TSTP Solution File: GRP004-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP004-1 : TPTP v8.1.2. Released v1.0.0.
% 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 : n002.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 01:16:31 EDT 2023
% Result : Unsatisfiable 0.14s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP004-1 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n002.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 28 20:58:19 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.40 Command-line arguments: --no-flatten-goal
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% 0.14/0.40 % SZS status Unsatisfiable
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% 0.14/0.41 % SZS output start Proof
% 0.14/0.41 Take the following subset of the input axioms:
% 0.14/0.41 fof(associativity1, axiom, ![X, Y, U, Z, V, W]: (~product(X, Y, U) | (~product(Y, Z, V) | (~product(U, Z, W) | product(X, V, W))))).
% 0.14/0.41 fof(associativity2, axiom, ![X2, Y2, U2, Z2, V2, W2]: (~product(X2, Y2, U2) | (~product(Y2, Z2, V2) | (~product(X2, V2, W2) | product(U2, Z2, W2))))).
% 0.14/0.41 fof(left_identity, axiom, ![X2]: product(identity, X2, X2)).
% 0.14/0.41 fof(left_inverse, axiom, ![X2]: product(inverse(X2), X2, identity)).
% 0.14/0.41 fof(prove_there_is_a_right_inverse, negated_conjecture, ![X2]: ~product(a, X2, identity)).
% 0.14/0.41
% 0.14/0.41 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.14/0.41 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.14/0.41 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.14/0.41 fresh(y, y, x1...xn) = u
% 0.14/0.41 C => fresh(s, t, x1...xn) = v
% 0.14/0.41 where fresh is a fresh function symbol and x1..xn are the free
% 0.14/0.41 variables of u and v.
% 0.14/0.41 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.14/0.41 input problem has no model of domain size 1).
% 0.14/0.41
% 0.14/0.41 The encoding turns the above axioms into the following unit equations and goals:
% 0.14/0.41
% 0.14/0.41 Axiom 1 (left_identity): product(identity, X, X) = true2.
% 0.14/0.41 Axiom 2 (left_inverse): product(inverse(X), X, identity) = true2.
% 0.14/0.41 Axiom 3 (associativity1): fresh6(X, X, Y, Z, W) = true2.
% 0.14/0.41 Axiom 4 (associativity2): fresh4(X, X, Y, Z, W) = true2.
% 0.14/0.41 Axiom 5 (associativity2): fresh(X, X, Y, Z, W, V, U) = product(W, V, U).
% 0.14/0.41 Axiom 6 (associativity1): fresh2(X, X, Y, Z, W, V, U) = product(Y, V, U).
% 0.14/0.41 Axiom 7 (associativity1): fresh5(X, X, Y, Z, W, V, U, T) = fresh6(product(Y, Z, W), true2, Y, U, T).
% 0.14/0.41 Axiom 8 (associativity2): fresh3(X, X, Y, Z, W, V, U, T) = fresh4(product(Y, Z, W), true2, W, V, T).
% 0.14/0.41 Axiom 9 (associativity1): fresh5(product(X, Y, Z), true2, W, V, X, Y, U, Z) = fresh2(product(V, Y, U), true2, W, V, X, U, Z).
% 0.21/0.41 Axiom 10 (associativity2): fresh3(product(X, Y, Z), true2, W, X, V, Y, Z, U) = fresh(product(W, Z, U), true2, W, X, V, Y, U).
% 0.21/0.41
% 0.21/0.41 Goal 1 (prove_there_is_a_right_inverse): product(a, X, identity) = true2.
% 0.21/0.41 The goal is true when:
% 0.21/0.41 X = inverse(a)
% 0.21/0.41
% 0.21/0.41 Proof:
% 0.21/0.41 product(a, inverse(a), identity)
% 0.21/0.41 = { by axiom 5 (associativity2) R->L }
% 0.21/0.41 fresh(true2, true2, inverse(inverse(a)), identity, a, inverse(a), identity)
% 0.21/0.41 = { by axiom 2 (left_inverse) R->L }
% 0.21/0.41 fresh(product(inverse(inverse(a)), inverse(a), identity), true2, inverse(inverse(a)), identity, a, inverse(a), identity)
% 0.21/0.41 = { by axiom 10 (associativity2) R->L }
% 0.21/0.41 fresh3(product(identity, inverse(a), inverse(a)), true2, inverse(inverse(a)), identity, a, inverse(a), inverse(a), identity)
% 0.21/0.41 = { by axiom 1 (left_identity) }
% 0.21/0.41 fresh3(true2, true2, inverse(inverse(a)), identity, a, inverse(a), inverse(a), identity)
% 0.21/0.41 = { by axiom 8 (associativity2) }
% 0.21/0.41 fresh4(product(inverse(inverse(a)), identity, a), true2, a, inverse(a), identity)
% 0.21/0.41 = { by axiom 6 (associativity1) R->L }
% 0.21/0.41 fresh4(fresh2(true2, true2, inverse(inverse(a)), inverse(a), identity, identity, a), true2, a, inverse(a), identity)
% 0.21/0.41 = { by axiom 2 (left_inverse) R->L }
% 0.21/0.41 fresh4(fresh2(product(inverse(a), a, identity), true2, inverse(inverse(a)), inverse(a), identity, identity, a), true2, a, inverse(a), identity)
% 0.21/0.41 = { by axiom 9 (associativity1) R->L }
% 0.21/0.41 fresh4(fresh5(product(identity, a, a), true2, inverse(inverse(a)), inverse(a), identity, a, identity, a), true2, a, inverse(a), identity)
% 0.21/0.41 = { by axiom 1 (left_identity) }
% 0.21/0.41 fresh4(fresh5(true2, true2, inverse(inverse(a)), inverse(a), identity, a, identity, a), true2, a, inverse(a), identity)
% 0.21/0.41 = { by axiom 7 (associativity1) }
% 0.21/0.41 fresh4(fresh6(product(inverse(inverse(a)), inverse(a), identity), true2, inverse(inverse(a)), identity, a), true2, a, inverse(a), identity)
% 0.21/0.41 = { by axiom 2 (left_inverse) }
% 0.21/0.41 fresh4(fresh6(true2, true2, inverse(inverse(a)), identity, a), true2, a, inverse(a), identity)
% 0.21/0.41 = { by axiom 3 (associativity1) }
% 0.21/0.41 fresh4(true2, true2, a, inverse(a), identity)
% 0.21/0.41 = { by axiom 4 (associativity2) }
% 0.21/0.41 true2
% 0.21/0.41 % SZS output end Proof
% 0.21/0.41
% 0.21/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
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