TSTP Solution File: SYN155-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN155-1 : 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 : n013.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 03:33:23 EDT 2023
% Result : Unsatisfiable 30.29s 4.25s
% Output : Proof 30.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN155-1 : TPTP v8.1.2. Released v1.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n013.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 20:01:47 EDT 2023
% 0.14/0.34 % CPUTime :
% 30.29/4.25 Command-line arguments: --no-flatten-goal
% 30.29/4.25
% 30.29/4.25 % SZS status Unsatisfiable
% 30.29/4.25
% 30.44/4.27 % SZS output start Proof
% 30.44/4.27 Take the following subset of the input axioms:
% 30.44/4.27 fof(axiom_13, axiom, r0(e)).
% 30.44/4.27 fof(axiom_14, axiom, ![X]: p0(b, X)).
% 30.44/4.27 fof(axiom_18, axiom, p0(c, b)).
% 30.44/4.27 fof(axiom_19, axiom, ![Y, X2]: m0(X2, d, Y)).
% 30.44/4.27 fof(axiom_27, axiom, m0(e, b, c)).
% 30.44/4.27 fof(axiom_30, axiom, n0(e, e)).
% 30.44/4.27 fof(axiom_34, axiom, n0(c, d)).
% 30.44/4.27 fof(axiom_5, axiom, s0(b)).
% 30.44/4.27 fof(prove_this, negated_conjecture, ![X2]: ~n4(X2, a)).
% 30.44/4.27 fof(rule_003, axiom, ![C, D, E, F]: (l1(C, D) | (~p0(E, C) | (~r0(F) | ~m0(D, C, E))))).
% 30.44/4.27 fof(rule_029, axiom, ![I, H]: (m1(H, I, H) | (~p0(H, I) | ~s0(H)))).
% 30.44/4.27 fof(rule_110, axiom, ![B, D2, C2]: (q1(B, B, B) | ~m0(C2, D2, B))).
% 30.44/4.27 fof(rule_154, axiom, ![A2]: (p2(A2, A2, A2) | ~q1(A2, A2, A2))).
% 30.44/4.27 fof(rule_176, axiom, ![D2, E2]: (p2(D2, E2, D2) | ~m1(E2, D2, E2))).
% 30.44/4.27 fof(rule_186, axiom, ![G, H2]: (q2(G, G, H2) | ~l1(H2, G))).
% 30.44/4.27 fof(rule_238, axiom, ![I2]: (m3(I2, I2, I2) | ~p2(I2, I2, I2))).
% 30.44/4.27 fof(rule_240, axiom, ![D2, E2, F2]: (n3(D2) | ~p2(E2, F2, D2))).
% 30.44/4.27 fof(rule_255, axiom, ![I2, H2, G2]: (q3(G2, H2) | (~q2(I2, G2, H2) | ~n0(I2, G2)))).
% 30.44/4.27 fof(rule_274, axiom, k4(c) | (~n0(c, d) | (~q3(e, b) | ~n3(e)))).
% 30.44/4.27 fof(rule_284, axiom, ![I2, H2]: (n4(H2, H2) | (~k4(I2) | ~m3(H2, H2, H2)))).
% 30.44/4.27
% 30.44/4.27 Now clausify the problem and encode Horn clauses using encoding 3 of
% 30.44/4.27 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 30.44/4.27 We repeatedly replace C & s=t => u=v by the two clauses:
% 30.44/4.27 fresh(y, y, x1...xn) = u
% 30.44/4.27 C => fresh(s, t, x1...xn) = v
% 30.44/4.27 where fresh is a fresh function symbol and x1..xn are the free
% 30.44/4.27 variables of u and v.
% 30.44/4.27 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 30.44/4.27 input problem has no model of domain size 1).
% 30.44/4.27
% 30.44/4.27 The encoding turns the above axioms into the following unit equations and goals:
% 30.44/4.27
% 30.44/4.27 Axiom 1 (axiom_5): s0(b) = true2.
% 30.44/4.27 Axiom 2 (axiom_13): r0(e) = true2.
% 30.44/4.27 Axiom 3 (rule_274): fresh473(X, X) = k4(c).
% 30.44/4.27 Axiom 4 (rule_274): fresh81(X, X) = true2.
% 30.44/4.27 Axiom 5 (axiom_34): n0(c, d) = true2.
% 30.44/4.27 Axiom 6 (axiom_30): n0(e, e) = true2.
% 30.44/4.27 Axiom 7 (axiom_18): p0(c, b) = true2.
% 30.44/4.27 Axiom 8 (axiom_14): p0(b, X) = true2.
% 30.44/4.27 Axiom 9 (rule_274): fresh472(X, X) = fresh473(n3(e), true2).
% 30.44/4.27 Axiom 10 (rule_110): fresh297(X, X, Y) = true2.
% 30.44/4.27 Axiom 11 (rule_154): fresh241(X, X, Y) = true2.
% 30.44/4.27 Axiom 12 (rule_238): fresh129(X, X, Y) = true2.
% 30.44/4.27 Axiom 13 (rule_240): fresh127(X, X, Y) = true2.
% 30.44/4.27 Axiom 14 (rule_284): fresh68(X, X, Y) = n4(Y, Y).
% 30.44/4.27 Axiom 15 (rule_284): fresh67(X, X, Y) = true2.
% 30.44/4.27 Axiom 16 (axiom_19): m0(X, d, Y) = true2.
% 30.44/4.27 Axiom 17 (axiom_27): m0(e, b, c) = true2.
% 30.44/4.27 Axiom 18 (rule_003): fresh439(X, X, Y, Z) = true2.
% 30.44/4.27 Axiom 19 (rule_029): fresh404(X, X, Y, Z) = m1(Y, Z, Y).
% 30.44/4.27 Axiom 20 (rule_029): fresh403(X, X, Y, Z) = true2.
% 30.44/4.27 Axiom 21 (rule_176): fresh208(X, X, Y, Z) = true2.
% 30.44/4.27 Axiom 22 (rule_186): fresh195(X, X, Y, Z) = true2.
% 30.44/4.27 Axiom 23 (rule_255): fresh103(X, X, Y, Z) = true2.
% 30.44/4.27 Axiom 24 (rule_274): fresh472(q3(e, b), true2) = fresh81(n0(c, d), true2).
% 30.44/4.27 Axiom 25 (rule_003): fresh673(X, X, Y, Z, W) = l1(Y, Z).
% 30.44/4.27 Axiom 26 (rule_255): fresh104(X, X, Y, Z, W) = q3(Y, Z).
% 30.44/4.27 Axiom 27 (rule_003): fresh672(X, X, Y, Z, W, V) = fresh673(r0(V), true2, Y, Z, W).
% 30.44/4.27 Axiom 28 (rule_029): fresh404(p0(X, Y), true2, X, Y) = fresh403(s0(X), true2, X, Y).
% 30.44/4.27 Axiom 29 (rule_110): fresh297(m0(X, Y, Z), true2, Z) = q1(Z, Z, Z).
% 30.44/4.27 Axiom 30 (rule_154): fresh241(q1(X, X, X), true2, X) = p2(X, X, X).
% 30.44/4.27 Axiom 31 (rule_186): fresh195(l1(X, Y), true2, Y, X) = q2(Y, Y, X).
% 30.44/4.27 Axiom 32 (rule_238): fresh129(p2(X, X, X), true2, X) = m3(X, X, X).
% 30.44/4.27 Axiom 33 (rule_240): fresh127(p2(X, Y, Z), true2, Z) = n3(Z).
% 30.44/4.27 Axiom 34 (rule_284): fresh68(k4(X), true2, Y) = fresh67(m3(Y, Y, Y), true2, Y).
% 30.44/4.27 Axiom 35 (rule_176): fresh208(m1(X, Y, X), true2, Y, X) = p2(Y, X, Y).
% 30.44/4.27 Axiom 36 (rule_003): fresh672(p0(X, Y), true2, Y, Z, X, W) = fresh439(m0(Z, Y, X), true2, Y, Z).
% 30.44/4.27 Axiom 37 (rule_255): fresh104(q2(X, Y, Z), true2, Y, Z, X) = fresh103(n0(X, Y), true2, Y, Z).
% 30.44/4.27
% 30.44/4.27 Goal 1 (prove_this): n4(X, a) = true2.
% 30.44/4.27 The goal is true when:
% 30.44/4.27 X = a
% 30.44/4.27
% 30.44/4.27 Proof:
% 30.44/4.27 n4(a, a)
% 30.44/4.27 = { by axiom 14 (rule_284) R->L }
% 30.44/4.27 fresh68(true2, true2, a)
% 30.44/4.27 = { by axiom 4 (rule_274) R->L }
% 30.44/4.27 fresh68(fresh81(true2, true2), true2, a)
% 30.44/4.27 = { by axiom 5 (axiom_34) R->L }
% 30.44/4.27 fresh68(fresh81(n0(c, d), true2), true2, a)
% 30.44/4.27 = { by axiom 24 (rule_274) R->L }
% 30.44/4.27 fresh68(fresh472(q3(e, b), true2), true2, a)
% 30.44/4.27 = { by axiom 26 (rule_255) R->L }
% 30.44/4.27 fresh68(fresh472(fresh104(true2, true2, e, b, e), true2), true2, a)
% 30.44/4.27 = { by axiom 22 (rule_186) R->L }
% 30.44/4.27 fresh68(fresh472(fresh104(fresh195(true2, true2, e, b), true2, e, b, e), true2), true2, a)
% 30.44/4.27 = { by axiom 18 (rule_003) R->L }
% 30.44/4.27 fresh68(fresh472(fresh104(fresh195(fresh439(true2, true2, b, e), true2, e, b), true2, e, b, e), true2), true2, a)
% 30.44/4.27 = { by axiom 17 (axiom_27) R->L }
% 30.44/4.27 fresh68(fresh472(fresh104(fresh195(fresh439(m0(e, b, c), true2, b, e), true2, e, b), true2, e, b, e), true2), true2, a)
% 30.44/4.27 = { by axiom 36 (rule_003) R->L }
% 30.44/4.27 fresh68(fresh472(fresh104(fresh195(fresh672(p0(c, b), true2, b, e, c, e), true2, e, b), true2, e, b, e), true2), true2, a)
% 30.44/4.27 = { by axiom 7 (axiom_18) }
% 30.44/4.27 fresh68(fresh472(fresh104(fresh195(fresh672(true2, true2, b, e, c, e), true2, e, b), true2, e, b, e), true2), true2, a)
% 30.44/4.27 = { by axiom 27 (rule_003) }
% 30.44/4.27 fresh68(fresh472(fresh104(fresh195(fresh673(r0(e), true2, b, e, c), true2, e, b), true2, e, b, e), true2), true2, a)
% 30.44/4.27 = { by axiom 2 (axiom_13) }
% 30.44/4.27 fresh68(fresh472(fresh104(fresh195(fresh673(true2, true2, b, e, c), true2, e, b), true2, e, b, e), true2), true2, a)
% 30.44/4.27 = { by axiom 25 (rule_003) }
% 30.44/4.27 fresh68(fresh472(fresh104(fresh195(l1(b, e), true2, e, b), true2, e, b, e), true2), true2, a)
% 30.44/4.27 = { by axiom 31 (rule_186) }
% 30.44/4.27 fresh68(fresh472(fresh104(q2(e, e, b), true2, e, b, e), true2), true2, a)
% 30.44/4.27 = { by axiom 37 (rule_255) }
% 30.44/4.27 fresh68(fresh472(fresh103(n0(e, e), true2, e, b), true2), true2, a)
% 30.44/4.27 = { by axiom 6 (axiom_30) }
% 30.44/4.27 fresh68(fresh472(fresh103(true2, true2, e, b), true2), true2, a)
% 30.44/4.27 = { by axiom 23 (rule_255) }
% 30.44/4.27 fresh68(fresh472(true2, true2), true2, a)
% 30.44/4.27 = { by axiom 9 (rule_274) }
% 30.44/4.27 fresh68(fresh473(n3(e), true2), true2, a)
% 30.44/4.27 = { by axiom 33 (rule_240) R->L }
% 30.44/4.27 fresh68(fresh473(fresh127(p2(e, b, e), true2, e), true2), true2, a)
% 30.44/4.27 = { by axiom 35 (rule_176) R->L }
% 30.44/4.27 fresh68(fresh473(fresh127(fresh208(m1(b, e, b), true2, e, b), true2, e), true2), true2, a)
% 30.44/4.27 = { by axiom 19 (rule_029) R->L }
% 30.44/4.27 fresh68(fresh473(fresh127(fresh208(fresh404(true2, true2, b, e), true2, e, b), true2, e), true2), true2, a)
% 30.44/4.27 = { by axiom 8 (axiom_14) R->L }
% 30.44/4.27 fresh68(fresh473(fresh127(fresh208(fresh404(p0(b, e), true2, b, e), true2, e, b), true2, e), true2), true2, a)
% 30.44/4.27 = { by axiom 28 (rule_029) }
% 30.44/4.27 fresh68(fresh473(fresh127(fresh208(fresh403(s0(b), true2, b, e), true2, e, b), true2, e), true2), true2, a)
% 30.44/4.27 = { by axiom 1 (axiom_5) }
% 30.44/4.27 fresh68(fresh473(fresh127(fresh208(fresh403(true2, true2, b, e), true2, e, b), true2, e), true2), true2, a)
% 30.44/4.27 = { by axiom 20 (rule_029) }
% 30.44/4.27 fresh68(fresh473(fresh127(fresh208(true2, true2, e, b), true2, e), true2), true2, a)
% 30.44/4.27 = { by axiom 21 (rule_176) }
% 30.44/4.27 fresh68(fresh473(fresh127(true2, true2, e), true2), true2, a)
% 30.44/4.27 = { by axiom 13 (rule_240) }
% 30.44/4.27 fresh68(fresh473(true2, true2), true2, a)
% 30.44/4.28 = { by axiom 3 (rule_274) }
% 30.44/4.28 fresh68(k4(c), true2, a)
% 30.44/4.28 = { by axiom 34 (rule_284) }
% 30.44/4.28 fresh67(m3(a, a, a), true2, a)
% 30.44/4.28 = { by axiom 32 (rule_238) R->L }
% 30.44/4.28 fresh67(fresh129(p2(a, a, a), true2, a), true2, a)
% 30.44/4.28 = { by axiom 30 (rule_154) R->L }
% 30.44/4.28 fresh67(fresh129(fresh241(q1(a, a, a), true2, a), true2, a), true2, a)
% 30.44/4.28 = { by axiom 29 (rule_110) R->L }
% 30.44/4.28 fresh67(fresh129(fresh241(fresh297(m0(X, d, a), true2, a), true2, a), true2, a), true2, a)
% 30.44/4.28 = { by axiom 16 (axiom_19) }
% 30.44/4.28 fresh67(fresh129(fresh241(fresh297(true2, true2, a), true2, a), true2, a), true2, a)
% 30.44/4.28 = { by axiom 10 (rule_110) }
% 30.44/4.28 fresh67(fresh129(fresh241(true2, true2, a), true2, a), true2, a)
% 30.44/4.28 = { by axiom 11 (rule_154) }
% 30.44/4.28 fresh67(fresh129(true2, true2, a), true2, a)
% 30.44/4.28 = { by axiom 12 (rule_238) }
% 30.44/4.28 fresh67(true2, true2, a)
% 30.44/4.28 = { by axiom 15 (rule_284) }
% 30.44/4.28 true2
% 30.44/4.28 % SZS output end Proof
% 30.44/4.28
% 30.44/4.28 RESULT: Unsatisfiable (the axioms are contradictory).
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