TSTP Solution File: LCL226-3 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL226-3 : TPTP v8.1.2. Released v2.3.0.
% 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 : n017.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 : Thu Aug 31 08:18:08 EDT 2023
% Result : Unsatisfiable 0.28s 0.62s
% Output : Proof 0.28s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.18 % Problem : LCL226-3 : TPTP v8.1.2. Released v2.3.0.
% 0.11/0.19 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.19/0.42 % Computer : n017.cluster.edu
% 0.19/0.42 % Model : x86_64 x86_64
% 0.19/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.42 % Memory : 8042.1875MB
% 0.19/0.42 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.42 % CPULimit : 300
% 0.19/0.42 % WCLimit : 300
% 0.19/0.42 % DateTime : Fri Aug 25 01:39:40 EDT 2023
% 0.19/0.42 % CPUTime :
% 0.28/0.62 Command-line arguments: --ground-connectedness --complete-subsets
% 0.28/0.62
% 0.28/0.62 % SZS status Unsatisfiable
% 0.28/0.62
% 0.28/0.62 % SZS output start Proof
% 0.28/0.62 Take the following subset of the input axioms:
% 0.28/0.62 fof(axiom_1_5, axiom, ![A, B, C]: axiom(implies(or(A, or(B, C)), or(B, or(A, C))))).
% 0.28/0.62 fof(axiom_1_6, axiom, ![A2, B2, C2]: axiom(implies(implies(A2, B2), implies(or(C2, A2), or(C2, B2))))).
% 0.28/0.62 fof(implies_definition, axiom, ![X, Y]: implies(X, Y)=or(not(X), Y)).
% 0.28/0.62 fof(prove_this, negated_conjecture, ~theorem(implies(or(q, r), implies(or(not(r), s), or(q, s))))).
% 0.28/0.62 fof(rule_1, axiom, ![X2]: (theorem(X2) | ~axiom(X2))).
% 0.28/0.62 fof(rule_2, axiom, ![X2, Y2]: (theorem(X2) | (~theorem(implies(Y2, X2)) | ~theorem(Y2)))).
% 0.28/0.62
% 0.28/0.62 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.28/0.62 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.28/0.62 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.28/0.62 fresh(y, y, x1...xn) = u
% 0.28/0.62 C => fresh(s, t, x1...xn) = v
% 0.28/0.62 where fresh is a fresh function symbol and x1..xn are the free
% 0.28/0.62 variables of u and v.
% 0.28/0.62 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.28/0.62 input problem has no model of domain size 1).
% 0.28/0.62
% 0.28/0.62 The encoding turns the above axioms into the following unit equations and goals:
% 0.28/0.62
% 0.28/0.62 Axiom 1 (rule_2): fresh(X, X, Y) = true.
% 0.28/0.62 Axiom 2 (rule_1): fresh2(X, X, Y) = true.
% 0.28/0.62 Axiom 3 (implies_definition): implies(X, Y) = or(not(X), Y).
% 0.28/0.62 Axiom 4 (rule_2): fresh3(X, X, Y, Z) = theorem(Y).
% 0.28/0.62 Axiom 5 (rule_1): fresh2(axiom(X), true, X) = theorem(X).
% 0.28/0.62 Axiom 6 (rule_2): fresh3(theorem(implies(X, Y)), true, Y, X) = fresh(theorem(X), true, Y).
% 0.28/0.62 Axiom 7 (axiom_1_6): axiom(implies(implies(X, Y), implies(or(Z, X), or(Z, Y)))) = true.
% 0.28/0.62 Axiom 8 (axiom_1_5): axiom(implies(or(X, or(Y, Z)), or(Y, or(X, Z)))) = true.
% 0.28/0.62
% 0.28/0.62 Goal 1 (prove_this): theorem(implies(or(q, r), implies(or(not(r), s), or(q, s)))) = true.
% 0.28/0.62 Proof:
% 0.28/0.62 theorem(implies(or(q, r), implies(or(not(r), s), or(q, s))))
% 0.28/0.62 = { by axiom 4 (rule_2) R->L }
% 0.28/0.63 fresh3(true, true, implies(or(q, r), implies(or(not(r), s), or(q, s))), implies(or(not(r), s), implies(or(q, r), or(q, s))))
% 0.28/0.63 = { by axiom 2 (rule_1) R->L }
% 0.28/0.63 fresh3(fresh2(true, true, implies(implies(or(not(r), s), implies(or(q, r), or(q, s))), implies(or(q, r), implies(or(not(r), s), or(q, s))))), true, implies(or(q, r), implies(or(not(r), s), or(q, s))), implies(or(not(r), s), implies(or(q, r), or(q, s))))
% 0.28/0.63 = { by axiom 8 (axiom_1_5) R->L }
% 0.28/0.63 fresh3(fresh2(axiom(implies(or(not(or(not(r), s)), or(not(or(q, r)), or(q, s))), or(not(or(q, r)), or(not(or(not(r), s)), or(q, s))))), true, implies(implies(or(not(r), s), implies(or(q, r), or(q, s))), implies(or(q, r), implies(or(not(r), s), or(q, s))))), true, implies(or(q, r), implies(or(not(r), s), or(q, s))), implies(or(not(r), s), implies(or(q, r), or(q, s))))
% 0.28/0.63 = { by axiom 3 (implies_definition) R->L }
% 0.28/0.63 fresh3(fresh2(axiom(implies(implies(or(not(r), s), or(not(or(q, r)), or(q, s))), or(not(or(q, r)), or(not(or(not(r), s)), or(q, s))))), true, implies(implies(or(not(r), s), implies(or(q, r), or(q, s))), implies(or(q, r), implies(or(not(r), s), or(q, s))))), true, implies(or(q, r), implies(or(not(r), s), or(q, s))), implies(or(not(r), s), implies(or(q, r), or(q, s))))
% 0.28/0.63 = { by axiom 3 (implies_definition) R->L }
% 0.28/0.63 fresh3(fresh2(axiom(implies(implies(or(not(r), s), or(not(or(q, r)), or(q, s))), or(not(or(q, r)), implies(or(not(r), s), or(q, s))))), true, implies(implies(or(not(r), s), implies(or(q, r), or(q, s))), implies(or(q, r), implies(or(not(r), s), or(q, s))))), true, implies(or(q, r), implies(or(not(r), s), or(q, s))), implies(or(not(r), s), implies(or(q, r), or(q, s))))
% 0.28/0.63 = { by axiom 3 (implies_definition) R->L }
% 0.28/0.63 fresh3(fresh2(axiom(implies(implies(or(not(r), s), implies(or(q, r), or(q, s))), or(not(or(q, r)), implies(or(not(r), s), or(q, s))))), true, implies(implies(or(not(r), s), implies(or(q, r), or(q, s))), implies(or(q, r), implies(or(not(r), s), or(q, s))))), true, implies(or(q, r), implies(or(not(r), s), or(q, s))), implies(or(not(r), s), implies(or(q, r), or(q, s))))
% 0.28/0.63 = { by axiom 3 (implies_definition) R->L }
% 0.28/0.63 fresh3(fresh2(axiom(implies(implies(or(not(r), s), implies(or(q, r), or(q, s))), implies(or(q, r), implies(or(not(r), s), or(q, s))))), true, implies(implies(or(not(r), s), implies(or(q, r), or(q, s))), implies(or(q, r), implies(or(not(r), s), or(q, s))))), true, implies(or(q, r), implies(or(not(r), s), or(q, s))), implies(or(not(r), s), implies(or(q, r), or(q, s))))
% 0.28/0.63 = { by axiom 5 (rule_1) }
% 0.28/0.63 fresh3(theorem(implies(implies(or(not(r), s), implies(or(q, r), or(q, s))), implies(or(q, r), implies(or(not(r), s), or(q, s))))), true, implies(or(q, r), implies(or(not(r), s), or(q, s))), implies(or(not(r), s), implies(or(q, r), or(q, s))))
% 0.28/0.63 = { by axiom 6 (rule_2) }
% 0.28/0.63 fresh(theorem(implies(or(not(r), s), implies(or(q, r), or(q, s)))), true, implies(or(q, r), implies(or(not(r), s), or(q, s))))
% 0.28/0.63 = { by axiom 5 (rule_1) R->L }
% 0.28/0.63 fresh(fresh2(axiom(implies(or(not(r), s), implies(or(q, r), or(q, s)))), true, implies(or(not(r), s), implies(or(q, r), or(q, s)))), true, implies(or(q, r), implies(or(not(r), s), or(q, s))))
% 0.28/0.63 = { by axiom 3 (implies_definition) R->L }
% 0.28/0.63 fresh(fresh2(axiom(implies(implies(r, s), implies(or(q, r), or(q, s)))), true, implies(or(not(r), s), implies(or(q, r), or(q, s)))), true, implies(or(q, r), implies(or(not(r), s), or(q, s))))
% 0.28/0.63 = { by axiom 7 (axiom_1_6) }
% 0.28/0.63 fresh(fresh2(true, true, implies(or(not(r), s), implies(or(q, r), or(q, s)))), true, implies(or(q, r), implies(or(not(r), s), or(q, s))))
% 0.28/0.63 = { by axiom 2 (rule_1) }
% 0.28/0.63 fresh(true, true, implies(or(q, r), implies(or(not(r), s), or(q, s))))
% 0.28/0.63 = { by axiom 1 (rule_2) }
% 0.28/0.63 true
% 0.28/0.63 % SZS output end Proof
% 0.28/0.63
% 0.28/0.63 RESULT: Unsatisfiable (the axioms are contradictory).
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