TSTP Solution File: SYN099-1.003 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SYN099-1.003 : 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 : n018.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 03:33:09 EDT 2023
% Result : Unsatisfiable 0.13s 0.43s
% Output : Proof 0.20s
% 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 : SYN099-1.003 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.13/0.13 % 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 : n018.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 19:31:45 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.43 Command-line arguments: --no-flatten-goal
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% 0.13/0.43 % SZS status Unsatisfiable
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% 0.20/0.43 % SZS output start Proof
% 0.20/0.43 Take the following subset of the input axioms:
% 0.20/0.43 fof(m_s2_goal_1, negated_conjecture, ![X]: ~p_1_3(X)).
% 0.20/0.43 fof(m_s2_type11_4, axiom, ![X2]: (p_1_3(X2) | (~q_2_3(X2) | ~q_1_2(X2)))).
% 0.20/0.43 fof(m_s2_type12_1, axiom, ![X2]: (q_1_2(X2) | (~p_2_2(X2) | ~q_1_1(X2)))).
% 0.20/0.43 fof(m_s2_type12_5, axiom, ![X2]: (q_2_3(X2) | (~p_3_3(X2) | ~q_2_2(X2)))).
% 0.20/0.43 fof(m_t2_2, axiom, q_1_1(a)).
% 0.20/0.43 fof(m_t2_3, axiom, p_2_2(a)).
% 0.20/0.43 fof(m_t2_4, axiom, q_2_2(a)).
% 0.20/0.43 fof(m_t2_5, axiom, p_3_3(a)).
% 0.20/0.43
% 0.20/0.43 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.43 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.43 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.43 fresh(y, y, x1...xn) = u
% 0.20/0.43 C => fresh(s, t, x1...xn) = v
% 0.20/0.43 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.43 variables of u and v.
% 0.20/0.43 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.43 input problem has no model of domain size 1).
% 0.20/0.43
% 0.20/0.43 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.43
% 0.20/0.43 Axiom 1 (m_t2_2): q_1_1(a) = true2.
% 0.20/0.43 Axiom 2 (m_t2_5): p_3_3(a) = true2.
% 0.20/0.43 Axiom 3 (m_t2_3): p_2_2(a) = true2.
% 0.20/0.43 Axiom 4 (m_t2_4): q_2_2(a) = true2.
% 0.20/0.43 Axiom 5 (m_s2_type11_4): fresh30(X, X, Y) = p_1_3(Y).
% 0.20/0.43 Axiom 6 (m_s2_type11_4): fresh29(X, X, Y) = true2.
% 0.20/0.43 Axiom 7 (m_s2_type12_1): fresh24(X, X, Y) = q_1_2(Y).
% 0.20/0.43 Axiom 8 (m_s2_type12_1): fresh23(X, X, Y) = true2.
% 0.20/0.43 Axiom 9 (m_s2_type12_5): fresh16(X, X, Y) = q_2_3(Y).
% 0.20/0.43 Axiom 10 (m_s2_type12_5): fresh15(X, X, Y) = true2.
% 0.20/0.43 Axiom 11 (m_s2_type11_4): fresh30(q_1_2(X), true2, X) = fresh29(q_2_3(X), true2, X).
% 0.20/0.43 Axiom 12 (m_s2_type12_1): fresh24(q_1_1(X), true2, X) = fresh23(p_2_2(X), true2, X).
% 0.20/0.43 Axiom 13 (m_s2_type12_5): fresh16(p_3_3(X), true2, X) = fresh15(q_2_2(X), true2, X).
% 0.20/0.43
% 0.20/0.43 Goal 1 (m_s2_goal_1): p_1_3(X) = true2.
% 0.20/0.43 The goal is true when:
% 0.20/0.43 X = a
% 0.20/0.43
% 0.20/0.43 Proof:
% 0.20/0.43 p_1_3(a)
% 0.20/0.43 = { by axiom 5 (m_s2_type11_4) R->L }
% 0.20/0.43 fresh30(true2, true2, a)
% 0.20/0.43 = { by axiom 8 (m_s2_type12_1) R->L }
% 0.20/0.43 fresh30(fresh23(true2, true2, a), true2, a)
% 0.20/0.43 = { by axiom 3 (m_t2_3) R->L }
% 0.20/0.43 fresh30(fresh23(p_2_2(a), true2, a), true2, a)
% 0.20/0.43 = { by axiom 12 (m_s2_type12_1) R->L }
% 0.20/0.43 fresh30(fresh24(q_1_1(a), true2, a), true2, a)
% 0.20/0.43 = { by axiom 1 (m_t2_2) }
% 0.20/0.43 fresh30(fresh24(true2, true2, a), true2, a)
% 0.20/0.43 = { by axiom 7 (m_s2_type12_1) }
% 0.20/0.43 fresh30(q_1_2(a), true2, a)
% 0.20/0.43 = { by axiom 11 (m_s2_type11_4) }
% 0.20/0.43 fresh29(q_2_3(a), true2, a)
% 0.20/0.43 = { by axiom 9 (m_s2_type12_5) R->L }
% 0.20/0.43 fresh29(fresh16(true2, true2, a), true2, a)
% 0.20/0.43 = { by axiom 2 (m_t2_5) R->L }
% 0.20/0.43 fresh29(fresh16(p_3_3(a), true2, a), true2, a)
% 0.20/0.43 = { by axiom 13 (m_s2_type12_5) }
% 0.20/0.43 fresh29(fresh15(q_2_2(a), true2, a), true2, a)
% 0.20/0.43 = { by axiom 4 (m_t2_4) }
% 0.20/0.43 fresh29(fresh15(true2, true2, a), true2, a)
% 0.20/0.43 = { by axiom 10 (m_s2_type12_5) }
% 0.20/0.43 fresh29(true2, true2, a)
% 0.20/0.43 = { by axiom 6 (m_s2_type11_4) }
% 0.20/0.43 true2
% 0.20/0.43 % SZS output end Proof
% 0.20/0.43
% 0.20/0.43 RESULT: Unsatisfiable (the axioms are contradictory).
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