TSTP Solution File: SYN233-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SYN233-1 : 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 : n023.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 03:33:42 EDT 2023
% Result : Unsatisfiable 14.17s 2.16s
% Output : Proof 14.17s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN233-1 : TPTP v8.1.2. Released v1.1.0.
% 0.06/0.13 % 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 : n023.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 21:37:11 EDT 2023
% 0.13/0.34 % CPUTime :
% 14.17/2.16 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 14.17/2.16
% 14.17/2.16 % SZS status Unsatisfiable
% 14.17/2.16
% 14.17/2.17 % SZS output start Proof
% 14.17/2.17 Take the following subset of the input axioms:
% 14.17/2.17 fof(axiom_13, axiom, r0(e)).
% 14.17/2.17 fof(axiom_19, axiom, ![X, Y]: m0(X, d, Y)).
% 14.17/2.17 fof(prove_this, negated_conjecture, ![X2]: ~l3(e, X2)).
% 14.17/2.17 fof(rule_107, axiom, ![A2]: (q1(e, A2, A2) | (~m0(A2, d, A2) | ~m0(e, d, A2)))).
% 14.17/2.17 fof(rule_154, axiom, ![A2_2]: (p2(A2_2, A2_2, A2_2) | ~q1(A2_2, A2_2, A2_2))).
% 14.17/2.17 fof(rule_215, axiom, ![G, H]: (l3(G, H) | (~r0(G) | ~p2(G, H, G)))).
% 14.17/2.17
% 14.17/2.17 Now clausify the problem and encode Horn clauses using encoding 3 of
% 14.17/2.17 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 14.17/2.17 We repeatedly replace C & s=t => u=v by the two clauses:
% 14.17/2.17 fresh(y, y, x1...xn) = u
% 14.17/2.17 C => fresh(s, t, x1...xn) = v
% 14.17/2.17 where fresh is a fresh function symbol and x1..xn are the free
% 14.17/2.17 variables of u and v.
% 14.17/2.17 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 14.17/2.17 input problem has no model of domain size 1).
% 14.17/2.17
% 14.17/2.17 The encoding turns the above axioms into the following unit equations and goals:
% 14.17/2.17
% 14.17/2.17 Axiom 1 (axiom_13): r0(e) = true2.
% 14.17/2.17 Axiom 2 (axiom_19): m0(X, d, Y) = true2.
% 14.17/2.17 Axiom 3 (rule_107): fresh301(X, X, Y) = q1(e, Y, Y).
% 14.17/2.17 Axiom 4 (rule_107): fresh300(X, X, Y) = true2.
% 14.17/2.17 Axiom 5 (rule_154): fresh241(X, X, Y) = true2.
% 14.17/2.17 Axiom 6 (rule_215): fresh160(X, X, Y, Z) = l3(Y, Z).
% 14.17/2.17 Axiom 7 (rule_215): fresh159(X, X, Y, Z) = true2.
% 14.17/2.17 Axiom 8 (rule_107): fresh301(m0(e, d, X), true2, X) = fresh300(m0(X, d, X), true2, X).
% 14.17/2.17 Axiom 9 (rule_154): fresh241(q1(X, X, X), true2, X) = p2(X, X, X).
% 14.17/2.17 Axiom 10 (rule_215): fresh160(p2(X, Y, X), true2, X, Y) = fresh159(r0(X), true2, X, Y).
% 14.17/2.17
% 14.17/2.17 Goal 1 (prove_this): l3(e, X) = true2.
% 14.17/2.17 The goal is true when:
% 14.17/2.17 X = e
% 14.17/2.17
% 14.17/2.17 Proof:
% 14.17/2.17 l3(e, e)
% 14.17/2.17 = { by axiom 6 (rule_215) R->L }
% 14.17/2.17 fresh160(true2, true2, e, e)
% 14.17/2.17 = { by axiom 5 (rule_154) R->L }
% 14.17/2.17 fresh160(fresh241(true2, true2, e), true2, e, e)
% 14.17/2.17 = { by axiom 4 (rule_107) R->L }
% 14.17/2.17 fresh160(fresh241(fresh300(true2, true2, e), true2, e), true2, e, e)
% 14.17/2.17 = { by axiom 2 (axiom_19) R->L }
% 14.17/2.17 fresh160(fresh241(fresh300(m0(e, d, e), true2, e), true2, e), true2, e, e)
% 14.17/2.17 = { by axiom 8 (rule_107) R->L }
% 14.17/2.17 fresh160(fresh241(fresh301(m0(e, d, e), true2, e), true2, e), true2, e, e)
% 14.17/2.17 = { by axiom 2 (axiom_19) }
% 14.17/2.17 fresh160(fresh241(fresh301(true2, true2, e), true2, e), true2, e, e)
% 14.17/2.17 = { by axiom 3 (rule_107) }
% 14.17/2.17 fresh160(fresh241(q1(e, e, e), true2, e), true2, e, e)
% 14.17/2.17 = { by axiom 9 (rule_154) }
% 14.17/2.17 fresh160(p2(e, e, e), true2, e, e)
% 14.17/2.17 = { by axiom 10 (rule_215) }
% 14.17/2.17 fresh159(r0(e), true2, e, e)
% 14.17/2.17 = { by axiom 1 (axiom_13) }
% 14.17/2.17 fresh159(true2, true2, e, e)
% 14.17/2.17 = { by axiom 7 (rule_215) }
% 14.17/2.17 true2
% 14.17/2.17 % SZS output end Proof
% 14.17/2.17
% 14.17/2.17 RESULT: Unsatisfiable (the axioms are contradictory).
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