TSTP Solution File: GRP770-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP770-1 : 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 : n028.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 57.25s 7.63s
% Output : Proof 57.60s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP770-1 : TPTP v8.1.2. Released v4.1.0.
% 0.06/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 28 23:05:55 EDT 2023
% 0.12/0.33 % CPUTime :
% 57.25/7.63 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 57.25/7.63
% 57.25/7.63 % SZS status Unsatisfiable
% 57.25/7.63
% 57.60/7.65 % SZS output start Proof
% 57.60/7.65 Axiom 1 (sos01): product(X, one) = X.
% 57.60/7.65 Axiom 2 (sos02): product(one, X) = X.
% 57.60/7.65 Axiom 3 (sos10): j(X) = quotient(one, X).
% 57.60/7.65 Axiom 4 (sos09): i(X) = difference(X, one).
% 57.60/7.65 Axiom 5 (sos12): eta(X) = product(i(X), X).
% 57.60/7.65 Axiom 6 (sos11): product(i(X), X) = product(X, j(X)).
% 57.60/7.65 Axiom 7 (sos03): product(X, difference(X, Y)) = Y.
% 57.60/7.65 Axiom 8 (sos06): product(quotient(X, Y), Y) = X.
% 57.60/7.65 Axiom 9 (sos05): quotient(product(X, Y), Y) = X.
% 57.60/7.65 Axiom 10 (sos04): difference(X, product(X, Y)) = Y.
% 57.60/7.65 Axiom 11 (sos14): product(X, product(eta(X), Y)) = product(j(j(X)), Y).
% 57.60/7.65 Axiom 12 (sos23): product(X, i(product(Y, X))) = i(Y).
% 57.60/7.65 Axiom 13 (sos13): product(i(i(X)), Y) = product(eta(X), product(X, Y)).
% 57.60/7.65 Axiom 14 (sos16): product(eta(X), product(Y, Z)) = product(product(eta(X), Y), Z).
% 57.60/7.65 Axiom 15 (sos24): product(j(product(X, Y)), X) = j(Y).
% 57.60/7.65 Axiom 16 (sos07): difference(X, product(product(X, Y), Z)) = quotient(product(Y, product(Z, X)), X).
% 57.60/7.65 Axiom 17 (sos21): product(i(product(X, Y)), i(i(X))) = i(Y).
% 57.60/7.65
% 57.60/7.65 Lemma 18: i(j(X)) = X.
% 57.60/7.65 Proof:
% 57.60/7.65 i(j(X))
% 57.60/7.65 = { by axiom 4 (sos09) }
% 57.60/7.65 difference(j(X), one)
% 57.60/7.65 = { by axiom 8 (sos06) R->L }
% 57.60/7.65 difference(j(X), product(quotient(one, X), X))
% 57.60/7.65 = { by axiom 3 (sos10) R->L }
% 57.60/7.65 difference(j(X), product(j(X), X))
% 57.60/7.65 = { by axiom 10 (sos04) }
% 57.60/7.65 X
% 57.60/7.65
% 57.60/7.65 Lemma 19: product(X, i(X)) = one.
% 57.60/7.65 Proof:
% 57.60/7.65 product(X, i(X))
% 57.60/7.65 = { by axiom 4 (sos09) }
% 57.60/7.65 product(X, difference(X, one))
% 57.60/7.65 = { by axiom 7 (sos03) }
% 57.60/7.65 one
% 57.60/7.65
% 57.60/7.65 Lemma 20: eta(i(X)) = eta(X).
% 57.60/7.65 Proof:
% 57.60/7.65 eta(i(X))
% 57.60/7.65 = { by axiom 5 (sos12) }
% 57.60/7.65 product(i(i(X)), i(X))
% 57.60/7.65 = { by axiom 13 (sos13) }
% 57.60/7.65 product(eta(X), product(X, i(X)))
% 57.60/7.65 = { by lemma 19 }
% 57.60/7.65 product(eta(X), one)
% 57.60/7.65 = { by axiom 1 (sos01) }
% 57.60/7.65 eta(X)
% 57.60/7.65
% 57.60/7.65 Lemma 21: product(X, j(X)) = eta(X).
% 57.60/7.65 Proof:
% 57.60/7.65 product(X, j(X))
% 57.60/7.65 = { by axiom 6 (sos11) R->L }
% 57.60/7.65 product(i(X), X)
% 57.60/7.65 = { by axiom 5 (sos12) R->L }
% 57.60/7.65 eta(X)
% 57.60/7.65
% 57.60/7.65 Lemma 22: difference(X, i(Y)) = i(product(Y, X)).
% 57.60/7.65 Proof:
% 57.60/7.65 difference(X, i(Y))
% 57.60/7.65 = { by axiom 12 (sos23) R->L }
% 57.60/7.65 difference(X, product(X, i(product(Y, X))))
% 57.60/7.65 = { by axiom 10 (sos04) }
% 57.60/7.65 i(product(Y, X))
% 57.60/7.65
% 57.60/7.65 Lemma 23: quotient(i(X), i(Y)) = difference(X, Y).
% 57.60/7.65 Proof:
% 57.60/7.65 quotient(i(X), i(Y))
% 57.60/7.65 = { by axiom 12 (sos23) R->L }
% 57.60/7.65 quotient(product(difference(X, Y), i(product(X, difference(X, Y)))), i(Y))
% 57.60/7.65 = { by axiom 7 (sos03) }
% 57.60/7.65 quotient(product(difference(X, Y), i(Y)), i(Y))
% 57.60/7.65 = { by axiom 9 (sos05) }
% 57.60/7.65 difference(X, Y)
% 57.60/7.65
% 57.60/7.65 Lemma 24: product(eta(X), product(j(eta(X)), Y)) = Y.
% 57.60/7.65 Proof:
% 57.60/7.65 product(eta(X), product(j(eta(X)), Y))
% 57.60/7.65 = { by lemma 20 R->L }
% 57.60/7.65 product(eta(X), product(j(eta(i(X))), Y))
% 57.60/7.65 = { by lemma 20 R->L }
% 57.60/7.65 product(eta(X), product(j(eta(i(i(X)))), Y))
% 57.60/7.65 = { by axiom 5 (sos12) }
% 57.60/7.65 product(eta(X), product(j(product(i(i(i(X))), i(i(X)))), Y))
% 57.60/7.65 = { by axiom 12 (sos23) R->L }
% 57.60/7.65 product(eta(X), product(j(product(i(product(X, i(product(i(X), X)))), i(i(X)))), Y))
% 57.60/7.65 = { by axiom 5 (sos12) R->L }
% 57.60/7.65 product(eta(X), product(j(product(i(product(X, i(eta(X)))), i(i(X)))), Y))
% 57.60/7.65 = { by axiom 17 (sos21) }
% 57.60/7.65 product(eta(X), product(j(i(i(eta(X)))), Y))
% 57.60/7.65 = { by axiom 3 (sos10) }
% 57.60/7.65 product(eta(X), product(quotient(one, i(i(eta(X)))), Y))
% 57.60/7.65 = { by lemma 19 R->L }
% 57.60/7.65 product(eta(X), product(quotient(product(i(eta(X)), i(i(eta(X)))), i(i(eta(X)))), Y))
% 57.60/7.65 = { by axiom 9 (sos05) }
% 57.60/7.65 product(eta(X), product(i(eta(X)), Y))
% 57.60/7.65 = { by axiom 14 (sos16) }
% 57.60/7.65 product(product(eta(X), i(eta(X))), Y)
% 57.60/7.65 = { by lemma 19 }
% 57.60/7.65 product(one, Y)
% 57.60/7.65 = { by axiom 2 (sos02) }
% 57.60/7.65 Y
% 57.60/7.65
% 57.60/7.65 Goal 1 (goals): product(x0, product(x1, x2)) = product(quotient(product(x0, x1), x0), product(x0, x2)).
% 57.60/7.65 Proof:
% 57.60/7.65 product(x0, product(x1, x2))
% 57.60/7.65 = { by axiom 7 (sos03) R->L }
% 57.60/7.65 product(x0, product(product(eta(x0), difference(eta(x0), x1)), x2))
% 57.60/7.65 = { by axiom 14 (sos16) R->L }
% 57.60/7.65 product(x0, product(eta(x0), product(difference(eta(x0), x1), x2)))
% 57.60/7.65 = { by lemma 24 R->L }
% 57.60/7.65 product(x0, product(eta(x0), product(difference(eta(x0), product(eta(x0), product(j(eta(x0)), x1))), x2)))
% 57.60/7.65 = { by axiom 10 (sos04) }
% 57.60/7.65 product(x0, product(eta(x0), product(product(j(eta(x0)), x1), x2)))
% 57.60/7.65 = { by axiom 7 (sos03) R->L }
% 57.60/7.65 product(x0, product(eta(x0), product(product(j(product(x1, difference(x1, eta(x0)))), x1), x2)))
% 57.60/7.65 = { by axiom 15 (sos24) }
% 57.60/7.65 product(x0, product(eta(x0), product(j(difference(x1, eta(x0))), x2)))
% 57.60/7.65 = { by lemma 20 R->L }
% 57.60/7.65 product(x0, product(eta(x0), product(j(difference(x1, eta(i(x0)))), x2)))
% 57.60/7.65 = { by axiom 12 (sos23) R->L }
% 57.60/7.65 product(x0, product(eta(x0), product(j(difference(x1, eta(product(x1, i(product(x0, x1)))))), x2)))
% 57.60/7.65 = { by lemma 21 R->L }
% 57.60/7.65 product(x0, product(eta(x0), product(j(difference(x1, product(product(x1, i(product(x0, x1))), j(product(x1, i(product(x0, x1))))))), x2)))
% 57.60/7.65 = { by axiom 16 (sos07) }
% 57.60/7.65 product(x0, product(eta(x0), product(j(quotient(product(i(product(x0, x1)), product(j(product(x1, i(product(x0, x1)))), x1)), x1)), x2)))
% 57.60/7.65 = { by axiom 15 (sos24) }
% 57.60/7.65 product(x0, product(eta(x0), product(j(quotient(product(i(product(x0, x1)), j(i(product(x0, x1)))), x1)), x2)))
% 57.60/7.65 = { by lemma 21 }
% 57.60/7.65 product(x0, product(eta(x0), product(j(quotient(eta(i(product(x0, x1))), x1)), x2)))
% 57.60/7.65 = { by lemma 20 }
% 57.60/7.65 product(x0, product(eta(x0), product(j(quotient(eta(product(x0, x1)), x1)), x2)))
% 57.60/7.65 = { by lemma 24 R->L }
% 57.60/7.65 product(x0, product(eta(x0), product(j(product(eta(product(x0, x1)), product(j(eta(product(x0, x1))), quotient(eta(product(x0, x1)), x1)))), x2)))
% 57.60/7.65 = { by axiom 8 (sos06) R->L }
% 57.60/7.65 product(x0, product(eta(x0), product(j(product(eta(product(x0, x1)), product(j(product(quotient(eta(product(x0, x1)), x1), x1)), quotient(eta(product(x0, x1)), x1)))), x2)))
% 57.60/7.65 = { by axiom 15 (sos24) }
% 57.60/7.65 product(x0, product(eta(x0), product(j(product(eta(product(x0, x1)), j(x1))), x2)))
% 57.60/7.65 = { by lemma 21 R->L }
% 57.60/7.65 product(x0, product(eta(x0), product(j(product(product(product(x0, x1), j(product(x0, x1))), j(x1))), x2)))
% 57.60/7.65 = { by lemma 18 R->L }
% 57.60/7.65 product(x0, product(eta(x0), product(j(product(product(i(j(product(x0, x1))), j(product(x0, x1))), j(x1))), x2)))
% 57.60/7.65 = { by axiom 5 (sos12) R->L }
% 57.60/7.65 product(x0, product(eta(x0), product(j(product(eta(j(product(x0, x1))), j(x1))), x2)))
% 57.60/7.65 = { by axiom 15 (sos24) R->L }
% 57.60/7.65 product(x0, product(eta(x0), product(j(product(eta(j(product(x0, x1))), product(j(product(x0, x1)), x0))), x2)))
% 57.60/7.65 = { by axiom 13 (sos13) R->L }
% 57.60/7.65 product(x0, product(eta(x0), product(j(product(i(i(j(product(x0, x1)))), x0)), x2)))
% 57.60/7.65 = { by lemma 18 }
% 57.60/7.65 product(x0, product(eta(x0), product(j(product(i(product(x0, x1)), x0)), x2)))
% 57.60/7.65 = { by axiom 8 (sos06) R->L }
% 57.60/7.65 product(x0, product(eta(x0), product(j(product(i(product(quotient(product(x0, x1), x0), x0)), x0)), x2)))
% 57.60/7.65 = { by lemma 22 R->L }
% 57.60/7.65 product(x0, product(eta(x0), product(j(product(difference(x0, i(quotient(product(x0, x1), x0))), x0)), x2)))
% 57.60/7.65 = { by axiom 12 (sos23) R->L }
% 57.60/7.65 product(x0, product(eta(x0), product(j(product(difference(x0, product(product(x0, x2), i(product(quotient(product(x0, x1), x0), product(x0, x2))))), x0)), x2)))
% 57.60/7.65 = { by axiom 16 (sos07) }
% 57.60/7.65 product(x0, product(eta(x0), product(j(product(quotient(product(x2, product(i(product(quotient(product(x0, x1), x0), product(x0, x2))), x0)), x0), x0)), x2)))
% 57.60/7.65 = { by axiom 8 (sos06) }
% 57.60/7.66 product(x0, product(eta(x0), product(j(product(x2, product(i(product(quotient(product(x0, x1), x0), product(x0, x2))), x0))), x2)))
% 57.60/7.66 = { by axiom 15 (sos24) }
% 57.60/7.66 product(x0, product(eta(x0), j(product(i(product(quotient(product(x0, x1), x0), product(x0, x2))), x0))))
% 57.60/7.66 = { by axiom 10 (sos04) R->L }
% 57.60/7.66 product(x0, difference(x0, product(x0, product(eta(x0), j(product(i(product(quotient(product(x0, x1), x0), product(x0, x2))), x0))))))
% 57.60/7.66 = { by axiom 11 (sos14) }
% 57.60/7.66 product(x0, difference(x0, product(j(j(x0)), j(product(i(product(quotient(product(x0, x1), x0), product(x0, x2))), x0)))))
% 57.60/7.66 = { by lemma 23 R->L }
% 57.60/7.66 product(x0, quotient(i(x0), i(product(j(j(x0)), j(product(i(product(quotient(product(x0, x1), x0), product(x0, x2))), x0))))))
% 57.60/7.66 = { by lemma 22 R->L }
% 57.60/7.66 product(x0, quotient(i(x0), difference(j(product(i(product(quotient(product(x0, x1), x0), product(x0, x2))), x0)), i(j(j(x0))))))
% 57.60/7.66 = { by lemma 18 }
% 57.60/7.66 product(x0, quotient(i(x0), difference(j(product(i(product(quotient(product(x0, x1), x0), product(x0, x2))), x0)), j(x0))))
% 57.60/7.66 = { by lemma 23 R->L }
% 57.60/7.66 product(x0, quotient(i(x0), quotient(i(j(product(i(product(quotient(product(x0, x1), x0), product(x0, x2))), x0))), i(j(x0)))))
% 57.60/7.66 = { by lemma 18 }
% 57.60/7.66 product(x0, quotient(i(x0), quotient(i(j(product(i(product(quotient(product(x0, x1), x0), product(x0, x2))), x0))), x0)))
% 57.60/7.66 = { by lemma 18 }
% 57.60/7.66 product(x0, quotient(i(x0), quotient(product(i(product(quotient(product(x0, x1), x0), product(x0, x2))), x0), x0)))
% 57.60/7.66 = { by axiom 9 (sos05) }
% 57.60/7.66 product(x0, quotient(i(x0), i(product(quotient(product(x0, x1), x0), product(x0, x2)))))
% 57.60/7.66 = { by lemma 23 }
% 57.60/7.66 product(x0, difference(x0, product(quotient(product(x0, x1), x0), product(x0, x2))))
% 57.60/7.66 = { by axiom 7 (sos03) }
% 57.60/7.66 product(quotient(product(x0, x1), x0), product(x0, x2))
% 57.60/7.66 % SZS output end Proof
% 57.60/7.66
% 57.60/7.66 RESULT: Unsatisfiable (the axioms are contradictory).
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