TSTP Solution File: SYN210-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN210-1 : 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 : n022.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 03:33:36 EDT 2023
% Result : Unsatisfiable 27.10s 3.84s
% Output : Proof 27.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN210-1 : TPTP v8.1.2. Released v1.1.0.
% 0.11/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n022.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.20/0.35 % CPULimit : 300
% 0.20/0.35 % WCLimit : 300
% 0.20/0.35 % DateTime : Sat Aug 26 20:28:40 EDT 2023
% 0.20/0.35 % CPUTime :
% 27.10/3.84 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 27.10/3.84
% 27.10/3.84 % SZS status Unsatisfiable
% 27.10/3.84
% 27.10/3.85 % SZS output start Proof
% 27.10/3.85 Take the following subset of the input axioms:
% 27.10/3.85 fof(axiom_19, axiom, ![X, Y]: m0(X, d, Y)).
% 27.10/3.85 fof(axiom_26, axiom, n0(d, c)).
% 27.10/3.85 fof(prove_this, negated_conjecture, ~s4(c)).
% 27.10/3.85 fof(rule_002, axiom, ![G, H]: (l1(G, G) | ~n0(H, G))).
% 27.10/3.85 fof(rule_122, axiom, ![G2, H2]: (q1(G2, G2, G2) | ~m0(G2, H2, G2))).
% 27.10/3.85 fof(rule_154, axiom, ![A2]: (p2(A2, A2, A2) | ~q1(A2, A2, A2))).
% 27.10/3.85 fof(rule_240, axiom, ![D, E, F]: (n3(D) | ~p2(E, F, D))).
% 27.10/3.85 fof(rule_248, axiom, ![I, J]: (p3(I, I, I) | (~p2(J, I, I) | ~n3(I)))).
% 27.10/3.85 fof(rule_299, axiom, ![C, B, D2, A2_2]: (s4(A2_2) | (~p3(B, C, D2) | ~l1(A2_2, C)))).
% 27.10/3.85
% 27.10/3.85 Now clausify the problem and encode Horn clauses using encoding 3 of
% 27.10/3.85 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 27.10/3.85 We repeatedly replace C & s=t => u=v by the two clauses:
% 27.10/3.85 fresh(y, y, x1...xn) = u
% 27.10/3.85 C => fresh(s, t, x1...xn) = v
% 27.10/3.85 where fresh is a fresh function symbol and x1..xn are the free
% 27.10/3.85 variables of u and v.
% 27.10/3.85 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 27.10/3.85 input problem has no model of domain size 1).
% 27.10/3.85
% 27.10/3.85 The encoding turns the above axioms into the following unit equations and goals:
% 27.10/3.85
% 27.10/3.85 Axiom 1 (axiom_26): n0(d, c) = true.
% 27.10/3.85 Axiom 2 (axiom_19): m0(X, d, Y) = true.
% 27.10/3.85 Axiom 3 (rule_002): fresh441(X, X, Y) = true.
% 27.10/3.85 Axiom 4 (rule_122): fresh279(X, X, Y) = true.
% 27.10/3.85 Axiom 5 (rule_154): fresh241(X, X, Y) = true.
% 27.10/3.85 Axiom 6 (rule_240): fresh127(X, X, Y) = true.
% 27.10/3.85 Axiom 7 (rule_248): fresh116(X, X, Y) = true.
% 27.10/3.85 Axiom 8 (rule_299): fresh45(X, X, Y) = true.
% 27.10/3.85 Axiom 9 (rule_002): fresh441(n0(X, Y), true, Y) = l1(Y, Y).
% 27.10/3.85 Axiom 10 (rule_248): fresh117(X, X, Y, Z) = p3(Y, Y, Y).
% 27.10/3.85 Axiom 11 (rule_299): fresh46(X, X, Y, Z) = s4(Y).
% 27.10/3.85 Axiom 12 (rule_122): fresh279(m0(X, Y, X), true, X) = q1(X, X, X).
% 27.10/3.85 Axiom 13 (rule_154): fresh241(q1(X, X, X), true, X) = p2(X, X, X).
% 27.10/3.85 Axiom 14 (rule_240): fresh127(p2(X, Y, Z), true, Z) = n3(Z).
% 27.10/3.85 Axiom 15 (rule_248): fresh117(n3(X), true, X, Y) = fresh116(p2(Y, X, X), true, X).
% 27.10/3.85 Axiom 16 (rule_299): fresh46(p3(X, Y, Z), true, W, Y) = fresh45(l1(W, Y), true, W).
% 27.10/3.85
% 27.10/3.85 Lemma 17: p2(X, X, X) = true.
% 27.10/3.85 Proof:
% 27.10/3.85 p2(X, X, X)
% 27.10/3.85 = { by axiom 13 (rule_154) R->L }
% 27.10/3.85 fresh241(q1(X, X, X), true, X)
% 27.10/3.85 = { by axiom 12 (rule_122) R->L }
% 27.10/3.85 fresh241(fresh279(m0(X, d, X), true, X), true, X)
% 27.10/3.85 = { by axiom 2 (axiom_19) }
% 27.10/3.85 fresh241(fresh279(true, true, X), true, X)
% 27.10/3.85 = { by axiom 4 (rule_122) }
% 27.10/3.85 fresh241(true, true, X)
% 27.10/3.85 = { by axiom 5 (rule_154) }
% 27.10/3.85 true
% 27.10/3.85
% 27.10/3.85 Goal 1 (prove_this): s4(c) = true.
% 27.10/3.85 Proof:
% 27.10/3.85 s4(c)
% 27.10/3.85 = { by axiom 11 (rule_299) R->L }
% 27.10/3.85 fresh46(true, true, c, c)
% 27.10/3.85 = { by axiom 7 (rule_248) R->L }
% 27.10/3.85 fresh46(fresh116(true, true, c), true, c, c)
% 27.10/3.85 = { by lemma 17 R->L }
% 27.10/3.85 fresh46(fresh116(p2(c, c, c), true, c), true, c, c)
% 27.10/3.85 = { by axiom 15 (rule_248) R->L }
% 27.10/3.85 fresh46(fresh117(n3(c), true, c, c), true, c, c)
% 27.10/3.85 = { by axiom 14 (rule_240) R->L }
% 27.10/3.85 fresh46(fresh117(fresh127(p2(c, c, c), true, c), true, c, c), true, c, c)
% 27.10/3.85 = { by lemma 17 }
% 27.10/3.85 fresh46(fresh117(fresh127(true, true, c), true, c, c), true, c, c)
% 27.10/3.85 = { by axiom 6 (rule_240) }
% 27.10/3.85 fresh46(fresh117(true, true, c, c), true, c, c)
% 27.10/3.85 = { by axiom 10 (rule_248) }
% 27.10/3.85 fresh46(p3(c, c, c), true, c, c)
% 27.10/3.85 = { by axiom 16 (rule_299) }
% 27.10/3.85 fresh45(l1(c, c), true, c)
% 27.10/3.85 = { by axiom 9 (rule_002) R->L }
% 27.10/3.85 fresh45(fresh441(n0(d, c), true, c), true, c)
% 27.10/3.85 = { by axiom 1 (axiom_26) }
% 27.10/3.85 fresh45(fresh441(true, true, c), true, c)
% 27.10/3.85 = { by axiom 3 (rule_002) }
% 27.10/3.85 fresh45(true, true, c)
% 27.10/3.85 = { by axiom 8 (rule_299) }
% 27.10/3.85 true
% 27.10/3.85 % SZS output end Proof
% 27.10/3.85
% 27.10/3.85 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------