TSTP Solution File: SYN205-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN205-1 : 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 : n015.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 03:33:35 EDT 2023
% Result : Unsatisfiable 64.46s 8.87s
% Output : Proof 65.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYN205-1 : 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
% 0.13/0.35 % Computer : n015.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 17:40:38 EDT 2023
% 0.13/0.35 % CPUTime :
% 64.46/8.87 Command-line arguments: --no-flatten-goal
% 64.46/8.87
% 64.46/8.87 % SZS status Unsatisfiable
% 64.46/8.87
% 65.20/8.90 % SZS output start Proof
% 65.20/8.90 Take the following subset of the input axioms:
% 65.20/8.90 fof(axiom_14, axiom, ![X]: p0(b, X)).
% 65.20/8.90 fof(axiom_19, axiom, ![Y, X2]: m0(X2, d, Y)).
% 65.20/8.90 fof(axiom_20, axiom, l0(a)).
% 65.20/8.90 fof(axiom_28, axiom, k0(e)).
% 65.20/8.90 fof(axiom_31, axiom, m0(b, b, e)).
% 65.20/8.90 fof(axiom_32, axiom, k0(b)).
% 65.20/8.90 fof(axiom_37, axiom, n0(b, a)).
% 65.20/8.90 fof(axiom_5, axiom, s0(b)).
% 65.20/8.90 fof(axiom_7, axiom, n0(d, b)).
% 65.20/8.90 fof(prove_this, negated_conjecture, ~s3(a, d)).
% 65.20/8.90 fof(rule_002, axiom, ![G, H]: (l1(G, G) | ~n0(H, G))).
% 65.20/8.90 fof(rule_050, axiom, ![D, E]: (n1(D, E, D) | (~s0(b) | (~l0(D) | ~p0(b, E))))).
% 65.20/8.90 fof(rule_054, axiom, ![F, G2, E2]: (n1(E2, F, F) | (~l0(G2) | (~l1(G2, E2) | ~n1(E2, F, E2))))).
% 65.20/8.90 fof(rule_063, axiom, ![E2, D2]: (p1(D2, D2, E2) | (~n0(d, D2) | ~k0(E2)))).
% 65.20/8.90 fof(rule_082, axiom, ![I, J, A2, H2]: (p1(H2, I, J) | (~m0(J, H2, A2) | ~p1(J, H2, A2)))).
% 65.20/8.90 fof(rule_085, axiom, ![C, B]: (p1(B, B, B) | ~p0(C, B))).
% 65.20/8.90 fof(rule_125, axiom, ![I2]: (s1(I2) | ~p0(I2, I2))).
% 65.20/8.90 fof(rule_177, axiom, ![F2, E2]: (q2(E2, F2, F2) | (~k0(F2) | ~p1(E2, E2, E2)))).
% 65.20/8.90 fof(rule_182, axiom, ![H2, G2, F2]: (q2(F2, G2, F2) | (~p1(F2, F2, H2) | (~n1(G2, F2, H2) | ~q2(G2, H2, F2))))).
% 65.20/8.90 fof(rule_189, axiom, ![H2]: (s2(H2) | (~q2(b, H2, b) | ~s1(b)))).
% 65.20/8.90 fof(rule_273, axiom, ![I2, J2, B2, A2_2]: (s3(I2, J2) | (~q2(A2_2, I2, A2_2) | (~s2(I2) | ~m0(A2_2, B2, J2))))).
% 65.20/8.90
% 65.20/8.90 Now clausify the problem and encode Horn clauses using encoding 3 of
% 65.20/8.90 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 65.20/8.90 We repeatedly replace C & s=t => u=v by the two clauses:
% 65.20/8.90 fresh(y, y, x1...xn) = u
% 65.20/8.90 C => fresh(s, t, x1...xn) = v
% 65.20/8.90 where fresh is a fresh function symbol and x1..xn are the free
% 65.20/8.90 variables of u and v.
% 65.20/8.90 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 65.20/8.90 input problem has no model of domain size 1).
% 65.20/8.90
% 65.20/8.90 The encoding turns the above axioms into the following unit equations and goals:
% 65.20/8.90
% 65.20/8.90 Axiom 1 (axiom_28): k0(e) = true.
% 65.20/8.90 Axiom 2 (axiom_32): k0(b) = true.
% 65.20/8.90 Axiom 3 (axiom_20): l0(a) = true.
% 65.20/8.90 Axiom 4 (axiom_5): s0(b) = true.
% 65.20/8.90 Axiom 5 (axiom_7): n0(d, b) = true.
% 65.20/8.90 Axiom 6 (axiom_37): n0(b, a) = true.
% 65.20/8.90 Axiom 7 (axiom_14): p0(b, X) = true.
% 65.20/8.90 Axiom 8 (rule_002): fresh441(X, X, Y) = true.
% 65.20/8.90 Axiom 9 (rule_085): fresh328(X, X, Y) = true.
% 65.20/8.90 Axiom 10 (rule_125): fresh275(X, X, Y) = true.
% 65.20/8.90 Axiom 11 (rule_189): fresh192(X, X, Y) = s2(Y).
% 65.20/8.90 Axiom 12 (rule_189): fresh191(X, X, Y) = true.
% 65.20/8.90 Axiom 13 (rule_073): fresh627(X, X, Y) = p1(Y, Y, Y).
% 65.20/8.90 Axiom 14 (axiom_19): m0(X, d, Y) = true.
% 65.20/8.90 Axiom 15 (axiom_31): m0(b, b, e) = true.
% 65.20/8.90 Axiom 16 (rule_050): fresh645(X, X, Y, Z) = true.
% 65.20/8.90 Axiom 17 (rule_054): fresh637(X, X, Y, Z) = true.
% 65.20/8.90 Axiom 18 (rule_182): fresh551(X, X, Y, Z) = true.
% 65.20/8.90 Axiom 19 (rule_273): fresh475(X, X, Y, Z) = true.
% 65.20/8.90 Axiom 20 (rule_050): fresh375(X, X, Y, Z) = n1(Y, Z, Y).
% 65.20/8.90 Axiom 21 (rule_063): fresh357(X, X, Y, Z) = p1(Y, Y, Z).
% 65.20/8.90 Axiom 22 (rule_063): fresh356(X, X, Y, Z) = true.
% 65.20/8.90 Axiom 23 (rule_177): fresh207(X, X, Y, Z) = q2(Y, Z, Z).
% 65.20/8.90 Axiom 24 (rule_177): fresh206(X, X, Y, Z) = true.
% 65.20/8.90 Axiom 25 (rule_050): fresh644(X, X, Y, Z) = fresh645(s0(b), true, Y, Z).
% 65.20/8.90 Axiom 26 (rule_054): fresh636(X, X, Y, Z, W) = fresh637(l0(W), true, Y, Z).
% 65.20/8.90 Axiom 27 (rule_002): fresh441(n0(X, Y), true, Y) = l1(Y, Y).
% 65.20/8.90 Axiom 28 (rule_054): fresh371(X, X, Y, Z, W) = n1(Y, Z, Z).
% 65.20/8.90 Axiom 29 (rule_082): fresh333(X, X, Y, Z, W) = true.
% 65.20/8.90 Axiom 30 (rule_085): fresh328(p0(X, Y), true, Y) = p1(Y, Y, Y).
% 65.20/8.90 Axiom 31 (rule_125): fresh275(p0(X, X), true, X) = s1(X).
% 65.20/8.90 Axiom 32 (rule_182): fresh199(X, X, Y, Z, W) = q2(Y, Z, Y).
% 65.20/8.90 Axiom 33 (rule_050): fresh644(l0(X), true, X, Y) = fresh375(p0(b, Y), true, X, Y).
% 65.20/8.90 Axiom 34 (rule_063): fresh357(k0(X), true, Y, X) = fresh356(n0(d, Y), true, Y, X).
% 65.20/8.90 Axiom 35 (rule_082): fresh334(X, X, Y, Z, W, V) = p1(Y, Z, W).
% 65.20/8.90 Axiom 36 (rule_189): fresh192(q2(b, X, b), true, X) = fresh191(s1(b), true, X).
% 65.20/8.90 Axiom 37 (rule_273): fresh82(X, X, Y, Z, W, V) = s3(Y, Z).
% 65.20/8.90 Axiom 38 (rule_182): fresh550(X, X, Y, Z, W) = fresh551(n1(Z, Y, W), true, Y, Z).
% 65.20/8.90 Axiom 39 (rule_273): fresh474(X, X, Y, Z, W, V) = fresh475(m0(W, V, Z), true, Y, Z).
% 65.20/8.90 Axiom 40 (rule_177): fresh207(p1(X, X, X), true, X, Y) = fresh206(k0(Y), true, X, Y).
% 65.20/8.90 Axiom 41 (rule_054): fresh636(n1(X, Y, X), true, X, Y, Z) = fresh371(l1(Z, X), true, X, Y, Z).
% 65.20/8.90 Axiom 42 (rule_182): fresh550(q2(X, Y, Z), true, Z, X, Y) = fresh199(p1(Z, Z, Y), true, Z, X, Y).
% 65.20/8.90 Axiom 43 (rule_082): fresh334(p1(X, Y, Z), true, Y, W, X, Z) = fresh333(m0(X, Y, Z), true, Y, W, X).
% 65.20/8.90 Axiom 44 (rule_273): fresh474(s2(X), true, X, Y, Z, W) = fresh82(q2(Z, X, Z), true, X, Y, Z, W).
% 65.20/8.90
% 65.20/8.90 Lemma 45: n1(a, X, X) = true.
% 65.20/8.90 Proof:
% 65.20/8.90 n1(a, X, X)
% 65.20/8.90 = { by axiom 28 (rule_054) R->L }
% 65.20/8.90 fresh371(true, true, a, X, a)
% 65.20/8.90 = { by axiom 8 (rule_002) R->L }
% 65.20/8.90 fresh371(fresh441(true, true, a), true, a, X, a)
% 65.20/8.90 = { by axiom 6 (axiom_37) R->L }
% 65.20/8.90 fresh371(fresh441(n0(b, a), true, a), true, a, X, a)
% 65.20/8.90 = { by axiom 27 (rule_002) }
% 65.20/8.90 fresh371(l1(a, a), true, a, X, a)
% 65.20/8.90 = { by axiom 41 (rule_054) R->L }
% 65.20/8.90 fresh636(n1(a, X, a), true, a, X, a)
% 65.20/8.90 = { by axiom 20 (rule_050) R->L }
% 65.20/8.90 fresh636(fresh375(true, true, a, X), true, a, X, a)
% 65.20/8.90 = { by axiom 7 (axiom_14) R->L }
% 65.20/8.90 fresh636(fresh375(p0(b, X), true, a, X), true, a, X, a)
% 65.20/8.90 = { by axiom 33 (rule_050) R->L }
% 65.20/8.90 fresh636(fresh644(l0(a), true, a, X), true, a, X, a)
% 65.20/8.90 = { by axiom 3 (axiom_20) }
% 65.20/8.90 fresh636(fresh644(true, true, a, X), true, a, X, a)
% 65.20/8.90 = { by axiom 25 (rule_050) }
% 65.20/8.90 fresh636(fresh645(s0(b), true, a, X), true, a, X, a)
% 65.20/8.90 = { by axiom 4 (axiom_5) }
% 65.20/8.90 fresh636(fresh645(true, true, a, X), true, a, X, a)
% 65.20/8.90 = { by axiom 16 (rule_050) }
% 65.20/8.90 fresh636(true, true, a, X, a)
% 65.20/8.90 = { by axiom 26 (rule_054) }
% 65.20/8.90 fresh637(l0(a), true, a, X)
% 65.20/8.90 = { by axiom 3 (axiom_20) }
% 65.20/8.90 fresh637(true, true, a, X)
% 65.20/8.90 = { by axiom 17 (rule_054) }
% 65.20/8.90 true
% 65.20/8.90
% 65.20/8.90 Lemma 46: fresh627(X, X, Y) = true.
% 65.20/8.90 Proof:
% 65.20/8.90 fresh627(X, X, Y)
% 65.20/8.90 = { by axiom 13 (rule_073) }
% 65.20/8.90 p1(Y, Y, Y)
% 65.20/8.90 = { by axiom 30 (rule_085) R->L }
% 65.20/8.90 fresh328(p0(b, Y), true, Y)
% 65.20/8.90 = { by axiom 7 (axiom_14) }
% 65.20/8.90 fresh328(true, true, Y)
% 65.20/8.90 = { by axiom 9 (rule_085) }
% 65.20/8.90 true
% 65.20/8.90
% 65.20/8.90 Lemma 47: fresh206(k0(X), true, Y, X) = fresh207(Z, Z, Y, X).
% 65.20/8.90 Proof:
% 65.20/8.90 fresh206(k0(X), true, Y, X)
% 65.20/8.90 = { by axiom 40 (rule_177) R->L }
% 65.20/8.90 fresh207(p1(Y, Y, Y), true, Y, X)
% 65.20/8.90 = { by axiom 13 (rule_073) R->L }
% 65.20/8.90 fresh207(fresh627(W, W, Y), true, Y, X)
% 65.20/8.90 = { by lemma 46 }
% 65.20/8.90 fresh207(true, true, Y, X)
% 65.20/8.90 = { by axiom 23 (rule_177) }
% 65.20/8.90 q2(Y, X, X)
% 65.20/8.90 = { by axiom 23 (rule_177) R->L }
% 65.20/8.91 fresh207(Z, Z, Y, X)
% 65.20/8.91
% 65.20/8.91 Goal 1 (prove_this): s3(a, d) = true.
% 65.20/8.91 Proof:
% 65.20/8.91 s3(a, d)
% 65.20/8.91 = { by axiom 37 (rule_273) R->L }
% 65.20/8.91 fresh82(true, true, a, d, e, d)
% 65.20/8.91 = { by axiom 18 (rule_182) R->L }
% 65.20/8.91 fresh82(fresh551(true, true, e, a), true, a, d, e, d)
% 65.20/8.91 = { by lemma 45 R->L }
% 65.20/8.91 fresh82(fresh551(n1(a, e, e), true, e, a), true, a, d, e, d)
% 65.20/8.91 = { by axiom 38 (rule_182) R->L }
% 65.20/8.91 fresh82(fresh550(true, true, e, a, e), true, a, d, e, d)
% 65.20/8.91 = { by axiom 24 (rule_177) R->L }
% 65.20/8.91 fresh82(fresh550(fresh206(true, true, a, e), true, e, a, e), true, a, d, e, d)
% 65.20/8.91 = { by axiom 1 (axiom_28) R->L }
% 65.20/8.91 fresh82(fresh550(fresh206(k0(e), true, a, e), true, e, a, e), true, a, d, e, d)
% 65.20/8.91 = { by lemma 47 }
% 65.20/8.91 fresh82(fresh550(fresh207(X, X, a, e), true, e, a, e), true, a, d, e, d)
% 65.20/8.91 = { by axiom 23 (rule_177) }
% 65.20/8.91 fresh82(fresh550(q2(a, e, e), true, e, a, e), true, a, d, e, d)
% 65.20/8.91 = { by axiom 42 (rule_182) }
% 65.20/8.91 fresh82(fresh199(p1(e, e, e), true, e, a, e), true, a, d, e, d)
% 65.20/8.91 = { by axiom 13 (rule_073) R->L }
% 65.20/8.91 fresh82(fresh199(fresh627(Y, Y, e), true, e, a, e), true, a, d, e, d)
% 65.20/8.91 = { by lemma 46 }
% 65.20/8.91 fresh82(fresh199(true, true, e, a, e), true, a, d, e, d)
% 65.20/8.91 = { by axiom 32 (rule_182) }
% 65.20/8.91 fresh82(q2(e, a, e), true, a, d, e, d)
% 65.20/8.91 = { by axiom 44 (rule_273) R->L }
% 65.20/8.91 fresh474(s2(a), true, a, d, e, d)
% 65.20/8.91 = { by axiom 11 (rule_189) R->L }
% 65.20/8.91 fresh474(fresh192(true, true, a), true, a, d, e, d)
% 65.20/8.91 = { by axiom 18 (rule_182) R->L }
% 65.20/8.91 fresh474(fresh192(fresh551(true, true, b, a), true, a), true, a, d, e, d)
% 65.20/8.91 = { by lemma 45 R->L }
% 65.20/8.91 fresh474(fresh192(fresh551(n1(a, b, b), true, b, a), true, a), true, a, d, e, d)
% 65.20/8.91 = { by axiom 38 (rule_182) R->L }
% 65.20/8.91 fresh474(fresh192(fresh550(true, true, b, a, b), true, a), true, a, d, e, d)
% 65.20/8.91 = { by axiom 24 (rule_177) R->L }
% 65.20/8.91 fresh474(fresh192(fresh550(fresh206(true, true, a, b), true, b, a, b), true, a), true, a, d, e, d)
% 65.20/8.91 = { by axiom 2 (axiom_32) R->L }
% 65.20/8.91 fresh474(fresh192(fresh550(fresh206(k0(b), true, a, b), true, b, a, b), true, a), true, a, d, e, d)
% 65.20/8.91 = { by lemma 47 }
% 65.20/8.91 fresh474(fresh192(fresh550(fresh207(Z, Z, a, b), true, b, a, b), true, a), true, a, d, e, d)
% 65.20/8.91 = { by axiom 23 (rule_177) }
% 65.20/8.91 fresh474(fresh192(fresh550(q2(a, b, b), true, b, a, b), true, a), true, a, d, e, d)
% 65.20/8.91 = { by axiom 42 (rule_182) }
% 65.20/8.91 fresh474(fresh192(fresh199(p1(b, b, b), true, b, a, b), true, a), true, a, d, e, d)
% 65.20/8.91 = { by axiom 35 (rule_082) R->L }
% 65.20/8.91 fresh474(fresh192(fresh199(fresh334(true, true, b, b, b, e), true, b, a, b), true, a), true, a, d, e, d)
% 65.20/8.91 = { by axiom 22 (rule_063) R->L }
% 65.20/8.91 fresh474(fresh192(fresh199(fresh334(fresh356(true, true, b, e), true, b, b, b, e), true, b, a, b), true, a), true, a, d, e, d)
% 65.20/8.91 = { by axiom 5 (axiom_7) R->L }
% 65.20/8.91 fresh474(fresh192(fresh199(fresh334(fresh356(n0(d, b), true, b, e), true, b, b, b, e), true, b, a, b), true, a), true, a, d, e, d)
% 65.20/8.91 = { by axiom 34 (rule_063) R->L }
% 65.20/8.91 fresh474(fresh192(fresh199(fresh334(fresh357(k0(e), true, b, e), true, b, b, b, e), true, b, a, b), true, a), true, a, d, e, d)
% 65.20/8.91 = { by axiom 1 (axiom_28) }
% 65.20/8.91 fresh474(fresh192(fresh199(fresh334(fresh357(true, true, b, e), true, b, b, b, e), true, b, a, b), true, a), true, a, d, e, d)
% 65.20/8.91 = { by axiom 21 (rule_063) }
% 65.20/8.91 fresh474(fresh192(fresh199(fresh334(p1(b, b, e), true, b, b, b, e), true, b, a, b), true, a), true, a, d, e, d)
% 65.20/8.91 = { by axiom 43 (rule_082) }
% 65.20/8.91 fresh474(fresh192(fresh199(fresh333(m0(b, b, e), true, b, b, b), true, b, a, b), true, a), true, a, d, e, d)
% 65.20/8.91 = { by axiom 15 (axiom_31) }
% 65.20/8.91 fresh474(fresh192(fresh199(fresh333(true, true, b, b, b), true, b, a, b), true, a), true, a, d, e, d)
% 65.20/8.91 = { by axiom 29 (rule_082) }
% 65.20/8.91 fresh474(fresh192(fresh199(true, true, b, a, b), true, a), true, a, d, e, d)
% 65.20/8.91 = { by axiom 32 (rule_182) }
% 65.20/8.91 fresh474(fresh192(q2(b, a, b), true, a), true, a, d, e, d)
% 65.20/8.91 = { by axiom 36 (rule_189) }
% 65.20/8.91 fresh474(fresh191(s1(b), true, a), true, a, d, e, d)
% 65.20/8.91 = { by axiom 31 (rule_125) R->L }
% 65.20/8.91 fresh474(fresh191(fresh275(p0(b, b), true, b), true, a), true, a, d, e, d)
% 65.20/8.91 = { by axiom 7 (axiom_14) }
% 65.20/8.91 fresh474(fresh191(fresh275(true, true, b), true, a), true, a, d, e, d)
% 65.20/8.91 = { by axiom 10 (rule_125) }
% 65.20/8.91 fresh474(fresh191(true, true, a), true, a, d, e, d)
% 65.20/8.91 = { by axiom 12 (rule_189) }
% 65.20/8.91 fresh474(true, true, a, d, e, d)
% 65.20/8.91 = { by axiom 39 (rule_273) }
% 65.20/8.91 fresh475(m0(e, d, d), true, a, d)
% 65.20/8.91 = { by axiom 14 (axiom_19) }
% 65.20/8.91 fresh475(true, true, a, d)
% 65.20/8.91 = { by axiom 19 (rule_273) }
% 65.20/8.91 true
% 65.20/8.91 % SZS output end Proof
% 65.20/8.91
% 65.20/8.91 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------