axiom 27 (rule_295) R->L }
% 33.11/4.60 fresh51(true, true, a, e, a)
% 33.11/4.60 = { by axiom 17 (rule_205) R->L }
% 33.11/4.60 fresh51(fresh170(true, true, a), true, a, e, a)
% 33.11/4.60 = { by lemma 35 R->L }
% 33.11/4.60 fresh51(fresh170(p2(a, a, a), true, a), true, a, e, a)
% 33.11/4.60 = { by axiom 25 (rule_205) }
% 33.11/4.60 fresh51(k3(a, a, a), true, a, e, a)
% 33.11/4.60 = { by axiom 34 (rule_295) R->L }
% 33.11/4.60 fresh462(m3(a, a, a), true, a, e, a, a)
% 33.11/4.60 = { by axiom 26 (rule_238) R->L }
% 33.11/4.60 fresh462(fresh129(p2(a, a, a), true, a), true, a, e, a, a)
% 33.11/4.60 = { by lemma 35 }
% 33.11/4.60 fresh462(fresh129(true, true, a), true, a, e, a, a)
% 33.11/4.60 = { by axiom 18 (rule_238) }
% 33.11/4.60 fresh462(true, true, a, e, a, a)
% 33.11/4.60 = { by axiom 31 (rule_295) }
% 33.11/4.60 fresh463(q2(a, e, a), true, a, e)
% 33.11/4.60 = { by axiom 30 (rule_187) R->L }
% 33.11/4.60 fresh463(fresh543(true, true, a, e, X, d), true, a, e)
% 33.11/4.60 = { by axiom 4 (axiom_28) R->L }
% 33.11/4.60 fresh463(fresh543(k0(e), true, a, e, X, d), true, a, e)
% 33.11/4.60 = { by axiom 32 (rule_187) R->L }
% 33.11/4.60 fresh463(fresh542(true, true, a, e, X, d), true, a, e)
% 33.11/4.60 = { by axiom 16 (rule_181) R->L }
% 33.11/4.60 fresh463(fresh542(fresh200(true, true, e), true, a, e, X, d), true, a, e)
% 33.11/4.60 = { by axiom 5 (rule_090) R->L }
% 33.11/4.60 fresh463(fresh542(fresh200(fresh320(true, true), true, e), true, a, e, X, d), true, a, e)
% 33.11/4.60 = { by axiom 2 (axiom_13) R->L }
% 33.11/4.60 fresh463(fresh542(fresh200(fresh320(r0(e), true), true, e), true, a, e, X, d), true, a, e)
% 33.11/4.60 = { by axiom 11 (rule_090) R->L }
% 33.11/4.60 fresh463(fresh542(fresh200(fresh321(k0(e), true), true, e), true, a, e, X, d), true, a, e)
% 33.11/4.60 = { by axiom 4 (axiom_28) }
% 33.11/4.60 fresh463(fresh542(fresh200(fresh321(true, true), true, e), true, a, e, X, d), true, a, e)
% 33.11/4.60 = { by axiom 9 (rule_090) }
% 33.11/4.60 fresh463(fresh542(fresh200(p1(e, e, e), true, e), true, a, e, X, d), true, a, e)
% 33.11/4.60 = { by axiom 24 (rule_181) }
% 33.11/4.60 fresh463(fresh542(q2(e, e, e), true, a, e, X, d), true, a, e)
% 33.11/4.60 = { by axiom 33 (rule_187) }
% 33.11/4.60 fresh463(fresh544(r1(e), true, a, e, X, d), true, a, e)
% 33.11/4.60 = { by axiom 14 (rule_124) R->L }
% 33.11/4.60 fresh463(fresh544(fresh276(true, true, e), true, a, e, X, d), true, a, e)
% 33.11/4.60 = { by axiom 1 (axiom_17) R->L }
% 33.11/4.60 fresh463(fresh544(fresh276(q0(e, d), true, e), true, a, e, X, d), true, a, e)
% 33.11/4.60 = { by axiom 28 (rule_124) R->L }
% 33.11/4.60 fresh463(fresh544(fresh592(q1(d, d, d), true, e, d), true, a, e, X, d), true, a, e)
% 33.11/4.60 = { by axiom 8 (rule_117) R->L }
% 33.11/4.60 fresh463(fresh544(fresh592(fresh286(true, true), true, e, d), true, a, e, X, d), true, a, e)
% 33.11/4.60 = { by axiom 4 (axiom_28) R->L }
% 33.11/4.60 fresh463(fresh544(fresh592(fresh286(k0(e), true), true, e, d), true, a, e, X, d), true, a, e)
% 33.11/4.60 = { by axiom 12 (rule_117) }
% 33.11/4.60 fresh463(fresh544(fresh592(fresh285(s0(d), true), true, e, d), true, a, e, X, d), true, a, e)
% 33.11/4.60 = { by axiom 3 (axiom_1) }
% 33.11/4.60 fresh463(fresh544(fresh592(fresh285(true, true), true, e, d), true, a, e, X, d), true, a, e)
% 33.11/4.60 = { by axiom 6 (rule_117) }
% 33.11/4.60 fresh463(fresh544(fresh592(true, true, e, d), true, a, e, X, d), true, a, e)
% 33.11/4.60 = { by axiom 19 (rule_124) }
% 33.11/4.60 fresh463(fresh544(fresh593(s0(d), true, e), true, a, e, X, d), true, a, e)
% 33.11/4.60 = { by axiom 3 (axiom_1) }
% 33.11/4.60 fresh463(fresh544(fresh593(true, true, e), true, a, e, X, d), true, a, e)
% 33.11/4.60 = { by axiom 10 (rule_124) }
% 33.11/4.60 fresh463(fresh544(true, true, a, e, X, d), true, a, e)
% 33.11/4.60 = { by axiom 29 (rule_187) }
% 33.11/4.60 fresh463(fresh545(m0(X, d, a), true, a, e), true, a, e)
% 33.11/4.60 = { by axiom 7 (axiom_19) }
% 33.11/4.60 fresh463(fresh545(true, true, a, e), true, a, e)
% 33.11/4.60 = { by axiom 20 (rule_187) }
% 33.11/4.60 fresh463(true, true, a, e)
% 33.11/4.60 = { by axiom 21 (rule_295) }
% 33.11/4.60 true
% 33.11/4.60 % SZS output end Proof
% 33.11/4.60
% 33.11/4.60 RESULT: Unsatisfiable (the axioms are contradictory).
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