TSTP Solution File: GRP766-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP766-1 : 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 : n018.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 25.32s 3.65s
% Output : Proof 25.32s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP766-1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.13 % 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 : n018.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 : Mon Aug 28 23:20:47 EDT 2023
% 0.13/0.34 % CPUTime :
% 25.32/3.65 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 25.32/3.65
% 25.32/3.65 % SZS status Unsatisfiable
% 25.32/3.65
% 25.32/3.66 % SZS output start Proof
% 25.32/3.66 Axiom 1 (sos04): difference(X, product(X, Y)) = Y.
% 25.32/3.66 Axiom 2 (sos18): t(X, Y) = quotient(product(X, Y), X).
% 25.32/3.66 Axiom 3 (sos05): quotient(product(X, Y), Y) = X.
% 25.32/3.66 Axiom 4 (sos03): product(X, difference(X, Y)) = Y.
% 25.32/3.66 Axiom 5 (sos06): product(quotient(X, Y), Y) = X.
% 25.32/3.66 Axiom 6 (sos07): difference(X, product(product(X, Y), Z)) = quotient(product(Y, product(Z, X)), X).
% 25.32/3.66 Axiom 7 (sos13): l(X, Y, Z) = difference(product(X, Y), product(X, product(Y, Z))).
% 25.32/3.66 Axiom 8 (sos08): difference(product(X, Y), product(X, product(Y, Z))) = quotient(quotient(product(Z, product(X, Y)), Y), X).
% 25.32/3.66 Axiom 9 (sos19): t(eta(X), product(Y, Z)) = product(t(eta(X), Y), t(eta(X), Z)).
% 25.32/3.66
% 25.32/3.66 Lemma 10: t(eta(X), product(Y, eta(X))) = product(eta(X), Y).
% 25.32/3.66 Proof:
% 25.32/3.66 t(eta(X), product(Y, eta(X)))
% 25.32/3.66 = { by axiom 9 (sos19) }
% 25.32/3.66 product(t(eta(X), Y), t(eta(X), eta(X)))
% 25.32/3.66 = { by axiom 2 (sos18) }
% 25.32/3.66 product(t(eta(X), Y), quotient(product(eta(X), eta(X)), eta(X)))
% 25.32/3.66 = { by axiom 3 (sos05) }
% 25.32/3.66 product(t(eta(X), Y), eta(X))
% 25.32/3.66 = { by axiom 2 (sos18) }
% 25.32/3.66 product(quotient(product(eta(X), Y), eta(X)), eta(X))
% 25.32/3.66 = { by axiom 5 (sos06) }
% 25.32/3.66 product(eta(X), Y)
% 25.32/3.66
% 25.32/3.66 Lemma 11: product(product(X, Y), l(X, Y, Z)) = product(X, product(Y, Z)).
% 25.32/3.66 Proof:
% 25.32/3.66 product(product(X, Y), l(X, Y, Z))
% 25.32/3.66 = { by axiom 7 (sos13) }
% 25.32/3.66 product(product(X, Y), difference(product(X, Y), product(X, product(Y, Z))))
% 25.32/3.66 = { by axiom 4 (sos03) }
% 25.32/3.66 product(X, product(Y, Z))
% 25.32/3.66
% 25.32/3.66 Lemma 12: product(difference(X, product(product(X, Y), Z)), X) = product(Y, product(Z, X)).
% 25.32/3.66 Proof:
% 25.32/3.66 product(difference(X, product(product(X, Y), Z)), X)
% 25.32/3.66 = { by axiom 6 (sos07) }
% 25.32/3.66 product(quotient(product(Y, product(Z, X)), X), X)
% 25.32/3.66 = { by axiom 5 (sos06) }
% 25.32/3.66 product(Y, product(Z, X))
% 25.32/3.66
% 25.32/3.66 Goal 1 (goals): product(eta(x0), product(x1, x2)) = product(product(eta(x0), x1), x2).
% 25.32/3.66 Proof:
% 25.32/3.66 product(eta(x0), product(x1, x2))
% 25.32/3.66 = { by axiom 1 (sos04) R->L }
% 25.32/3.66 product(eta(x0), product(difference(product(x2, eta(x0)), product(product(x2, eta(x0)), x1)), x2))
% 25.32/3.66 = { by axiom 4 (sos03) R->L }
% 25.32/3.66 product(eta(x0), product(difference(product(x2, eta(x0)), product(product(eta(x0), difference(eta(x0), product(x2, eta(x0)))), x1)), x2))
% 25.32/3.66 = { by axiom 4 (sos03) R->L }
% 25.32/3.66 product(eta(x0), product(difference(product(x2, eta(x0)), product(eta(x0), difference(eta(x0), product(product(eta(x0), difference(eta(x0), product(x2, eta(x0)))), x1)))), x2))
% 25.32/3.66 = { by lemma 10 R->L }
% 25.32/3.66 product(eta(x0), product(difference(product(x2, eta(x0)), t(eta(x0), product(difference(eta(x0), product(product(eta(x0), difference(eta(x0), product(x2, eta(x0)))), x1)), eta(x0)))), x2))
% 25.32/3.66 = { by lemma 12 }
% 25.32/3.66 product(eta(x0), product(difference(product(x2, eta(x0)), t(eta(x0), product(difference(eta(x0), product(x2, eta(x0))), product(x1, eta(x0))))), x2))
% 25.32/3.66 = { by axiom 9 (sos19) }
% 25.32/3.66 product(eta(x0), product(difference(product(x2, eta(x0)), product(t(eta(x0), difference(eta(x0), product(x2, eta(x0)))), t(eta(x0), product(x1, eta(x0))))), x2))
% 25.32/3.66 = { by lemma 10 }
% 25.32/3.66 product(eta(x0), product(difference(product(x2, eta(x0)), product(t(eta(x0), difference(eta(x0), product(x2, eta(x0)))), product(eta(x0), x1))), x2))
% 25.32/3.66 = { by axiom 4 (sos03) R->L }
% 25.32/3.66 product(eta(x0), product(difference(product(x2, eta(x0)), product(t(eta(x0), difference(eta(x0), product(product(eta(x0), difference(eta(x0), x2)), eta(x0)))), product(eta(x0), x1))), x2))
% 25.32/3.66 = { by axiom 5 (sos06) R->L }
% 25.32/3.66 product(eta(x0), product(difference(product(x2, eta(x0)), product(t(eta(x0), product(quotient(difference(eta(x0), product(product(eta(x0), difference(eta(x0), x2)), eta(x0))), eta(x0)), eta(x0))), product(eta(x0), x1))), x2))
% 25.32/3.66 = { by axiom 6 (sos07) }
% 25.32/3.66 product(eta(x0), product(difference(product(x2, eta(x0)), product(t(eta(x0), product(quotient(quotient(product(difference(eta(x0), x2), product(eta(x0), eta(x0))), eta(x0)), eta(x0)), eta(x0))), product(eta(x0), x1))), x2))
% 25.32/3.66 = { by axiom 8 (sos08) R->L }
% 25.32/3.66 product(eta(x0), product(difference(product(x2, eta(x0)), product(t(eta(x0), product(difference(product(eta(x0), eta(x0)), product(eta(x0), product(eta(x0), difference(eta(x0), x2)))), eta(x0))), product(eta(x0), x1))), x2))
% 25.32/3.66 = { by axiom 7 (sos13) R->L }
% 25.32/3.66 product(eta(x0), product(difference(product(x2, eta(x0)), product(t(eta(x0), product(l(eta(x0), eta(x0), difference(eta(x0), x2)), eta(x0))), product(eta(x0), x1))), x2))
% 25.32/3.66 = { by axiom 2 (sos18) }
% 25.32/3.66 product(eta(x0), product(difference(product(x2, eta(x0)), product(quotient(product(eta(x0), product(l(eta(x0), eta(x0), difference(eta(x0), x2)), eta(x0))), eta(x0)), product(eta(x0), x1))), x2))
% 25.32/3.66 = { by axiom 6 (sos07) R->L }
% 25.32/3.66 product(eta(x0), product(difference(product(x2, eta(x0)), product(difference(eta(x0), product(product(eta(x0), eta(x0)), l(eta(x0), eta(x0), difference(eta(x0), x2)))), product(eta(x0), x1))), x2))
% 25.32/3.66 = { by lemma 11 }
% 25.32/3.66 product(eta(x0), product(difference(product(x2, eta(x0)), product(difference(eta(x0), product(eta(x0), product(eta(x0), difference(eta(x0), x2)))), product(eta(x0), x1))), x2))
% 25.32/3.66 = { by axiom 1 (sos04) }
% 25.32/3.66 product(eta(x0), product(difference(product(x2, eta(x0)), product(product(eta(x0), difference(eta(x0), x2)), product(eta(x0), x1))), x2))
% 25.32/3.66 = { by axiom 4 (sos03) }
% 25.32/3.66 product(eta(x0), product(difference(product(x2, eta(x0)), product(x2, product(eta(x0), x1))), x2))
% 25.32/3.66 = { by axiom 7 (sos13) R->L }
% 25.32/3.66 product(eta(x0), product(l(x2, eta(x0), x1), x2))
% 25.32/3.66 = { by lemma 12 R->L }
% 25.32/3.66 product(difference(x2, product(product(x2, eta(x0)), l(x2, eta(x0), x1))), x2)
% 25.32/3.66 = { by lemma 11 }
% 25.32/3.66 product(difference(x2, product(x2, product(eta(x0), x1))), x2)
% 25.32/3.66 = { by axiom 1 (sos04) }
% 25.32/3.66 product(product(eta(x0), x1), x2)
% 25.32/3.66 % SZS output end Proof
% 25.32/3.66
% 25.32/3.66 RESULT: Unsatisfiable (the axioms are contradictory).
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