TSTP Solution File: SYN191-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN191-1 : 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 03:33:31 EDT 2023
% Result : Unsatisfiable 44.73s 6.08s
% Output : Proof 44.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYN191-1 : TPTP v8.1.2. Released v1.1.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n025.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 21:56:38 EDT 2023
% 0.14/0.35 % CPUTime :
% 44.73/6.08 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 44.73/6.08
% 44.73/6.08 % SZS status Unsatisfiable
% 44.73/6.08
% 44.89/6.09 % SZS output start Proof
% 44.89/6.09 Take the following subset of the input axioms:
% 44.89/6.10 fof(axiom_1, axiom, s0(d)).
% 44.89/6.10 fof(axiom_14, axiom, ![X]: p0(b, X)).
% 44.89/6.10 fof(axiom_17, axiom, ![X2]: q0(X2, d)).
% 44.89/6.10 fof(axiom_19, axiom, ![Y, X2]: m0(X2, d, Y)).
% 44.89/6.10 fof(axiom_24, axiom, l0(c)).
% 44.89/6.10 fof(axiom_26, axiom, n0(d, c)).
% 44.89/6.10 fof(axiom_28, axiom, k0(e)).
% 44.89/6.10 fof(axiom_5, axiom, s0(b)).
% 44.89/6.10 fof(prove_this, negated_conjecture, ~r3(c, b, c)).
% 44.89/6.10 fof(rule_001, axiom, ![I, J]: (k1(I) | ~n0(J, I))).
% 44.89/6.10 fof(rule_029, axiom, ![H, I2]: (m1(H, I2, H) | (~p0(H, I2) | ~s0(H)))).
% 44.89/6.10 fof(rule_107, axiom, ![A2]: (q1(e, A2, A2) | (~m0(A2, d, A2) | ~m0(e, d, A2)))).
% 44.89/6.10 fof(rule_117, axiom, q1(d, d, d) | (~k0(e) | ~s0(d))).
% 44.89/6.10 fof(rule_122, axiom, ![G, H2]: (q1(G, G, G) | ~m0(G, H2, G))).
% 44.89/6.10 fof(rule_124, axiom, ![D, E]: (r1(D) | (~q0(D, E) | (~s0(d) | ~q1(d, E, d))))).
% 44.89/6.10 fof(rule_127, axiom, ![C, F, D2, E2]: (k2(C, D2) | (~m1(E2, D2, C) | (~k1(F) | ~k2(F, D2))))).
% 44.89/6.10 fof(rule_129, axiom, ![A, J2]: (k2(J2, J2) | ~q1(A, J2, J2))).
% 44.89/6.10 fof(rule_154, axiom, ![A2_2]: (p2(A2_2, A2_2, A2_2) | ~q1(A2_2, A2_2, A2_2))).
% 44.89/6.10 fof(rule_188, axiom, ![G2]: (r2(G2) | (~r1(G2) | ~l0(G2)))).
% 44.89/6.10 fof(rule_267, axiom, ![B, C2, D2]: (r3(B, C2, B) | ~p2(B, D2, C2))).
% 44.89/6.10 fof(rule_272, axiom, ![J2, B2, A2_2]: (r3(J2, A2_2, B2) | (~k2(A2_2, B2) | (~r2(B2) | ~r3(B2, J2, J2))))).
% 44.89/6.10
% 44.89/6.10 Now clausify the problem and encode Horn clauses using encoding 3 of
% 44.89/6.10 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 44.89/6.10 We repeatedly replace C & s=t => u=v by the two clauses:
% 44.89/6.10 fresh(y, y, x1...xn) = u
% 44.89/6.10 C => fresh(s, t, x1...xn) = v
% 44.89/6.10 where fresh is a fresh function symbol and x1..xn are the free
% 44.89/6.10 variables of u and v.
% 44.89/6.10 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 44.89/6.10 input problem has no model of domain size 1).
% 44.89/6.10
% 44.89/6.10 The encoding turns the above axioms into the following unit equations and goals:
% 44.89/6.10
% 44.89/6.10 Axiom 1 (axiom_5): s0(b) = true.
% 44.89/6.10 Axiom 2 (axiom_1): s0(d) = true.
% 44.89/6.10 Axiom 3 (axiom_24): l0(c) = true.
% 44.89/6.10 Axiom 4 (axiom_28): k0(e) = true.
% 44.89/6.10 Axiom 5 (axiom_14): p0(b, X) = true.
% 44.89/6.10 Axiom 6 (axiom_17): q0(X, d) = true.
% 44.89/6.10 Axiom 7 (axiom_26): n0(d, c) = true.
% 44.89/6.10 Axiom 8 (rule_117): fresh285(X, X) = true.
% 44.89/6.10 Axiom 9 (axiom_19): m0(X, d, Y) = true.
% 44.89/6.10 Axiom 10 (rule_117): fresh286(X, X) = q1(d, d, d).
% 44.89/6.10 Axiom 11 (rule_124): fresh593(X, X, Y) = true.
% 44.89/6.10 Axiom 12 (rule_001): fresh440(X, X, Y) = true.
% 44.89/6.10 Axiom 13 (rule_107): fresh301(X, X, Y) = q1(e, Y, Y).
% 44.89/6.10 Axiom 14 (rule_107): fresh300(X, X, Y) = true.
% 44.89/6.10 Axiom 15 (rule_117): fresh286(k0(e), true) = fresh285(s0(d), true).
% 44.89/6.10 Axiom 16 (rule_122): fresh279(X, X, Y) = true.
% 44.89/6.10 Axiom 17 (rule_124): fresh276(X, X, Y) = r1(Y).
% 44.89/6.10 Axiom 18 (rule_129): fresh270(X, X, Y) = true.
% 44.89/6.10 Axiom 19 (rule_154): fresh241(X, X, Y) = true.
% 44.89/6.10 Axiom 20 (rule_188): fresh194(X, X, Y) = r2(Y).
% 44.89/6.10 Axiom 21 (rule_188): fresh193(X, X, Y) = true.
% 44.89/6.10 Axiom 22 (rule_124): fresh592(X, X, Y, Z) = fresh593(s0(d), true, Y).
% 44.89/6.10 Axiom 23 (rule_127): fresh591(X, X, Y, Z) = true.
% 44.89/6.10 Axiom 24 (rule_029): fresh404(X, X, Y, Z) = m1(Y, Z, Y).
% 44.89/6.10 Axiom 25 (rule_029): fresh403(X, X, Y, Z) = true.
% 44.89/6.10 Axiom 26 (rule_188): fresh194(r1(X), true, X) = fresh193(l0(X), true, X).
% 44.89/6.10 Axiom 27 (rule_267): fresh88(X, X, Y, Z) = true.
% 44.89/6.10 Axiom 28 (rule_272): fresh477(X, X, Y, Z, W) = r3(Y, Z, W).
% 44.89/6.10 Axiom 29 (rule_001): fresh440(n0(X, Y), true, Y) = k1(Y).
% 44.89/6.10 Axiom 30 (rule_127): fresh272(X, X, Y, Z, W) = k2(Y, Z).
% 44.89/6.10 Axiom 31 (rule_272): fresh83(X, X, Y, Z, W) = true.
% 44.89/6.10 Axiom 32 (rule_127): fresh590(X, X, Y, Z, W, V) = fresh591(k1(W), true, Y, Z).
% 44.89/6.10 Axiom 33 (rule_272): fresh476(X, X, Y, Z, W) = fresh477(r2(W), true, Y, Z, W).
% 44.89/6.10 Axiom 34 (rule_029): fresh404(p0(X, Y), true, X, Y) = fresh403(s0(X), true, X, Y).
% 44.89/6.10 Axiom 35 (rule_107): fresh301(m0(e, d, X), true, X) = fresh300(m0(X, d, X), true, X).
% 44.89/6.10 Axiom 36 (rule_122): fresh279(m0(X, Y, X), true, X) = q1(X, X, X).
% 44.89/6.10 Axiom 37 (rule_129): fresh270(q1(X, Y, Y), true, Y) = k2(Y, Y).
% 44.89/6.10 Axiom 38 (rule_154): fresh241(q1(X, X, X), true, X) = p2(X, X, X).
% 44.89/6.10 Axiom 39 (rule_124): fresh592(q1(d, X, d), true, Y, X) = fresh276(q0(Y, X), true, Y).
% 44.89/6.10 Axiom 40 (rule_267): fresh88(p2(X, Y, Z), true, X, Z) = r3(X, Z, X).
% 44.89/6.10 Axiom 41 (rule_272): fresh476(r3(X, Y, Y), true, Y, Z, X) = fresh83(k2(Z, X), true, Y, Z, X).
% 44.89/6.10 Axiom 42 (rule_127): fresh590(k2(X, Y), true, Z, Y, X, W) = fresh272(m1(W, Y, Z), true, Z, Y, X).
% 44.89/6.10
% 44.89/6.10 Goal 1 (prove_this): r3(c, b, c) = true.
% 44.89/6.10 Proof:
% 44.89/6.10 r3(c, b, c)
% 44.89/6.10 = { by axiom 28 (rule_272) R->L }
% 44.89/6.10 fresh477(true, true, c, b, c)
% 44.89/6.10 = { by axiom 21 (rule_188) R->L }
% 44.89/6.10 fresh477(fresh193(true, true, c), true, c, b, c)
% 44.89/6.10 = { by axiom 3 (axiom_24) R->L }
% 44.89/6.10 fresh477(fresh193(l0(c), true, c), true, c, b, c)
% 44.89/6.10 = { by axiom 26 (rule_188) R->L }
% 44.89/6.10 fresh477(fresh194(r1(c), true, c), true, c, b, c)
% 44.89/6.10 = { by axiom 17 (rule_124) R->L }
% 44.89/6.10 fresh477(fresh194(fresh276(true, true, c), true, c), true, c, b, c)
% 44.89/6.10 = { by axiom 6 (axiom_17) R->L }
% 44.89/6.10 fresh477(fresh194(fresh276(q0(c, d), true, c), true, c), true, c, b, c)
% 44.89/6.10 = { by axiom 39 (rule_124) R->L }
% 44.89/6.10 fresh477(fresh194(fresh592(q1(d, d, d), true, c, d), true, c), true, c, b, c)
% 44.89/6.10 = { by axiom 10 (rule_117) R->L }
% 44.89/6.10 fresh477(fresh194(fresh592(fresh286(true, true), true, c, d), true, c), true, c, b, c)
% 44.89/6.10 = { by axiom 4 (axiom_28) R->L }
% 44.89/6.10 fresh477(fresh194(fresh592(fresh286(k0(e), true), true, c, d), true, c), true, c, b, c)
% 44.89/6.10 = { by axiom 15 (rule_117) }
% 44.89/6.10 fresh477(fresh194(fresh592(fresh285(s0(d), true), true, c, d), true, c), true, c, b, c)
% 44.89/6.10 = { by axiom 2 (axiom_1) }
% 44.89/6.10 fresh477(fresh194(fresh592(fresh285(true, true), true, c, d), true, c), true, c, b, c)
% 44.89/6.10 = { by axiom 8 (rule_117) }
% 44.89/6.10 fresh477(fresh194(fresh592(true, true, c, d), true, c), true, c, b, c)
% 44.89/6.10 = { by axiom 22 (rule_124) }
% 44.89/6.10 fresh477(fresh194(fresh593(s0(d), true, c), true, c), true, c, b, c)
% 44.89/6.10 = { by axiom 2 (axiom_1) }
% 44.89/6.10 fresh477(fresh194(fresh593(true, true, c), true, c), true, c, b, c)
% 44.89/6.10 = { by axiom 11 (rule_124) }
% 44.89/6.10 fresh477(fresh194(true, true, c), true, c, b, c)
% 44.89/6.10 = { by axiom 20 (rule_188) }
% 44.89/6.10 fresh477(r2(c), true, c, b, c)
% 44.89/6.10 = { by axiom 33 (rule_272) R->L }
% 44.89/6.10 fresh476(true, true, c, b, c)
% 44.89/6.10 = { by axiom 27 (rule_267) R->L }
% 44.89/6.10 fresh476(fresh88(true, true, c, c), true, c, b, c)
% 44.89/6.10 = { by axiom 19 (rule_154) R->L }
% 44.89/6.10 fresh476(fresh88(fresh241(true, true, c), true, c, c), true, c, b, c)
% 44.89/6.10 = { by axiom 16 (rule_122) R->L }
% 44.89/6.10 fresh476(fresh88(fresh241(fresh279(true, true, c), true, c), true, c, c), true, c, b, c)
% 44.89/6.10 = { by axiom 9 (axiom_19) R->L }
% 44.89/6.10 fresh476(fresh88(fresh241(fresh279(m0(c, d, c), true, c), true, c), true, c, c), true, c, b, c)
% 44.89/6.10 = { by axiom 36 (rule_122) }
% 44.89/6.10 fresh476(fresh88(fresh241(q1(c, c, c), true, c), true, c, c), true, c, b, c)
% 44.89/6.10 = { by axiom 38 (rule_154) }
% 44.89/6.10 fresh476(fresh88(p2(c, c, c), true, c, c), true, c, b, c)
% 44.89/6.10 = { by axiom 40 (rule_267) }
% 44.89/6.10 fresh476(r3(c, c, c), true, c, b, c)
% 44.89/6.10 = { by axiom 41 (rule_272) }
% 44.89/6.10 fresh83(k2(b, c), true, c, b, c)
% 44.89/6.10 = { by axiom 30 (rule_127) R->L }
% 44.89/6.10 fresh83(fresh272(true, true, b, c, c), true, c, b, c)
% 44.89/6.10 = { by axiom 25 (rule_029) R->L }
% 44.89/6.10 fresh83(fresh272(fresh403(true, true, b, c), true, b, c, c), true, c, b, c)
% 44.89/6.10 = { by axiom 1 (axiom_5) R->L }
% 44.89/6.10 fresh83(fresh272(fresh403(s0(b), true, b, c), true, b, c, c), true, c, b, c)
% 44.89/6.10 = { by axiom 34 (rule_029) R->L }
% 44.89/6.10 fresh83(fresh272(fresh404(p0(b, c), true, b, c), true, b, c, c), true, c, b, c)
% 44.89/6.10 = { by axiom 5 (axiom_14) }
% 44.89/6.10 fresh83(fresh272(fresh404(true, true, b, c), true, b, c, c), true, c, b, c)
% 44.89/6.10 = { by axiom 24 (rule_029) }
% 44.89/6.10 fresh83(fresh272(m1(b, c, b), true, b, c, c), true, c, b, c)
% 44.89/6.10 = { by axiom 42 (rule_127) R->L }
% 44.89/6.10 fresh83(fresh590(k2(c, c), true, b, c, c, b), true, c, b, c)
% 44.89/6.10 = { by axiom 37 (rule_129) R->L }
% 44.89/6.10 fresh83(fresh590(fresh270(q1(e, c, c), true, c), true, b, c, c, b), true, c, b, c)
% 44.89/6.10 = { by axiom 13 (rule_107) R->L }
% 44.89/6.10 fresh83(fresh590(fresh270(fresh301(true, true, c), true, c), true, b, c, c, b), true, c, b, c)
% 44.89/6.10 = { by axiom 9 (axiom_19) R->L }
% 44.89/6.10 fresh83(fresh590(fresh270(fresh301(m0(e, d, c), true, c), true, c), true, b, c, c, b), true, c, b, c)
% 44.89/6.10 = { by axiom 35 (rule_107) }
% 44.89/6.10 fresh83(fresh590(fresh270(fresh300(m0(c, d, c), true, c), true, c), true, b, c, c, b), true, c, b, c)
% 44.89/6.10 = { by axiom 9 (axiom_19) }
% 44.89/6.10 fresh83(fresh590(fresh270(fresh300(true, true, c), true, c), true, b, c, c, b), true, c, b, c)
% 44.89/6.10 = { by axiom 14 (rule_107) }
% 44.89/6.10 fresh83(fresh590(fresh270(true, true, c), true, b, c, c, b), true, c, b, c)
% 44.89/6.10 = { by axiom 18 (rule_129) }
% 44.89/6.10 fresh83(fresh590(true, true, b, c, c, b), true, c, b, c)
% 44.89/6.10 = { by axiom 32 (rule_127) }
% 44.89/6.10 fresh83(fresh591(k1(c), true, b, c), true, c, b, c)
% 44.89/6.10 = { by axiom 29 (rule_001) R->L }
% 44.89/6.10 fresh83(fresh591(fresh440(n0(d, c), true, c), true, b, c), true, c, b, c)
% 44.89/6.10 = { by axiom 7 (axiom_26) }
% 44.89/6.10 fresh83(fresh591(fresh440(true, true, c), true, b, c), true, c, b, c)
% 44.89/6.10 = { by axiom 12 (rule_001) }
% 44.89/6.10 fresh83(fresh591(true, true, b, c), true, c, b, c)
% 44.89/6.10 = { by axiom 23 (rule_127) }
% 44.89/6.10 fresh83(true, true, c, b, c)
% 44.89/6.10 = { by axiom 31 (rule_272) }
% 44.89/6.10 true
% 44.89/6.10 % SZS output end Proof
% 44.89/6.10
% 44.89/6.10 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------