TSTP Solution File: GRP767-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP767-1 : 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 : 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 : Thu Aug 31 01:20:02 EDT 2023
% Result : Unsatisfiable 1.38s 0.58s
% Output : Proof 1.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP767-1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.35 % Computer : n029.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon Aug 28 23:13:41 EDT 2023
% 0.15/0.35 % CPUTime :
% 1.38/0.58 Command-line arguments: --no-flatten-goal
% 1.38/0.58
% 1.38/0.58 % SZS status Unsatisfiable
% 1.38/0.58
% 1.38/0.60 % SZS output start Proof
% 1.38/0.60 Axiom 1 (sos09): i(X) = difference(X, one).
% 1.38/0.60 Axiom 2 (sos10): j(X) = quotient(one, X).
% 1.38/0.60 Axiom 3 (sos01): product(X, one) = X.
% 1.38/0.60 Axiom 4 (sos12): eta(X) = product(i(X), X).
% 1.38/0.60 Axiom 5 (sos11): product(i(X), X) = product(X, j(X)).
% 1.38/0.60 Axiom 6 (sos04): difference(X, product(X, Y)) = Y.
% 1.38/0.60 Axiom 7 (sos05): quotient(product(X, Y), Y) = X.
% 1.38/0.60 Axiom 8 (sos03): product(X, difference(X, Y)) = Y.
% 1.38/0.60 Axiom 9 (sos06): product(quotient(X, Y), Y) = X.
% 1.38/0.60 Axiom 10 (sos14): product(X, product(eta(X), Y)) = product(j(j(X)), Y).
% 1.38/0.60 Axiom 11 (sos13): product(i(i(X)), Y) = product(eta(X), product(X, Y)).
% 1.38/0.60 Axiom 12 (sos16): product(eta(X), product(Y, Z)) = product(product(eta(X), Y), Z).
% 1.38/0.60 Axiom 13 (sos07): difference(X, product(product(X, Y), Z)) = quotient(product(Y, product(Z, X)), X).
% 1.38/0.60 Axiom 14 (sos08): difference(product(X, Y), product(X, product(Y, Z))) = quotient(quotient(product(Z, product(X, Y)), Y), X).
% 1.38/0.60
% 1.38/0.60 Lemma 15: product(X, i(X)) = one.
% 1.38/0.60 Proof:
% 1.38/0.60 product(X, i(X))
% 1.38/0.60 = { by axiom 1 (sos09) }
% 1.38/0.60 product(X, difference(X, one))
% 1.38/0.60 = { by axiom 8 (sos03) }
% 1.38/0.60 one
% 1.38/0.60
% 1.38/0.60 Lemma 16: j(i(X)) = X.
% 1.38/0.60 Proof:
% 1.38/0.60 j(i(X))
% 1.38/0.60 = { by axiom 2 (sos10) }
% 1.38/0.60 quotient(one, i(X))
% 1.38/0.60 = { by lemma 15 R->L }
% 1.38/0.60 quotient(product(X, i(X)), i(X))
% 1.38/0.60 = { by axiom 7 (sos05) }
% 1.38/0.60 X
% 1.38/0.60
% 1.38/0.60 Lemma 17: eta(i(X)) = eta(X).
% 1.38/0.60 Proof:
% 1.38/0.60 eta(i(X))
% 1.38/0.60 = { by axiom 4 (sos12) }
% 1.38/0.60 product(i(i(X)), i(X))
% 1.38/0.60 = { by axiom 11 (sos13) }
% 1.38/0.60 product(eta(X), product(X, i(X)))
% 1.38/0.60 = { by lemma 15 }
% 1.38/0.60 product(eta(X), one)
% 1.38/0.60 = { by axiom 3 (sos01) }
% 1.38/0.60 eta(X)
% 1.38/0.60
% 1.38/0.60 Lemma 18: product(X, eta(X)) = j(j(X)).
% 1.38/0.60 Proof:
% 1.38/0.60 product(X, eta(X))
% 1.38/0.60 = { by axiom 3 (sos01) R->L }
% 1.38/0.60 product(X, product(eta(X), one))
% 1.38/0.60 = { by axiom 10 (sos14) }
% 1.38/0.60 product(j(j(X)), one)
% 1.38/0.60 = { by axiom 3 (sos01) }
% 1.38/0.60 j(j(X))
% 1.38/0.60
% 1.38/0.60 Lemma 19: product(j(X), X) = one.
% 1.38/0.60 Proof:
% 1.38/0.60 product(j(X), X)
% 1.38/0.60 = { by axiom 2 (sos10) }
% 1.38/0.60 product(quotient(one, X), X)
% 1.38/0.60 = { by axiom 9 (sos06) }
% 1.38/0.60 one
% 1.38/0.60
% 1.38/0.60 Goal 1 (goals): product(j(j(x0)), j(product(x1, x0))) = j(x1).
% 1.38/0.60 Proof:
% 1.38/0.60 product(j(j(x0)), j(product(x1, x0)))
% 1.38/0.60 = { by axiom 7 (sos05) R->L }
% 1.38/0.60 product(quotient(product(j(j(x0)), j(product(x1, x0))), j(product(x1, x0))), j(product(x1, x0)))
% 1.38/0.60 = { by axiom 6 (sos04) R->L }
% 1.38/0.60 product(quotient(difference(eta(x0), product(eta(x0), product(j(j(x0)), j(product(x1, x0))))), j(product(x1, x0))), j(product(x1, x0)))
% 1.38/0.60 = { by axiom 12 (sos16) }
% 1.38/0.60 product(quotient(difference(eta(x0), product(product(eta(x0), j(j(x0))), j(product(x1, x0)))), j(product(x1, x0))), j(product(x1, x0)))
% 1.38/0.60 = { by axiom 9 (sos06) }
% 1.38/0.60 difference(eta(x0), product(product(eta(x0), j(j(x0))), j(product(x1, x0))))
% 1.38/0.60 = { by lemma 18 R->L }
% 1.38/0.60 difference(eta(x0), product(product(eta(x0), product(x0, eta(x0))), j(product(x1, x0))))
% 1.38/0.60 = { by axiom 11 (sos13) R->L }
% 1.38/0.60 difference(eta(x0), product(product(i(i(x0)), eta(x0)), j(product(x1, x0))))
% 1.38/0.60 = { by lemma 17 R->L }
% 1.38/0.60 difference(eta(x0), product(product(i(i(x0)), eta(i(x0))), j(product(x1, x0))))
% 1.38/0.60 = { by lemma 17 R->L }
% 1.38/0.60 difference(eta(x0), product(product(i(i(x0)), eta(i(i(x0)))), j(product(x1, x0))))
% 1.38/0.60 = { by lemma 18 }
% 1.38/0.60 difference(eta(x0), product(j(j(i(i(x0)))), j(product(x1, x0))))
% 1.38/0.60 = { by lemma 16 }
% 1.38/0.60 difference(eta(x0), product(j(i(x0)), j(product(x1, x0))))
% 1.38/0.60 = { by lemma 16 }
% 1.38/0.60 difference(eta(x0), product(x0, j(product(x1, x0))))
% 1.38/0.60 = { by lemma 16 R->L }
% 1.38/0.60 j(i(difference(eta(x0), product(x0, j(product(x1, x0))))))
% 1.38/0.60 = { by axiom 6 (sos04) R->L }
% 1.38/0.60 j(difference(product(x0, j(product(x1, x0))), product(product(x0, j(product(x1, x0))), i(difference(eta(x0), product(x0, j(product(x1, x0))))))))
% 1.38/0.60 = { by axiom 8 (sos03) R->L }
% 1.38/0.60 j(difference(product(X, difference(X, product(x0, j(product(x1, x0))))), product(product(x0, j(product(x1, x0))), i(difference(eta(x0), product(x0, j(product(x1, x0))))))))
% 1.38/0.60 = { by axiom 8 (sos03) R->L }
% 1.38/0.60 j(difference(product(X, difference(X, product(x0, j(product(x1, x0))))), product(product(eta(x0), difference(eta(x0), product(x0, j(product(x1, x0))))), i(difference(eta(x0), product(x0, j(product(x1, x0))))))))
% 1.38/0.60 = { by axiom 12 (sos16) R->L }
% 1.38/0.60 j(difference(product(X, difference(X, product(x0, j(product(x1, x0))))), product(eta(x0), product(difference(eta(x0), product(x0, j(product(x1, x0)))), i(difference(eta(x0), product(x0, j(product(x1, x0)))))))))
% 1.38/0.60 = { by lemma 15 }
% 1.38/0.60 j(difference(product(X, difference(X, product(x0, j(product(x1, x0))))), product(eta(x0), one)))
% 1.38/0.60 = { by axiom 3 (sos01) }
% 1.38/0.60 j(difference(product(X, difference(X, product(x0, j(product(x1, x0))))), eta(x0)))
% 1.38/0.60 = { by axiom 8 (sos03) }
% 1.38/0.60 j(difference(product(x0, j(product(x1, x0))), eta(x0)))
% 1.38/0.60 = { by axiom 4 (sos12) }
% 1.38/0.60 j(difference(product(x0, j(product(x1, x0))), product(i(x0), x0)))
% 1.38/0.60 = { by axiom 5 (sos11) }
% 1.38/0.60 j(difference(product(x0, j(product(x1, x0))), product(x0, j(x0))))
% 1.38/0.60 = { by axiom 8 (sos03) R->L }
% 1.38/0.60 j(difference(product(x0, j(product(x1, x0))), product(x0, product(j(product(x1, x0)), difference(j(product(x1, x0)), j(x0))))))
% 1.38/0.60 = { by axiom 14 (sos08) }
% 1.38/0.60 j(quotient(quotient(product(difference(j(product(x1, x0)), j(x0)), product(x0, j(product(x1, x0)))), j(product(x1, x0))), x0))
% 1.38/0.60 = { by axiom 13 (sos07) R->L }
% 1.38/0.60 j(quotient(difference(j(product(x1, x0)), product(product(j(product(x1, x0)), difference(j(product(x1, x0)), j(x0))), x0)), x0))
% 1.38/0.60 = { by axiom 8 (sos03) }
% 1.38/0.60 j(quotient(difference(j(product(x1, x0)), product(j(x0), x0)), x0))
% 1.38/0.61 = { by lemma 19 }
% 1.38/0.61 j(quotient(difference(j(product(x1, x0)), one), x0))
% 1.38/0.61 = { by lemma 19 R->L }
% 1.38/0.61 j(quotient(difference(j(product(x1, x0)), product(j(product(x1, x0)), product(x1, x0))), x0))
% 1.38/0.61 = { by axiom 6 (sos04) }
% 1.38/0.61 j(quotient(product(x1, x0), x0))
% 1.38/0.61 = { by axiom 7 (sos05) }
% 1.38/0.61 j(x1)
% 1.38/0.61 % SZS output end Proof
% 1.38/0.61
% 1.38/0.61 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------