TSTP Solution File: SYN190-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN190-1 : 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 : n016.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 03:33:31 EDT 2023
% Result : Unsatisfiable 53.31s 7.18s
% Output : Proof 53.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN190-1 : 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
% 0.13/0.34 % Computer : n016.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 19:20:12 EDT 2023
% 0.13/0.34 % CPUTime :
% 53.31/7.18 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 53.31/7.18
% 53.31/7.18 % SZS status Unsatisfiable
% 53.31/7.18
% 53.60/7.21 % SZS output start Proof
% 53.60/7.21 Take the following subset of the input axioms:
% 53.60/7.21 fof(axiom_1, axiom, s0(d)).
% 53.60/7.21 fof(axiom_14, axiom, ![X]: p0(b, X)).
% 53.60/7.21 fof(axiom_17, axiom, ![X2]: q0(X2, d)).
% 53.60/7.21 fof(axiom_19, axiom, ![Y, X2]: m0(X2, d, Y)).
% 53.60/7.21 fof(axiom_20, axiom, l0(a)).
% 53.60/7.21 fof(axiom_28, axiom, k0(e)).
% 53.60/7.21 fof(axiom_37, axiom, n0(b, a)).
% 53.60/7.21 fof(prove_this, negated_conjecture, ![X2]: ~r3(a, X2, d)).
% 53.60/7.21 fof(rule_002, axiom, ![G, H]: (l1(G, G) | ~n0(H, G))).
% 53.60/7.21 fof(rule_092, axiom, ![J, C, B, A2]: (q1(J, A2, J) | (~n0(B, A2) | ~p0(C, J)))).
% 53.60/7.21 fof(rule_117, axiom, q1(d, d, d) | (~k0(e) | ~s0(d))).
% 53.60/7.21 fof(rule_122, axiom, ![H2, G2]: (q1(G2, G2, G2) | ~m0(G2, H2, G2))).
% 53.60/7.21 fof(rule_124, axiom, ![D, E]: (r1(D) | (~q0(D, E) | (~s0(d) | ~q1(d, E, d))))).
% 53.60/7.21 fof(rule_125, axiom, ![I]: (s1(I) | ~p0(I, I))).
% 53.60/7.21 fof(rule_126, axiom, ![F, H2, G2]: (s1(F) | (~q0(F, G2) | ~s1(H2)))).
% 53.60/7.21 fof(rule_135, axiom, ![H2, G2, F2]: (m2(F2) | (~s0(F2) | ~l1(G2, H2)))).
% 53.60/7.21 fof(rule_141, axiom, ![B2]: (p2(B2, a, B2) | ~q1(B2, a, B2))).
% 53.60/7.21 fof(rule_154, axiom, ![A2_2]: (p2(A2_2, A2_2, A2_2) | ~q1(A2_2, A2_2, A2_2))).
% 53.60/7.21 fof(rule_188, axiom, ![G2]: (r2(G2) | (~r1(G2) | ~l0(G2)))).
% 53.60/7.21 fof(rule_192, axiom, ![J2, C2, B2, A2_2]: (k3(J2, A2_2, J2) | (~s1(A2_2) | (~p2(B2, A2_2, C2) | ~n0(J2, C2))))).
% 53.60/7.21 fof(rule_235, axiom, ![C2, B2]: (m3(B2, B2, C2) | (~r2(C2) | ~k3(B2, C2, B2)))).
% 53.60/7.21 fof(rule_267, axiom, ![C2, D2, B2]: (r3(B2, C2, B2) | ~p2(B2, D2, C2))).
% 53.60/7.21 fof(rule_268, axiom, ![A, I2, J2, H2]: (r3(H2, H2, I2) | (~m2(I2) | (~m3(J2, b, H2) | ~r3(I2, A, A))))).
% 53.60/7.21
% 53.60/7.21 Now clausify the problem and encode Horn clauses using encoding 3 of
% 53.60/7.21 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 53.60/7.21 We repeatedly replace C & s=t => u=v by the two clauses:
% 53.60/7.21 fresh(y, y, x1...xn) = u
% 53.60/7.21 C => fresh(s, t, x1...xn) = v
% 53.60/7.21 where fresh is a fresh function symbol and x1..xn are the free
% 53.60/7.21 variables of u and v.
% 53.60/7.21 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 53.60/7.21 input problem has no model of domain size 1).
% 53.60/7.21
% 53.60/7.21 The encoding turns the above axioms into the following unit equations and goals:
% 53.60/7.21
% 53.60/7.22 Axiom 1 (axiom_14): p0(b, X) = true2.
% 53.60/7.22 Axiom 2 (axiom_17): q0(X, d) = true2.
% 53.60/7.22 Axiom 3 (axiom_1): s0(d) = true2.
% 53.60/7.22 Axiom 4 (axiom_20): l0(a) = true2.
% 53.60/7.22 Axiom 5 (axiom_37): n0(b, a) = true2.
% 53.60/7.22 Axiom 6 (axiom_28): k0(e) = true2.
% 53.60/7.22 Axiom 7 (rule_117): fresh285(X, X) = true2.
% 53.60/7.22 Axiom 8 (axiom_19): m0(X, d, Y) = true2.
% 53.60/7.22 Axiom 9 (rule_117): fresh286(X, X) = q1(d, d, d).
% 53.60/7.22 Axiom 10 (rule_124): fresh593(X, X, Y) = true2.
% 53.60/7.22 Axiom 11 (rule_002): fresh441(X, X, Y) = true2.
% 53.60/7.22 Axiom 12 (rule_117): fresh286(k0(e), true2) = fresh285(s0(d), true2).
% 53.60/7.22 Axiom 13 (rule_122): fresh279(X, X, Y) = true2.
% 53.60/7.22 Axiom 14 (rule_124): fresh276(X, X, Y) = r1(Y).
% 53.60/7.22 Axiom 15 (rule_125): fresh275(X, X, Y) = true2.
% 53.60/7.22 Axiom 16 (rule_126): fresh273(X, X, Y) = true2.
% 53.60/7.22 Axiom 17 (rule_135): fresh265(X, X, Y) = m2(Y).
% 53.60/7.22 Axiom 18 (rule_135): fresh264(X, X, Y) = true2.
% 53.60/7.22 Axiom 19 (rule_141): fresh258(X, X, Y) = true2.
% 53.60/7.22 Axiom 20 (rule_154): fresh241(X, X, Y) = true2.
% 53.60/7.22 Axiom 21 (rule_188): fresh194(X, X, Y) = r2(Y).
% 53.60/7.22 Axiom 22 (rule_188): fresh193(X, X, Y) = true2.
% 53.60/7.22 Axiom 23 (rule_124): fresh592(X, X, Y, Z) = fresh593(s0(d), true2, Y).
% 53.60/7.22 Axiom 24 (rule_192): fresh541(X, X, Y, Z) = true2.
% 53.60/7.22 Axiom 25 (rule_268): fresh485(X, X, Y, Z) = true2.
% 53.60/7.22 Axiom 26 (rule_002): fresh441(n0(X, Y), true2, Y) = l1(Y, Y).
% 53.60/7.22 Axiom 27 (rule_092): fresh317(X, X, Y, Z) = true2.
% 53.60/7.22 Axiom 28 (rule_125): fresh275(p0(X, X), true2, X) = s1(X).
% 53.60/7.22 Axiom 29 (rule_126): fresh274(X, X, Y, Z) = s1(Y).
% 53.60/7.22 Axiom 30 (rule_135): fresh265(l1(X, Y), true2, Z) = fresh264(s0(Z), true2, Z).
% 53.60/7.22 Axiom 31 (rule_188): fresh194(r1(X), true2, X) = fresh193(l0(X), true2, X).
% 53.60/7.22 Axiom 32 (rule_235): fresh134(X, X, Y, Z) = m3(Y, Y, Z).
% 53.60/7.22 Axiom 33 (rule_235): fresh133(X, X, Y, Z) = true2.
% 53.60/7.22 Axiom 34 (rule_267): fresh88(X, X, Y, Z) = true2.
% 53.60/7.22 Axiom 35 (rule_268): fresh87(X, X, Y, Z) = r3(Y, Y, Z).
% 53.60/7.22 Axiom 36 (rule_192): fresh540(X, X, Y, Z, W) = fresh541(n0(Y, W), true2, Y, Z).
% 53.60/7.22 Axiom 37 (rule_268): fresh484(X, X, Y, Z, W) = fresh485(m2(Z), true2, Y, Z).
% 53.60/7.22 Axiom 38 (rule_092): fresh318(X, X, Y, Z, W) = q1(Y, Z, Y).
% 53.60/7.22 Axiom 39 (rule_122): fresh279(m0(X, Y, X), true2, X) = q1(X, X, X).
% 53.60/7.22 Axiom 40 (rule_126): fresh274(s1(X), true2, Y, Z) = fresh273(q0(Y, Z), true2, Y).
% 53.60/7.22 Axiom 41 (rule_141): fresh258(q1(X, a, X), true2, X) = p2(X, a, X).
% 53.60/7.22 Axiom 42 (rule_154): fresh241(q1(X, X, X), true2, X) = p2(X, X, X).
% 53.60/7.22 Axiom 43 (rule_192): fresh186(X, X, Y, Z, W) = k3(Y, Z, Y).
% 53.60/7.22 Axiom 44 (rule_124): fresh592(q1(d, X, d), true2, Y, X) = fresh276(q0(Y, X), true2, Y).
% 53.60/7.22 Axiom 45 (rule_092): fresh318(p0(X, Y), true2, Y, Z, W) = fresh317(n0(W, Z), true2, Y, Z).
% 53.60/7.22 Axiom 46 (rule_235): fresh134(k3(X, Y, X), true2, X, Y) = fresh133(r2(Y), true2, X, Y).
% 53.60/7.22 Axiom 47 (rule_267): fresh88(p2(X, Y, Z), true2, X, Z) = r3(X, Z, X).
% 53.60/7.22 Axiom 48 (rule_192): fresh540(p2(X, Y, Z), true2, W, Y, Z) = fresh186(s1(Y), true2, W, Y, Z).
% 53.60/7.22 Axiom 49 (rule_268): fresh484(r3(X, Y, Y), true2, Z, X, W) = fresh87(m3(W, b, Z), true2, Z, X).
% 53.60/7.22
% 53.60/7.22 Goal 1 (prove_this): r3(a, X, d) = true2.
% 53.60/7.22 The goal is true when:
% 53.60/7.22 X = a
% 53.60/7.22
% 53.60/7.22 Proof:
% 53.60/7.22 r3(a, a, d)
% 53.60/7.22 = { by axiom 35 (rule_268) R->L }
% 53.60/7.22 fresh87(true2, true2, a, d)
% 53.60/7.22 = { by axiom 33 (rule_235) R->L }
% 53.60/7.22 fresh87(fresh133(true2, true2, b, a), true2, a, d)
% 53.60/7.22 = { by axiom 22 (rule_188) R->L }
% 53.60/7.22 fresh87(fresh133(fresh193(true2, true2, a), true2, b, a), true2, a, d)
% 53.60/7.22 = { by axiom 4 (axiom_20) R->L }
% 53.60/7.22 fresh87(fresh133(fresh193(l0(a), true2, a), true2, b, a), true2, a, d)
% 53.60/7.22 = { by axiom 31 (rule_188) R->L }
% 53.60/7.22 fresh87(fresh133(fresh194(r1(a), true2, a), true2, b, a), true2, a, d)
% 53.60/7.22 = { by axiom 14 (rule_124) R->L }
% 53.60/7.22 fresh87(fresh133(fresh194(fresh276(true2, true2, a), true2, a), true2, b, a), true2, a, d)
% 53.60/7.22 = { by axiom 2 (axiom_17) R->L }
% 53.60/7.22 fresh87(fresh133(fresh194(fresh276(q0(a, d), true2, a), true2, a), true2, b, a), true2, a, d)
% 53.60/7.22 = { by axiom 44 (rule_124) R->L }
% 53.60/7.22 fresh87(fresh133(fresh194(fresh592(q1(d, d, d), true2, a, d), true2, a), true2, b, a), true2, a, d)
% 53.60/7.22 = { by axiom 9 (rule_117) R->L }
% 53.60/7.22 fresh87(fresh133(fresh194(fresh592(fresh286(true2, true2), true2, a, d), true2, a), true2, b, a), true2, a, d)
% 53.60/7.22 = { by axiom 6 (axiom_28) R->L }
% 53.60/7.22 fresh87(fresh133(fresh194(fresh592(fresh286(k0(e), true2), true2, a, d), true2, a), true2, b, a), true2, a, d)
% 53.60/7.22 = { by axiom 12 (rule_117) }
% 53.60/7.22 fresh87(fresh133(fresh194(fresh592(fresh285(s0(d), true2), true2, a, d), true2, a), true2, b, a), true2, a, d)
% 53.60/7.22 = { by axiom 3 (axiom_1) }
% 53.60/7.22 fresh87(fresh133(fresh194(fresh592(fresh285(true2, true2), true2, a, d), true2, a), true2, b, a), true2, a, d)
% 53.60/7.22 = { by axiom 7 (rule_117) }
% 53.60/7.22 fresh87(fresh133(fresh194(fresh592(true2, true2, a, d), true2, a), true2, b, a), true2, a, d)
% 53.60/7.22 = { by axiom 23 (rule_124) }
% 53.60/7.22 fresh87(fresh133(fresh194(fresh593(s0(d), true2, a), true2, a), true2, b, a), true2, a, d)
% 53.60/7.22 = { by axiom 3 (axiom_1) }
% 53.60/7.22 fresh87(fresh133(fresh194(fresh593(true2, true2, a), true2, a), true2, b, a), true2, a, d)
% 53.60/7.22 = { by axiom 10 (rule_124) }
% 53.60/7.22 fresh87(fresh133(fresh194(true2, true2, a), true2, b, a), true2, a, d)
% 53.60/7.22 = { by axiom 21 (rule_188) }
% 53.60/7.22 fresh87(fresh133(r2(a), true2, b, a), true2, a, d)
% 53.60/7.22 = { by axiom 46 (rule_235) R->L }
% 53.60/7.22 fresh87(fresh134(k3(b, a, b), true2, b, a), true2, a, d)
% 53.60/7.22 = { by axiom 43 (rule_192) R->L }
% 53.60/7.22 fresh87(fresh134(fresh186(true2, true2, b, a, a), true2, b, a), true2, a, d)
% 53.60/7.22 = { by axiom 16 (rule_126) R->L }
% 53.60/7.22 fresh87(fresh134(fresh186(fresh273(true2, true2, a), true2, b, a, a), true2, b, a), true2, a, d)
% 53.60/7.22 = { by axiom 2 (axiom_17) R->L }
% 53.60/7.22 fresh87(fresh134(fresh186(fresh273(q0(a, d), true2, a), true2, b, a, a), true2, b, a), true2, a, d)
% 53.60/7.22 = { by axiom 40 (rule_126) R->L }
% 53.60/7.22 fresh87(fresh134(fresh186(fresh274(s1(b), true2, a, d), true2, b, a, a), true2, b, a), true2, a, d)
% 53.60/7.22 = { by axiom 28 (rule_125) R->L }
% 53.60/7.22 fresh87(fresh134(fresh186(fresh274(fresh275(p0(b, b), true2, b), true2, a, d), true2, b, a, a), true2, b, a), true2, a, d)
% 53.60/7.22 = { by axiom 1 (axiom_14) }
% 53.60/7.22 fresh87(fresh134(fresh186(fresh274(fresh275(true2, true2, b), true2, a, d), true2, b, a, a), true2, b, a), true2, a, d)
% 53.60/7.22 = { by axiom 15 (rule_125) }
% 53.60/7.22 fresh87(fresh134(fresh186(fresh274(true2, true2, a, d), true2, b, a, a), true2, b, a), true2, a, d)
% 53.60/7.22 = { by axiom 29 (rule_126) }
% 53.60/7.22 fresh87(fresh134(fresh186(s1(a), true2, b, a, a), true2, b, a), true2, a, d)
% 53.60/7.22 = { by axiom 48 (rule_192) R->L }
% 53.60/7.22 fresh87(fresh134(fresh540(p2(a, a, a), true2, b, a, a), true2, b, a), true2, a, d)
% 53.60/7.22 = { by axiom 41 (rule_141) R->L }
% 53.60/7.22 fresh87(fresh134(fresh540(fresh258(q1(a, a, a), true2, a), true2, b, a, a), true2, b, a), true2, a, d)
% 53.60/7.22 = { by axiom 38 (rule_092) R->L }
% 53.60/7.22 fresh87(fresh134(fresh540(fresh258(fresh318(true2, true2, a, a, b), true2, a), true2, b, a, a), true2, b, a), true2, a, d)
% 53.60/7.22 = { by axiom 1 (axiom_14) R->L }
% 53.60/7.22 fresh87(fresh134(fresh540(fresh258(fresh318(p0(b, a), true2, a, a, b), true2, a), true2, b, a, a), true2, b, a), true2, a, d)
% 53.60/7.22 = { by axiom 45 (rule_092) }
% 53.60/7.22 fresh87(fresh134(fresh540(fresh258(fresh317(n0(b, a), true2, a, a), true2, a), true2, b, a, a), true2, b, a), true2, a, d)
% 53.60/7.22 = { by axiom 5 (axiom_37) }
% 53.60/7.22 fresh87(fresh134(fresh540(fresh258(fresh317(true2, true2, a, a), true2, a), true2, b, a, a), true2, b, a), true2, a, d)
% 53.60/7.22 = { by axiom 27 (rule_092) }
% 53.60/7.22 fresh87(fresh134(fresh540(fresh258(true2, true2, a), true2, b, a, a), true2, b, a), true2, a, d)
% 53.60/7.22 = { by axiom 19 (rule_141) }
% 53.60/7.22 fresh87(fresh134(fresh540(true2, true2, b, a, a), true2, b, a), true2, a, d)
% 53.60/7.22 = { by axiom 36 (rule_192) }
% 53.60/7.22 fresh87(fresh134(fresh541(n0(b, a), true2, b, a), true2, b, a), true2, a, d)
% 53.60/7.22 = { by axiom 5 (axiom_37) }
% 53.60/7.22 fresh87(fresh134(fresh541(true2, true2, b, a), true2, b, a), true2, a, d)
% 53.60/7.22 = { by axiom 24 (rule_192) }
% 53.60/7.22 fresh87(fresh134(true2, true2, b, a), true2, a, d)
% 53.60/7.22 = { by axiom 32 (rule_235) }
% 53.60/7.22 fresh87(m3(b, b, a), true2, a, d)
% 53.60/7.22 = { by axiom 49 (rule_268) R->L }
% 53.60/7.22 fresh484(r3(d, d, d), true2, a, d, b)
% 53.60/7.22 = { by axiom 47 (rule_267) R->L }
% 53.60/7.22 fresh484(fresh88(p2(d, d, d), true2, d, d), true2, a, d, b)
% 53.60/7.22 = { by axiom 42 (rule_154) R->L }
% 53.60/7.22 fresh484(fresh88(fresh241(q1(d, d, d), true2, d), true2, d, d), true2, a, d, b)
% 53.60/7.22 = { by axiom 39 (rule_122) R->L }
% 53.60/7.22 fresh484(fresh88(fresh241(fresh279(m0(d, d, d), true2, d), true2, d), true2, d, d), true2, a, d, b)
% 53.60/7.22 = { by axiom 8 (axiom_19) }
% 53.60/7.22 fresh484(fresh88(fresh241(fresh279(true2, true2, d), true2, d), true2, d, d), true2, a, d, b)
% 53.60/7.22 = { by axiom 13 (rule_122) }
% 53.60/7.22 fresh484(fresh88(fresh241(true2, true2, d), true2, d, d), true2, a, d, b)
% 53.60/7.22 = { by axiom 20 (rule_154) }
% 53.60/7.22 fresh484(fresh88(true2, true2, d, d), true2, a, d, b)
% 53.60/7.22 = { by axiom 34 (rule_267) }
% 53.60/7.22 fresh484(true2, true2, a, d, b)
% 53.60/7.22 = { by axiom 37 (rule_268) }
% 53.60/7.22 fresh485(m2(d), true2, a, d)
% 53.60/7.22 = { by axiom 17 (rule_135) R->L }
% 53.60/7.22 fresh485(fresh265(true2, true2, d), true2, a, d)
% 53.60/7.22 = { by axiom 11 (rule_002) R->L }
% 53.60/7.22 fresh485(fresh265(fresh441(true2, true2, a), true2, d), true2, a, d)
% 53.60/7.22 = { by axiom 5 (axiom_37) R->L }
% 53.60/7.22 fresh485(fresh265(fresh441(n0(b, a), true2, a), true2, d), true2, a, d)
% 53.60/7.22 = { by axiom 26 (rule_002) }
% 53.60/7.22 fresh485(fresh265(l1(a, a), true2, d), true2, a, d)
% 53.60/7.22 = { by axiom 30 (rule_135) }
% 53.60/7.22 fresh485(fresh264(s0(d), true2, d), true2, a, d)
% 53.60/7.22 = { by axiom 3 (axiom_1) }
% 53.60/7.22 fresh485(fresh264(true2, true2, d), true2, a, d)
% 53.60/7.22 = { by axiom 18 (rule_135) }
% 53.60/7.22 fresh485(true2, true2, a, d)
% 53.60/7.22 = { by axiom 25 (rule_268) }
% 53.60/7.22 true2
% 53.60/7.22 % SZS output end Proof
% 53.60/7.22
% 53.60/7.22 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------