TSTP Solution File: BOO004-10 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : BOO004-10 : 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 : n008.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 18:11:16 EDT 2023
% Result : Unsatisfiable 0.21s 0.48s
% 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
% 0.00/0.12 % Problem : BOO004-10 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 08:40:47 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.21/0.48 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.21/0.48
% 0.21/0.48 % SZS status Unsatisfiable
% 0.21/0.48
% 0.21/0.49 % SZS output start Proof
% 0.21/0.49 Axiom 1 (additive_identity1): sum(additive_identity, X, X) = true.
% 0.21/0.49 Axiom 2 (multiplicative_identity2): product(X, multiplicative_identity, X) = true.
% 0.21/0.49 Axiom 3 (ifeq_axiom_001): ifeq(X, X, Y, Z) = Y.
% 0.21/0.49 Axiom 4 (additive_inverse1): sum(inverse(X), X, multiplicative_identity) = true.
% 0.21/0.49 Axiom 5 (multiplicative_inverse2): product(X, inverse(X), additive_identity) = true.
% 0.21/0.49 Axiom 6 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.21/0.49 Axiom 7 (closure_of_addition): sum(X, Y, add(X, Y)) = true.
% 0.21/0.49 Axiom 8 (multiplication_is_well_defined): ifeq2(product(X, Y, Z), true, ifeq2(product(X, Y, W), true, W, Z), Z) = Z.
% 0.21/0.49 Axiom 9 (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.
% 0.21/0.49
% 0.21/0.49 Goal 1 (prove_both_equalities): sum(x, x, x) = true.
% 0.21/0.49 Proof:
% 0.21/0.49 sum(x, x, x)
% 0.21/0.49 = { by axiom 6 (ifeq_axiom) R->L }
% 0.21/0.49 sum(x, x, ifeq2(true, true, x, add(x, x)))
% 0.21/0.49 = { by axiom 9 (distributivity7) R->L }
% 0.21/0.49 sum(x, x, ifeq2(ifeq(product(x, inverse(x), additive_identity), true, ifeq(sum(additive_identity, x, x), true, ifeq(sum(inverse(x), x, multiplicative_identity), true, ifeq(sum(x, x, add(x, x)), true, product(add(x, x), multiplicative_identity, x), true), true), true), true), true, x, add(x, x)))
% 0.21/0.49 = { by axiom 1 (additive_identity1) }
% 0.21/0.49 sum(x, x, ifeq2(ifeq(product(x, inverse(x), additive_identity), true, ifeq(true, true, ifeq(sum(inverse(x), x, multiplicative_identity), true, ifeq(sum(x, x, add(x, x)), true, product(add(x, x), multiplicative_identity, x), true), true), true), true), true, x, add(x, x)))
% 0.21/0.49 = { by axiom 3 (ifeq_axiom_001) }
% 0.21/0.49 sum(x, x, ifeq2(ifeq(product(x, inverse(x), additive_identity), true, ifeq(sum(inverse(x), x, multiplicative_identity), true, ifeq(sum(x, x, add(x, x)), true, product(add(x, x), multiplicative_identity, x), true), true), true), true, x, add(x, x)))
% 0.21/0.49 = { by axiom 5 (multiplicative_inverse2) }
% 0.21/0.49 sum(x, x, ifeq2(ifeq(true, true, ifeq(sum(inverse(x), x, multiplicative_identity), true, ifeq(sum(x, x, add(x, x)), true, product(add(x, x), multiplicative_identity, x), true), true), true), true, x, add(x, x)))
% 0.21/0.49 = { by axiom 3 (ifeq_axiom_001) }
% 0.21/0.49 sum(x, x, ifeq2(ifeq(sum(inverse(x), x, multiplicative_identity), true, ifeq(sum(x, x, add(x, x)), true, product(add(x, x), multiplicative_identity, x), true), true), true, x, add(x, x)))
% 0.21/0.49 = { by axiom 4 (additive_inverse1) }
% 0.21/0.49 sum(x, x, ifeq2(ifeq(true, true, ifeq(sum(x, x, add(x, x)), true, product(add(x, x), multiplicative_identity, x), true), true), true, x, add(x, x)))
% 0.21/0.49 = { by axiom 3 (ifeq_axiom_001) }
% 0.21/0.49 sum(x, x, ifeq2(ifeq(sum(x, x, add(x, x)), true, product(add(x, x), multiplicative_identity, x), true), true, x, add(x, x)))
% 0.21/0.49 = { by axiom 7 (closure_of_addition) }
% 0.21/0.49 sum(x, x, ifeq2(ifeq(true, true, product(add(x, x), multiplicative_identity, x), true), true, x, add(x, x)))
% 0.21/0.49 = { by axiom 3 (ifeq_axiom_001) }
% 0.21/0.49 sum(x, x, ifeq2(product(add(x, x), multiplicative_identity, x), true, x, add(x, x)))
% 0.21/0.49 = { by axiom 6 (ifeq_axiom) R->L }
% 0.21/0.49 sum(x, x, ifeq2(true, true, ifeq2(product(add(x, x), multiplicative_identity, x), true, x, add(x, x)), add(x, x)))
% 0.21/0.49 = { by axiom 2 (multiplicative_identity2) R->L }
% 0.21/0.49 sum(x, x, ifeq2(product(add(x, x), multiplicative_identity, add(x, x)), true, ifeq2(product(add(x, x), multiplicative_identity, x), true, x, add(x, x)), add(x, x)))
% 0.21/0.49 = { by axiom 8 (multiplication_is_well_defined) }
% 0.21/0.49 sum(x, x, add(x, x))
% 0.21/0.49 = { by axiom 7 (closure_of_addition) }
% 0.21/0.49 true
% 0.21/0.49 % SZS output end Proof
% 0.21/0.49
% 0.21/0.49 RESULT: Unsatisfiable (the axioms are contradictory).
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