TSTP Solution File: SYN117-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN117-1 : 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 : 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 03:33:14 EDT 2023
% Result : Unsatisfiable 39.27s 5.47s
% Output : Proof 39.27s
% 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 : SYN117-1 : 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 : 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 21:04:00 EDT 2023
% 0.13/0.35 % CPUTime :
% 39.27/5.47 Command-line arguments: --no-flatten-goal
% 39.27/5.47
% 39.27/5.47 % SZS status Unsatisfiable
% 39.27/5.47
% 39.27/5.48 % SZS output start Proof
% 39.27/5.48 Take the following subset of the input axioms:
% 39.27/5.48 fof(axiom_13, axiom, r0(e)).
% 39.27/5.48 fof(axiom_14, axiom, ![X]: p0(b, X)).
% 39.27/5.48 fof(axiom_19, axiom, ![Y, X2]: m0(X2, d, Y)).
% 39.27/5.48 fof(axiom_5, axiom, s0(b)).
% 39.27/5.48 fof(prove_this, negated_conjecture, ~k5(e)).
% 39.27/5.48 fof(rule_003, axiom, ![C, D, E, F]: (l1(C, D) | (~p0(E, C) | (~r0(F) | ~m0(D, C, E))))).
% 39.27/5.48 fof(rule_029, axiom, ![I, H]: (m1(H, I, H) | (~p0(H, I) | ~s0(H)))).
% 39.27/5.48 fof(rule_110, axiom, ![B, C2, D2]: (q1(B, B, B) | ~m0(C2, D2, B))).
% 39.27/5.48 fof(rule_154, axiom, ![A2]: (p2(A2, A2, A2) | ~q1(A2, A2, A2))).
% 39.27/5.48 fof(rule_176, axiom, ![E2, D2]: (p2(D2, E2, D2) | ~m1(E2, D2, E2))).
% 39.27/5.48 fof(rule_240, axiom, ![E2, F2, D2]: (n3(D2) | ~p2(E2, F2, D2))).
% 39.27/5.48 fof(rule_248, axiom, ![J, I2]: (p3(I2, I2, I2) | (~p2(J, I2, I2) | ~n3(I2)))).
% 39.27/5.48 fof(rule_267, axiom, ![C2, D2, B2]: (r3(B2, C2, B2) | ~p2(B2, D2, C2))).
% 39.27/5.48 fof(rule_299, axiom, ![C2, D2, B2, A2_2]: (s4(A2_2) | (~p3(B2, C2, D2) | ~l1(A2_2, C2)))).
% 39.27/5.48 fof(rule_300, axiom, ![G, E2, F2]: (k5(E2) | (~s4(F2) | ~r3(G, E2, E2)))).
% 39.27/5.48
% 39.27/5.48 Now clausify the problem and encode Horn clauses using encoding 3 of
% 39.27/5.48 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 39.27/5.48 We repeatedly replace C & s=t => u=v by the two clauses:
% 39.27/5.48 fresh(y, y, x1...xn) = u
% 39.27/5.48 C => fresh(s, t, x1...xn) = v
% 39.27/5.48 where fresh is a fresh function symbol and x1..xn are the free
% 39.27/5.48 variables of u and v.
% 39.27/5.48 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 39.27/5.48 input problem has no model of domain size 1).
% 39.27/5.48
% 39.27/5.48 The encoding turns the above axioms into the following unit equations and goals:
% 39.27/5.48
% 39.27/5.48 Axiom 1 (axiom_5): s0(b) = true.
% 39.27/5.48 Axiom 2 (axiom_13): r0(e) = true.
% 39.27/5.48 Axiom 3 (axiom_14): p0(b, X) = true.
% 39.27/5.48 Axiom 4 (rule_110): fresh297(X, X, Y) = true.
% 39.27/5.48 Axiom 5 (rule_154): fresh241(X, X, Y) = true.
% 39.27/5.48 Axiom 6 (rule_240): fresh127(X, X, Y) = true.
% 39.27/5.48 Axiom 7 (rule_248): fresh116(X, X, Y) = true.
% 39.27/5.48 Axiom 8 (rule_299): fresh45(X, X, Y) = true.
% 39.27/5.48 Axiom 9 (rule_300): fresh43(X, X, Y) = true.
% 39.27/5.48 Axiom 10 (axiom_19): m0(X, d, Y) = true.
% 39.27/5.48 Axiom 11 (rule_003): fresh439(X, X, Y, Z) = true.
% 39.27/5.48 Axiom 12 (rule_029): fresh404(X, X, Y, Z) = m1(Y, Z, Y).
% 39.27/5.48 Axiom 13 (rule_029): fresh403(X, X, Y, Z) = true.
% 39.27/5.48 Axiom 14 (rule_176): fresh208(X, X, Y, Z) = true.
% 39.27/5.48 Axiom 15 (rule_248): fresh117(X, X, Y, Z) = p3(Y, Y, Y).
% 39.27/5.48 Axiom 16 (rule_267): fresh88(X, X, Y, Z) = true.
% 39.27/5.48 Axiom 17 (rule_299): fresh46(X, X, Y, Z) = s4(Y).
% 39.27/5.48 Axiom 18 (rule_300): fresh44(X, X, Y, Z) = k5(Y).
% 39.27/5.48 Axiom 19 (rule_003): fresh673(X, X, Y, Z, W) = l1(Y, Z).
% 39.27/5.48 Axiom 20 (rule_003): fresh672(X, X, Y, Z, W, V) = fresh673(r0(V), true, Y, Z, W).
% 39.27/5.48 Axiom 21 (rule_029): fresh404(p0(X, Y), true, X, Y) = fresh403(s0(X), true, X, Y).
% 39.27/5.48 Axiom 22 (rule_110): fresh297(m0(X, Y, Z), true, Z) = q1(Z, Z, Z).
% 39.27/5.48 Axiom 23 (rule_154): fresh241(q1(X, X, X), true, X) = p2(X, X, X).
% 39.27/5.48 Axiom 24 (rule_240): fresh127(p2(X, Y, Z), true, Z) = n3(Z).
% 39.27/5.48 Axiom 25 (rule_248): fresh117(n3(X), true, X, Y) = fresh116(p2(Y, X, X), true, X).
% 39.27/5.48 Axiom 26 (rule_300): fresh44(s4(X), true, Y, Z) = fresh43(r3(Z, Y, Y), true, Y).
% 39.27/5.48 Axiom 27 (rule_176): fresh208(m1(X, Y, X), true, Y, X) = p2(Y, X, Y).
% 39.27/5.48 Axiom 28 (rule_267): fresh88(p2(X, Y, Z), true, X, Z) = r3(X, Z, X).
% 39.27/5.48 Axiom 29 (rule_299): fresh46(p3(X, Y, Z), true, W, Y) = fresh45(l1(W, Y), true, W).
% 39.27/5.48 Axiom 30 (rule_003): fresh672(p0(X, Y), true, Y, Z, X, W) = fresh439(m0(Z, Y, X), true, Y, Z).
% 39.27/5.48
% 39.27/5.48 Lemma 31: p2(X, b, X) = true.
% 39.27/5.48 Proof:
% 39.27/5.48 p2(X, b, X)
% 39.27/5.48 = { by axiom 27 (rule_176) R->L }
% 39.27/5.48 fresh208(m1(b, X, b), true, X, b)
% 39.27/5.48 = { by axiom 12 (rule_029) R->L }
% 39.27/5.48 fresh208(fresh404(true, true, b, X), true, X, b)
% 39.27/5.48 = { by axiom 3 (axiom_14) R->L }
% 39.27/5.48 fresh208(fresh404(p0(b, X), true, b, X), true, X, b)
% 39.27/5.48 = { by axiom 21 (rule_029) }
% 39.27/5.48 fresh208(fresh403(s0(b), true, b, X), true, X, b)
% 39.27/5.48 = { by axiom 1 (axiom_5) }
% 39.27/5.48 fresh208(fresh403(true, true, b, X), true, X, b)
% 39.27/5.48 = { by axiom 13 (rule_029) }
% 39.27/5.48 fresh208(true, true, X, b)
% 39.27/5.49 = { by axiom 14 (rule_176) }
% 39.27/5.49 true
% 39.27/5.49
% 39.27/5.49 Goal 1 (prove_this): k5(e) = true.
% 39.27/5.49 Proof:
% 39.27/5.49 k5(e)
% 39.27/5.49 = { by axiom 18 (rule_300) R->L }
% 39.27/5.49 fresh44(true, true, e, e)
% 39.27/5.49 = { by axiom 8 (rule_299) R->L }
% 39.27/5.49 fresh44(fresh45(true, true, d), true, e, e)
% 39.27/5.49 = { by axiom 11 (rule_003) R->L }
% 39.27/5.49 fresh44(fresh45(fresh439(true, true, d, X), true, d), true, e, e)
% 39.27/5.49 = { by axiom 10 (axiom_19) R->L }
% 39.27/5.49 fresh44(fresh45(fresh439(m0(X, d, b), true, d, X), true, d), true, e, e)
% 39.27/5.49 = { by axiom 30 (rule_003) R->L }
% 39.27/5.49 fresh44(fresh45(fresh672(p0(b, d), true, d, X, b, e), true, d), true, e, e)
% 39.27/5.49 = { by axiom 3 (axiom_14) }
% 39.27/5.49 fresh44(fresh45(fresh672(true, true, d, X, b, e), true, d), true, e, e)
% 39.27/5.49 = { by axiom 20 (rule_003) }
% 39.27/5.49 fresh44(fresh45(fresh673(r0(e), true, d, X, b), true, d), true, e, e)
% 39.27/5.49 = { by axiom 2 (axiom_13) }
% 39.27/5.49 fresh44(fresh45(fresh673(true, true, d, X, b), true, d), true, e, e)
% 39.27/5.49 = { by axiom 19 (rule_003) }
% 39.27/5.49 fresh44(fresh45(l1(d, X), true, d), true, e, e)
% 39.27/5.49 = { by axiom 29 (rule_299) R->L }
% 39.27/5.49 fresh44(fresh46(p3(X, X, X), true, d, X), true, e, e)
% 39.27/5.49 = { by axiom 15 (rule_248) R->L }
% 39.27/5.49 fresh44(fresh46(fresh117(true, true, X, X), true, d, X), true, e, e)
% 39.27/5.49 = { by axiom 6 (rule_240) R->L }
% 39.27/5.49 fresh44(fresh46(fresh117(fresh127(true, true, X), true, X, X), true, d, X), true, e, e)
% 39.27/5.49 = { by lemma 31 R->L }
% 39.27/5.49 fresh44(fresh46(fresh117(fresh127(p2(X, b, X), true, X), true, X, X), true, d, X), true, e, e)
% 39.27/5.49 = { by axiom 24 (rule_240) }
% 39.27/5.49 fresh44(fresh46(fresh117(n3(X), true, X, X), true, d, X), true, e, e)
% 39.27/5.49 = { by axiom 25 (rule_248) }
% 39.27/5.49 fresh44(fresh46(fresh116(p2(X, X, X), true, X), true, d, X), true, e, e)
% 39.27/5.49 = { by axiom 23 (rule_154) R->L }
% 39.27/5.49 fresh44(fresh46(fresh116(fresh241(q1(X, X, X), true, X), true, X), true, d, X), true, e, e)
% 39.27/5.49 = { by axiom 22 (rule_110) R->L }
% 39.27/5.49 fresh44(fresh46(fresh116(fresh241(fresh297(m0(Y, d, X), true, X), true, X), true, X), true, d, X), true, e, e)
% 39.27/5.49 = { by axiom 10 (axiom_19) }
% 39.27/5.49 fresh44(fresh46(fresh116(fresh241(fresh297(true, true, X), true, X), true, X), true, d, X), true, e, e)
% 39.27/5.49 = { by axiom 4 (rule_110) }
% 39.27/5.49 fresh44(fresh46(fresh116(fresh241(true, true, X), true, X), true, d, X), true, e, e)
% 39.27/5.49 = { by axiom 5 (rule_154) }
% 39.27/5.49 fresh44(fresh46(fresh116(true, true, X), true, d, X), true, e, e)
% 39.27/5.49 = { by axiom 7 (rule_248) }
% 39.27/5.49 fresh44(fresh46(true, true, d, X), true, e, e)
% 39.27/5.49 = { by axiom 17 (rule_299) }
% 39.27/5.49 fresh44(s4(d), true, e, e)
% 39.27/5.49 = { by axiom 26 (rule_300) }
% 39.27/5.49 fresh43(r3(e, e, e), true, e)
% 39.27/5.49 = { by axiom 28 (rule_267) R->L }
% 39.27/5.49 fresh43(fresh88(p2(e, b, e), true, e, e), true, e)
% 39.27/5.49 = { by lemma 31 }
% 39.27/5.49 fresh43(fresh88(true, true, e, e), true, e)
% 39.27/5.49 = { by axiom 16 (rule_267) }
% 39.27/5.49 fresh43(true, true, e)
% 39.27/5.49 = { by axiom 9 (rule_300) }
% 39.27/5.49 true
% 39.27/5.49 % SZS output end Proof
% 39.27/5.49
% 39.27/5.49 RESULT: Unsatisfiable (the axioms are contradictory).
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