TSTP Solution File: GRP029-2 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP029-2 : 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 : n026.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 01:16:41 EDT 2023
% Result : Unsatisfiable 0.21s 0.45s
% 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
% 0.00/0.13 % Problem : GRP029-2 : TPTP v8.1.2. Released v1.0.0.
% 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 : n026.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 : Tue Aug 29 00:36:20 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.45 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.21/0.45
% 0.21/0.45 % SZS status Unsatisfiable
% 0.21/0.45
% 0.21/0.47 % SZS output start Proof
% 0.21/0.47 Take the following subset of the input axioms:
% 0.21/0.47 fof(associativity1, axiom, ![X, Y, Z, W, U, V]: (~product(X, Y, U) | (~product(Y, Z, V) | (~product(U, Z, W) | product(X, V, W))))).
% 0.21/0.47 fof(associativity2, axiom, ![X2, Y2, Z2, W2, U2, V2]: (~product(X2, Y2, U2) | (~product(Y2, Z2, V2) | (~product(X2, V2, W2) | product(U2, Z2, W2))))).
% 0.21/0.47 fof(left_identity, axiom, ![A]: product(identity, A, A)).
% 0.21/0.47 fof(left_inverse, axiom, ![A2]: product(inverse(A2), A2, identity)).
% 0.21/0.47 fof(prove_there_is_a_right_identity, negated_conjecture, ![A2]: ~product(not_right_identity(A2), A2, not_right_identity(A2))).
% 0.21/0.47
% 0.21/0.47 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.47 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.47 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.47 fresh(y, y, x1...xn) = u
% 0.21/0.47 C => fresh(s, t, x1...xn) = v
% 0.21/0.47 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.47 variables of u and v.
% 0.21/0.47 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.47 input problem has no model of domain size 1).
% 0.21/0.47
% 0.21/0.47 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.47
% 0.21/0.47 Axiom 1 (left_identity): product(identity, X, X) = true2.
% 0.21/0.47 Axiom 2 (left_inverse): product(inverse(X), X, identity) = true2.
% 0.21/0.47 Axiom 3 (associativity1): fresh20(X, X, Y, Z, W) = true2.
% 0.21/0.47 Axiom 4 (associativity2): fresh18(X, X, Y, Z, W) = true2.
% 0.21/0.47 Axiom 5 (associativity1): fresh16(X, X, Y, Z, W, V, U) = product(Y, V, U).
% 0.21/0.47 Axiom 6 (associativity2): fresh15(X, X, Y, Z, W, V, U) = product(W, V, U).
% 0.21/0.47 Axiom 7 (associativity1): fresh19(X, X, Y, Z, W, V, U, T) = fresh20(product(Y, Z, W), true2, Y, U, T).
% 0.21/0.47 Axiom 8 (associativity2): fresh17(X, X, Y, Z, W, V, U, T) = fresh18(product(Y, Z, W), true2, W, V, T).
% 0.21/0.47 Axiom 9 (associativity1): fresh19(product(X, Y, Z), true2, W, V, X, Y, U, Z) = fresh16(product(V, Y, U), true2, W, V, X, U, Z).
% 0.21/0.47 Axiom 10 (associativity2): fresh17(product(X, Y, Z), true2, W, X, V, Y, Z, U) = fresh15(product(W, Z, U), true2, W, X, V, Y, U).
% 0.21/0.47
% 0.21/0.47 Lemma 11: fresh19(X, X, Y, inverse(Z), identity, W, identity, Z) = product(Y, identity, Z).
% 0.21/0.47 Proof:
% 0.21/0.47 fresh19(X, X, Y, inverse(Z), identity, W, identity, Z)
% 0.21/0.47 = { by axiom 7 (associativity1) }
% 0.21/0.47 fresh20(product(Y, inverse(Z), identity), true2, Y, identity, Z)
% 0.21/0.47 = { by axiom 7 (associativity1) R->L }
% 0.21/0.47 fresh19(true2, true2, Y, inverse(Z), identity, Z, identity, Z)
% 0.21/0.47 = { by axiom 1 (left_identity) R->L }
% 0.21/0.47 fresh19(product(identity, Z, Z), true2, Y, inverse(Z), identity, Z, identity, Z)
% 0.21/0.47 = { by axiom 9 (associativity1) }
% 0.21/0.47 fresh16(product(inverse(Z), Z, identity), true2, Y, inverse(Z), identity, identity, Z)
% 0.21/0.47 = { by axiom 2 (left_inverse) }
% 0.21/0.47 fresh16(true2, true2, Y, inverse(Z), identity, identity, Z)
% 0.21/0.47 = { by axiom 5 (associativity1) }
% 0.21/0.47 product(Y, identity, Z)
% 0.21/0.47
% 0.21/0.47 Goal 1 (prove_there_is_a_right_identity): product(not_right_identity(X), X, not_right_identity(X)) = true2.
% 0.21/0.47 The goal is true when:
% 0.21/0.47 X = identity
% 0.21/0.47
% 0.21/0.47 Proof:
% 0.21/0.47 product(not_right_identity(identity), identity, not_right_identity(identity))
% 0.21/0.47 = { by lemma 11 R->L }
% 0.21/0.47 fresh19(Z, Z, not_right_identity(identity), inverse(not_right_identity(identity)), identity, W, identity, not_right_identity(identity))
% 0.21/0.47 = { by axiom 7 (associativity1) }
% 0.21/0.47 fresh20(product(not_right_identity(identity), inverse(not_right_identity(identity)), identity), true2, not_right_identity(identity), identity, not_right_identity(identity))
% 0.21/0.47 = { by axiom 6 (associativity2) R->L }
% 0.21/0.47 fresh20(fresh15(true2, true2, inverse(inverse(not_right_identity(identity))), identity, not_right_identity(identity), inverse(not_right_identity(identity)), identity), true2, not_right_identity(identity), identity, not_right_identity(identity))
% 0.21/0.47 = { by axiom 2 (left_inverse) R->L }
% 0.21/0.47 fresh20(fresh15(product(inverse(inverse(not_right_identity(identity))), inverse(not_right_identity(identity)), identity), true2, inverse(inverse(not_right_identity(identity))), identity, not_right_identity(identity), inverse(not_right_identity(identity)), identity), true2, not_right_identity(identity), identity, not_right_identity(identity))
% 0.21/0.47 = { by axiom 10 (associativity2) R->L }
% 0.21/0.47 fresh20(fresh17(product(identity, inverse(not_right_identity(identity)), inverse(not_right_identity(identity))), true2, inverse(inverse(not_right_identity(identity))), identity, not_right_identity(identity), inverse(not_right_identity(identity)), inverse(not_right_identity(identity)), identity), true2, not_right_identity(identity), identity, not_right_identity(identity))
% 0.21/0.47 = { by axiom 1 (left_identity) }
% 0.21/0.47 fresh20(fresh17(true2, true2, inverse(inverse(not_right_identity(identity))), identity, not_right_identity(identity), inverse(not_right_identity(identity)), inverse(not_right_identity(identity)), identity), true2, not_right_identity(identity), identity, not_right_identity(identity))
% 0.21/0.47 = { by axiom 8 (associativity2) }
% 0.21/0.47 fresh20(fresh18(product(inverse(inverse(not_right_identity(identity))), identity, not_right_identity(identity)), true2, not_right_identity(identity), inverse(not_right_identity(identity)), identity), true2, not_right_identity(identity), identity, not_right_identity(identity))
% 0.21/0.47 = { by lemma 11 R->L }
% 0.21/0.47 fresh20(fresh18(fresh19(X, X, inverse(inverse(not_right_identity(identity))), inverse(not_right_identity(identity)), identity, Y, identity, not_right_identity(identity)), true2, not_right_identity(identity), inverse(not_right_identity(identity)), identity), true2, not_right_identity(identity), identity, not_right_identity(identity))
% 0.21/0.47 = { by axiom 7 (associativity1) }
% 0.21/0.47 fresh20(fresh18(fresh20(product(inverse(inverse(not_right_identity(identity))), inverse(not_right_identity(identity)), identity), true2, inverse(inverse(not_right_identity(identity))), identity, not_right_identity(identity)), true2, not_right_identity(identity), inverse(not_right_identity(identity)), identity), true2, not_right_identity(identity), identity, not_right_identity(identity))
% 0.21/0.47 = { by axiom 2 (left_inverse) }
% 0.21/0.47 fresh20(fresh18(fresh20(true2, true2, inverse(inverse(not_right_identity(identity))), identity, not_right_identity(identity)), true2, not_right_identity(identity), inverse(not_right_identity(identity)), identity), true2, not_right_identity(identity), identity, not_right_identity(identity))
% 0.21/0.47 = { by axiom 3 (associativity1) }
% 0.21/0.47 fresh20(fresh18(true2, true2, not_right_identity(identity), inverse(not_right_identity(identity)), identity), true2, not_right_identity(identity), identity, not_right_identity(identity))
% 0.21/0.47 = { by axiom 4 (associativity2) }
% 0.21/0.47 fresh20(true2, true2, not_right_identity(identity), identity, not_right_identity(identity))
% 0.21/0.47 = { by axiom 3 (associativity1) }
% 0.21/0.47 true2
% 0.21/0.47 % SZS output end Proof
% 0.21/0.47
% 0.21/0.47 RESULT: Unsatisfiable (the axioms are contradictory).
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