TSTP Solution File: FLD025-5 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : FLD025-5 : TPTP v8.1.2. Bugfixed v2.1.0.
% 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 : n029.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 : Wed Aug 30 22:36:54 EDT 2023
% Result : Unsatisfiable 19.70s 2.93s
% Output : Proof 19.70s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD025-5 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.34 % Computer : n029.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Sun Aug 27 23:36:40 EDT 2023
% 0.15/0.34 % CPUTime :
% 19.70/2.93 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 19.70/2.93
% 19.70/2.93 % SZS status Unsatisfiable
% 19.70/2.93
% 19.70/2.93 % SZS output start Proof
% 19.70/2.93 Take the following subset of the input axioms:
% 19.70/2.93 fof(associativity_multiplication_1, axiom, ![X, V, W, Y, U, Z]: (product(X, V, W) | (~product(X, Y, U) | (~product(Y, Z, V) | ~product(U, Z, W))))).
% 19.70/2.93 fof(associativity_multiplication_2, axiom, ![X2, Y2, Z2, V2, W2, U2]: (product(U2, Z2, W2) | (~product(X2, Y2, U2) | (~product(Y2, Z2, V2) | ~product(X2, V2, W2))))).
% 19.70/2.93 fof(commutativity_multiplication, axiom, ![X2, Y2, Z2]: (product(Y2, X2, Z2) | ~product(X2, Y2, Z2))).
% 19.70/2.93 fof(existence_of_identity_multiplication, axiom, ![X2]: (product(multiplicative_identity, X2, X2) | ~defined(X2))).
% 19.70/2.93 fof(not_product_11, negated_conjecture, ~product(multiplicative_identity, u, v)).
% 19.70/2.93 fof(product_10, negated_conjecture, product(d, b, v)).
% 19.70/2.93 fof(product_7, negated_conjecture, product(multiplicative_identity, a, b)).
% 19.70/2.93 fof(product_8, negated_conjecture, product(multiplicative_identity, c, d)).
% 19.70/2.93 fof(product_9, negated_conjecture, product(a, c, u)).
% 19.70/2.93 fof(u_is_defined, hypothesis, defined(u)).
% 19.70/2.93
% 19.70/2.93 Now clausify the problem and encode Horn clauses using encoding 3 of
% 19.70/2.93 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 19.70/2.93 We repeatedly replace C & s=t => u=v by the two clauses:
% 19.70/2.93 fresh(y, y, x1...xn) = u
% 19.70/2.93 C => fresh(s, t, x1...xn) = v
% 19.70/2.93 where fresh is a fresh function symbol and x1..xn are the free
% 19.70/2.93 variables of u and v.
% 19.70/2.93 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 19.70/2.93 input problem has no model of domain size 1).
% 19.70/2.93
% 19.70/2.93 The encoding turns the above axioms into the following unit equations and goals:
% 19.70/2.93
% 19.70/2.93 Axiom 1 (u_is_defined): defined(u) = true.
% 19.70/2.93 Axiom 2 (existence_of_identity_multiplication): fresh13(X, X, Y) = true.
% 19.70/2.93 Axiom 3 (product_9): product(a, c, u) = true.
% 19.70/2.93 Axiom 4 (product_10): product(d, b, v) = true.
% 19.70/2.93 Axiom 5 (product_7): product(multiplicative_identity, a, b) = true.
% 19.70/2.93 Axiom 6 (product_8): product(multiplicative_identity, c, d) = true.
% 19.70/2.93 Axiom 7 (existence_of_identity_multiplication): fresh13(defined(X), true, X) = product(multiplicative_identity, X, X).
% 19.70/2.93 Axiom 8 (associativity_multiplication_1): fresh40(X, X, Y, Z, W) = true.
% 19.70/2.93 Axiom 9 (associativity_multiplication_2): fresh38(X, X, Y, Z, W) = true.
% 19.70/2.93 Axiom 10 (commutativity_multiplication): fresh17(X, X, Y, Z, W) = true.
% 19.70/2.93 Axiom 11 (associativity_multiplication_1): fresh20(X, X, Y, Z, W, V, U) = product(Y, Z, W).
% 19.70/2.93 Axiom 12 (associativity_multiplication_2): fresh19(X, X, Y, Z, W, V, U) = product(Y, Z, W).
% 19.70/2.93 Axiom 13 (associativity_multiplication_1): fresh39(X, X, Y, Z, W, V, U, T) = fresh40(product(Y, V, U), true, Y, Z, W).
% 19.70/2.93 Axiom 14 (associativity_multiplication_2): fresh37(X, X, Y, Z, W, V, U, T) = fresh38(product(V, U, Y), true, Y, Z, W).
% 19.70/2.93 Axiom 15 (commutativity_multiplication): fresh17(product(X, Y, Z), true, Y, X, Z) = product(Y, X, Z).
% 19.70/2.93 Axiom 16 (associativity_multiplication_1): fresh39(product(X, Y, Z), true, W, V, Z, U, X, Y) = fresh20(product(U, Y, V), true, W, V, Z, U, X).
% 19.70/2.93 Axiom 17 (associativity_multiplication_2): fresh37(product(X, Y, Z), true, W, Y, V, U, X, Z) = fresh19(product(U, Z, V), true, W, Y, V, U, X).
% 19.70/2.93
% 19.70/2.93 Goal 1 (not_product_11): product(multiplicative_identity, u, v) = true.
% 19.70/2.93 Proof:
% 19.70/2.93 product(multiplicative_identity, u, v)
% 19.70/2.93 = { by axiom 11 (associativity_multiplication_1) R->L }
% 19.70/2.93 fresh20(true, true, multiplicative_identity, u, v, c, d)
% 19.70/2.93 = { by axiom 10 (commutativity_multiplication) R->L }
% 19.70/2.93 fresh20(fresh17(true, true, c, b, u), true, multiplicative_identity, u, v, c, d)
% 19.70/2.93 = { by axiom 9 (associativity_multiplication_2) R->L }
% 19.70/2.94 fresh20(fresh17(fresh38(true, true, b, c, u), true, c, b, u), true, multiplicative_identity, u, v, c, d)
% 19.70/2.94 = { by axiom 5 (product_7) R->L }
% 19.70/2.94 fresh20(fresh17(fresh38(product(multiplicative_identity, a, b), true, b, c, u), true, c, b, u), true, multiplicative_identity, u, v, c, d)
% 19.70/2.94 = { by axiom 14 (associativity_multiplication_2) R->L }
% 19.70/2.94 fresh20(fresh17(fresh37(true, true, b, c, u, multiplicative_identity, a, u), true, c, b, u), true, multiplicative_identity, u, v, c, d)
% 19.70/2.94 = { by axiom 3 (product_9) R->L }
% 19.70/2.94 fresh20(fresh17(fresh37(product(a, c, u), true, b, c, u, multiplicative_identity, a, u), true, c, b, u), true, multiplicative_identity, u, v, c, d)
% 19.70/2.94 = { by axiom 17 (associativity_multiplication_2) }
% 19.70/2.94 fresh20(fresh17(fresh19(product(multiplicative_identity, u, u), true, b, c, u, multiplicative_identity, a), true, c, b, u), true, multiplicative_identity, u, v, c, d)
% 19.70/2.94 = { by axiom 7 (existence_of_identity_multiplication) R->L }
% 19.70/2.94 fresh20(fresh17(fresh19(fresh13(defined(u), true, u), true, b, c, u, multiplicative_identity, a), true, c, b, u), true, multiplicative_identity, u, v, c, d)
% 19.70/2.94 = { by axiom 1 (u_is_defined) }
% 19.70/2.94 fresh20(fresh17(fresh19(fresh13(true, true, u), true, b, c, u, multiplicative_identity, a), true, c, b, u), true, multiplicative_identity, u, v, c, d)
% 19.70/2.94 = { by axiom 2 (existence_of_identity_multiplication) }
% 19.70/2.94 fresh20(fresh17(fresh19(true, true, b, c, u, multiplicative_identity, a), true, c, b, u), true, multiplicative_identity, u, v, c, d)
% 19.70/2.94 = { by axiom 12 (associativity_multiplication_2) }
% 19.70/2.94 fresh20(fresh17(product(b, c, u), true, c, b, u), true, multiplicative_identity, u, v, c, d)
% 19.70/2.94 = { by axiom 15 (commutativity_multiplication) }
% 19.70/2.94 fresh20(product(c, b, u), true, multiplicative_identity, u, v, c, d)
% 19.70/2.94 = { by axiom 16 (associativity_multiplication_1) R->L }
% 19.70/2.94 fresh39(product(d, b, v), true, multiplicative_identity, u, v, c, d, b)
% 19.70/2.94 = { by axiom 4 (product_10) }
% 19.70/2.94 fresh39(true, true, multiplicative_identity, u, v, c, d, b)
% 19.70/2.94 = { by axiom 13 (associativity_multiplication_1) }
% 19.70/2.94 fresh40(product(multiplicative_identity, c, d), true, multiplicative_identity, u, v)
% 19.70/2.94 = { by axiom 6 (product_8) }
% 19.70/2.94 fresh40(true, true, multiplicative_identity, u, v)
% 19.70/2.94 = { by axiom 8 (associativity_multiplication_1) }
% 19.70/2.94 true
% 19.70/2.94 % SZS output end Proof
% 19.70/2.94
% 19.70/2.94 RESULT: Unsatisfiable (the axioms are contradictory).
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