TSTP Solution File: SYN166-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SYN166-1 : 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 : n009.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 03:33:26 EDT 2023
% Result : Unsatisfiable 37.78s 5.16s
% Output : Proof 37.78s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09 % Problem : SYN166-1 : TPTP v8.1.2. Released v1.1.0.
% 0.04/0.09 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.09/0.29 % Computer : n009.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Sat Aug 26 19:51:05 EDT 2023
% 0.09/0.29 % CPUTime :
% 37.78/5.16 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 37.78/5.16
% 37.78/5.16 % SZS status Unsatisfiable
% 37.78/5.16
% 37.78/5.16 % SZS output start Proof
% 37.78/5.16 Take the following subset of the input axioms:
% 37.78/5.16 fof(axiom_12, axiom, ![X]: m0(a, X, a)).
% 37.78/5.16 fof(axiom_14, axiom, ![X2]: p0(b, X2)).
% 37.78/5.16 fof(axiom_38, axiom, m0(b, a, a)).
% 37.78/5.16 fof(axiom_9, axiom, r0(b)).
% 37.78/5.16 fof(prove_this, negated_conjecture, ~p1(a, b, b)).
% 37.78/5.16 fof(rule_075, axiom, p1(a, a, a) | ~p0(b, a)).
% 37.78/5.16 fof(rule_082, axiom, ![I, J, H, A2]: (p1(H, I, J) | (~m0(J, H, A2) | ~p1(J, H, A2)))).
% 37.78/5.16 fof(rule_087, axiom, p1(a, b, a) | (~r0(b) | ~p1(a, a, a))).
% 37.78/5.16
% 37.78/5.16 Now clausify the problem and encode Horn clauses using encoding 3 of
% 37.78/5.16 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 37.78/5.16 We repeatedly replace C & s=t => u=v by the two clauses:
% 37.78/5.16 fresh(y, y, x1...xn) = u
% 37.78/5.16 C => fresh(s, t, x1...xn) = v
% 37.78/5.16 where fresh is a fresh function symbol and x1..xn are the free
% 37.78/5.16 variables of u and v.
% 37.78/5.16 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 37.78/5.16 input problem has no model of domain size 1).
% 37.78/5.16
% 37.78/5.16 The encoding turns the above axioms into the following unit equations and goals:
% 37.78/5.16
% 37.78/5.16 Axiom 1 (axiom_14): p0(b, X) = true.
% 37.78/5.16 Axiom 2 (axiom_9): r0(b) = true.
% 37.78/5.16 Axiom 3 (rule_075): fresh341(X, X) = true.
% 37.78/5.16 Axiom 4 (rule_087): fresh324(X, X) = true.
% 37.78/5.16 Axiom 5 (axiom_38): m0(b, a, a) = true.
% 37.78/5.16 Axiom 6 (axiom_12): m0(a, X, a) = true.
% 37.78/5.16 Axiom 7 (rule_087): fresh325(X, X) = p1(a, b, a).
% 37.78/5.16 Axiom 8 (rule_075): fresh341(p0(b, a), true) = p1(a, a, a).
% 37.78/5.16 Axiom 9 (rule_087): fresh325(p1(a, a, a), true) = fresh324(r0(b), true).
% 37.78/5.16 Axiom 10 (rule_082): fresh333(X, X, Y, Z, W) = true.
% 37.78/5.16 Axiom 11 (rule_082): fresh334(X, X, Y, Z, W, V) = p1(Y, Z, W).
% 37.78/5.16 Axiom 12 (rule_082): fresh334(p1(X, Y, Z), true, Y, W, X, Z) = fresh333(m0(X, Y, Z), true, Y, W, X).
% 37.78/5.16
% 37.78/5.16 Goal 1 (prove_this): p1(a, b, b) = true.
% 37.78/5.16 Proof:
% 37.78/5.16 p1(a, b, b)
% 37.78/5.16 = { by axiom 11 (rule_082) R->L }
% 37.78/5.16 fresh334(true, true, a, b, b, a)
% 37.78/5.16 = { by axiom 10 (rule_082) R->L }
% 37.78/5.16 fresh334(fresh333(true, true, b, a, a), true, a, b, b, a)
% 37.78/5.16 = { by axiom 6 (axiom_12) R->L }
% 37.78/5.16 fresh334(fresh333(m0(a, b, a), true, b, a, a), true, a, b, b, a)
% 37.78/5.16 = { by axiom 12 (rule_082) R->L }
% 37.78/5.16 fresh334(fresh334(p1(a, b, a), true, b, a, a, a), true, a, b, b, a)
% 37.78/5.16 = { by axiom 7 (rule_087) R->L }
% 37.78/5.16 fresh334(fresh334(fresh325(true, true), true, b, a, a, a), true, a, b, b, a)
% 37.78/5.16 = { by axiom 3 (rule_075) R->L }
% 37.78/5.16 fresh334(fresh334(fresh325(fresh341(true, true), true), true, b, a, a, a), true, a, b, b, a)
% 37.78/5.16 = { by axiom 1 (axiom_14) R->L }
% 37.78/5.16 fresh334(fresh334(fresh325(fresh341(p0(b, a), true), true), true, b, a, a, a), true, a, b, b, a)
% 37.78/5.16 = { by axiom 8 (rule_075) }
% 37.78/5.17 fresh334(fresh334(fresh325(p1(a, a, a), true), true, b, a, a, a), true, a, b, b, a)
% 37.78/5.17 = { by axiom 9 (rule_087) }
% 37.78/5.17 fresh334(fresh334(fresh324(r0(b), true), true, b, a, a, a), true, a, b, b, a)
% 37.78/5.17 = { by axiom 2 (axiom_9) }
% 37.78/5.17 fresh334(fresh334(fresh324(true, true), true, b, a, a, a), true, a, b, b, a)
% 37.78/5.17 = { by axiom 4 (rule_087) }
% 37.78/5.17 fresh334(fresh334(true, true, b, a, a, a), true, a, b, b, a)
% 37.78/5.17 = { by axiom 11 (rule_082) }
% 37.78/5.17 fresh334(p1(b, a, a), true, a, b, b, a)
% 37.78/5.17 = { by axiom 12 (rule_082) }
% 37.78/5.17 fresh333(m0(b, a, a), true, a, b, b)
% 37.78/5.17 = { by axiom 5 (axiom_38) }
% 37.78/5.17 fresh333(true, true, a, b, b)
% 37.78/5.17 = { by axiom 10 (rule_082) }
% 37.78/5.17 true
% 37.78/5.17 % SZS output end Proof
% 37.78/5.17
% 37.78/5.17 RESULT: Unsatisfiable (the axioms are contradictory).
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