TSTP Solution File: SYN250-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN250-1 : 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 : n025.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 03:33:46 EDT 2023
% Result : Unsatisfiable 26.19s 4.04s
% Output : Proof 26.19s
% 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 : SYN250-1 : 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 : n025.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 21:19:53 EDT 2023
% 0.13/0.34 % CPUTime :
% 26.19/4.04 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 26.19/4.04
% 26.19/4.04 % SZS status Unsatisfiable
% 26.19/4.04
% 26.19/4.04 % SZS output start Proof
% 26.19/4.04 Take the following subset of the input axioms:
% 26.19/4.05 fof(axiom_12, axiom, ![X]: m0(a, X, a)).
% 26.19/4.05 fof(axiom_13, axiom, r0(e)).
% 26.19/4.05 fof(axiom_21, axiom, q0(b, e)).
% 26.19/4.05 fof(axiom_24, axiom, l0(c)).
% 26.19/4.05 fof(axiom_37, axiom, n0(b, a)).
% 26.19/4.05 fof(axiom_6, axiom, q0(b, b)).
% 26.19/4.05 fof(prove_this, negated_conjecture, ~m1(e, a, a)).
% 26.19/4.05 fof(rule_001, axiom, ![I, J]: (k1(I) | ~n0(J, I))).
% 26.19/4.05 fof(rule_016, axiom, ![H, A, I2, J2]: (m1(H, I2, I2) | (~m1(J2, I2, H) | ~m1(J2, A, I2)))).
% 26.19/4.05 fof(rule_024, axiom, ![G, F, H2]: (m1(F, a, G) | (~m0(a, H2, a) | (~q0(F, G) | ~m1(G, c, G))))).
% 26.19/4.05 fof(rule_034, axiom, ![B, A2]: (m1(A2, B, B) | (~k1(a) | (~k1(B) | ~q0(A2, A2))))).
% 26.19/4.05 fof(rule_035, axiom, ![I2, J2]: (m1(I2, J2, I2) | (~r0(I2) | ~l0(J2)))).
% 26.19/4.05
% 26.19/4.05 Now clausify the problem and encode Horn clauses using encoding 3 of
% 26.19/4.05 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 26.19/4.05 We repeatedly replace C & s=t => u=v by the two clauses:
% 26.19/4.05 fresh(y, y, x1...xn) = u
% 26.19/4.05 C => fresh(s, t, x1...xn) = v
% 26.19/4.05 where fresh is a fresh function symbol and x1..xn are the free
% 26.19/4.05 variables of u and v.
% 26.19/4.05 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 26.19/4.05 input problem has no model of domain size 1).
% 26.19/4.05
% 26.19/4.05 The encoding turns the above axioms into the following unit equations and goals:
% 26.19/4.05
% 26.19/4.05 Axiom 1 (axiom_6): q0(b, b) = true.
% 26.19/4.05 Axiom 2 (axiom_21): q0(b, e) = true.
% 26.19/4.05 Axiom 3 (axiom_13): r0(e) = true.
% 26.19/4.05 Axiom 4 (axiom_24): l0(c) = true.
% 26.19/4.05 Axiom 5 (axiom_37): n0(b, a) = true.
% 26.19/4.05 Axiom 6 (axiom_12): m0(a, X, a) = true.
% 26.19/4.05 Axiom 7 (rule_001): fresh440(X, X, Y) = true.
% 26.19/4.05 Axiom 8 (rule_024): fresh662(X, X, Y, Z) = true.
% 26.19/4.05 Axiom 9 (rule_034): fresh653(X, X, Y, Z) = m1(Y, Z, Z).
% 26.19/4.05 Axiom 10 (rule_001): fresh440(n0(X, Y), true, Y) = k1(Y).
% 26.19/4.05 Axiom 11 (rule_016): fresh422(X, X, Y, Z) = true.
% 26.19/4.05 Axiom 12 (rule_024): fresh410(X, X, Y, Z) = m1(Y, a, Z).
% 26.19/4.05 Axiom 13 (rule_034): fresh397(X, X, Y, Z) = true.
% 26.19/4.05 Axiom 14 (rule_035): fresh396(X, X, Y, Z) = m1(Y, Z, Y).
% 26.19/4.05 Axiom 15 (rule_035): fresh395(X, X, Y, Z) = true.
% 26.19/4.05 Axiom 16 (rule_024): fresh661(X, X, Y, Z, W) = fresh662(q0(Y, Z), true, Y, Z).
% 26.19/4.05 Axiom 17 (rule_034): fresh652(X, X, Y, Z) = fresh653(k1(Z), true, Y, Z).
% 26.19/4.05 Axiom 18 (rule_016): fresh423(X, X, Y, Z, W) = m1(Y, Z, Z).
% 26.19/4.05 Axiom 19 (rule_034): fresh652(k1(a), true, X, Y) = fresh397(q0(X, X), true, X, Y).
% 26.19/4.05 Axiom 20 (rule_035): fresh396(l0(X), true, Y, X) = fresh395(r0(Y), true, Y, X).
% 26.19/4.05 Axiom 21 (rule_024): fresh661(m1(X, c, X), true, Y, X, Z) = fresh410(m0(a, Z, a), true, Y, X).
% 26.19/4.05 Axiom 22 (rule_016): fresh423(m1(X, Y, Z), true, W, Z, X) = fresh422(m1(X, Z, W), true, W, Z).
% 26.19/4.05
% 26.19/4.05 Lemma 23: k1(a) = true.
% 26.19/4.05 Proof:
% 26.19/4.05 k1(a)
% 26.19/4.05 = { by axiom 10 (rule_001) R->L }
% 26.19/4.05 fresh440(n0(b, a), true, a)
% 26.19/4.05 = { by axiom 5 (axiom_37) }
% 26.19/4.05 fresh440(true, true, a)
% 26.19/4.05 = { by axiom 7 (rule_001) }
% 26.19/4.05 true
% 26.19/4.05
% 26.19/4.05 Goal 1 (prove_this): m1(e, a, a) = true.
% 26.19/4.05 Proof:
% 26.19/4.05 m1(e, a, a)
% 26.19/4.05 = { by axiom 18 (rule_016) R->L }
% 26.19/4.05 fresh423(true, true, e, a, b)
% 26.19/4.05 = { by axiom 13 (rule_034) R->L }
% 26.19/4.05 fresh423(fresh397(true, true, b, a), true, e, a, b)
% 26.19/4.05 = { by axiom 1 (axiom_6) R->L }
% 26.19/4.05 fresh423(fresh397(q0(b, b), true, b, a), true, e, a, b)
% 26.19/4.05 = { by axiom 19 (rule_034) R->L }
% 26.19/4.05 fresh423(fresh652(k1(a), true, b, a), true, e, a, b)
% 26.19/4.05 = { by lemma 23 }
% 26.19/4.05 fresh423(fresh652(true, true, b, a), true, e, a, b)
% 26.19/4.05 = { by axiom 17 (rule_034) }
% 26.19/4.05 fresh423(fresh653(k1(a), true, b, a), true, e, a, b)
% 26.19/4.05 = { by lemma 23 }
% 26.19/4.05 fresh423(fresh653(true, true, b, a), true, e, a, b)
% 26.19/4.05 = { by axiom 9 (rule_034) }
% 26.19/4.05 fresh423(m1(b, a, a), true, e, a, b)
% 26.19/4.05 = { by axiom 22 (rule_016) }
% 26.19/4.05 fresh422(m1(b, a, e), true, e, a)
% 26.19/4.05 = { by axiom 12 (rule_024) R->L }
% 26.19/4.05 fresh422(fresh410(true, true, b, e), true, e, a)
% 26.19/4.05 = { by axiom 6 (axiom_12) R->L }
% 26.19/4.05 fresh422(fresh410(m0(a, X, a), true, b, e), true, e, a)
% 26.19/4.05 = { by axiom 21 (rule_024) R->L }
% 26.19/4.05 fresh422(fresh661(m1(e, c, e), true, b, e, X), true, e, a)
% 26.19/4.05 = { by axiom 14 (rule_035) R->L }
% 26.19/4.05 fresh422(fresh661(fresh396(true, true, e, c), true, b, e, X), true, e, a)
% 26.19/4.05 = { by axiom 4 (axiom_24) R->L }
% 26.19/4.05 fresh422(fresh661(fresh396(l0(c), true, e, c), true, b, e, X), true, e, a)
% 26.19/4.05 = { by axiom 20 (rule_035) }
% 26.19/4.05 fresh422(fresh661(fresh395(r0(e), true, e, c), true, b, e, X), true, e, a)
% 26.19/4.05 = { by axiom 3 (axiom_13) }
% 26.19/4.05 fresh422(fresh661(fresh395(true, true, e, c), true, b, e, X), true, e, a)
% 26.19/4.05 = { by axiom 15 (rule_035) }
% 26.19/4.05 fresh422(fresh661(true, true, b, e, X), true, e, a)
% 26.19/4.05 = { by axiom 16 (rule_024) }
% 26.19/4.05 fresh422(fresh662(q0(b, e), true, b, e), true, e, a)
% 26.19/4.05 = { by axiom 2 (axiom_21) }
% 26.19/4.05 fresh422(fresh662(true, true, b, e), true, e, a)
% 26.19/4.05 = { by axiom 8 (rule_024) }
% 26.19/4.05 fresh422(true, true, e, a)
% 26.19/4.05 = { by axiom 11 (rule_016) }
% 26.19/4.05 true
% 26.19/4.05 % SZS output end Proof
% 26.19/4.05
% 26.19/4.05 RESULT: Unsatisfiable (the axioms are contradictory).
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