TSTP Solution File: SYN101-1.002.002 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SYN101-1.002.002 : TPTP v8.1.2. Bugfixed v1.2.1.
% 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 : n008.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 03:33:10 EDT 2023
% Result : Unsatisfiable 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN101-1.002.002 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n008.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 : Sat Aug 26 21:11:47 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.40 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.19/0.40
% 0.19/0.40 % SZS status Unsatisfiable
% 0.19/0.40
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 Take the following subset of the input axioms:
% 0.19/0.41 fof(n_1, axiom, nq_1(a)).
% 0.19/0.41 fof(n_3, axiom, nq_2(a)).
% 0.19/0.41 fof(n_s2_goal_1, negated_conjecture, ~p_1_2(a, a)).
% 0.19/0.41 fof(n_s2_type11_2, axiom, ![X_1, X_2]: (p_1_2(X_1, X_2) | (~q_2_2(X_1, X_2) | ~q_1_1(X_1, X_2)))).
% 0.19/0.41 fof(n_s2_type12_1, axiom, ![X_1_2, X_2_2]: (q_1_2(X_1_2, X_2_2) | (~p_2_2(X_1_2, X_2_2) | ~q_1_1(X_1_2, X_2_2)))).
% 0.19/0.41 fof(n_s2_type22_2, axiom, ![X_1_2, X_2_2]: (q_2_2(X_1_2, X_2_2) | ~q_1_2(X_1_2, X_2_2))).
% 0.19/0.41 fof(n_t2_2, axiom, ![X_1_2, X_2_2]: (q_1_1(X_1_2, X_2_2) | (~nq_1(X_1_2) | ~nq_2(X_2_2)))).
% 0.19/0.41 fof(n_t2_3, axiom, ![X_1_2, X_2_2]: (p_2_2(X_1_2, X_2_2) | (~nq_1(X_1_2) | ~nq_2(X_2_2)))).
% 0.19/0.41
% 0.19/0.41 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.41 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.41 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.41 fresh(y, y, x1...xn) = u
% 0.19/0.41 C => fresh(s, t, x1...xn) = v
% 0.19/0.41 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.41 variables of u and v.
% 0.19/0.41 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.41 input problem has no model of domain size 1).
% 0.19/0.41
% 0.19/0.41 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.41
% 0.19/0.41 Axiom 1 (n_1): nq_1(a) = true.
% 0.19/0.41 Axiom 2 (n_3): nq_2(a) = true.
% 0.19/0.41 Axiom 3 (n_s2_type11_2): fresh18(X, X, Y, Z) = p_1_2(Y, Z).
% 0.19/0.41 Axiom 4 (n_s2_type11_2): fresh17(X, X, Y, Z) = true.
% 0.19/0.41 Axiom 5 (n_s2_type12_1): fresh16(X, X, Y, Z) = q_1_2(Y, Z).
% 0.19/0.41 Axiom 6 (n_s2_type12_1): fresh15(X, X, Y, Z) = true.
% 0.19/0.41 Axiom 7 (n_s2_type22_2): fresh9(X, X, Y, Z) = true.
% 0.19/0.41 Axiom 8 (n_t2_2): fresh6(X, X, Y, Z) = q_1_1(Y, Z).
% 0.19/0.41 Axiom 9 (n_t2_2): fresh5(X, X, Y, Z) = true.
% 0.19/0.41 Axiom 10 (n_t2_3): fresh4(X, X, Y, Z) = p_2_2(Y, Z).
% 0.19/0.41 Axiom 11 (n_t2_3): fresh3(X, X, Y, Z) = true.
% 0.19/0.41 Axiom 12 (n_t2_2): fresh6(nq_2(X), true, Y, X) = fresh5(nq_1(Y), true, Y, X).
% 0.19/0.41 Axiom 13 (n_t2_3): fresh4(nq_2(X), true, Y, X) = fresh3(nq_1(Y), true, Y, X).
% 0.19/0.41 Axiom 14 (n_s2_type11_2): fresh18(q_1_1(X, Y), true, X, Y) = fresh17(q_2_2(X, Y), true, X, Y).
% 0.19/0.41 Axiom 15 (n_s2_type12_1): fresh16(q_1_1(X, Y), true, X, Y) = fresh15(p_2_2(X, Y), true, X, Y).
% 0.19/0.41 Axiom 16 (n_s2_type22_2): fresh9(q_1_2(X, Y), true, X, Y) = q_2_2(X, Y).
% 0.19/0.41
% 0.19/0.41 Lemma 17: q_1_1(a, a) = true.
% 0.19/0.41 Proof:
% 0.19/0.41 q_1_1(a, a)
% 0.19/0.41 = { by axiom 8 (n_t2_2) R->L }
% 0.19/0.41 fresh6(true, true, a, a)
% 0.19/0.41 = { by axiom 2 (n_3) R->L }
% 0.19/0.41 fresh6(nq_2(a), true, a, a)
% 0.19/0.41 = { by axiom 12 (n_t2_2) }
% 0.19/0.41 fresh5(nq_1(a), true, a, a)
% 0.19/0.41 = { by axiom 1 (n_1) }
% 0.19/0.41 fresh5(true, true, a, a)
% 0.19/0.41 = { by axiom 9 (n_t2_2) }
% 0.19/0.41 true
% 0.19/0.41
% 0.19/0.41 Goal 1 (n_s2_goal_1): p_1_2(a, a) = true.
% 0.19/0.41 Proof:
% 0.19/0.41 p_1_2(a, a)
% 0.19/0.41 = { by axiom 3 (n_s2_type11_2) R->L }
% 0.19/0.41 fresh18(true, true, a, a)
% 0.19/0.41 = { by lemma 17 R->L }
% 0.19/0.41 fresh18(q_1_1(a, a), true, a, a)
% 0.19/0.41 = { by axiom 14 (n_s2_type11_2) }
% 0.19/0.41 fresh17(q_2_2(a, a), true, a, a)
% 0.19/0.41 = { by axiom 16 (n_s2_type22_2) R->L }
% 0.19/0.41 fresh17(fresh9(q_1_2(a, a), true, a, a), true, a, a)
% 0.19/0.41 = { by axiom 5 (n_s2_type12_1) R->L }
% 0.19/0.41 fresh17(fresh9(fresh16(true, true, a, a), true, a, a), true, a, a)
% 0.19/0.41 = { by lemma 17 R->L }
% 0.19/0.41 fresh17(fresh9(fresh16(q_1_1(a, a), true, a, a), true, a, a), true, a, a)
% 0.19/0.41 = { by axiom 15 (n_s2_type12_1) }
% 0.19/0.41 fresh17(fresh9(fresh15(p_2_2(a, a), true, a, a), true, a, a), true, a, a)
% 0.19/0.41 = { by axiom 10 (n_t2_3) R->L }
% 0.19/0.41 fresh17(fresh9(fresh15(fresh4(true, true, a, a), true, a, a), true, a, a), true, a, a)
% 0.19/0.41 = { by axiom 2 (n_3) R->L }
% 0.19/0.41 fresh17(fresh9(fresh15(fresh4(nq_2(a), true, a, a), true, a, a), true, a, a), true, a, a)
% 0.19/0.41 = { by axiom 13 (n_t2_3) }
% 0.19/0.41 fresh17(fresh9(fresh15(fresh3(nq_1(a), true, a, a), true, a, a), true, a, a), true, a, a)
% 0.19/0.41 = { by axiom 1 (n_1) }
% 0.19/0.41 fresh17(fresh9(fresh15(fresh3(true, true, a, a), true, a, a), true, a, a), true, a, a)
% 0.19/0.41 = { by axiom 11 (n_t2_3) }
% 0.19/0.41 fresh17(fresh9(fresh15(true, true, a, a), true, a, a), true, a, a)
% 0.19/0.42 = { by axiom 6 (n_s2_type12_1) }
% 0.19/0.42 fresh17(fresh9(true, true, a, a), true, a, a)
% 0.19/0.42 = { by axiom 7 (n_s2_type22_2) }
% 0.19/0.42 fresh17(true, true, a, a)
% 0.19/0.42 = { by axiom 4 (n_s2_type11_2) }
% 0.19/0.42 true
% 0.19/0.42 % SZS output end Proof
% 0.19/0.42
% 0.19/0.42 RESULT: Unsatisfiable (the axioms are contradictory).
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