TSTP Solution File: SYN202-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN202-1 : 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 : n029.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 03:33:34 EDT 2023
% Result : Unsatisfiable 32.81s 4.63s
% Output : Proof 32.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SYN202-1 : TPTP v8.1.2. Released v1.1.0.
% 0.00/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.36 % Computer : n029.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat Aug 26 18:15:55 EDT 2023
% 0.14/0.37 % CPUTime :
% 32.81/4.63 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 32.81/4.63
% 32.81/4.63 % SZS status Unsatisfiable
% 32.81/4.63
% 32.81/4.64 % SZS output start Proof
% 32.81/4.64 Take the following subset of the input axioms:
% 32.81/4.64 fof(axiom_1, axiom, s0(d)).
% 32.81/4.64 fof(axiom_13, axiom, r0(e)).
% 32.81/4.64 fof(axiom_14, axiom, ![X]: p0(b, X)).
% 32.81/4.64 fof(axiom_17, axiom, ![X2]: q0(X2, d)).
% 32.81/4.64 fof(axiom_19, axiom, ![Y, X2]: m0(X2, d, Y)).
% 32.81/4.64 fof(axiom_28, axiom, k0(e)).
% 32.81/4.64 fof(prove_this, negated_conjecture, ~s2(e)).
% 32.81/4.64 fof(rule_090, axiom, p1(e, e, e) | (~r0(e) | ~k0(e))).
% 32.81/4.64 fof(rule_117, axiom, q1(d, d, d) | (~k0(e) | ~s0(d))).
% 32.81/4.64 fof(rule_124, axiom, ![D, E]: (r1(D) | (~q0(D, E) | (~s0(d) | ~q1(d, E, d))))).
% 32.81/4.64 fof(rule_125, axiom, ![I]: (s1(I) | ~p0(I, I))).
% 32.81/4.64 fof(rule_181, axiom, ![I2]: (q2(I2, I2, I2) | ~p1(I2, I2, I2))).
% 32.81/4.64 fof(rule_187, axiom, ![C, F, D2, E2]: (q2(C, D2, C) | (~r1(D2) | (~m0(E2, F, C) | (~k0(D2) | ~q2(D2, D2, D2)))))).
% 32.81/4.64 fof(rule_189, axiom, ![H]: (s2(H) | (~q2(b, H, b) | ~s1(b)))).
% 32.81/4.64
% 32.81/4.64 Now clausify the problem and encode Horn clauses using encoding 3 of
% 32.81/4.64 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 32.81/4.64 We repeatedly replace C & s=t => u=v by the two clauses:
% 32.81/4.64 fresh(y, y, x1...xn) = u
% 32.81/4.64 C => fresh(s, t, x1...xn) = v
% 32.81/4.64 where fresh is a fresh function symbol and x1..xn are the free
% 32.81/4.64 variables of u and v.
% 32.81/4.64 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 32.81/4.64 input problem has no model of domain size 1).
% 32.81/4.64
% 32.81/4.64 The encoding turns the above axioms into the following unit equations and goals:
% 32.81/4.64
% 32.81/4.64 Axiom 1 (axiom_14): p0(b, X) = true.
% 32.81/4.64 Axiom 2 (axiom_17): q0(X, d) = true.
% 32.81/4.64 Axiom 3 (axiom_13): r0(e) = true.
% 32.81/4.64 Axiom 4 (axiom_1): s0(d) = true.
% 32.81/4.64 Axiom 5 (axiom_28): k0(e) = true.
% 32.81/4.64 Axiom 6 (rule_090): fresh320(X, X) = true.
% 32.81/4.64 Axiom 7 (rule_117): fresh285(X, X) = true.
% 32.81/4.64 Axiom 8 (axiom_19): m0(X, d, Y) = true.
% 32.81/4.64 Axiom 9 (rule_117): fresh286(X, X) = q1(d, d, d).
% 32.81/4.64 Axiom 10 (rule_090): fresh321(X, X) = p1(e, e, e).
% 32.81/4.64 Axiom 11 (rule_124): fresh593(X, X, Y) = true.
% 32.81/4.64 Axiom 12 (rule_090): fresh321(k0(e), true) = fresh320(r0(e), true).
% 32.81/4.64 Axiom 13 (rule_117): fresh286(k0(e), true) = fresh285(s0(d), true).
% 32.81/4.64 Axiom 14 (rule_124): fresh276(X, X, Y) = r1(Y).
% 32.81/4.64 Axiom 15 (rule_125): fresh275(X, X, Y) = true.
% 32.81/4.64 Axiom 16 (rule_181): fresh200(X, X, Y) = true.
% 32.81/4.64 Axiom 17 (rule_189): fresh192(X, X, Y) = s2(Y).
% 32.81/4.64 Axiom 18 (rule_189): fresh191(X, X, Y) = true.
% 32.81/4.64 Axiom 19 (rule_124): fresh592(X, X, Y, Z) = fresh593(s0(d), true, Y).
% 32.81/4.64 Axiom 20 (rule_187): fresh545(X, X, Y, Z) = true.
% 32.81/4.64 Axiom 21 (rule_125): fresh275(p0(X, X), true, X) = s1(X).
% 32.81/4.64 Axiom 22 (rule_181): fresh200(p1(X, X, X), true, X) = q2(X, X, X).
% 32.81/4.64 Axiom 23 (rule_189): fresh192(q2(b, X, b), true, X) = fresh191(s1(b), true, X).
% 32.81/4.64 Axiom 24 (rule_124): fresh592(q1(d, X, d), true, Y, X) = fresh276(q0(Y, X), true, Y).
% 32.81/4.64 Axiom 25 (rule_187): fresh544(X, X, Y, Z, W, V) = fresh545(m0(W, V, Y), true, Y, Z).
% 32.81/4.64 Axiom 26 (rule_187): fresh543(X, X, Y, Z, W, V) = q2(Y, Z, Y).
% 32.81/4.64 Axiom 27 (rule_187): fresh542(X, X, Y, Z, W, V) = fresh543(k0(Z), true, Y, Z, W, V).
% 32.81/4.64 Axiom 28 (rule_187): fresh542(q2(X, X, X), true, Y, X, Z, W) = fresh544(r1(X), true, Y, X, Z, W).
% 32.81/4.64
% 32.81/4.64 Goal 1 (prove_this): s2(e) = true.
% 32.81/4.64 Proof:
% 32.81/4.64 s2(e)
% 32.81/4.64 = { by axiom 17 (rule_189) R->L }
% 32.81/4.64 fresh192(true, true, e)
% 32.81/4.64 = { by axiom 20 (rule_187) R->L }
% 32.81/4.64 fresh192(fresh545(true, true, b, e), true, e)
% 32.81/4.64 = { by axiom 8 (axiom_19) R->L }
% 32.81/4.64 fresh192(fresh545(m0(X, d, b), true, b, e), true, e)
% 32.81/4.64 = { by axiom 25 (rule_187) R->L }
% 32.81/4.64 fresh192(fresh544(true, true, b, e, X, d), true, e)
% 32.81/4.64 = { by axiom 11 (rule_124) R->L }
% 32.81/4.64 fresh192(fresh544(fresh593(true, true, e), true, b, e, X, d), true, e)
% 32.81/4.64 = { by axiom 4 (axiom_1) R->L }
% 32.81/4.64 fresh192(fresh544(fresh593(s0(d), true, e), true, b, e, X, d), true, e)
% 32.81/4.64 = { by axiom 19 (rule_124) R->L }
% 32.81/4.64 fresh192(fresh544(fresh592(true, true, e, d), true, b, e, X, d), true, e)
% 32.81/4.64 = { by axiom 7 (rule_117) R->L }
% 32.81/4.64 fresh192(fresh544(fresh592(fresh285(true, true), true, e, d), true, b, e, X, d), true, e)
% 32.81/4.64 = { by axiom 4 (axiom_1) R->L }
% 32.81/4.64 fresh192(fresh544(fresh592(fresh285(s0(d), true), true, e, d), true, b, e, X, d), true, e)
% 32.81/4.64 = { by axiom 13 (rule_117) R->L }
% 32.81/4.64 fresh192(fresh544(fresh592(fresh286(k0(e), true), true, e, d), true, b, e, X, d), true, e)
% 32.81/4.64 = { by axiom 5 (axiom_28) }
% 32.81/4.64 fresh192(fresh544(fresh592(fresh286(true, true), true, e, d), true, b, e, X, d), true, e)
% 32.81/4.64 = { by axiom 9 (rule_117) }
% 32.81/4.64 fresh192(fresh544(fresh592(q1(d, d, d), true, e, d), true, b, e, X, d), true, e)
% 32.81/4.64 = { by axiom 24 (rule_124) }
% 32.81/4.64 fresh192(fresh544(fresh276(q0(e, d), true, e), true, b, e, X, d), true, e)
% 32.81/4.64 = { by axiom 2 (axiom_17) }
% 32.81/4.64 fresh192(fresh544(fresh276(true, true, e), true, b, e, X, d), true, e)
% 32.81/4.64 = { by axiom 14 (rule_124) }
% 32.81/4.64 fresh192(fresh544(r1(e), true, b, e, X, d), true, e)
% 32.81/4.64 = { by axiom 28 (rule_187) R->L }
% 32.81/4.64 fresh192(fresh542(q2(e, e, e), true, b, e, X, d), true, e)
% 32.81/4.64 = { by axiom 22 (rule_181) R->L }
% 32.81/4.64 fresh192(fresh542(fresh200(p1(e, e, e), true, e), true, b, e, X, d), true, e)
% 32.81/4.64 = { by axiom 10 (rule_090) R->L }
% 32.81/4.64 fresh192(fresh542(fresh200(fresh321(true, true), true, e), true, b, e, X, d), true, e)
% 32.81/4.64 = { by axiom 5 (axiom_28) R->L }
% 32.81/4.64 fresh192(fresh542(fresh200(fresh321(k0(e), true), true, e), true, b, e, X, d), true, e)
% 32.81/4.64 = { by axiom 12 (rule_090) }
% 32.81/4.64 fresh192(fresh542(fresh200(fresh320(r0(e), true), true, e), true, b, e, X, d), true, e)
% 32.81/4.64 = { by axiom 3 (axiom_13) }
% 32.81/4.64 fresh192(fresh542(fresh200(fresh320(true, true), true, e), true, b, e, X, d), true, e)
% 32.81/4.64 = { by axiom 6 (rule_090) }
% 32.81/4.64 fresh192(fresh542(fresh200(true, true, e), true, b, e, X, d), true, e)
% 32.81/4.64 = { by axiom 16 (rule_181) }
% 32.81/4.64 fresh192(fresh542(true, true, b, e, X, d), true, e)
% 32.81/4.64 = { by axiom 27 (rule_187) }
% 32.81/4.64 fresh192(fresh543(k0(e), true, b, e, X, d), true, e)
% 32.81/4.64 = { by axiom 5 (axiom_28) }
% 32.81/4.64 fresh192(fresh543(true, true, b, e, X, d), true, e)
% 32.81/4.64 = { by axiom 26 (rule_187) }
% 32.81/4.64 fresh192(q2(b, e, b), true, e)
% 32.81/4.64 = { by axiom 23 (rule_189) }
% 32.81/4.64 fresh191(s1(b), true, e)
% 32.81/4.64 = { by axiom 21 (rule_125) R->L }
% 32.81/4.64 fresh191(fresh275(p0(b, b), true, b), true, e)
% 32.81/4.64 = { by axiom 1 (axiom_14) }
% 32.81/4.64 fresh191(fresh275(true, true, b), true, e)
% 32.81/4.64 = { by axiom 15 (rule_125) }
% 32.81/4.64 fresh191(true, true, e)
% 32.81/4.64 = { by axiom 18 (rule_189) }
% 32.81/4.64 true
% 32.81/4.64 % SZS output end Proof
% 32.81/4.64
% 32.81/4.64 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------