TSTP Solution File: SYN201-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SYN201-1 : 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 : n001.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 03:33:34 EDT 2023
% Result : Unsatisfiable 17.10s 2.64s
% Output : Proof 17.10s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYN201-1 : TPTP v8.1.2. Released v1.1.0.
% 0.00/0.14 % 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 : n001.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 21:18:46 EDT 2023
% 0.13/0.35 % CPUTime :
% 17.10/2.64 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 17.10/2.64
% 17.10/2.64 % SZS status Unsatisfiable
% 17.10/2.64
% 17.10/2.64 % SZS output start Proof
% 17.10/2.64 Take the following subset of the input axioms:
% 17.10/2.64 fof(axiom_11, axiom, n0(e, b)).
% 17.10/2.64 fof(axiom_14, axiom, ![X]: p0(b, X)).
% 17.10/2.64 fof(prove_this, negated_conjecture, ~s2(b)).
% 17.10/2.64 fof(rule_002, axiom, ![G, H]: (l1(G, G) | ~n0(H, G))).
% 17.10/2.64 fof(rule_125, axiom, ![I]: (s1(I) | ~p0(I, I))).
% 17.10/2.64 fof(rule_186, axiom, ![H2, G2]: (q2(G2, G2, H2) | ~l1(H2, G2))).
% 17.10/2.64 fof(rule_189, axiom, ![H2]: (s2(H2) | (~q2(b, H2, b) | ~s1(b)))).
% 17.10/2.64
% 17.10/2.64 Now clausify the problem and encode Horn clauses using encoding 3 of
% 17.10/2.64 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 17.10/2.64 We repeatedly replace C & s=t => u=v by the two clauses:
% 17.10/2.64 fresh(y, y, x1...xn) = u
% 17.10/2.64 C => fresh(s, t, x1...xn) = v
% 17.10/2.64 where fresh is a fresh function symbol and x1..xn are the free
% 17.10/2.64 variables of u and v.
% 17.10/2.64 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 17.10/2.64 input problem has no model of domain size 1).
% 17.10/2.64
% 17.10/2.64 The encoding turns the above axioms into the following unit equations and goals:
% 17.10/2.64
% 17.10/2.64 Axiom 1 (axiom_14): p0(b, X) = true.
% 17.10/2.64 Axiom 2 (axiom_11): n0(e, b) = true.
% 17.10/2.64 Axiom 3 (rule_002): fresh441(X, X, Y) = true.
% 17.10/2.64 Axiom 4 (rule_125): fresh275(X, X, Y) = true.
% 17.10/2.64 Axiom 5 (rule_189): fresh192(X, X, Y) = s2(Y).
% 17.10/2.64 Axiom 6 (rule_189): fresh191(X, X, Y) = true.
% 17.10/2.64 Axiom 7 (rule_002): fresh441(n0(X, Y), true, Y) = l1(Y, Y).
% 17.10/2.64 Axiom 8 (rule_125): fresh275(p0(X, X), true, X) = s1(X).
% 17.10/2.64 Axiom 9 (rule_186): fresh195(X, X, Y, Z) = true.
% 17.10/2.64 Axiom 10 (rule_186): fresh195(l1(X, Y), true, Y, X) = q2(Y, Y, X).
% 17.10/2.64 Axiom 11 (rule_189): fresh192(q2(b, X, b), true, X) = fresh191(s1(b), true, X).
% 17.10/2.64
% 17.10/2.64 Goal 1 (prove_this): s2(b) = true.
% 17.10/2.64 Proof:
% 17.10/2.64 s2(b)
% 17.10/2.64 = { by axiom 5 (rule_189) R->L }
% 17.10/2.64 fresh192(true, true, b)
% 17.10/2.64 = { by axiom 9 (rule_186) R->L }
% 17.10/2.64 fresh192(fresh195(true, true, b, b), true, b)
% 17.10/2.64 = { by axiom 3 (rule_002) R->L }
% 17.10/2.64 fresh192(fresh195(fresh441(true, true, b), true, b, b), true, b)
% 17.10/2.64 = { by axiom 2 (axiom_11) R->L }
% 17.10/2.64 fresh192(fresh195(fresh441(n0(e, b), true, b), true, b, b), true, b)
% 17.10/2.64 = { by axiom 7 (rule_002) }
% 17.10/2.64 fresh192(fresh195(l1(b, b), true, b, b), true, b)
% 17.10/2.64 = { by axiom 10 (rule_186) }
% 17.10/2.64 fresh192(q2(b, b, b), true, b)
% 17.10/2.64 = { by axiom 11 (rule_189) }
% 17.10/2.64 fresh191(s1(b), true, b)
% 17.10/2.64 = { by axiom 8 (rule_125) R->L }
% 17.10/2.64 fresh191(fresh275(p0(b, b), true, b), true, b)
% 17.10/2.64 = { by axiom 1 (axiom_14) }
% 17.10/2.64 fresh191(fresh275(true, true, b), true, b)
% 17.10/2.64 = { by axiom 4 (rule_125) }
% 17.10/2.64 fresh191(true, true, b)
% 17.10/2.64 = { by axiom 6 (rule_189) }
% 17.10/2.64 true
% 17.10/2.64 % SZS output end Proof
% 17.10/2.64
% 17.10/2.64 RESULT: Unsatisfiable (the axioms are contradictory).
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