TSTP Solution File: BOO017-10 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : BOO017-10 : TPTP v8.1.2. Released v7.5.0.
% 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 : n020.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 18:11:26 EDT 2023
% Result : Unsatisfiable 56.25s 7.73s
% Output : Proof 56.66s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15 % Problem : BOO017-10 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.36 % Computer : n020.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8042.1875MB
% 0.12/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Sun Aug 27 08:25:14 EDT 2023
% 0.12/0.36 % CPUTime :
% 56.25/7.73 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 56.25/7.73
% 56.25/7.73 % SZS status Unsatisfiable
% 56.25/7.73
% 56.25/7.75 % SZS output start Proof
% 56.25/7.75 Axiom 1 (additive_identity2): sum(X, additive_identity, X) = true.
% 56.25/7.75 Axiom 2 (x_plus_y): sum(x, y, z) = true.
% 56.25/7.75 Axiom 3 (additive_identity1): sum(additive_identity, X, X) = true.
% 56.25/7.75 Axiom 4 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 56.25/7.75 Axiom 5 (multiplicative_inverse2): product(X, inverse(X), additive_identity) = true.
% 56.25/7.75 Axiom 6 (ifeq_axiom_001): ifeq(X, X, Y, Z) = Y.
% 56.25/7.75 Axiom 7 (closure_of_multiplication): product(X, Y, multiply(X, Y)) = true.
% 56.25/7.75 Axiom 8 (commutativity_of_addition): ifeq(sum(X, Y, Z), true, sum(Y, X, Z), true) = true.
% 56.66/7.75 Axiom 9 (commutativity_of_multiplication): ifeq(product(X, Y, Z), true, product(Y, X, Z), true) = true.
% 56.66/7.75 Axiom 10 (multiplication_is_well_defined): ifeq2(product(X, Y, Z), true, ifeq2(product(X, Y, W), true, W, Z), Z) = Z.
% 56.66/7.75 Axiom 11 (distributivity7): ifeq(product(X, Y, Z), true, ifeq(sum(Z, W, V), true, ifeq(sum(Y, W, U), true, ifeq(sum(X, W, T), true, product(T, U, V), true), true), true), true) = true.
% 56.66/7.75 Axiom 12 (distributivity2): ifeq(product(X, Y, Z), true, ifeq(product(X, W, V), true, ifeq(sum(V, Z, U), true, ifeq(sum(W, Y, T), true, product(X, T, U), true), true), true), true) = true.
% 56.66/7.75
% 56.66/7.75 Goal 1 (prove_product): product(x, z, x) = true.
% 56.66/7.75 Proof:
% 56.66/7.75 product(x, z, x)
% 56.66/7.75 = { by axiom 6 (ifeq_axiom_001) R->L }
% 56.66/7.75 ifeq(true, true, product(x, z, x), true)
% 56.66/7.75 = { by axiom 9 (commutativity_of_multiplication) R->L }
% 56.66/7.75 ifeq(ifeq(product(y, additive_identity, additive_identity), true, product(additive_identity, y, additive_identity), true), true, product(x, z, x), true)
% 56.66/7.75 = { by axiom 4 (ifeq_axiom) R->L }
% 56.66/7.75 ifeq(ifeq(product(y, additive_identity, ifeq2(true, true, additive_identity, multiply(y, additive_identity))), true, product(additive_identity, y, additive_identity), true), true, product(x, z, x), true)
% 56.66/7.75 = { by axiom 12 (distributivity2) R->L }
% 56.66/7.75 ifeq(ifeq(product(y, additive_identity, ifeq2(ifeq(product(y, inverse(y), additive_identity), true, ifeq(product(y, additive_identity, multiply(y, additive_identity)), true, ifeq(sum(multiply(y, additive_identity), additive_identity, multiply(y, additive_identity)), true, ifeq(sum(additive_identity, inverse(y), inverse(y)), true, product(y, inverse(y), multiply(y, additive_identity)), true), true), true), true), true, additive_identity, multiply(y, additive_identity))), true, product(additive_identity, y, additive_identity), true), true, product(x, z, x), true)
% 56.66/7.75 = { by axiom 1 (additive_identity2) }
% 56.66/7.75 ifeq(ifeq(product(y, additive_identity, ifeq2(ifeq(product(y, inverse(y), additive_identity), true, ifeq(product(y, additive_identity, multiply(y, additive_identity)), true, ifeq(true, true, ifeq(sum(additive_identity, inverse(y), inverse(y)), true, product(y, inverse(y), multiply(y, additive_identity)), true), true), true), true), true, additive_identity, multiply(y, additive_identity))), true, product(additive_identity, y, additive_identity), true), true, product(x, z, x), true)
% 56.66/7.75 = { by axiom 6 (ifeq_axiom_001) }
% 56.66/7.75 ifeq(ifeq(product(y, additive_identity, ifeq2(ifeq(product(y, inverse(y), additive_identity), true, ifeq(product(y, additive_identity, multiply(y, additive_identity)), true, ifeq(sum(additive_identity, inverse(y), inverse(y)), true, product(y, inverse(y), multiply(y, additive_identity)), true), true), true), true, additive_identity, multiply(y, additive_identity))), true, product(additive_identity, y, additive_identity), true), true, product(x, z, x), true)
% 56.66/7.75 = { by axiom 3 (additive_identity1) }
% 56.66/7.75 ifeq(ifeq(product(y, additive_identity, ifeq2(ifeq(product(y, inverse(y), additive_identity), true, ifeq(product(y, additive_identity, multiply(y, additive_identity)), true, ifeq(true, true, product(y, inverse(y), multiply(y, additive_identity)), true), true), true), true, additive_identity, multiply(y, additive_identity))), true, product(additive_identity, y, additive_identity), true), true, product(x, z, x), true)
% 56.66/7.75 = { by axiom 6 (ifeq_axiom_001) }
% 56.66/7.75 ifeq(ifeq(product(y, additive_identity, ifeq2(ifeq(product(y, inverse(y), additive_identity), true, ifeq(product(y, additive_identity, multiply(y, additive_identity)), true, product(y, inverse(y), multiply(y, additive_identity)), true), true), true, additive_identity, multiply(y, additive_identity))), true, product(additive_identity, y, additive_identity), true), true, product(x, z, x), true)
% 56.66/7.75 = { by axiom 5 (multiplicative_inverse2) }
% 56.66/7.75 ifeq(ifeq(product(y, additive_identity, ifeq2(ifeq(true, true, ifeq(product(y, additive_identity, multiply(y, additive_identity)), true, product(y, inverse(y), multiply(y, additive_identity)), true), true), true, additive_identity, multiply(y, additive_identity))), true, product(additive_identity, y, additive_identity), true), true, product(x, z, x), true)
% 56.66/7.75 = { by axiom 6 (ifeq_axiom_001) }
% 56.66/7.75 ifeq(ifeq(product(y, additive_identity, ifeq2(ifeq(product(y, additive_identity, multiply(y, additive_identity)), true, product(y, inverse(y), multiply(y, additive_identity)), true), true, additive_identity, multiply(y, additive_identity))), true, product(additive_identity, y, additive_identity), true), true, product(x, z, x), true)
% 56.66/7.75 = { by axiom 7 (closure_of_multiplication) }
% 56.66/7.75 ifeq(ifeq(product(y, additive_identity, ifeq2(ifeq(true, true, product(y, inverse(y), multiply(y, additive_identity)), true), true, additive_identity, multiply(y, additive_identity))), true, product(additive_identity, y, additive_identity), true), true, product(x, z, x), true)
% 56.66/7.75 = { by axiom 6 (ifeq_axiom_001) }
% 56.66/7.75 ifeq(ifeq(product(y, additive_identity, ifeq2(product(y, inverse(y), multiply(y, additive_identity)), true, additive_identity, multiply(y, additive_identity))), true, product(additive_identity, y, additive_identity), true), true, product(x, z, x), true)
% 56.66/7.75 = { by axiom 4 (ifeq_axiom) R->L }
% 56.66/7.75 ifeq(ifeq(product(y, additive_identity, ifeq2(product(y, inverse(y), multiply(y, additive_identity)), true, ifeq2(true, true, additive_identity, multiply(y, additive_identity)), multiply(y, additive_identity))), true, product(additive_identity, y, additive_identity), true), true, product(x, z, x), true)
% 56.66/7.75 = { by axiom 5 (multiplicative_inverse2) R->L }
% 56.66/7.75 ifeq(ifeq(product(y, additive_identity, ifeq2(product(y, inverse(y), multiply(y, additive_identity)), true, ifeq2(product(y, inverse(y), additive_identity), true, additive_identity, multiply(y, additive_identity)), multiply(y, additive_identity))), true, product(additive_identity, y, additive_identity), true), true, product(x, z, x), true)
% 56.66/7.75 = { by axiom 10 (multiplication_is_well_defined) }
% 56.66/7.75 ifeq(ifeq(product(y, additive_identity, multiply(y, additive_identity)), true, product(additive_identity, y, additive_identity), true), true, product(x, z, x), true)
% 56.66/7.75 = { by axiom 7 (closure_of_multiplication) }
% 56.66/7.75 ifeq(ifeq(true, true, product(additive_identity, y, additive_identity), true), true, product(x, z, x), true)
% 56.66/7.75 = { by axiom 6 (ifeq_axiom_001) }
% 56.66/7.75 ifeq(product(additive_identity, y, additive_identity), true, product(x, z, x), true)
% 56.66/7.75 = { by axiom 6 (ifeq_axiom_001) R->L }
% 56.66/7.76 ifeq(product(additive_identity, y, additive_identity), true, ifeq(true, true, product(x, z, x), true), true)
% 56.66/7.76 = { by axiom 8 (commutativity_of_addition) R->L }
% 56.66/7.76 ifeq(product(additive_identity, y, additive_identity), true, ifeq(ifeq(sum(x, y, z), true, sum(y, x, z), true), true, product(x, z, x), true), true)
% 56.66/7.76 = { by axiom 2 (x_plus_y) }
% 56.66/7.76 ifeq(product(additive_identity, y, additive_identity), true, ifeq(ifeq(true, true, sum(y, x, z), true), true, product(x, z, x), true), true)
% 56.66/7.76 = { by axiom 6 (ifeq_axiom_001) }
% 56.66/7.76 ifeq(product(additive_identity, y, additive_identity), true, ifeq(sum(y, x, z), true, product(x, z, x), true), true)
% 56.66/7.76 = { by axiom 6 (ifeq_axiom_001) R->L }
% 56.66/7.76 ifeq(product(additive_identity, y, additive_identity), true, ifeq(sum(y, x, z), true, ifeq(true, true, product(x, z, x), true), true), true)
% 56.66/7.76 = { by axiom 3 (additive_identity1) R->L }
% 56.66/7.76 ifeq(product(additive_identity, y, additive_identity), true, ifeq(sum(y, x, z), true, ifeq(sum(additive_identity, x, x), true, product(x, z, x), true), true), true)
% 56.66/7.76 = { by axiom 6 (ifeq_axiom_001) R->L }
% 56.66/7.76 ifeq(product(additive_identity, y, additive_identity), true, ifeq(true, true, ifeq(sum(y, x, z), true, ifeq(sum(additive_identity, x, x), true, product(x, z, x), true), true), true), true)
% 56.66/7.76 = { by axiom 3 (additive_identity1) R->L }
% 56.66/7.76 ifeq(product(additive_identity, y, additive_identity), true, ifeq(sum(additive_identity, x, x), true, ifeq(sum(y, x, z), true, ifeq(sum(additive_identity, x, x), true, product(x, z, x), true), true), true), true)
% 56.66/7.76 = { by axiom 11 (distributivity7) }
% 56.66/7.76 true
% 56.66/7.76 % SZS output end Proof
% 56.66/7.76
% 56.66/7.76 RESULT: Unsatisfiable (the axioms are contradictory).
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