TSTP Solution File: GRP772-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP772-1 : TPTP v8.1.2. Released v4.1.0.
% 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 : n025.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 01:20:03 EDT 2023
% Result : Unsatisfiable 0.19s 0.53s
% Output : Proof 0.19s
% 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 : GRP772-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 29 01:23:24 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.53 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.19/0.53
% 0.19/0.53 % SZS status Unsatisfiable
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% 0.19/0.53 % SZS output start Proof
% 0.19/0.53 Axiom 1 (sos09): i(X) = difference(X, one).
% 0.19/0.53 Axiom 2 (sos10): j(X) = quotient(one, X).
% 0.19/0.53 Axiom 3 (sos04): difference(X, product(X, Y)) = Y.
% 0.19/0.53 Axiom 4 (sos19): t(X, Y) = quotient(product(X, Y), X).
% 0.19/0.53 Axiom 5 (sos05): quotient(product(X, Y), Y) = X.
% 0.19/0.53 Axiom 6 (sos30): a(X, i(Y), Z) = a(X, j(Y), Z).
% 0.19/0.53 Axiom 7 (sos32): a(j(X), Y, Z) = a(Y, Z, X).
% 0.19/0.53 Axiom 8 (sos03): product(X, difference(X, Y)) = Y.
% 0.19/0.53 Axiom 9 (sos07): difference(X, product(product(X, Y), Z)) = quotient(product(Y, product(Z, X)), X).
% 0.19/0.53 Axiom 10 (sos27): product(a(X, Y, Z), product(W, V)) = product(product(a(X, Y, Z), W), V).
% 0.19/0.53 Axiom 11 (sos08): difference(product(X, Y), product(X, product(Y, Z))) = quotient(quotient(product(Z, product(X, Y)), Y), X).
% 0.19/0.53 Axiom 12 (sos29): product(a(X, Y, Z), difference(Z, product(a(Z, X, Y), Z))) = one.
% 0.19/0.53
% 0.19/0.53 Lemma 13: a(X, Y, i(Z)) = a(Z, X, Y).
% 0.19/0.53 Proof:
% 0.19/0.53 a(X, Y, i(Z))
% 0.19/0.53 = { by axiom 7 (sos32) R->L }
% 0.19/0.53 a(j(i(Z)), X, Y)
% 0.19/0.53 = { by axiom 2 (sos10) }
% 0.19/0.53 a(quotient(one, i(Z)), X, Y)
% 0.19/0.53 = { by axiom 8 (sos03) R->L }
% 0.19/0.53 a(quotient(product(Z, difference(Z, one)), i(Z)), X, Y)
% 0.19/0.53 = { by axiom 1 (sos09) R->L }
% 0.19/0.53 a(quotient(product(Z, i(Z)), i(Z)), X, Y)
% 0.19/0.53 = { by axiom 5 (sos05) }
% 0.19/0.53 a(Z, X, Y)
% 0.19/0.53
% 0.19/0.53 Lemma 14: difference(product(X, a(Y, Z, W)), product(X, product(a(Y, Z, W), V))) = V.
% 0.19/0.53 Proof:
% 0.19/0.53 difference(product(X, a(Y, Z, W)), product(X, product(a(Y, Z, W), V)))
% 0.19/0.53 = { by axiom 11 (sos08) }
% 0.19/0.53 quotient(quotient(product(V, product(X, a(Y, Z, W))), a(Y, Z, W)), X)
% 0.19/0.53 = { by axiom 9 (sos07) R->L }
% 0.19/0.53 quotient(difference(a(Y, Z, W), product(product(a(Y, Z, W), V), X)), X)
% 0.19/0.53 = { by axiom 10 (sos27) R->L }
% 0.19/0.53 quotient(difference(a(Y, Z, W), product(a(Y, Z, W), product(V, X))), X)
% 0.19/0.53 = { by axiom 3 (sos04) }
% 0.19/0.53 quotient(product(V, X), X)
% 0.19/0.53 = { by axiom 5 (sos05) }
% 0.19/0.53 V
% 0.19/0.53
% 0.19/0.53 Lemma 15: t(X, i(a(Y, Z, X))) = a(X, Y, Z).
% 0.19/0.53 Proof:
% 0.19/0.53 t(X, i(a(Y, Z, X)))
% 0.19/0.53 = { by axiom 1 (sos09) }
% 0.19/0.53 t(X, difference(a(Y, Z, X), one))
% 0.19/0.53 = { by lemma 14 R->L }
% 0.19/0.53 t(X, difference(product(W, a(Y, Z, X)), product(W, product(a(Y, Z, X), difference(a(Y, Z, X), one)))))
% 0.19/0.53 = { by axiom 8 (sos03) }
% 0.19/0.53 t(X, difference(product(W, a(Y, Z, X)), product(W, one)))
% 0.19/0.53 = { by axiom 12 (sos29) R->L }
% 0.19/0.53 t(X, difference(product(W, a(Y, Z, X)), product(W, product(a(Y, Z, X), difference(X, product(a(X, Y, Z), X))))))
% 0.19/0.53 = { by lemma 14 }
% 0.19/0.53 t(X, difference(X, product(a(X, Y, Z), X)))
% 0.19/0.53 = { by axiom 4 (sos19) }
% 0.19/0.53 quotient(product(X, difference(X, product(a(X, Y, Z), X))), X)
% 0.19/0.53 = { by axiom 8 (sos03) }
% 0.19/0.53 quotient(product(a(X, Y, Z), X), X)
% 0.19/0.53 = { by axiom 5 (sos05) }
% 0.19/0.53 a(X, Y, Z)
% 0.19/0.53
% 0.19/0.53 Goal 1 (goals): a(x0, x1, x1) = a(x1, x1, x0).
% 0.19/0.53 Proof:
% 0.19/0.53 a(x0, x1, x1)
% 0.19/0.53 = { by lemma 13 R->L }
% 0.19/0.53 a(x1, x1, i(x0))
% 0.19/0.53 = { by lemma 15 R->L }
% 0.19/0.53 t(x1, i(a(x1, i(x0), x1)))
% 0.19/0.53 = { by lemma 15 R->L }
% 0.19/0.53 t(x1, i(t(x1, i(a(i(x0), x1, x1)))))
% 0.19/0.53 = { by axiom 7 (sos32) R->L }
% 0.19/0.53 t(x1, i(t(x1, i(a(j(x1), i(x0), x1)))))
% 0.19/0.53 = { by lemma 15 }
% 0.19/0.53 t(x1, i(a(x1, j(x1), i(x0))))
% 0.19/0.53 = { by axiom 6 (sos30) R->L }
% 0.19/0.53 t(x1, i(a(x1, i(x1), i(x0))))
% 0.19/0.53 = { by lemma 13 }
% 0.19/0.53 t(x1, i(a(x0, x1, i(x1))))
% 0.19/0.53 = { by lemma 13 }
% 0.19/0.53 t(x1, i(a(x1, x0, x1)))
% 0.19/0.53 = { by lemma 15 }
% 0.19/0.53 a(x1, x1, x0)
% 0.19/0.53 % SZS output end Proof
% 0.19/0.53
% 0.19/0.53 RESULT: Unsatisfiable (the axioms are contradictory).
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