TSTP Solution File: SYN286-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SYN286-1 : 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 : n016.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 03:33:55 EDT 2023
% Result : Unsatisfiable 22.45s 3.48s
% Output : Proof 22.45s
% 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 : SYN286-1 : 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 : n016.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 17:53:42 EDT 2023
% 0.13/0.35 % CPUTime :
% 22.45/3.48 Command-line arguments: --no-flatten-goal
% 22.45/3.48
% 22.45/3.48 % SZS status Unsatisfiable
% 22.45/3.48
% 22.45/3.48 % SZS output start Proof
% 22.45/3.48 Take the following subset of the input axioms:
% 22.45/3.48 fof(axiom_19, axiom, ![X, Y]: m0(X, d, Y)).
% 22.45/3.48 fof(axiom_20, axiom, l0(a)).
% 22.45/3.48 fof(axiom_28, axiom, k0(e)).
% 22.45/3.48 fof(prove_this, negated_conjecture, ![X2]: ~q1(a, e, X2)).
% 22.45/3.48 fof(rule_099, axiom, ![G, E, F]: (q1(E, F, F) | (~k0(G) | (~l0(E) | ~q1(F, F, G))))).
% 22.45/3.48 fof(rule_107, axiom, ![A2]: (q1(e, A2, A2) | (~m0(A2, d, A2) | ~m0(e, d, A2)))).
% 22.45/3.48
% 22.45/3.48 Now clausify the problem and encode Horn clauses using encoding 3 of
% 22.45/3.48 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 22.45/3.48 We repeatedly replace C & s=t => u=v by the two clauses:
% 22.45/3.48 fresh(y, y, x1...xn) = u
% 22.45/3.48 C => fresh(s, t, x1...xn) = v
% 22.45/3.48 where fresh is a fresh function symbol and x1..xn are the free
% 22.45/3.48 variables of u and v.
% 22.45/3.48 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 22.45/3.48 input problem has no model of domain size 1).
% 22.45/3.48
% 22.45/3.48 The encoding turns the above axioms into the following unit equations and goals:
% 22.45/3.48
% 22.45/3.48 Axiom 1 (axiom_28): k0(e) = true2.
% 22.45/3.48 Axiom 2 (axiom_20): l0(a) = true2.
% 22.45/3.48 Axiom 3 (rule_107): fresh300(X, X, Y) = true2.
% 22.45/3.48 Axiom 4 (rule_107): fresh301(X, X, Y) = q1(e, Y, Y).
% 22.45/3.48 Axiom 5 (axiom_19): m0(X, d, Y) = true2.
% 22.45/3.48 Axiom 6 (rule_099): fresh607(X, X, Y, Z) = true2.
% 22.45/3.48 Axiom 7 (rule_099): fresh310(X, X, Y, Z) = q1(Y, Z, Z).
% 22.45/3.48 Axiom 8 (rule_099): fresh606(X, X, Y, Z, W) = fresh607(l0(Y), true2, Y, Z).
% 22.45/3.48 Axiom 9 (rule_107): fresh301(m0(e, d, X), true2, X) = fresh300(m0(X, d, X), true2, X).
% 22.45/3.48 Axiom 10 (rule_099): fresh606(q1(X, X, Y), true2, Z, X, Y) = fresh310(k0(Y), true2, Z, X).
% 22.45/3.48
% 22.45/3.48 Goal 1 (prove_this): q1(a, e, X) = true2.
% 22.45/3.48 The goal is true when:
% 22.45/3.48 X = e
% 22.45/3.48
% 22.45/3.48 Proof:
% 22.45/3.48 q1(a, e, e)
% 22.45/3.48 = { by axiom 7 (rule_099) R->L }
% 22.45/3.48 fresh310(true2, true2, a, e)
% 22.45/3.48 = { by axiom 1 (axiom_28) R->L }
% 22.45/3.48 fresh310(k0(e), true2, a, e)
% 22.45/3.48 = { by axiom 10 (rule_099) R->L }
% 22.45/3.48 fresh606(q1(e, e, e), true2, a, e, e)
% 22.45/3.48 = { by axiom 4 (rule_107) R->L }
% 22.45/3.48 fresh606(fresh301(true2, true2, e), true2, a, e, e)
% 22.45/3.48 = { by axiom 5 (axiom_19) R->L }
% 22.45/3.48 fresh606(fresh301(m0(e, d, e), true2, e), true2, a, e, e)
% 22.45/3.48 = { by axiom 9 (rule_107) }
% 22.45/3.48 fresh606(fresh300(m0(e, d, e), true2, e), true2, a, e, e)
% 22.45/3.48 = { by axiom 5 (axiom_19) }
% 22.45/3.48 fresh606(fresh300(true2, true2, e), true2, a, e, e)
% 22.45/3.48 = { by axiom 3 (rule_107) }
% 22.45/3.48 fresh606(true2, true2, a, e, e)
% 22.45/3.48 = { by axiom 8 (rule_099) }
% 22.45/3.48 fresh607(l0(a), true2, a, e)
% 22.45/3.48 = { by axiom 2 (axiom_20) }
% 22.45/3.48 fresh607(true2, true2, a, e)
% 22.45/3.48 = { by axiom 6 (rule_099) }
% 22.45/3.48 true2
% 22.45/3.48 % SZS output end Proof
% 22.45/3.48
% 22.45/3.48 RESULT: Unsatisfiable (the axioms are contradictory).
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