TSTP Solution File: SYN265-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN265-1 : 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 : n012.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 03:33:50 EDT 2023
% Result : Unsatisfiable 16.65s 2.56s
% Output : Proof 16.65s
% 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 : SYN265-1 : 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 : n012.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 20:13:40 EDT 2023
% 0.14/0.34 % CPUTime :
% 16.65/2.56 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 16.65/2.56
% 16.65/2.56 % SZS status Unsatisfiable
% 16.65/2.56
% 16.65/2.56 % SZS output start Proof
% 16.65/2.56 Take the following subset of the input axioms:
% 16.65/2.56 fof(axiom_1, axiom, s0(d)).
% 16.65/2.56 fof(axiom_17, axiom, ![X]: q0(X, d)).
% 16.65/2.56 fof(axiom_20, axiom, l0(a)).
% 16.65/2.56 fof(axiom_28, axiom, k0(e)).
% 16.65/2.56 fof(prove_this, negated_conjecture, ![X2]: ~p3(X2, X2, a)).
% 16.65/2.56 fof(rule_117, axiom, q1(d, d, d) | (~k0(e) | ~s0(d))).
% 16.65/2.56 fof(rule_124, axiom, ![D, E]: (r1(D) | (~q0(D, E) | (~s0(d) | ~q1(d, E, d))))).
% 16.65/2.56 fof(rule_188, axiom, ![G]: (r2(G) | (~r1(G) | ~l0(G)))).
% 16.65/2.56 fof(rule_204, axiom, k3(a, a, a) | ~r2(a)).
% 16.65/2.56 fof(rule_242, axiom, ![J, B, A2]: (p3(J, A2, B) | (~r2(A2) | ~k3(A2, B, J)))).
% 16.65/2.56
% 16.65/2.56 Now clausify the problem and encode Horn clauses using encoding 3 of
% 16.65/2.56 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 16.65/2.56 We repeatedly replace C & s=t => u=v by the two clauses:
% 16.65/2.56 fresh(y, y, x1...xn) = u
% 16.65/2.56 C => fresh(s, t, x1...xn) = v
% 16.65/2.56 where fresh is a fresh function symbol and x1..xn are the free
% 16.65/2.56 variables of u and v.
% 16.65/2.56 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 16.65/2.56 input problem has no model of domain size 1).
% 16.65/2.56
% 16.65/2.56 The encoding turns the above axioms into the following unit equations and goals:
% 16.65/2.56
% 16.65/2.56 Axiom 1 (axiom_1): s0(d) = true2.
% 16.65/2.56 Axiom 2 (axiom_20): l0(a) = true2.
% 16.65/2.56 Axiom 3 (axiom_28): k0(e) = true2.
% 16.65/2.56 Axiom 4 (axiom_17): q0(X, d) = true2.
% 16.65/2.56 Axiom 5 (rule_117): fresh285(X, X) = true2.
% 16.65/2.56 Axiom 6 (rule_204): fresh171(X, X) = true2.
% 16.65/2.56 Axiom 7 (rule_117): fresh286(X, X) = q1(d, d, d).
% 16.65/2.56 Axiom 8 (rule_124): fresh593(X, X, Y) = true2.
% 16.65/2.56 Axiom 9 (rule_117): fresh286(k0(e), true2) = fresh285(s0(d), true2).
% 16.65/2.56 Axiom 10 (rule_124): fresh276(X, X, Y) = r1(Y).
% 16.65/2.56 Axiom 11 (rule_188): fresh194(X, X, Y) = r2(Y).
% 16.65/2.56 Axiom 12 (rule_188): fresh193(X, X, Y) = true2.
% 16.65/2.56 Axiom 13 (rule_204): fresh171(r2(a), true2) = k3(a, a, a).
% 16.65/2.56 Axiom 14 (rule_124): fresh592(X, X, Y, Z) = fresh593(s0(d), true2, Y).
% 16.65/2.56 Axiom 15 (rule_188): fresh194(r1(X), true2, X) = fresh193(l0(X), true2, X).
% 16.65/2.56 Axiom 16 (rule_242): fresh124(X, X, Y, Z, W) = p3(Y, Z, W).
% 16.65/2.56 Axiom 17 (rule_242): fresh123(X, X, Y, Z, W) = true2.
% 16.65/2.56 Axiom 18 (rule_124): fresh592(q1(d, X, d), true2, Y, X) = fresh276(q0(Y, X), true2, Y).
% 16.65/2.56 Axiom 19 (rule_242): fresh124(k3(X, Y, Z), true2, Z, X, Y) = fresh123(r2(X), true2, Z, X, Y).
% 16.65/2.56
% 16.65/2.56 Lemma 20: r2(a) = true2.
% 16.65/2.56 Proof:
% 16.65/2.56 r2(a)
% 16.65/2.56 = { by axiom 11 (rule_188) R->L }
% 16.65/2.56 fresh194(true2, true2, a)
% 16.65/2.56 = { by axiom 8 (rule_124) R->L }
% 16.65/2.56 fresh194(fresh593(true2, true2, a), true2, a)
% 16.65/2.56 = { by axiom 1 (axiom_1) R->L }
% 16.65/2.56 fresh194(fresh593(s0(d), true2, a), true2, a)
% 16.65/2.56 = { by axiom 14 (rule_124) R->L }
% 16.65/2.56 fresh194(fresh592(true2, true2, a, d), true2, a)
% 16.65/2.56 = { by axiom 5 (rule_117) R->L }
% 16.65/2.56 fresh194(fresh592(fresh285(true2, true2), true2, a, d), true2, a)
% 16.65/2.56 = { by axiom 1 (axiom_1) R->L }
% 16.65/2.56 fresh194(fresh592(fresh285(s0(d), true2), true2, a, d), true2, a)
% 16.65/2.56 = { by axiom 9 (rule_117) R->L }
% 16.65/2.56 fresh194(fresh592(fresh286(k0(e), true2), true2, a, d), true2, a)
% 16.65/2.56 = { by axiom 3 (axiom_28) }
% 16.65/2.56 fresh194(fresh592(fresh286(true2, true2), true2, a, d), true2, a)
% 16.65/2.56 = { by axiom 7 (rule_117) }
% 16.65/2.56 fresh194(fresh592(q1(d, d, d), true2, a, d), true2, a)
% 16.65/2.56 = { by axiom 18 (rule_124) }
% 16.65/2.56 fresh194(fresh276(q0(a, d), true2, a), true2, a)
% 16.65/2.56 = { by axiom 4 (axiom_17) }
% 16.65/2.56 fresh194(fresh276(true2, true2, a), true2, a)
% 16.65/2.56 = { by axiom 10 (rule_124) }
% 16.65/2.56 fresh194(r1(a), true2, a)
% 16.65/2.56 = { by axiom 15 (rule_188) }
% 16.65/2.56 fresh193(l0(a), true2, a)
% 16.65/2.56 = { by axiom 2 (axiom_20) }
% 16.65/2.56 fresh193(true2, true2, a)
% 16.65/2.56 = { by axiom 12 (rule_188) }
% 16.65/2.56 true2
% 16.65/2.56
% 16.65/2.56 Goal 1 (prove_this): p3(X, X, a) = true2.
% 16.65/2.56 The goal is true when:
% 16.65/2.56 X = a
% 16.65/2.56
% 16.65/2.56 Proof:
% 16.65/2.56 p3(a, a, a)
% 16.65/2.56 = { by axiom 16 (rule_242) R->L }
% 16.65/2.56 fresh124(true2, true2, a, a, a)
% 16.65/2.56 = { by axiom 6 (rule_204) R->L }
% 16.65/2.56 fresh124(fresh171(true2, true2), true2, a, a, a)
% 16.65/2.56 = { by lemma 20 R->L }
% 16.65/2.56 fresh124(fresh171(r2(a), true2), true2, a, a, a)
% 16.65/2.56 = { by axiom 13 (rule_204) }
% 16.65/2.56 fresh124(k3(a, a, a), true2, a, a, a)
% 16.65/2.56 = { by axiom 19 (rule_242) }
% 16.65/2.56 fresh123(r2(a), true2, a, a, a)
% 16.65/2.56 = { by lemma 20 }
% 16.65/2.56 fresh123(true2, true2, a, a, a)
% 16.65/2.57 = { by axiom 17 (rule_242) }
% 16.65/2.57 true2
% 16.65/2.57 % SZS output end Proof
% 16.65/2.57
% 16.65/2.57 RESULT: Unsatisfiable (the axioms are contradictory).
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