TSTP Solution File: SYN223-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SYN223-1 : 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 : n028.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 03:33:40 EDT 2023
% Result : Unsatisfiable 12.79s 2.01s
% Output : Proof 12.79s
% 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 : SYN223-1 : 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 : n028.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 17:17:22 EDT 2023
% 0.13/0.34 % CPUTime :
% 12.79/2.01 Command-line arguments: --no-flatten-goal
% 12.79/2.01
% 12.79/2.01 % SZS status Unsatisfiable
% 12.79/2.01
% 12.79/2.01 % SZS output start Proof
% 12.79/2.01 Take the following subset of the input axioms:
% 12.79/2.01 fof(axiom_31, axiom, m0(b, b, e)).
% 12.79/2.01 fof(axiom_9, axiom, r0(b)).
% 12.79/2.01 fof(prove_this, negated_conjecture, ![X]: ~l3(X, e)).
% 12.79/2.01 fof(rule_005, axiom, ![C, B]: (m1(B, C, B) | ~m0(C, C, B))).
% 12.79/2.01 fof(rule_176, axiom, ![D, E]: (p2(D, E, D) | ~m1(E, D, E))).
% 12.79/2.01 fof(rule_215, axiom, ![G, H]: (l3(G, H) | (~r0(G) | ~p2(G, H, G)))).
% 12.79/2.01
% 12.79/2.01 Now clausify the problem and encode Horn clauses using encoding 3 of
% 12.79/2.01 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 12.79/2.01 We repeatedly replace C & s=t => u=v by the two clauses:
% 12.79/2.01 fresh(y, y, x1...xn) = u
% 12.79/2.01 C => fresh(s, t, x1...xn) = v
% 12.79/2.01 where fresh is a fresh function symbol and x1..xn are the free
% 12.79/2.01 variables of u and v.
% 12.79/2.01 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 12.79/2.01 input problem has no model of domain size 1).
% 12.79/2.01
% 12.79/2.01 The encoding turns the above axioms into the following unit equations and goals:
% 12.79/2.01
% 12.79/2.01 Axiom 1 (axiom_9): r0(b) = true2.
% 12.79/2.02 Axiom 2 (axiom_31): m0(b, b, e) = true2.
% 12.79/2.02 Axiom 3 (rule_005): fresh437(X, X, Y, Z) = true2.
% 12.79/2.02 Axiom 4 (rule_176): fresh208(X, X, Y, Z) = true2.
% 12.79/2.02 Axiom 5 (rule_215): fresh160(X, X, Y, Z) = l3(Y, Z).
% 12.79/2.02 Axiom 6 (rule_215): fresh159(X, X, Y, Z) = true2.
% 12.79/2.02 Axiom 7 (rule_005): fresh437(m0(X, X, Y), true2, Y, X) = m1(Y, X, Y).
% 12.79/2.02 Axiom 8 (rule_176): fresh208(m1(X, Y, X), true2, Y, X) = p2(Y, X, Y).
% 12.79/2.02 Axiom 9 (rule_215): fresh160(p2(X, Y, X), true2, X, Y) = fresh159(r0(X), true2, X, Y).
% 12.79/2.02
% 12.79/2.02 Goal 1 (prove_this): l3(X, e) = true2.
% 12.79/2.02 The goal is true when:
% 12.79/2.02 X = b
% 12.79/2.02
% 12.79/2.02 Proof:
% 12.79/2.02 l3(b, e)
% 12.79/2.02 = { by axiom 5 (rule_215) R->L }
% 12.79/2.02 fresh160(true2, true2, b, e)
% 12.79/2.02 = { by axiom 4 (rule_176) R->L }
% 12.79/2.02 fresh160(fresh208(true2, true2, b, e), true2, b, e)
% 12.79/2.02 = { by axiom 3 (rule_005) R->L }
% 12.79/2.02 fresh160(fresh208(fresh437(true2, true2, e, b), true2, b, e), true2, b, e)
% 12.79/2.02 = { by axiom 2 (axiom_31) R->L }
% 12.79/2.02 fresh160(fresh208(fresh437(m0(b, b, e), true2, e, b), true2, b, e), true2, b, e)
% 12.79/2.02 = { by axiom 7 (rule_005) }
% 12.79/2.02 fresh160(fresh208(m1(e, b, e), true2, b, e), true2, b, e)
% 12.79/2.02 = { by axiom 8 (rule_176) }
% 12.79/2.02 fresh160(p2(b, e, b), true2, b, e)
% 12.79/2.02 = { by axiom 9 (rule_215) }
% 12.79/2.02 fresh159(r0(b), true2, b, e)
% 12.79/2.02 = { by axiom 1 (axiom_9) }
% 12.79/2.02 fresh159(true2, true2, b, e)
% 12.79/2.02 = { by axiom 6 (rule_215) }
% 12.79/2.02 true2
% 12.79/2.02 % SZS output end Proof
% 12.79/2.02
% 12.79/2.02 RESULT: Unsatisfiable (the axioms are contradictory).
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